The kinetic molecular theory of gases

WEBVTT
Kind: captions
Language: en

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- [Instructor] In this video,

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we're gonna talk about something called

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kinetic molecular theory,
which sounds very fancy.

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But as we'll see in the next few seconds,

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or the next few minutes,

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it actually helps build our intuition

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for what is actually going on with the gas

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or at least an approximation

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of what's going on with the gas.

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So first, let's think
about the types of things

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that we know we can measure about a gas

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at a macro level.

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Now, what do I mean at a macro?

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I'm saying at a large scale,
at a scale that's much larger

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than the scale of atoms or molecules.

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And we know the types of
things that we can measure.

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We can measure pressure.

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How do we do you do that?

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Well, pressure is just
force per unit area.

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So, you can do this.

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There's various contraptions
you can use to measure pressure

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depending what you're using it for.

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Force, you can measure with springs

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and you can apply a certain
forces to certain square areas.

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But these are all ways that
you can measure pressure

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and we can measure the pressure
of a gas in a container.

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You can measure volume of a container.

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That's actually pretty straightforward.

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You can imagine a container

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that looks something
like this, it's volume.

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We know how to find the volume

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of a rectangular prism like this,

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or even if it was sphere or
some other type of figure.

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There's many ways of measuring the volume

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without even being able to observe

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or even know that things
like molecules exist.

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We know how to measure temperature,

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and we can do that in different scales.

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Kelvin is what we use 'cause
it's more of an absolute scale,

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but you can use literally thermometers

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to measure temperature.

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And once again, you
can measure temperature

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without knowing anything
about atoms or molecules

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or whether they even exist.

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And you can also measure
an amount of a substance.

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And in particular, we could say,

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you can measure the number of moles.

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Now you might say don't moles
involve a certain number

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of a molecule or an atom.

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Well, they do, but the notion
of a mole actually existed

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even before we knew
exactly how many molecules,

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how many particles made up a mole.

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It was just viewed as an amount

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where people knew it must
be some number of particles,

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but they didn't know exactly.

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So all of these things, we
can measure at a macro level.

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And we know that we can connect them all

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with the ideal gas equation

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that tells us that pressure times volume

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is equal to the amount of
the gas we're dealing with.

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And this is, of course, we're
talking about an ideal gas

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and in future videos,

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we'll talk about how some gases
approach being an ideal gas

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while some are less than ideal.

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But the amount we have
measures the number of moles.

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You have your ideal gas constant

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that just helps us make
all the units work out

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depending on our units
for everything else.

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And then you have your
temperature measured in Kelvin.

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And, scientists long before
we were actually able

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to know about things like
atoms or even observe atoms

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or molecules directly, or even indirectly,

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they were able to
establish this relationship

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using these macro measurements.

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But how do these macro
measurements and this relationship

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actually make sense at a molecular level?

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And that's what kinetic
molecular theory provides us.

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It says, imagine the gas is being made up

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of a bunch of really,
really the small particles.

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Those are really the gas molecules.

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And their collective volume is very small

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compared to the volume of the container.

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So, it's mostly empty space
between those particles.

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Now, the pressure is
caused by these particles

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bouncing into the sides of the container.

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Because at any given moment,

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you have enough particles
bouncing off the side

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of any unit area that it's
providing a force per unit area.

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It's providing a pressure.

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It assumes that those collisions

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are what's known as elastic,

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which we'll study in much more
detail in a physics course,

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but it really says that your
kinetic energy is preserved.

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You might already be
familiar with the notion

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that kinetic energy is equal to one half

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times mass times velocity squared.

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And so the kinetic energy
of these particles,

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when they bounce off,
their mass doesn't change.

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The mass of the particles still there.

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And we're saying that the
velocity is going to be preserved.

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So you have all of these
really small particles,

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even their collective volume is small

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compared to the volume of the container.

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They're providing the pressure

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by having these elastic collisions

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with the side of the container.

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And temperature is related
to the average kinetic energy

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of these particles.

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It would be proportional.

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The higher the temperature,

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the higher average kinetic energy.

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Now average kinetic
energy is really important

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because some of these particles

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might be moving faster than others.

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And of course, N, the number of moles,

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tells us how many particles
we're dealing with.

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We know that each mole has
Avogadro's number of particles.

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So, if you just multiply the
most times Avogadro's number,

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you have the number of particles.

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And what's cool about
kinetic molecular theory,

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I know it's built as a theory,

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but this is fundamentally what chemists

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and physicists visualize

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when they imagine a gas in
a container of some kind.

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And just to make it a
little bit more clear,

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the axioms you could say of
kinetic molecular theory,

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the assumptions of it,
I'll give them here.

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And it's important to realize
that these are assumptions

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and the real world, we have
slight variation from it,

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but these assumptions get us a long way

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to explaining the behaviors of gases.

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So, we've already talked about it.

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Gas consists of particles
in constant random motion.

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We've already talked about that.

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They're bouncing off the
side of the container.

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The combined volume of the
particles is negligible

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compared to the total volume
in which the gas is contained.

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And that also matters

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when you talk about
things like ideal gases,

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because if it stops becoming negligible,

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then you have to start
thinking about the repulsive

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and attractive interactions,
a little bit more.

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The particles exert no attractive

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or repulsive forces on each other.

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And that kind of builds into
the last point I just made,

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which is if they did,

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then we're getting closer to
being a less than ideal gas.

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And we'll talk about that in other videos.

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The collisions between the
particles are completely elastic.

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So, they preserve kinetic energy

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and it's actually, they
would also preserve momentum.

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And that the average kinetic
energy of the particles

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is proportional to the Kelvin temperature.

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And we already talked about that,

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that the macro variable,

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the macro measurement of temperature

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is giving us an indication,

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it's proportional to the
average kinetic energy

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of the particles.


Kinetic molecular theory and the gas laws

WEBVTT
Kind: captions
Language: en

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- [Sal] In other videos,
we touched on the notion

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of kinetic molecular theory,
which I'll just shorten as KMT.

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And it's just this idea that
if you imagine a container,

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I'll just draw it in 2-dimensions here,

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that it contains some gas,
you can imagine the gas

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as being these particles
where their collective volume

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is much smaller than the
volume of the container.

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And the temperature we're dealing with

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is related to the average
kinetic energy of the particles.

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These particles are all
moving around, zooming around,

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and they each would have
some kinetic energy.

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Remember, kinetic energy,
you calculate that

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as MV squared over two.

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So, each of these particles
would have some mass

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and some velocity,

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but they could all have
different velocities for sure,

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even if they're the same type of particle.

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And if they're different
types of particles,

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they can have different masses as well.

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But, the average of these kinetic energies

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across all of these particles,

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that is proportional to temperature
when measured in Kelvin.

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And pressure, the pressure, remember,

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pressure is nothing but
force per unit area.

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And so, you can imagine this
surface of our container,

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this could be some type of a cube

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so I can draw it in 3-dimensions here,

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so there's some area over here.

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And you have your particles,

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let me do this in a different color,

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these particles are
constantly bouncing off of it

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and there's way more particles
then what I have drawn here,

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so at any given moment,
you're having some particles

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that are bouncing off of
this side of the container,

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actually all sides of the container.

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And these are perfectly
elastic collisions,

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they're preserving kinetic energy.

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And so, they're applying
some force, collectively,

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on this area, so the pressure is because

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of these particle
collisions on the surface.

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Now, what I wanna do in this
video is take these ideas

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that we conceptualize in
kinetic molecular theory

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and to understand why the ideal
gas law, PV is equal to nRT,

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make sense when we
conceptualize the world here.

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Just a reminder, P is
pressure, V is volume,

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n is the number of moles of
whatever gas we're dealing with,

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the amount of that gas,

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and then T is the temperature in Kelvin,

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and R is just the ideal gas constant,

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that's just whatever
constant you're doing,

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so that the units all work out together.

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So, let's first think about
how pressure relates to volume

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if we were to old
everything else constant.

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Well, the idea gas law tells
us that pressure times volume

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is going to be equal to this,
if we hold it at constant,

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I can even just write
a K here for constant,

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but that would also mean we could divide,

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let's say both sides by V,

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we can say that pressure is
equal to some constant over V.

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Another way to think about
it is is that pressure

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is proportional to the inverse of volume.

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You could also write this,
if we divide both sides by P,

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is that volume is proportional
to the inverse of pressure.

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Does that make sense

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from a kinetic molecular
theory point of view?

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Pause this video and think about it.

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Well, imagine we have our
original cube right over here.

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And I had the same number of particles,

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they have the same average kinetic energy,

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but let's say I were
to increase the volume.

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So, if I were to make the volume go up,

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so I were to some how expand this,

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or maybe put the exact number,

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the same particles with
the same temperature,

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in a larger container,
then at any given moment,

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you're just gonna have
fewer bounces of particles

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off of the container.

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Because they just have more
room to go in that volume,

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and even the surface area of the container

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is going to be high as well.

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So, it makes sense that
if the volume goes up,

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the pressure is going to go down.

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And you can think about it the other way.

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If you make this smaller,
that same number of particles

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with the same average kinetic energy,

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they're just gonna bump into the container

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that much more often.

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And that's going to increase the pressure,

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so volume goes down, pressure goes up.

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And this relationship, that pressure

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is inversely proportional
to volume, or vice versa,

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if you hold everything else constant,

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that's often known as Boyle's law.

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Now, another relationship,
what if we were to hold volume

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and the number of moles constant,

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and we wanna think about the relationship

00:04:09.370 --> 00:04:12.480
between pressure and temperature.

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Well, this is constant, this
constant, and this is constant,

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the ideal gas law would say that pressure

00:04:17.670 --> 00:04:20.230
is going to be proportional to temperature

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or that temperature's
proportional to pressure.

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Does that make sense?

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Well, let's go back to
our original container.

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If you were to increase the temperature,

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that means that the average
kinetic energy is increased.

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That means that these particles,

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when they hit the side of the container,

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they're going to hit
it with more velocity.

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That means that you're going
to have, at any given moment,

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you're gonna have more pressure

00:04:41.730 --> 00:04:44.780
exerted on the side of the container.

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And you could go the other way.

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Think about lowering the temperature,

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so the kinetic energy goes really low,

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then these particles are
just slowly drifting.

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And the speed with which they are hitting

00:04:54.920 --> 00:04:57.020
the side of the container
is going to go down

00:04:57.020 --> 00:04:58.890
and so the pressure would go down.

00:04:58.890 --> 00:05:00.120
So, it completely makes sense,

00:05:00.120 --> 00:05:02.280
if temperature goes up, pressure goes up,

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if temperature goes
down, pressure goes down,

00:05:04.770 --> 00:05:09.110
and this is often known
as Gay-Lussac's law.

00:05:09.110 --> 00:05:11.370
Now, another relationship, and
I'm really just going through

00:05:11.370 --> 00:05:13.490
all of the combinations over here,

00:05:13.490 --> 00:05:14.477
what if we were to hold pressure

00:05:14.477 --> 00:05:16.210
and the number of molecules constant?

00:05:16.210 --> 00:05:17.430
So, we're really looking
at the relationship

00:05:17.430 --> 00:05:19.350
between volume and temperature.

00:05:19.350 --> 00:05:22.520
So, once again, if P, n,
and R is always constant,

00:05:22.520 --> 00:05:25.100
if those are constant, the
ideal gas law would tell us

00:05:25.100 --> 00:05:28.460
that the volume is proportional
to the temperature,

00:05:28.460 --> 00:05:31.360
once again, holding
everything else constant.

00:05:31.360 --> 00:05:33.060
Well, to think about
that you can go through

00:05:33.060 --> 00:05:35.110
that same thought experiment we just had.

00:05:36.070 --> 00:05:37.690
If we increase the temperature,

00:05:37.690 --> 00:05:39.640
if these things are moving around faster,

00:05:39.640 --> 00:05:42.660
if you want to have the
same amount of force

00:05:42.660 --> 00:05:46.010
per area on the container,
on the side of the container,

00:05:46.010 --> 00:05:49.100
you're going to have
to increase the volume.

00:05:49.100 --> 00:05:51.240
So, this relationship, which
is completely consistent

00:05:51.240 --> 00:05:52.840
with kinetic molecular theory,

00:05:52.840 --> 00:05:55.610
is often known as Charles's law.

00:05:55.610 --> 00:05:59.050
Now, another one is the
relationship between volume

00:05:59.050 --> 00:06:01.070
and the number of moles.

00:06:01.070 --> 00:06:02.940
If everything else is held constant,

00:06:02.940 --> 00:06:05.080
the ideal gas law would
tell us that volume

00:06:05.080 --> 00:06:08.730
is going to be proportional
to the number of moles

00:06:08.730 --> 00:06:12.040
of our particle, or of our
gas that we are dealing with.

00:06:12.040 --> 00:06:13.770
And that makes sense 'cause, once again,

00:06:13.770 --> 00:06:15.040
you're holding everything else constant,

00:06:15.040 --> 00:06:16.670
you want pressure to be constant,

00:06:16.670 --> 00:06:18.140
temperature to be constant.

00:06:18.140 --> 00:06:21.660
If I were to double the
number of particles here,

00:06:21.660 --> 00:06:24.040
but I don't wanna change the
pressure or the temperature,

00:06:24.040 --> 00:06:26.110
makes sense that I would
have to double the volume.

00:06:26.110 --> 00:06:29.120
Likewise, if I wanted to
double the volume here

00:06:29.120 --> 00:06:31.310
and I didn't wanna change the
pressure or the temperature,

00:06:31.310 --> 00:06:33.590
I would have to put twice
as many particles in there,

00:06:33.590 --> 00:06:36.270
so I still have sufficient
number of interactions

00:06:36.270 --> 00:06:37.620
of bouncing of the particles

00:06:37.620 --> 00:06:39.120
with the sides of the container,

00:06:39.120 --> 00:06:41.690
so that I have sufficient pressure.

00:06:41.690 --> 00:06:44.550
And this notion is called Avogadro's law.

00:06:44.550 --> 00:06:45.890
Last but not least,

00:06:45.890 --> 00:06:48.013
let's say I have two identical containers.

00:06:49.090 --> 00:06:50.740
I have two identical containers,

00:06:50.740 --> 00:06:54.490
that's one there, that's one over here,

00:06:54.490 --> 00:06:57.653
actually I'm gonna draw that
same container a third time.

00:06:58.700 --> 00:07:03.670
And let's say over here, I have gas one

00:07:03.670 --> 00:07:08.220
and in this case, it has
some pressure due to gas one,

00:07:08.220 --> 00:07:10.150
we're gonna assume the
volume and the temperatures

00:07:10.150 --> 00:07:12.350
are the same across all three of these.

00:07:12.350 --> 00:07:14.820
And let's say we have gas two

00:07:14.820 --> 00:07:17.580
and it is exerting pressure too,

00:07:17.580 --> 00:07:20.280
if I were to take all of
the gas in both of them,

00:07:20.280 --> 00:07:22.910
and put them both into
this third container,

00:07:22.910 --> 00:07:26.040
so this third container is
gonna have all of the original

00:07:26.040 --> 00:07:30.140
of gas one and all of
the original of gas two,

00:07:30.140 --> 00:07:32.220
but we aren't changing the volume

00:07:32.220 --> 00:07:34.020
and we aren't changing the temperature.

00:07:34.020 --> 00:07:36.910
In any given unit area on
the surface of the container,

00:07:36.910 --> 00:07:38.910
you're gonna get the
collisions from particle one,

00:07:38.910 --> 00:07:43.150
which would give you P1 in
that force per unit area

00:07:43.150 --> 00:07:46.040
and you're going to get the
collisions from particle two,

00:07:46.040 --> 00:07:48.450
which would give you
that force per unit area.

00:07:48.450 --> 00:07:51.900
So, it makes sense that the
partial pressures would add up

00:07:51.900 --> 00:07:55.160
to be equal to the total
pressure in the container.

00:07:55.160 --> 00:07:57.400
And this is known as Dalton's law.

00:07:57.400 --> 00:08:00.380
But, the whole point of this
video is just appreciate

00:08:00.380 --> 00:08:01.840
that everything we've talked about

00:08:01.840 --> 00:08:04.630
with the ideal gas law,
actually makes a lot of sense,

00:08:04.630 --> 00:08:06.520
I would argue it makes the most sense,

00:08:06.520 --> 00:08:07.370
when you think about it

00:08:07.370 --> 00:08:09.883
in terms of kinetic molecular theory.


Representing solutions using particulate models

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:01.230
- [Instructor] The goal of this video

00:00:01.230 --> 00:00:04.710
is to help us visualize what's
going on with the solution

00:00:04.710 --> 00:00:07.730
at a microscopic really
at a molecular level.

00:00:07.730 --> 00:00:10.130
And also to get practice
drawing these types

00:00:10.130 --> 00:00:12.300
of visualizations, because
you might be asked to do so,

00:00:12.300 --> 00:00:15.220
depending on the type of
chemistry class you're in.

00:00:15.220 --> 00:00:18.120
So what I have here are three
different aqueous solutions,

00:00:18.120 --> 00:00:20.900
which means that the solute
is dissolved in water.

00:00:20.900 --> 00:00:22.320
The first one is sodium chloride.

00:00:22.320 --> 00:00:24.140
Then we have magnesium chloride.

00:00:24.140 --> 00:00:25.623
Then we have C12-H22-O11,

00:00:27.010 --> 00:00:29.220
which in other words is sucrose.

00:00:29.220 --> 00:00:30.640
And each of them are dissolved in water.

00:00:30.640 --> 00:00:31.880
What I'm gonna do is I'm gonna try to

00:00:31.880 --> 00:00:35.060
do a drawing of what's
happening at a particulate level

00:00:35.060 --> 00:00:39.150
in the respective
rectangles right below them.

00:00:39.150 --> 00:00:39.983
So, first of all,

00:00:39.983 --> 00:00:42.840
let's do think about what
happens with sodium chloride.

00:00:42.840 --> 00:00:44.720
So the first thing that you might realize,

00:00:44.720 --> 00:00:45.960
is that sodium chloride,

00:00:45.960 --> 00:00:47.760
this is an ionic compound.

00:00:47.760 --> 00:00:52.670
It's made of up of a
sodium positively charged

00:00:52.670 --> 00:00:54.360
ion or cation,

00:00:54.360 --> 00:00:58.593
and a chloride negatively charged ion.

00:00:59.570 --> 00:01:00.970
And if I wanna draw them,

00:01:00.970 --> 00:01:02.540
and they're going to be
in a one to one ratio.

00:01:02.540 --> 00:01:04.740
For every sodium there's one chloride.

00:01:04.740 --> 00:01:06.830
And I could think about
their relative sizes

00:01:06.830 --> 00:01:09.770
and to help us do so I'll
get out the periodic table

00:01:09.770 --> 00:01:13.030
of elements, and we can
see here that they're both

00:01:13.030 --> 00:01:15.020
in the third period.

00:01:15.020 --> 00:01:16.600
And if we were just looking at the atom,

00:01:16.600 --> 00:01:19.470
a sodium atom versus a chlorine atom,

00:01:19.470 --> 00:01:21.900
the general trend is
as you go to the right

00:01:21.900 --> 00:01:24.880
and you have more electrons
in that outer most shell,

00:01:24.880 --> 00:01:27.610
the radius tends to actually get smaller.

00:01:27.610 --> 00:01:29.870
So a chlorine atom is actually smaller

00:01:29.870 --> 00:01:33.380
than a sodium atom but we're
not talking about atoms.

00:01:33.380 --> 00:01:35.120
We're talking about ions.

00:01:35.120 --> 00:01:39.420
So positively charged sodium
ion that has lost an electron.

00:01:39.420 --> 00:01:43.000
So it actually has an electron
configuration of neon,

00:01:43.000 --> 00:01:44.940
while the chloride anion has

00:01:44.940 --> 00:01:47.200
an electron configuration of argon.

00:01:47.200 --> 00:01:50.445
So it actually turns out
that the chloride anion,

00:01:50.445 --> 00:01:54.190
is going to be larger
than the sodium cation.

00:01:54.190 --> 00:01:59.190
And so what I will do is I will represent

00:01:59.400 --> 00:02:03.600
the chloride anion looking like this.

00:02:03.600 --> 00:02:05.390
I'll put a negative charge there,

00:02:05.390 --> 00:02:10.020
and for the positively
charged sodium cation,

00:02:10.020 --> 00:02:12.510
I will make it a little bit smaller,

00:02:12.510 --> 00:02:15.530
something like that.

00:02:15.530 --> 00:02:19.720
And if I wanted to visualize
it for every sodium

00:02:19.720 --> 00:02:21.790
positively charged ion.

00:02:21.790 --> 00:02:26.040
I would also have to
draw a chloride anion.

00:02:26.040 --> 00:02:28.150
So that's one of them.

00:02:28.150 --> 00:02:30.660
And then you might say,
"okay, well that's the solute,

00:02:30.660 --> 00:02:31.760
but where is..."

00:02:31.760 --> 00:02:33.810
And sometimes they actually
just ask you just to draw

00:02:33.810 --> 00:02:35.950
the solute in which
case you would be done.

00:02:35.950 --> 00:02:37.040
But if you're wondering,

00:02:37.040 --> 00:02:38.890
well how is that
interacting with the water?

00:02:38.890 --> 00:02:41.060
And this will even help us
understand what's happening.

00:02:41.060 --> 00:02:42.660
Why sodium chloride,

00:02:42.660 --> 00:02:45.880
why ionic compounds
dissolve well into water.

00:02:45.880 --> 00:02:48.240
Well then we have to
draw the water molecules.

00:02:48.240 --> 00:02:50.650
And if we still wanna get
the relative sizing right,

00:02:50.650 --> 00:02:52.920
we can go back to our
periodic table of elements.

00:02:52.920 --> 00:02:56.760
And we know that the sodium cation,

00:02:56.760 --> 00:02:59.000
has an electron configuration of neon,

00:02:59.000 --> 00:03:01.850
and oxygen is pretty cool close to that.

00:03:01.850 --> 00:03:03.310
And when we're talking about water,

00:03:03.310 --> 00:03:06.540
the oxygen atom is hogging the electrons.

00:03:06.540 --> 00:03:08.280
The electrons are spending
a little bit more time

00:03:08.280 --> 00:03:10.610
around the oxygen than
around the hydrogens.

00:03:10.610 --> 00:03:12.530
So it's actually going
to be similar in size,

00:03:12.530 --> 00:03:15.360
and oxygen and water and a sodium cation.

00:03:15.360 --> 00:03:18.940
And obviously these aren't
going to be exact drawings,

00:03:18.940 --> 00:03:21.360
but we can imagine each water

00:03:21.360 --> 00:03:24.610
might look something like that.

00:03:24.610 --> 00:03:27.370
So it's an oxygen with two hydrogens.

00:03:27.370 --> 00:03:30.280
I'll just do it all in this
white color, right over here.

00:03:30.280 --> 00:03:32.610
And then the question is what
would their orientation be?

00:03:32.610 --> 00:03:34.250
And that's really important to get right,

00:03:34.250 --> 00:03:35.560
especially when you're dealing with water,

00:03:35.560 --> 00:03:37.770
which is a polar molecule.

00:03:37.770 --> 00:03:39.620
We know that the electrons spend more time

00:03:39.620 --> 00:03:40.500
around the oxygen.

00:03:40.500 --> 00:03:42.490
We talked about this in many videos.

00:03:42.490 --> 00:03:45.570
So the oxygen end has a
partial negative charge,

00:03:45.570 --> 00:03:49.550
while the hydrogen ends have
a partial positive charge.

00:03:49.550 --> 00:03:51.840
And so the orientation of
a water molecule is that

00:03:51.840 --> 00:03:55.400
the partially negative oxygen end,

00:03:55.400 --> 00:03:58.600
will be attracted to the positive ions.

00:03:58.600 --> 00:04:01.240
And then the positively
charged hydrogen ends

00:04:01.240 --> 00:04:04.720
will be attracted to the negative ions.

00:04:04.720 --> 00:04:06.150
So you might have something like that.

00:04:06.150 --> 00:04:09.260
That's oxygen and then the two hydrogens.

00:04:09.260 --> 00:04:11.420
You might have an oxygen,

00:04:11.420 --> 00:04:14.310
and then you have the two hydrogens.

00:04:14.310 --> 00:04:15.370
Because the hydrogens,

00:04:15.370 --> 00:04:16.890
that end of the water molecule has

00:04:16.890 --> 00:04:18.530
a partially positive charge.

00:04:18.530 --> 00:04:21.860
They're going to be attracted
to this chloride anion.

00:04:21.860 --> 00:04:24.230
You might have once again,

00:04:24.230 --> 00:04:26.730
the two hydrogens and then the oxygen.

00:04:26.730 --> 00:04:28.952
And once again, the oxygen
is going to be attracted

00:04:28.952 --> 00:04:32.780
to the sodium, the positively
charged sodium cations.

00:04:32.780 --> 00:04:35.600
And I could keep filling these in for,

00:04:35.600 --> 00:04:36.730
in this entire space.

00:04:36.730 --> 00:04:39.440
But I think you get the
idea of what the water

00:04:39.440 --> 00:04:42.590
would kind of look like and
how it would be oriented.

00:04:42.590 --> 00:04:43.860
Now for these next two,

00:04:43.860 --> 00:04:45.480
let's just focus on the solutes.

00:04:45.480 --> 00:04:48.093
What would the solute
look like in the solution?

00:04:49.640 --> 00:04:51.420
Well, magnesium chloride,

00:04:51.420 --> 00:04:54.080
this once again is an ionic compound.

00:04:54.080 --> 00:04:59.080
And so it is going to disassociate
into its constituent ions

00:04:59.180 --> 00:05:01.470
for every one magnesium ion,

00:05:01.470 --> 00:05:03.980
actually going to have a plus two charge.

00:05:03.980 --> 00:05:05.320
You're going to have two,

00:05:05.320 --> 00:05:08.330
negatively charged chloride anions.

00:05:08.330 --> 00:05:10.180
And what's the relative sizing?

00:05:10.180 --> 00:05:11.140
Well, to help us with that,

00:05:11.140 --> 00:05:13.790
we go back to the periodic
table of elements.

00:05:13.790 --> 00:05:16.520
And if we're talking
about a magnesium two plus

00:05:16.520 --> 00:05:18.900
or positively charged ion,

00:05:18.900 --> 00:05:22.070
it's still going to have an
electron configuration of neon,

00:05:22.070 --> 00:05:25.500
and it's going to have more
protons than the sodium ion.

00:05:25.500 --> 00:05:27.440
So it's gonna pull even harder on them.

00:05:27.440 --> 00:05:30.900
So it's gonna be even
smaller than the sodium ion.

00:05:30.900 --> 00:05:34.650
So we could draw the
magnesium ions like this.

00:05:34.650 --> 00:05:36.180
Maybe I'll do two of them.

00:05:36.180 --> 00:05:39.480
So I'm gonna do it even
smaller than the sodium

00:05:39.480 --> 00:05:41.910
and I'll write two plus,

00:05:41.910 --> 00:05:43.960
because it has a positive two charge.

00:05:43.960 --> 00:05:46.090
I will write two plus again,

00:05:46.090 --> 00:05:47.630
'cause it has a positive charge.

00:05:47.630 --> 00:05:50.020
And for every one of those,

00:05:50.020 --> 00:05:52.070
you're going to have two chloride anions.

00:05:53.060 --> 00:05:57.780
So maybe one there, maybe one there,

00:05:57.780 --> 00:06:02.420
maybe one there and then maybe one there.

00:06:02.420 --> 00:06:05.850
And then if you were
asked to draw the solvent,

00:06:05.850 --> 00:06:08.660
draw the water, you would
orient it similarly.

00:06:08.660 --> 00:06:11.510
Where the partially
positive the hydrogen ends

00:06:11.510 --> 00:06:14.270
of the water would be attracted to

00:06:14.270 --> 00:06:16.800
the negative chloride anions.

00:06:16.800 --> 00:06:20.640
And the oxygen end of the water
molecules would be attracted

00:06:20.640 --> 00:06:25.070
to these plus two charge magnesium ions.

00:06:25.070 --> 00:06:26.570
Now what about sucrose?

00:06:26.570 --> 00:06:28.560
It isn't an ionic compounds.

00:06:28.560 --> 00:06:29.393
So in this situation,

00:06:29.393 --> 00:06:31.390
it's not going to disassociate.

00:06:31.390 --> 00:06:35.500
So a sucrose molecule
is relatively larger.

00:06:35.500 --> 00:06:36.660
I'll draw it like that.

00:06:36.660 --> 00:06:40.800
Maybe we have another one just like that.

00:06:40.800 --> 00:06:43.210
And the reason why it
dissolves in water well is,

00:06:43.210 --> 00:06:46.620
a sucrose molecule has
parts of the molecule

00:06:46.620 --> 00:06:47.680
that have polarity to it.

00:06:47.680 --> 00:06:49.290
It has a lot of OH groups.

00:06:49.290 --> 00:06:52.470
So there's parts of the molecule
that are partially positive

00:06:52.470 --> 00:06:54.760
and other parts of the molecule
that are partially negative,

00:06:54.760 --> 00:06:56.560
other parts that are partially positive.

00:06:56.560 --> 00:07:01.420
And so that's able to be
attracted to the various ends

00:07:01.420 --> 00:07:03.130
depending on whether
it's partially positive,

00:07:03.130 --> 00:07:04.290
partially negative,

00:07:04.290 --> 00:07:06.480
of the water molecule.

00:07:06.480 --> 00:07:08.009
And so I'll just write it like this.

00:07:08.009 --> 00:07:11.979
C12-H22-O11.

00:07:11.979 --> 00:07:15.560
C12-H22-O11.

00:07:15.560 --> 00:07:16.393
For the sake of time,

00:07:16.393 --> 00:07:18.220
I haven't drawn the water molecules here

00:07:18.220 --> 00:07:20.280
and to actually make, to
draw them intelligently,

00:07:20.280 --> 00:07:22.640
you would have to know what
parts of this larger molecule

00:07:22.640 --> 00:07:26.460
have a partially positive
or partial negative charge.

00:07:26.460 --> 00:07:29.120
But as we'll see the
fact that you can either

00:07:29.120 --> 00:07:32.790
disassociate into ions
that clearly have charge,

00:07:32.790 --> 00:07:36.480
or then you have a larger
molecule where parts of it

00:07:36.480 --> 00:07:38.590
have a partial charge or have some charge

00:07:38.590 --> 00:07:39.670
associated with it.

00:07:39.670 --> 00:07:42.330
That's what allows it to dissolve well

00:07:42.330 --> 00:07:44.953
into a polar solvent like water.


Molarity

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:01.153
- [Instructor] In this video,

00:00:01.153 --> 00:00:02.980
we're gonna talk about one
of the most common ways

00:00:02.980 --> 00:00:06.350
to measure solute
concentration in a solution.

00:00:06.350 --> 00:00:08.313
And that is molarity.

00:00:09.540 --> 00:00:14.540
And molarity is defined as
the number of moles of solute,

00:00:17.430 --> 00:00:20.373
the thing that we are
dissolving in a solvent,

00:00:21.770 --> 00:00:26.770
that divided by the liters of solution.

00:00:28.410 --> 00:00:29.800
So let's just do an example

00:00:29.800 --> 00:00:34.130
and see if we can calculate
the molarity of a solution.

00:00:34.130 --> 00:00:38.640
So let's say that I have,
this is a container here.

00:00:38.640 --> 00:00:43.260
And I'm going to dissolve
some sodium sulfate in water.

00:00:43.260 --> 00:00:47.350
So sodium sulfate is the solute
and water is the solvent.

00:00:47.350 --> 00:00:49.820
Together, they give us this solution.

00:00:49.820 --> 00:00:51.780
And let's say we have a total,

00:00:51.780 --> 00:00:56.780
the total volume of solution
is 250 milliliters of solution.

00:00:59.040 --> 00:01:02.170
And that solution is made
up of just to give ourselves

00:01:02.170 --> 00:01:03.550
a bit of a refresher.

00:01:03.550 --> 00:01:07.790
We have the solvent, which is H2O,

00:01:07.790 --> 00:01:09.720
it is water in this situation.

00:01:09.720 --> 00:01:12.720
And you might say, do we have
250 milliliters of water?

00:01:12.720 --> 00:01:14.480
And the answer would be not quite

00:01:14.480 --> 00:01:17.920
because the 250 milliliters
that's the volume of the water

00:01:17.920 --> 00:01:20.540
plus the sodium sulfate.

00:01:20.540 --> 00:01:24.160
And so we're gonna have
some sodium sulfate in here.

00:01:24.160 --> 00:01:26.280
And let's say we know

00:01:26.280 --> 00:01:31.280
that we have 35.5 grams of sodium sulfate.

00:01:36.260 --> 00:01:39.780
That is the formula for sodium sulfate.

00:01:39.780 --> 00:01:41.530
And so given this information,

00:01:41.530 --> 00:01:43.380
how do we figure out molarity?

00:01:43.380 --> 00:01:44.820
Well, the first thing
you might say is okay,

00:01:44.820 --> 00:01:46.820
I know the number of
grams of sodium sulfate.

00:01:46.820 --> 00:01:48.680
I need to figure out the number of moles.

00:01:48.680 --> 00:01:50.240
And to figure out the number of moles,

00:01:50.240 --> 00:01:51.730
you'd have to look at the molar mass.

00:01:51.730 --> 00:01:54.630
You could figure that out from
a periodic table of elements.

00:01:54.630 --> 00:01:56.330
But just to speed us along,

00:01:56.330 --> 00:01:58.510
I will help you out a little bit here.

00:01:58.510 --> 00:02:01.530
The molar mass sodium sulfate,

00:02:02.990 --> 00:02:05.990
molar mass is 142.04 grams per mole.

00:02:13.870 --> 00:02:15.960
So given everything I've now told you,

00:02:15.960 --> 00:02:17.110
see if you can pause this video

00:02:17.110 --> 00:02:20.040
and figure out the
molarity of this solution.

00:02:20.040 --> 00:02:23.203
What's the molarity of the
sodium sulfate in this solution?

00:02:24.230 --> 00:02:26.020
All right, now let's work
through this together.

00:02:26.020 --> 00:02:31.020
So first, we wanna figure out
the number of moles of solute.

00:02:31.810 --> 00:02:34.250
So we can start with the mass of solute

00:02:34.250 --> 00:02:35.340
that we have right over here.

00:02:35.340 --> 00:02:40.340
So we have 35.5 grams of sodium sulfate.

00:02:42.820 --> 00:02:46.360
And now if we wanna figure
out the number of moles,

00:02:46.360 --> 00:02:48.000
see I'm gonna multiply
this times something

00:02:48.000 --> 00:02:49.940
that would cancel out the grams.

00:02:49.940 --> 00:02:51.960
And so I don't want grams per mole.

00:02:51.960 --> 00:02:54.090
I want moles per gram.

00:02:54.090 --> 00:02:55.160
And so I could write this.

00:02:55.160 --> 00:02:59.490
I could multiply this
times for every one mole

00:03:00.410 --> 00:03:05.410
of sodium sulfate, NA2SO4, we have 142.04.

00:03:09.590 --> 00:03:14.590
I'll write this way,
grams of sodium sulfate.

00:03:15.370 --> 00:03:16.920
And you can see very clearly

00:03:16.920 --> 00:03:18.510
that that will cancel with that

00:03:18.510 --> 00:03:20.870
and we're left with
moles of sodium sulfate.

00:03:20.870 --> 00:03:22.300
So we'll get a calculator out in a second

00:03:22.300 --> 00:03:26.787
and just take 35.5 and
divide that by 142.04.

00:03:29.300 --> 00:03:30.650
And then to figure out molarity,

00:03:30.650 --> 00:03:33.850
we wanna divide by the liters of solution.

00:03:33.850 --> 00:03:36.150
So up here we have a
calculation for number of moles

00:03:36.150 --> 00:03:37.600
and then the liters have solution,

00:03:37.600 --> 00:03:41.447
250 milliliters is the
same thing as 0.250 liters

00:03:44.290 --> 00:03:45.590
of our solution.

00:03:45.590 --> 00:03:47.820
And now we can just use our calculator

00:03:47.820 --> 00:03:49.170
to figure out what this is.

00:03:50.130 --> 00:03:55.130
35.5 divided by 142.04 equals that,

00:04:01.370 --> 00:04:05.233
and then we divide that by 0.25.

00:04:07.520 --> 00:04:09.080
I could just throw a zero in there.

00:04:09.080 --> 00:04:11.750
And then that gets us
that right over there.

00:04:11.750 --> 00:04:12.640
And then we can think about

00:04:12.640 --> 00:04:15.740
how many significant figures we have.

00:04:15.740 --> 00:04:17.330
So we have three over here.

00:04:17.330 --> 00:04:19.530
We have one, two, three,
four, five over here.

00:04:19.530 --> 00:04:21.960
We have three over here.

00:04:21.960 --> 00:04:25.170
So, I would say that we have
three significant figures.

00:04:25.170 --> 00:04:28.120
And so we would round this right most

00:04:28.120 --> 00:04:30.090
or this nine right over here.

00:04:30.090 --> 00:04:33.973
Well, if we round that up, we get 1.00,

00:04:35.640 --> 00:04:38.090
if we were to go to three
significant figures.

00:04:38.090 --> 00:04:40.633
So that gets us 1.00.

00:04:42.230 --> 00:04:44.800
And then you might say
what is the units here?

00:04:44.800 --> 00:04:49.600
And what people will normally
say is this is 1.00 molar.

00:04:49.600 --> 00:04:51.780
When you see this capital
M right over here,

00:04:51.780 --> 00:04:53.960
that is the unit for more molarity

00:04:53.960 --> 00:04:56.160
but they're really talking
about the number of moles

00:04:56.160 --> 00:04:59.310
of solute per liter of solution.

00:04:59.310 --> 00:05:02.073
And we are done.


Dilution

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:01.810
- [Instructor] In this
video, we're gonna talk

00:00:01.810 --> 00:00:04.620
about a concept in chemistry
that's quite important,

00:00:04.620 --> 00:00:07.060
known as dilutions.

00:00:07.060 --> 00:00:09.170
So let's do an example.

00:00:09.170 --> 00:00:13.610
So let's say we have a large
vat, as much as we need.

00:00:13.610 --> 00:00:16.730
It's a one-molar solution
of sodium sulfate,

00:00:16.730 --> 00:00:17.950
and it's an aqueous solution.

00:00:17.950 --> 00:00:20.760
So sodium sulfate is dissolved in water.

00:00:20.760 --> 00:00:24.020
And let's say we also have
as much water as we need,

00:00:24.020 --> 00:00:27.890
and what we want to do
is create a solution,

00:00:27.890 --> 00:00:30.750
another aqueous solution
of sodium sulfate,

00:00:30.750 --> 00:00:33.420
but one that has a
different concentration,

00:00:33.420 --> 00:00:36.040
in this case, one that
has a lower concentration.

00:00:36.040 --> 00:00:40.750
So we want to create
a 0.125-molar solution

00:00:40.750 --> 00:00:45.230
of sodium sulfate, and
we want 500 milliliters

00:00:45.230 --> 00:00:47.230
of this new solution.

00:00:47.230 --> 00:00:48.820
Pause this video and think about

00:00:48.820 --> 00:00:50.220
how you would approach that.

00:00:51.470 --> 00:00:53.430
All right, now let's
think about this together.

00:00:53.430 --> 00:00:55.890
So, first let's just
go over the intuition.

00:00:55.890 --> 00:00:58.010
You have a higher concentration here.

00:00:58.010 --> 00:01:00.130
You have a lower concentration here.

00:01:00.130 --> 00:01:02.070
So our intuition would tell us

00:01:02.070 --> 00:01:05.330
is that we're going to take
less than 500 milliliters

00:01:05.330 --> 00:01:09.240
of our original solution,
pour some of that in.

00:01:09.240 --> 00:01:11.960
That's going to have a
sufficient number of moles

00:01:11.960 --> 00:01:13.690
of sodium sulfate that,

00:01:13.690 --> 00:01:18.160
if we were to then fill
this up to 500 milliliters,

00:01:18.160 --> 00:01:22.770
that we would then have
a 0.125-molar solution.

00:01:22.770 --> 00:01:26.950
So the question really
is, is how much of this

00:01:26.950 --> 00:01:31.460
do we have to put in, which
we can then dilute with water

00:01:31.460 --> 00:01:34.730
to get to our goal solution?

00:01:34.730 --> 00:01:37.290
Well, to answer that question,
we just have to figure out

00:01:37.290 --> 00:01:40.080
how many moles of sodium sulfate

00:01:40.080 --> 00:01:44.350
need to be in this final
goal solution, this one

00:01:44.350 --> 00:01:46.630
or this one, depending
on how we visualize it?

00:01:46.630 --> 00:01:49.060
And then, how much of
our original solution,

00:01:49.060 --> 00:01:51.340
of our one-molar solution,
do we need to take out

00:01:51.340 --> 00:01:53.630
to have that many moles?

00:01:53.630 --> 00:01:55.930
And to think about how many moles,

00:01:55.930 --> 00:01:58.690
we just have to remind
ourselves what molarity is.

00:01:58.690 --> 00:02:03.690
We know already that molarity
is equal to number of moles,

00:02:04.610 --> 00:02:08.620
number of moles, of solute

00:02:10.270 --> 00:02:13.980
per liters of solution,

00:02:13.980 --> 00:02:16.213
liters of solution.

00:02:17.220 --> 00:02:19.370
Or another way to think about it is,

00:02:19.370 --> 00:02:22.760
if we multiply both sides
by liters of solution,

00:02:22.760 --> 00:02:27.550
we would get liters of solution

00:02:29.660 --> 00:02:33.893
times molarity, times molarity,

00:02:34.910 --> 00:02:37.740
is equal to the number of moles of solute,

00:02:37.740 --> 00:02:42.740
number of moles of solute.

00:02:43.400 --> 00:02:46.560
So what we can do is say,
all right, how many moles

00:02:46.560 --> 00:02:50.100
of our solute do we need in our goal?

00:02:50.100 --> 00:02:52.100
Well, to do that, we just
have to say, all right,

00:02:52.100 --> 00:02:56.700
we want to eventually have
500 milliliters of solution,

00:02:56.700 --> 00:02:58.400
or we could rewrite that

00:02:58.400 --> 00:03:00.207
as 0.500 liters,

00:03:04.730 --> 00:03:07.140
and this little decimal
point right over here

00:03:07.140 --> 00:03:08.110
makes it clear that we're dealing

00:03:08.110 --> 00:03:10.310
with three significant figures,

00:03:10.310 --> 00:03:12.340
that we've rounded to the nearest one,

00:03:12.340 --> 00:03:15.060
when we got to this, when we
have this goal right over here,

00:03:15.060 --> 00:03:16.660
or we would round to the nearest,

00:03:16.660 --> 00:03:18.410
to the ones place, I guess.

00:03:18.410 --> 00:03:21.640
So, our goal is to have half a liter

00:03:21.640 --> 00:03:24.060
of solution at a molarity

00:03:24.060 --> 00:03:28.750
of 0.125 molar,

00:03:28.750 --> 00:03:29.890
and then that is gonna give us

00:03:29.890 --> 00:03:31.270
the number of moles we need.

00:03:31.270 --> 00:03:33.560
And, if we multiply this
out, this is going to be

00:03:33.560 --> 00:03:37.630
zero point, let's see, half of 12 is 6

00:03:37.630 --> 00:03:39.810
and then half of 50 is 25,

00:03:39.810 --> 00:03:44.810
0.0625 moles,

00:03:45.180 --> 00:03:47.923
moles of solute.

00:03:49.080 --> 00:03:54.080
And, in this case, our
solute is sodium sulfate.

00:03:54.520 --> 00:03:57.330
And let's see if I got the
significant figures right.

00:03:57.330 --> 00:03:58.520
I have three right over here,

00:03:58.520 --> 00:04:00.560
one, two, three, one, two, three.

00:04:00.560 --> 00:04:01.580
So I take the product.

00:04:01.580 --> 00:04:05.060
I'd still have one, two,
three significant figures.

00:04:05.060 --> 00:04:06.300
So this is our goal.

00:04:06.300 --> 00:04:08.290
We want to have this many moles of solute.

00:04:08.290 --> 00:04:09.390
So we just have to figure out

00:04:09.390 --> 00:04:12.250
how much of our original
solution do we need

00:04:12.250 --> 00:04:15.650
in order to have that many
moles of sodium sulfate?

00:04:15.650 --> 00:04:17.360
So, one way to think about it is,

00:04:17.360 --> 00:04:20.530
there's some mystery volume
of our original solution

00:04:20.530 --> 00:04:23.930
we need, and we know what
its concentration is.

00:04:23.930 --> 00:04:27.120
It's a one-molar concentration that,

00:04:27.120 --> 00:04:28.450
when I take this product,

00:04:28.450 --> 00:04:32.920
I am going to get 0.0625 moles

00:04:33.780 --> 00:04:37.400
of sodium sulfate.

00:04:37.400 --> 00:04:39.840
And the math here is
pretty straightforward.

00:04:39.840 --> 00:04:42.930
We can divide both sides by one molar,

00:04:42.930 --> 00:04:44.830
and what are we going to get?

00:04:44.830 --> 00:04:46.060
And the units work out

00:04:46.060 --> 00:04:48.980
because we're in moles
where you have molar here.

00:04:48.980 --> 00:04:51.240
And so this is going to give
us our answer in liters.

00:04:51.240 --> 00:04:53.280
You divide both sides by one molar.

00:04:53.280 --> 00:04:58.280
You're going to get that
question mark is equal to

00:04:58.670 --> 00:05:03.670
0.0625 liters of solution.

00:05:04.850 --> 00:05:07.330
Or another way to think about
it is, this is equivalent

00:05:07.330 --> 00:05:12.100
to 62.5 milliliters

00:05:13.100 --> 00:05:14.930
of our original solution.

00:05:14.930 --> 00:05:17.300
I want to make sure I got all
the significant figures right.

00:05:17.300 --> 00:05:20.620
Had three over there. One,
two, three, one, two, three.

00:05:20.620 --> 00:05:21.860
And so, yes, right over here.

00:05:21.860 --> 00:05:24.670
I can still have one, two,
three significant figures

00:05:24.670 --> 00:05:26.480
or sometimes called significant digits.

00:05:26.480 --> 00:05:28.390
And so there we've answered our question.

00:05:28.390 --> 00:05:31.090
What I would do is I would take 62.5,

00:05:32.404 --> 00:05:36.020
62.5 milliliters of my original solution,

00:05:36.020 --> 00:05:37.550
so that's this over here,

00:05:37.550 --> 00:05:40.940
and then I would take my
water and then keep filling

00:05:40.940 --> 00:05:45.280
until I get to 500
milliliters, and we're done.

00:05:45.280 --> 00:05:48.930
At that point, I'm going
to have a 0.125 molar

00:05:48.930 --> 00:05:51.823
of sodium sulfate aqueous solution.


Types of mixtures

WEBVTT
Kind: captions
Language: en

00:00:00.470 --> 00:00:03.660
- [Instructor] I suspect that
you might already be familiar

00:00:03.660 --> 00:00:06.090
with the term mixture.

00:00:06.090 --> 00:00:08.310
It really does mean
what you think it means.

00:00:08.310 --> 00:00:09.980
If you take two or more substances

00:00:09.980 --> 00:00:11.830
and you were to mix them together,

00:00:11.830 --> 00:00:13.870
you are dealing with a mixture.

00:00:13.870 --> 00:00:17.610
And it could be a solid,
a liquid or a gas.

00:00:17.610 --> 00:00:20.800
Now there's fundamentally two
different types of mixtures.

00:00:20.800 --> 00:00:23.360
There's heterogeneous mixtures.

00:00:23.360 --> 00:00:26.020
And hetero, you're going
to see that prefix a lot,

00:00:26.020 --> 00:00:27.540
means different.

00:00:27.540 --> 00:00:32.540
So heterogeneous, this
is referring to mixtures

00:00:32.780 --> 00:00:36.090
that if you look at it
from a macro point of view,

00:00:36.090 --> 00:00:38.950
I'll do a heterogeneous liquid mixture.

00:00:38.950 --> 00:00:41.520
And what I often think of
here at the extreme form

00:00:41.520 --> 00:00:42.660
is where with my naked eye,

00:00:42.660 --> 00:00:45.130
I could see that different
parts of the mixtures

00:00:45.130 --> 00:00:47.960
have different concentrations
of the different things

00:00:47.960 --> 00:00:49.210
that have been mixed up.

00:00:49.210 --> 00:00:51.580
One example I often think
of is chocolate milk

00:00:51.580 --> 00:00:53.300
that's not well mixed.

00:00:53.300 --> 00:00:55.210
At the top you're going
to see these clumps

00:00:55.210 --> 00:00:57.120
and depending where you are in the milk,

00:00:57.120 --> 00:00:59.598
you can actually see it with your eye,

00:00:59.598 --> 00:01:02.190
that you don't have
consistent concentrations

00:01:02.190 --> 00:01:03.540
of the different substances.

00:01:03.540 --> 00:01:06.430
The properties of the
mixtures are different,

00:01:06.430 --> 00:01:10.240
depending on what part of
the mixture you look at.

00:01:10.240 --> 00:01:13.580
Now, you can imagine if
there's heterogeneous mixtures,

00:01:13.580 --> 00:01:17.140
the opposite would be
homogeneous mixtures.

00:01:17.140 --> 00:01:19.320
Those would be mixtures
that when you look at it

00:01:19.320 --> 00:01:22.230
from a macro point of
view, it looks consistent

00:01:22.230 --> 00:01:24.450
any point of the mixture.

00:01:24.450 --> 00:01:28.820
Homogeneous mixtures.

00:01:28.820 --> 00:01:32.500
And homogeneous mixtures,
there's another term for it,

00:01:32.500 --> 00:01:34.170
which you have probably heard.

00:01:34.170 --> 00:01:37.193
They're also known as solutions.

00:01:38.410 --> 00:01:40.460
And as I mentioned, when
we talk about mixtures,

00:01:40.460 --> 00:01:42.740
we could be talking about
solid, liquid or gas.

00:01:42.740 --> 00:01:44.810
Oftentimes in our head, we
think liquid immediately,

00:01:44.810 --> 00:01:46.360
but it can be solid liquid or gas.

00:01:46.360 --> 00:01:48.340
And so the same thing
is true for solutions.

00:01:48.340 --> 00:01:51.040
You can have solid liquids or gases.

00:01:51.040 --> 00:01:55.970
And an example of a
solid solution would be,

00:01:55.970 --> 00:01:58.960
say a metal alloy.

00:01:58.960 --> 00:02:02.010
Where at the macro level it's color,

00:02:02.010 --> 00:02:04.570
how well does it conduct electricity?

00:02:04.570 --> 00:02:06.400
How malleable is it?

00:02:06.400 --> 00:02:07.840
How hard is it?

00:02:07.840 --> 00:02:09.920
It looks like the properties are uniform

00:02:09.920 --> 00:02:11.050
throughout the alloy.

00:02:11.050 --> 00:02:13.220
If I have some type of metal alloy,

00:02:13.220 --> 00:02:17.610
if I were to just look at it like this,

00:02:17.610 --> 00:02:20.240
if I were to look at say bronze,

00:02:20.240 --> 00:02:22.010
well, from my point of view,

00:02:22.010 --> 00:02:24.920
it has the same properties
throughout the bronze.

00:02:24.920 --> 00:02:27.610
And I should probably do
bronze in a more bronze color

00:02:27.610 --> 00:02:28.660
right over here.

00:02:28.660 --> 00:02:29.970
But if you were to look at it

00:02:29.970 --> 00:02:32.030
with a very sensitive microscope

00:02:32.030 --> 00:02:33.160
or based on the models

00:02:33.160 --> 00:02:36.100
that we now know what is
going on in that metal,

00:02:36.100 --> 00:02:37.340
in that alloy,

00:02:37.340 --> 00:02:42.340
what's happening is you actually
have a mixture of metals.

00:02:42.810 --> 00:02:46.840
But it is a homogeneous mixture of metals

00:02:46.840 --> 00:02:49.070
because at a macro level,

00:02:49.070 --> 00:02:51.410
you can't really see the differences.

00:02:51.410 --> 00:02:53.280
Now at a micro level, you can,

00:02:53.280 --> 00:02:56.200
because there are different
metals mixed in together

00:02:56.200 --> 00:02:58.180
in this alloy.

00:02:58.180 --> 00:03:03.180
Now, as can imagine you
also have liquid solutions

00:03:03.440 --> 00:03:04.570
and in chemistry,

00:03:04.570 --> 00:03:06.640
these are the ones that
we'll often deal most.

00:03:06.640 --> 00:03:09.860
We will also deal with solid
and gas solutions as well.

00:03:09.860 --> 00:03:12.440
And when I think of a
homogeneous liquid mixture

00:03:12.440 --> 00:03:16.040
or a liquid solution, the one
that comes to mind for me,

00:03:16.040 --> 00:03:17.290
but we'll see a lot of these

00:03:17.290 --> 00:03:20.573
in our journey through
chemistry is salt water.

00:03:21.490 --> 00:03:23.410
Salt water.

00:03:23.410 --> 00:03:28.110
Salt water has sodium
chloride dissolved in water.

00:03:28.110 --> 00:03:29.850
And if you were to go to the ocean,

00:03:29.850 --> 00:03:31.940
and if you were to just
look at the salt water,

00:03:31.940 --> 00:03:34.550
or if you were to measure its
properties, even in a lab,

00:03:34.550 --> 00:03:37.560
you would see that the properties
throughout the salt water

00:03:37.560 --> 00:03:39.160
seem to be uniform.

00:03:39.160 --> 00:03:42.880
At a macro level, it
appears to be homogeneous.

00:03:42.880 --> 00:03:44.660
It appears to be uniform.

00:03:44.660 --> 00:03:46.730
But if you were to look
at what's happening

00:03:46.730 --> 00:03:48.160
at an atomic level,

00:03:48.160 --> 00:03:53.080
you would see that you
have your water molecules.

00:03:53.080 --> 00:03:54.340
Let me draw the water like that.

00:03:54.340 --> 00:03:58.600
That is the oxygen, each
of them has two hydrogens.

00:03:58.600 --> 00:04:02.330
And this end is partially positive,

00:04:02.330 --> 00:04:05.520
we've seen this multiple
times, the hydrogen end,

00:04:05.520 --> 00:04:08.300
the oxygen end is partially negative.

00:04:08.300 --> 00:04:11.610
And so when you dissolve
the sodium chloride,

00:04:11.610 --> 00:04:13.780
the chloride anions

00:04:13.780 --> 00:04:16.770
are attracted to the
positive ends of the water.

00:04:16.770 --> 00:04:20.070
So maybe you have a chloride anion there.

00:04:20.070 --> 00:04:22.660
And the sodium ions

00:04:22.660 --> 00:04:26.220
would be attracted to the
negative end of the H2O.

00:04:26.220 --> 00:04:29.250
So that's the sodium right over there.

00:04:29.250 --> 00:04:31.370
So when you look at it
at a micro perspective,

00:04:31.370 --> 00:04:33.290
you see that there are
different molecules,

00:04:33.290 --> 00:04:36.300
but at a macro perspective,
the macro properties,

00:04:36.300 --> 00:04:38.560
how it responds to different stimulus,

00:04:38.560 --> 00:04:42.010
how well it conducts electricity,
what it even looks like,

00:04:42.010 --> 00:04:44.340
it seems to be uniform.

00:04:44.340 --> 00:04:48.050
Now to be clear, saltwater is
not the only liquid solution.

00:04:48.050 --> 00:04:49.890
There's many types of liquid solutions.

00:04:49.890 --> 00:04:51.830
In chemistry, we'll often see water

00:04:51.830 --> 00:04:54.430
as our most common solvent.

00:04:54.430 --> 00:04:56.570
That's the thing that
you have the most of,

00:04:56.570 --> 00:04:59.200
the thing that other things
are getting dissolved in it.

00:04:59.200 --> 00:05:00.460
The things that are getting dissolved

00:05:00.460 --> 00:05:02.340
are called the solute,

00:05:02.340 --> 00:05:05.530
in this case it would
be the sodium chloride

00:05:05.530 --> 00:05:08.200
and the water is the solvent.

00:05:08.200 --> 00:05:09.883
Let me write that down, solvent.

00:05:11.810 --> 00:05:12.710
When you have a solution

00:05:12.710 --> 00:05:15.040
where you have something
dissolved in water,

00:05:15.040 --> 00:05:19.973
this is often called an
aqueous, aqueous solution.

00:05:21.370 --> 00:05:23.413
And sometimes it's abbreviated aq.

00:05:25.100 --> 00:05:28.700
Now, last but not least, we
haven't talked about gases yet.

00:05:28.700 --> 00:05:32.930
And you can for sure
have a solution of gas.

00:05:32.930 --> 00:05:34.330
And the one that's most common

00:05:34.330 --> 00:05:36.830
is the one that you and I
are breathing right now.

00:05:36.830 --> 00:05:40.113
The air around you is a gas solution.

00:05:41.619 --> 00:05:44.380
It's macroscopic
properties seem consistent,

00:05:44.380 --> 00:05:45.770
they seem uniform,

00:05:45.770 --> 00:05:50.190
but we know that the gas around
us is a mixture of nitrogen,

00:05:50.190 --> 00:05:52.710
of oxygen, of carbon dioxide,

00:05:52.710 --> 00:05:55.840
as well as molecules of other things.

00:05:55.840 --> 00:06:00.840
So a good example of a
gas solution would be air.

00:06:01.200 --> 00:06:02.570
So I'll let you go there.

00:06:02.570 --> 00:06:05.650
That's just a good primer
on what a mixture is,

00:06:05.650 --> 00:06:06.750
the types of mixtures

00:06:06.750 --> 00:06:09.700
and especially the subtype of a mixture,

00:06:09.700 --> 00:06:11.260
which is a homogeneous mixture,

00:06:11.260 --> 00:06:13.693
which we often call a solution.


Introduction to real gases

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:01.810
- [Instructor] In several other videos,

00:00:01.810 --> 00:00:05.970
we have talked about the ideal gas law,

00:00:05.970 --> 00:00:10.300
which tells us that pressure times volume

00:00:10.300 --> 00:00:12.540
is going to be equal to

00:00:12.540 --> 00:00:15.580
the number of moles times
the ideal gas constant,

00:00:15.580 --> 00:00:18.770
times the temperature, measured in Kelvin.

00:00:18.770 --> 00:00:22.320
Now in all of our studies
of the ideal gas law,

00:00:22.320 --> 00:00:23.990
we assumed that the gases

00:00:23.990 --> 00:00:26.930
that we were dealing with were ideal,

00:00:26.930 --> 00:00:28.400
And now we're gonna
think a little bit about

00:00:28.400 --> 00:00:31.670
what does it mean to be ideal
and what do real gasses,

00:00:31.670 --> 00:00:35.360
how do they vary from actual ideal gases?

00:00:35.360 --> 00:00:39.520
Well, in order for us to
assume that a gas is ideal,

00:00:39.520 --> 00:00:42.420
we assume that its volume,

00:00:42.420 --> 00:00:44.620
the volume that the gas takes up,

00:00:44.620 --> 00:00:49.620
volume of gas, is negligible, negligible,

00:00:49.990 --> 00:00:54.990
relative to container, to container.

00:00:55.710 --> 00:00:57.200
The other thing we assume

00:00:57.200 --> 00:00:59.400
is that the molecules of the gas

00:00:59.400 --> 00:01:01.310
don't interact with each other.

00:01:01.310 --> 00:01:05.673
Molecules don't interact.

00:01:07.810 --> 00:01:08.860
Now in the real world,

00:01:08.860 --> 00:01:13.310
we know that all molecules
take up some volume,

00:01:13.310 --> 00:01:15.130
but it could be a reasonable assumption,

00:01:15.130 --> 00:01:17.500
if we're talking about
a really huge container,

00:01:17.500 --> 00:01:21.100
and we don't have that high
a density of molecules in it,

00:01:21.100 --> 00:01:22.960
it's a reasonable assumption

00:01:22.960 --> 00:01:25.270
that the volume of the gas itself,

00:01:25.270 --> 00:01:29.610
that the molecules themselves
are small in volume,

00:01:29.610 --> 00:01:31.950
collectively, relative to the container,

00:01:31.950 --> 00:01:35.650
and it's reasonable in many
circumstances to assume

00:01:35.650 --> 00:01:38.280
that the molecules don't interact,

00:01:38.280 --> 00:01:41.570
maybe they don't have strong
intermolecular forces,

00:01:41.570 --> 00:01:43.560
once again, because they're taking up

00:01:43.560 --> 00:01:45.980
a small portion of the volume.

00:01:45.980 --> 00:01:48.950
They might even not get close
to each other too often.

00:01:48.950 --> 00:01:51.830
And so that's why these
are reasonable assumptions,

00:01:51.830 --> 00:01:54.740
and they allow us to say
that PV is equal to nRT,

00:01:54.740 --> 00:01:56.430
which is a valuable thing,

00:01:56.430 --> 00:01:59.540
a valuable approximation
in most circumstances.

00:01:59.540 --> 00:02:03.140
But in the real world, we
do know that in actuality,

00:02:03.140 --> 00:02:07.210
that each molecule takes up some volume,

00:02:07.210 --> 00:02:09.350
and that if you add up all
the molecules together,

00:02:09.350 --> 00:02:11.560
they're of course going
to take up some volume,

00:02:11.560 --> 00:02:13.270
and if there's enough molecules,

00:02:13.270 --> 00:02:15.040
or if the container is small enough,

00:02:15.040 --> 00:02:17.220
we know that the volume of
the gas relative to container

00:02:17.220 --> 00:02:18.830
won't be negligible.

00:02:18.830 --> 00:02:21.400
We also know that molecules

00:02:21.400 --> 00:02:25.110
will interact with each other
in some way, shape or form.

00:02:25.110 --> 00:02:26.790
Two molecules can't occupy

00:02:26.790 --> 00:02:28.810
the same space at the same time,

00:02:28.810 --> 00:02:31.410
so you definitely have
some repulsive forces,

00:02:31.410 --> 00:02:33.141
and you have, you might have some,

00:02:33.141 --> 00:02:35.790
even for fairly inert molecules,

00:02:35.790 --> 00:02:39.020
you might have some temporary
dipoles that get formed,

00:02:39.020 --> 00:02:42.760
some temporary attraction
or some temporary repulsion.

00:02:42.760 --> 00:02:44.700
So if you're dealing with a situation

00:02:44.700 --> 00:02:46.930
where things are less ideal,

00:02:46.930 --> 00:02:48.770
and I'm going to make a character of it,

00:02:48.770 --> 00:02:52.350
where the molecules are
taking up a significant volume

00:02:52.350 --> 00:02:53.620
relative to the container,

00:02:53.620 --> 00:02:56.810
you can't say that the
volume of the molecules

00:02:56.810 --> 00:02:58.990
are negligible relative to the container,

00:02:58.990 --> 00:03:02.130
and we assume that they are
interacting with each other,

00:03:02.130 --> 00:03:04.290
they're definitely going
to repulse each other,

00:03:04.290 --> 00:03:06.830
they can't occupy the same
space at the same time,

00:03:06.830 --> 00:03:08.820
but they might attract
each other at some points,

00:03:08.820 --> 00:03:11.200
or repulse each other at other points,

00:03:11.200 --> 00:03:13.190
and so in this situation,

00:03:13.190 --> 00:03:15.770
where we can't make these assumptions,

00:03:15.770 --> 00:03:19.363
we're going to have to
modify the ideal gas law.


Interpreting expressions with multiple variables: Cylinder

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:02.130
- [Instructor] We're told
that given the height h

00:00:02.130 --> 00:00:04.360
and volume V of a certain cylinder,

00:00:04.360 --> 00:00:06.460
Jill uses the formula r is equal

00:00:06.460 --> 00:00:08.570
to the square root of V over pi h

00:00:08.570 --> 00:00:11.440
to compute its radius to be 20 meters.

00:00:11.440 --> 00:00:14.730
If a second cylinder has the
same volume of the first,

00:00:14.730 --> 00:00:17.810
but is 100 times taller,

00:00:17.810 --> 00:00:20.350
what is its radius?

00:00:20.350 --> 00:00:21.310
Pause this video,

00:00:21.310 --> 00:00:24.440
and see if you can figure
this out on your own.

00:00:24.440 --> 00:00:26.120
All right, now let's do this together.

00:00:26.120 --> 00:00:28.900
So first, I always like to
approach things intuitively.

00:00:28.900 --> 00:00:32.190
So let's say the first cylinder
looks something like this,

00:00:32.190 --> 00:00:33.350
like this.

00:00:33.350 --> 00:00:36.510
And then the second cylinder,
here, it's 100 times taller.

00:00:36.510 --> 00:00:37.820
I would have trouble drawing something

00:00:37.820 --> 00:00:39.340
that's 100 times taller.

00:00:39.340 --> 00:00:41.030
But if it has the same volume,

00:00:41.030 --> 00:00:43.060
it's going to have to be a lot thinner.

00:00:43.060 --> 00:00:46.150
So if you want to maintain the volume,

00:00:46.150 --> 00:00:48.760
as you make the cylinder taller,

00:00:48.760 --> 00:00:51.820
and I'm not going anywhere
close to 100 times as tall here,

00:00:51.820 --> 00:00:54.030
you're going to have
to decrease the radius.

00:00:54.030 --> 00:00:55.780
So we would expect a radius

00:00:55.780 --> 00:00:59.070
to be a good bit less than 20 meters.

00:00:59.070 --> 00:01:00.640
So that's just the first intuition,

00:01:00.640 --> 00:01:02.540
just to make sure that we
somehow don't get some number

00:01:02.540 --> 00:01:04.350
that's larger than 20 meters.

00:01:04.350 --> 00:01:07.070
But how do we figure
out what that could be?

00:01:07.070 --> 00:01:09.140
Well, now we can go back to the formula,

00:01:09.140 --> 00:01:10.860
and we know that Jill calculated

00:01:10.860 --> 00:01:12.550
that 20 meters is the radius.

00:01:12.550 --> 00:01:17.080
So 20 is equal to the
square root of V over pi h.

00:01:17.080 --> 00:01:19.920
And if this formula
looks unfamiliar to you,

00:01:19.920 --> 00:01:24.300
just remember the volume of a cylinder is

00:01:24.300 --> 00:01:28.400
the area of either the top or the bottom,

00:01:28.400 --> 00:01:30.743
so pi r squared times the height.

00:01:31.600 --> 00:01:33.370
And if you were to just solve this for r,

00:01:33.370 --> 00:01:36.070
you would have this exact
formula that Jill uses.

00:01:36.070 --> 00:01:38.610
So this isn't some new formula.

00:01:38.610 --> 00:01:41.270
This is probably something
that you have seen already.

00:01:41.270 --> 00:01:43.880
So we know that 20
meters is equal to this,

00:01:43.880 --> 00:01:45.740
and now we're talking about a situation

00:01:45.740 --> 00:01:49.290
where we're at a height
that is 100 times taller.

00:01:49.290 --> 00:01:52.810
So this other cylinder
is going to have a radius

00:01:52.810 --> 00:01:54.090
of square root of,

00:01:54.090 --> 00:01:55.390
V is going to be the same,

00:01:55.390 --> 00:01:57.010
so let's just write that V there.

00:01:57.010 --> 00:01:58.060
Pi doesn't change.

00:01:58.060 --> 00:01:59.520
It's always going to be pi.

00:01:59.520 --> 00:02:00.850
And now instead of h,

00:02:00.850 --> 00:02:03.010
we have something that
is 100 times taller.

00:02:03.010 --> 00:02:05.710
So we could write that as 100h.

00:02:05.710 --> 00:02:08.360
And then what's another way to write this?

00:02:08.360 --> 00:02:10.930
Well, what I'm going to do
is try to bring out the 100,

00:02:10.930 --> 00:02:13.750
so I still get the square
root of V over pi h.

00:02:13.750 --> 00:02:17.810
So I could rewrite this
as the square root of

00:02:17.810 --> 00:02:19.800
one over 100

00:02:20.890 --> 00:02:24.660
times V over pi h,

00:02:24.660 --> 00:02:28.670
which I could write as the
square root of one over 100,

00:02:28.670 --> 00:02:31.350
and I'm just using
properties of radicals here,

00:02:31.350 --> 00:02:33.720
times the square root

00:02:33.720 --> 00:02:37.980
of V over pi h.

00:02:37.980 --> 00:02:40.420
Now, we know what the square
root of V over pi h is.

00:02:40.420 --> 00:02:43.260
We know that that is 20,
and our units are in meters.

00:02:43.260 --> 00:02:45.030
So this is 20.

00:02:45.030 --> 00:02:47.580
And then what's the square
root of one over 100?

00:02:47.580 --> 00:02:48.630
Well, this is the same thing

00:02:48.630 --> 00:02:51.660
as one over the square root of 100.

00:02:51.660 --> 00:02:54.520
And of course, now it's
going to be times 20,

00:02:54.520 --> 00:02:55.640
times 20.

00:02:55.640 --> 00:02:56.473
Well, the square root of 100,

00:02:56.473 --> 00:02:59.370
I should say the principal
root of 100 is 10.

00:02:59.370 --> 00:03:01.370
So the radius of our new cylinder,

00:03:01.370 --> 00:03:04.180
of the second cylinder is
going to be 1/10 of 20,

00:03:04.180 --> 00:03:06.900
which is equal to two meters.

00:03:06.900 --> 00:03:08.050
And we're done.

00:03:08.050 --> 00:03:12.130
The second cylinder is going
to have a radius of two meters,

00:03:12.130 --> 00:03:14.100
which meets our intuition.

00:03:14.100 --> 00:03:17.350
If we increase our height
by a factor of 100,

00:03:17.350 --> 00:03:20.530
then our radius decreases
by a factor of 10.

00:03:20.530 --> 00:03:21.363
The reason why is

00:03:21.363 --> 00:03:24.010
because you square the
radius right over here.

00:03:24.010 --> 00:03:27.070
So if height increases by a factor of 100,

00:03:27.070 --> 00:03:30.150
if radius just decreases
by a factor of 10,

00:03:30.150 --> 00:03:34.143
it'll make this whole expression
still have the same volume.


Sal Discusses the Safety of Reopening Schools on the Situation Room With Wolf Blitzer

WEBVTT
Kind: captions
Language: en

00:00:00.440 --> 00:00:02.870
- Doctor, when the CDC
Director, Robert Redfield,

00:00:02.870 --> 00:00:05.550
says these new guidelines
are meant to facilitate

00:00:05.550 --> 00:00:08.000
the opening of schools around the country,

00:00:08.000 --> 00:00:09.280
not keep them closed.

00:00:09.280 --> 00:00:11.930
Based on your reading
of these new guidelines,

00:00:11.930 --> 00:00:14.023
do you think they accomplish that goal?

00:00:16.070 --> 00:00:18.470
- Well Wolf, they sound
different from the guidelines

00:00:18.470 --> 00:00:19.820
that were released before.

00:00:19.820 --> 00:00:23.150
And I kept on thinking, what
is it that's so different?

00:00:23.150 --> 00:00:25.370
And what's different is the tone,

00:00:25.370 --> 00:00:27.320
because what I'm used
to seeing from the CDC

00:00:27.320 --> 00:00:29.670
is leading with the science and the facts.

00:00:29.670 --> 00:00:33.650
And these guidelines sound like
they're cherry picking data

00:00:33.650 --> 00:00:36.100
to make a specific policy point.

00:00:36.100 --> 00:00:38.300
And that's really concerning,
because what we need

00:00:38.300 --> 00:00:41.570
from the CDC is not a
justification of why children

00:00:41.570 --> 00:00:42.403
should be in school.

00:00:42.403 --> 00:00:44.440
We all know that, we all want that.

00:00:44.440 --> 00:00:46.370
But we want the CDC to lay out,

00:00:46.370 --> 00:00:48.920
what are the criteria
that we need to meet?

00:00:48.920 --> 00:00:51.947
For example, we need to test
positivity less than 5%,

00:00:51.947 --> 00:00:54.670
a consistent, 14 day decline
in the number of cases.

00:00:54.670 --> 00:00:55.580
Something like that.

00:00:55.580 --> 00:00:57.460
And also, here's a
checklist of what schools

00:00:57.460 --> 00:00:59.330
have to do in order for schools,

00:00:59.330 --> 00:01:01.690
for them to reopen safely, in person.

00:01:01.690 --> 00:01:03.840
That's not what the CDC
really has laid out.

00:01:03.840 --> 00:01:05.710
And I really worry, if we can't trust

00:01:05.710 --> 00:01:08.260
that what comes out from
them is based on science

00:01:08.260 --> 00:01:10.982
and not politics, then who can we trust?

00:01:10.982 --> 00:01:13.500
- Yeah, that's a real serious
potential problem out there.

00:01:13.500 --> 00:01:15.410
Sal, you just had an excellent interview

00:01:15.410 --> 00:01:17.560
with Dr. Anthony Fauci, yourself,

00:01:17.560 --> 00:01:19.410
and you asked him about bringing teachers

00:01:19.410 --> 00:01:21.010
and the students back to school.

00:01:21.010 --> 00:01:23.093
Let me play this clip. Listen to this.

00:01:24.220 --> 00:01:27.290
- When you talk about forcing teachers

00:01:27.290 --> 00:01:30.060
to come back to school, you
better be careful about that,

00:01:30.060 --> 00:01:35.060
and make sure you pay attention
to A, keeping them safe,

00:01:35.100 --> 00:01:36.853
and key, keeping them healthy.

00:01:38.070 --> 00:01:41.110
- Sal, I want you to elaborate
a little bit on that for us.

00:01:41.110 --> 00:01:44.843
What are some of the best
practices that Dr. Fauci outlined?

00:01:46.590 --> 00:01:48.260
- Yeah well, first of all,
just to completely agree

00:01:48.260 --> 00:01:49.430
with what was just said.

00:01:49.430 --> 00:01:51.500
What I think, we're talking
to school district leaders

00:01:51.500 --> 00:01:53.420
around the country, and
what they're craving

00:01:53.420 --> 00:01:55.490
is just very clear guidelines.

00:01:55.490 --> 00:01:58.520
What is the per capita
incidence rate, and for each

00:01:58.520 --> 00:02:01.560
of those levels, what is
the appropriate action?

00:02:01.560 --> 00:02:04.110
And there's good groups, like
the Harvard Global Health

00:02:04.110 --> 00:02:06.450
Initiative Institute, that have been

00:02:06.450 --> 00:02:08.200
doing very clear guidelines.

00:02:08.200 --> 00:02:11.680
And Dr. Fauci did seem to say
that those types of guidelines

00:02:11.680 --> 00:02:13.250
are what folks could index on.

00:02:13.250 --> 00:02:14.490
And the timing is super important,

00:02:14.490 --> 00:02:16.140
'cause we're only four to six weeks away

00:02:16.140 --> 00:02:18.230
from school starting, and school leaders

00:02:18.230 --> 00:02:19.760
really even haven't had a chance to think

00:02:19.760 --> 00:02:21.490
about how the instruction's
going to happen,

00:02:21.490 --> 00:02:23.280
'cause they don't know how
it's going to be structured.

00:02:23.280 --> 00:02:25.790
In terms of what we just
heard from the statement

00:02:25.790 --> 00:02:28.760
about teachers, I did
ask him very directly,

00:02:28.760 --> 00:02:30.750
should teachers be forced to go back?

00:02:30.750 --> 00:02:33.590
And he seemed pretty
empathetic with the situation,

00:02:33.590 --> 00:02:34.850
especially for older teachers,

00:02:34.850 --> 00:02:37.340
teachers who might have some
other health circumstances,

00:02:37.340 --> 00:02:40.030
that they shouldn't be
forced to go back to school.

00:02:40.030 --> 00:02:42.820
We talked about social
distancing, but once again,

00:02:42.820 --> 00:02:45.040
it would be valuable to
get very clear guidelines

00:02:45.040 --> 00:02:47.280
of what's good and what is not.

00:02:47.280 --> 00:02:49.610
And also, there's interesting ideas

00:02:49.610 --> 00:02:52.120
of maybe leveraging outdoor classrooms.

00:02:52.120 --> 00:02:53.620
There's a South Korean study talking

00:02:53.620 --> 00:02:56.060
about over 10 years old,
versus under 10 years old.

00:02:56.060 --> 00:02:57.880
What can we do with say, kindergarteners

00:02:57.880 --> 00:03:00.080
or first graders, outdoors?

00:03:00.080 --> 00:03:02.220
Some type of clear
guidance along those lines

00:03:02.220 --> 00:03:03.330
would be super valuable.

00:03:03.330 --> 00:03:04.640
- You're absolutely right.

00:03:04.640 --> 00:03:06.630
Dr. Wen, even as the white house pushes

00:03:06.630 --> 00:03:09.060
a complete return to schools, a key member

00:03:09.060 --> 00:03:12.100
of the corona virus task
force, Dr. Deborah Birx,

00:03:12.100 --> 00:03:15.730
is cautioning that it's unclear
how rapidly young children,

00:03:15.730 --> 00:03:19.890
even under the age of 10,
can transmit the virus.

00:03:19.890 --> 00:03:22.500
So we know this one study
that Sal was referring to,

00:03:22.500 --> 00:03:25.610
in South Korea, said that children over 10

00:03:25.610 --> 00:03:28.500
transmit the virus as
quickly and as thoroughly

00:03:28.500 --> 00:03:29.620
as adults do.

00:03:29.620 --> 00:03:31.790
What additional evidence
would you like to see

00:03:31.790 --> 00:03:33.683
on that critically important front?

00:03:35.350 --> 00:03:37.620
- Yeah, so that particular
study from South Korea,

00:03:37.620 --> 00:03:40.600
it actually only looked
at symptomatic people.

00:03:40.600 --> 00:03:43.300
So we don't know about
asymptomatic transmission,

00:03:43.300 --> 00:03:46.730
and since 40%, or even more,
of cases are transmitted

00:03:46.730 --> 00:03:49.340
by people without symptoms,
we really don't know

00:03:49.340 --> 00:03:51.750
whether asymptomatic
children, young children,

00:03:51.750 --> 00:03:54.680
can transmit just as
much as older people too.

00:03:54.680 --> 00:03:57.520
I think also, when you look at
the studies done of children,

00:03:57.520 --> 00:04:00.320
they have all been in countries
where the transmission

00:04:00.320 --> 00:04:03.410
rate is really low, and
so we really have no idea

00:04:03.410 --> 00:04:05.080
what it's going to look like in the US,

00:04:05.080 --> 00:04:07.100
if kids are going back in places

00:04:07.100 --> 00:04:08.630
where there are active surges.

00:04:08.630 --> 00:04:10.240
And I'm afraid that this looks like

00:04:10.240 --> 00:04:12.680
an uncontrolled environment,
where our children,

00:04:12.680 --> 00:04:16.470
and our teachers, and their
families, are guinea pigs.

00:04:16.470 --> 00:04:18.460
- You know Sal, in your interview,

00:04:18.460 --> 00:04:21.900
Dr. Fauci also spoke about
the potential downsides

00:04:21.900 --> 00:04:24.290
of relying on face shields in schools,

00:04:24.290 --> 00:04:27.460
rather than requiring students
and teachers to wear masks.

00:04:27.460 --> 00:04:29.473
I wanna play this clip, watch this.

00:04:31.350 --> 00:04:34.780
- My staff just brought this in. (laughs)

00:04:34.780 --> 00:04:35.613
- There you go.

00:04:35.613 --> 00:04:37.460
- This was a great-
- That's exactly what, yeah.

00:04:37.460 --> 00:04:39.067
- Like that? Yeah.

00:04:39.067 --> 00:04:40.740
- Good look.
- So this is good, yeah.

00:04:40.740 --> 00:04:43.730
This is good for droplets,
'cause it'll block it.

00:04:43.730 --> 00:04:47.140
The only trouble is if you
have any degree of aerosol,

00:04:47.140 --> 00:04:48.850
what's happens, is that all of this,

00:04:48.850 --> 00:04:50.930
see, it can go right in like that.

00:04:50.930 --> 00:04:52.720
That's the problem, you see?

00:04:52.720 --> 00:04:54.200
So these are good for droplets,

00:04:54.200 --> 00:04:56.250
but you have to be careful
if there's a degree

00:04:56.250 --> 00:04:58.330
of aerosolization.

00:04:58.330 --> 00:05:00.040
- So if you wear a face shield, Sal,

00:05:00.040 --> 00:05:01.880
you should also still wear a mask,

00:05:01.880 --> 00:05:03.430
I guess that's what he's suggesting.

00:05:03.430 --> 00:05:05.270
But for younger children, especially,

00:05:05.270 --> 00:05:07.750
it would be helpful to
see the teachers face.

00:05:07.750 --> 00:05:09.820
If face shields aren't very protective

00:05:09.820 --> 00:05:12.920
in a classroom setting, and
everyone has to wear a mask,

00:05:12.920 --> 00:05:15.250
which they clearly do,
what impact is all this

00:05:15.250 --> 00:05:18.093
going to have on the
critical issue of learning?

00:05:19.960 --> 00:05:21.460
- It's going to have a huge impact.

00:05:21.460 --> 00:05:24.570
Just from the school closures
that have already occurred,

00:05:24.570 --> 00:05:26.910
over the spring, a lot
of researchers think

00:05:26.910 --> 00:05:29.440
it's going to be as much
as a year of learning loss.

00:05:29.440 --> 00:05:30.840
'Cause not only were kids not learning,

00:05:30.840 --> 00:05:33.110
they were also forgetting,
they were atrophying.

00:05:33.110 --> 00:05:35.780
And basically the
conversation with Dr. Fauci,

00:05:35.780 --> 00:05:39.830
even if one of either the
Moderna, or one of the vaccines

00:05:39.830 --> 00:05:41.910
become successful, and we're
able to start deploying

00:05:41.910 --> 00:05:43.940
them in January, you're
still not going to get

00:05:43.940 --> 00:05:47.060
to herd immunity, get them all deployed,

00:05:47.060 --> 00:05:48.650
until several months later.

00:05:48.650 --> 00:05:51.260
It's a major public
health issue to be able

00:05:51.260 --> 00:05:53.260
to get hundreds of
millions of vaccines out.

00:05:53.260 --> 00:05:55.640
And so this is going to
be this entire school year

00:05:55.640 --> 00:05:58.640
in some form of socially-distanced
or hybrid learning.

00:05:58.640 --> 00:06:00.620
And so it's going to be a
really, really tough year.

00:06:00.620 --> 00:06:03.120
And the biggest fear is it's
going to drive more inequity.

00:06:03.120 --> 00:06:04.800
All of our children, my children, I think,

00:06:04.800 --> 00:06:06.590
are just going to be fine,
but there's a lot of kids

00:06:06.590 --> 00:06:08.780
who don't have the supports,
who don't have the access,

00:06:08.780 --> 00:06:10.430
and they're also going
to be going to schools

00:06:10.430 --> 00:06:11.860
that might not have the resources

00:06:11.860 --> 00:06:13.900
to be able to provide them adequately.

00:06:13.900 --> 00:06:15.550
So it's going to be a tough year.


Identifying value in digits

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:02.670
- [Narrator] So I'm going
to write down a number

00:00:02.670 --> 00:00:04.610
and I'm going to think about how much

00:00:04.610 --> 00:00:08.280
do each of these digits of the number,

00:00:08.280 --> 00:00:10.690
what value do they represent?

00:00:10.690 --> 00:00:13.310
And actually, let me
pick on this two here.

00:00:13.310 --> 00:00:14.930
What does that two represent?

00:00:14.930 --> 00:00:16.250
Does it just represent two,

00:00:16.250 --> 00:00:18.960
or does it represent something
different than just two?

00:00:18.960 --> 00:00:20.810
Pause the video and think about that.

00:00:21.950 --> 00:00:23.280
All right, now we'll
think about it together.

00:00:23.280 --> 00:00:25.860
And actually I'm going to
start with the seven here.

00:00:25.860 --> 00:00:28.910
The seven is in the one's place.

00:00:28.910 --> 00:00:32.200
So this seven represents seven ones,

00:00:32.200 --> 00:00:34.800
which is of course still just seven.

00:00:34.800 --> 00:00:36.920
So nothing too surprising there.

00:00:36.920 --> 00:00:39.150
Then we could go to the ten's place.

00:00:39.150 --> 00:00:41.690
So this one doesn't just represent one,

00:00:41.690 --> 00:00:44.030
it represents one 10.

00:00:44.030 --> 00:00:47.180
Or another way to think
about it, it represents 10.

00:00:47.180 --> 00:00:52.180
And then this two, it is
in the hundred's place.

00:00:52.270 --> 00:00:53.620
So it doesn't just represent two,

00:00:53.620 --> 00:00:57.940
it represents two hundreds,
we could write it that way,

00:00:57.940 --> 00:01:00.490
or it represents the value 200.

00:01:00.490 --> 00:01:02.780
So the number here is 217.

00:01:02.780 --> 00:01:06.950
The two represents two hundreds or 200.

00:01:06.950 --> 00:01:09.160
Now let me give you a
slightly different question.

00:01:09.160 --> 00:01:12.920
I'm going to write down three numbers.

00:01:12.920 --> 00:01:16.150
So we have this number
and I'm intentionally

00:01:16.150 --> 00:01:19.080
not saying it out loud, that number,

00:01:19.080 --> 00:01:24.080
I have this number and I have this number.

00:01:24.820 --> 00:01:26.760
And what I want you to
do is pause the video

00:01:26.760 --> 00:01:30.180
and tell me in which
of these three numbers

00:01:30.180 --> 00:01:33.543
does the seven represent 70?

00:01:34.510 --> 00:01:36.840
Pause the video and think about that.

00:01:36.840 --> 00:01:39.610
All right, now let's work
through this together.

00:01:39.610 --> 00:01:42.293
So let's start with this top number,

00:01:42.293 --> 00:01:45.380
In this number, the seven
is in the one's place,

00:01:45.380 --> 00:01:48.940
so that seven really just
represents seven ones,

00:01:48.940 --> 00:01:51.120
which is still just seven.

00:01:51.120 --> 00:01:54.640
So this seven does not represent 70.

00:01:54.640 --> 00:01:58.380
Now in this next number, the
two is in the one's place

00:01:58.380 --> 00:02:02.330
and we see that the seven
is in the ten's place.

00:02:02.330 --> 00:02:06.760
So this actually represents seven tens.

00:02:06.760 --> 00:02:11.760
Well, seven tens is the same thing as 70.

00:02:13.780 --> 00:02:16.580
So it's actually in this second situation

00:02:16.580 --> 00:02:19.800
where the seven does represent 70.

00:02:19.800 --> 00:02:24.580
This number is 572, the
seven represents 70.

00:02:24.580 --> 00:02:26.980
And let's just check
this last number here.

00:02:26.980 --> 00:02:29.010
Well, here are the seven
is not in the one's place,

00:02:29.010 --> 00:02:30.270
not in the ten's place,

00:02:30.270 --> 00:02:32.500
it is in the hundred's place.

00:02:32.500 --> 00:02:36.990
So this represents seven hundreds or 700.

00:02:36.990 --> 00:02:39.713
And that makes sense,
this number here is 705.


Inches and feet

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.060
- [Instructor] In this video,
I'm going to introduce you

00:00:02.060 --> 00:00:05.370
to two units of measuring length.

00:00:05.370 --> 00:00:09.520
The first is the inch, which
you might have heard about.

00:00:09.520 --> 00:00:13.460
And you're probably thinking,
"How long is an inch?"

00:00:13.460 --> 00:00:15.750
Well, if you're familiar with a quarter,

00:00:15.750 --> 00:00:18.560
a quarter looks something like this.

00:00:18.560 --> 00:00:21.083
You see George Washington on it.

00:00:22.090 --> 00:00:24.790
A quarter is almost an inch.

00:00:24.790 --> 00:00:28.550
So an inch might be something like that.

00:00:28.550 --> 00:00:30.960
One inch.

00:00:30.960 --> 00:00:32.900
Another way to think about
it is when I'm looking

00:00:32.900 --> 00:00:35.180
at my thumb, and I'm a grown man,

00:00:35.180 --> 00:00:36.730
at least physically (chuckles),

00:00:39.800 --> 00:00:43.420
my thumb is about two inches in length.

00:00:43.420 --> 00:00:47.410
So my thumb is about two inches in length.

00:00:47.410 --> 00:00:52.410
One inch and two inches.

00:00:52.740 --> 00:00:54.640
Depending on your age,
if you're watching this

00:00:54.640 --> 00:00:56.030
and let's say you're eight years old,

00:00:56.030 --> 00:00:57.160
seven or eight years old,

00:00:57.160 --> 00:01:00.080
your thumb might be closer to an inch

00:01:00.080 --> 00:01:02.680
or maybe a little bit over an inch.

00:01:02.680 --> 00:01:04.700
Now the other unit of measurement,

00:01:04.700 --> 00:01:08.070
you can view it as a bunch
of inches put together.

00:01:08.070 --> 00:01:10.400
And if you put 12 inches together,

00:01:10.400 --> 00:01:15.400
you get what is known as a foot, a foot.

00:01:16.150 --> 00:01:19.680
Now the word foot is used for
many things in our language,

00:01:19.680 --> 00:01:22.520
including for our individual feet,

00:01:22.520 --> 00:01:25.640
or the things at the ends of our legs.

00:01:25.640 --> 00:01:27.590
And I believe, I'm not sure

00:01:27.590 --> 00:01:30.530
where the unit of measurement
of the foot came from,

00:01:30.530 --> 00:01:31.980
but they might be related

00:01:31.980 --> 00:01:36.090
because actually my foot is almost a foot.

00:01:36.090 --> 00:01:39.720
And in fact, my shoes, and I wear a size,

00:01:39.720 --> 00:01:43.340
I wear a men's size 10 1/2,

00:01:43.340 --> 00:01:45.340
my sneakers that I wear

00:01:48.279 --> 00:01:50.063
are almost exactly one foot.

00:01:51.020 --> 00:01:54.600
And you can sometimes see it
written as ft, short for foot.

00:01:54.600 --> 00:01:58.660
Now, clearly not everyone's
foot is exactly a foot

00:01:58.660 --> 00:02:01.660
'cause everyone's feet and
shoes have different lengths,

00:02:01.660 --> 00:02:05.480
but that gets you a sense
of how large a foot is.

00:02:05.480 --> 00:02:06.313
Another way to think about it,

00:02:06.313 --> 00:02:07.320
and as I just mentioned,

00:02:07.320 --> 00:02:11.440
if you put 12 inches
together, you get one foot.

00:02:11.440 --> 00:02:13.400
12 inches

00:02:16.007 --> 00:02:19.340
equals one foot.

00:02:19.340 --> 00:02:23.090
So let me give you some objects.

00:02:23.090 --> 00:02:25.560
And I want you to pause
the video and think about,

00:02:25.560 --> 00:02:27.590
would you measure them in foot or inches

00:02:27.590 --> 00:02:29.700
or whether the measurements themselves

00:02:29.700 --> 00:02:32.700
sound like measurements in feet or inches.

00:02:32.700 --> 00:02:36.350
So if I give you a piece of paper,

00:02:36.350 --> 00:02:39.820
a regular piece of paper,

00:02:39.820 --> 00:02:43.580
kind with the holes on
it and the nice lines.

00:02:43.580 --> 00:02:47.000
So a piece of paper right over here.

00:02:47.000 --> 00:02:48.380
If I were to tell you

00:02:48.380 --> 00:02:52.760
that the height of this
paper is 11 something,

00:02:52.760 --> 00:02:56.803
would that be 11 inches or 11 feet?

00:02:58.440 --> 00:03:01.610
Well, if was 11 feet, that
would be a huge piece of paper.

00:03:01.610 --> 00:03:03.980
That would be a piece
of paper taller than me.

00:03:03.980 --> 00:03:06.370
That would be more of a
carpet than a piece of paper.

00:03:06.370 --> 00:03:07.410
So a piece of paper,

00:03:07.410 --> 00:03:12.410
actually a standard piece
of paper is 11 inches tall.

00:03:12.620 --> 00:03:16.720
Now, if we were to go outside
and play a little basketball,

00:03:16.720 --> 00:03:20.840
so this is the basketball,
or that's the backboard.

00:03:20.840 --> 00:03:24.610
And then we have the hoop, the hoop,

00:03:24.610 --> 00:03:26.163
we have the net,

00:03:27.290 --> 00:03:30.380
and then we have the post holding it up.

00:03:30.380 --> 00:03:32.370
Let me draw that in a different color.

00:03:32.370 --> 00:03:33.910
So we have the post.

00:03:33.910 --> 00:03:38.910
And this is a standard NBA basketball rim.

00:03:38.960 --> 00:03:42.240
If I were to say it's 10
something off the ground,

00:03:42.240 --> 00:03:45.313
is that 10 inches or 10 feet?

00:03:46.760 --> 00:03:48.290
Well, if it was 10 inches,

00:03:48.290 --> 00:03:52.280
it would be very easy to
dunk a basketball. (chuckles)

00:03:52.280 --> 00:03:54.750
Although it might be hard to
fit the basketball in the rim

00:03:54.750 --> 00:03:58.860
because if the rim was, it
might also be very, very small.

00:03:58.860 --> 00:04:01.390
That would be more of a basketball goal

00:04:01.390 --> 00:04:04.730
for an insect of some kind or
for a very, very small mouse.

00:04:04.730 --> 00:04:06.540
For normal human beings,

00:04:06.540 --> 00:04:10.440
the standard height of a
basketball goal is 10 feet.

00:04:10.440 --> 00:04:13.390
The one that they play with in the NBA.

00:04:13.390 --> 00:04:15.420
At your school, if you're
a little bit younger,

00:04:15.420 --> 00:04:16.970
you might see a basketball goal

00:04:16.970 --> 00:04:20.030
that is six feet or
eight feet or nine feet.

00:04:20.030 --> 00:04:20.870
But the standard ones

00:04:20.870 --> 00:04:25.480
that the professionals
play with are 10 feet tall.

00:04:25.480 --> 00:04:27.010
Now let me give you some things,

00:04:27.010 --> 00:04:28.400
and I wanna decide whether it's better

00:04:28.400 --> 00:04:32.340
to measure them with feet or with inches.

00:04:32.340 --> 00:04:35.240
So let's say that I have a swimming pool,

00:04:35.240 --> 00:04:38.720
say I have a swimming
pool right over here.

00:04:38.720 --> 00:04:42.270
And that is the pool.

00:04:42.270 --> 00:04:43.630
Would it be better to measure

00:04:43.630 --> 00:04:46.880
the length of this swimming
pool in feet or in inches?

00:04:46.880 --> 00:04:48.553
Pause the video and think about that.

00:04:50.350 --> 00:04:53.920
Well, a swimming pool is fairly large.

00:04:53.920 --> 00:04:56.820
It is much larger than even a foot.

00:04:56.820 --> 00:04:58.250
So you'd think you'd want to measure it,

00:04:58.250 --> 00:05:00.010
if you had to choose
between feet and inches,

00:05:00.010 --> 00:05:01.600
you would pick feet.

00:05:01.600 --> 00:05:04.290
And so this would be a situation

00:05:04.290 --> 00:05:06.620
where that pool might be, say,

00:05:06.620 --> 00:05:10.943
75 feet long.

00:05:12.130 --> 00:05:17.120
Now, if you were measuring
the length of a mouse,

00:05:17.120 --> 00:05:18.810
this is a mouse right over here.

00:05:18.810 --> 00:05:22.790
Not my best drawing of
a mouse with its tail,

00:05:22.790 --> 00:05:24.310
its feet right over there.

00:05:24.310 --> 00:05:27.470
Would you be best off
measuring it in feet or inches?

00:05:27.470 --> 00:05:30.563
A small mouse, a mouse that
could fit in your hand.

00:05:31.670 --> 00:05:34.270
Well, that's going to be a
good bit less than a foot.

00:05:34.270 --> 00:05:36.070
So it makes sense to
measure that in inches.

00:05:36.070 --> 00:05:40.710
I've seen mice that might only
be two or three inches long.

00:05:40.710 --> 00:05:41.780
So I'll leave you there.

00:05:41.780 --> 00:05:44.750
Hopefully that gives you a
rough sense of what an inch is,

00:05:44.750 --> 00:05:47.240
what a foot is, how they're
related to each other,

00:05:47.240 --> 00:05:49.553
and when you might use one or the other.