Energy at the microscopic scale

WEBVTT
Kind: captions
Language: en

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- [Instructor] Welcome.

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Today, we're going to take
a look at forms of energy,

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such as kinetic, electrical, thermal,

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gravitational, potential energy.

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It turns out when you start thinking

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about energy on smaller scales,
or the microscopic level,

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all of these forms of energy
are basically two things:

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one, kinetic energy,
particles moving around,

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and two, potential energy,
energy stored by a field,

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such as electric,
magnetic or gravitational.

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Let's start with a
deceivingly simple example

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and explore properties
of energy as we zoom in.

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I'm drawing a glass of water.

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This water has a temperature.

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I can warm up the water by adding energy

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from an electric stove,

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or cool down the water by
putting it in the fridge,

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thus removing energy in the liquid water.

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From this example, we
can see that temperature

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is related to energy.

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But how is it related to
kinetic or potential energy?

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Hmm.

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This big picture, the macroscopic scale,

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allows us to look at energy
in terms of temperature.

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But let's go to the
microscopic or small-scale

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to get a better picture
of the physics at play.

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As we look inside this liquid,

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we see lots of water
molecules moving around.

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Zoom, zoom, zoom.

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Well, they don't actually make a sound.

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The average speed at
which these molecules move

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is related to their kinetic
energy and its temperature.

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This is thermal motion.

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If we zoom in again, we can
look into the strong chemical

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bonds within molecules.

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Here, the individual atoms,
in this case for water,

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is hydrogen and oxygen.

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They can vibrate back
and forth and rotate,

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so they also have kinetic energy.

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Let's look at another example

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between macro and microscale
energy interactions.

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When you burn something, think of a fire.

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A chemical reaction takes place,

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and it releases a lot of energy.

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How does it do that?

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Let's look at the microscopic
scale to find out.

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In this example, I'm
gonna burn methane gas,

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and the chemical reaction that takes place

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is methane, CH4, and oxygen, O2.

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They rearrange to create water, H2O,

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and carbon dioxide, CO2, plus energy.

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Before the reaction,

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there is a greater
chemical potential energy

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than afterwards.

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But don't worry.

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Energy is still conserved
because that potential energy

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is converted to kinetic
energy and radiation.

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What is the source of
chemical potential energy?

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At this level, we can
think of individual bonds

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between atoms storing energy

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so that energy can be absorbed or released

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as bonds are broken and reformed.

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But where does the energy
and chemical bonds come from?

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We need to zoom in again.

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In a single atom,

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there's a nucleus that
contains protons and neutrons

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and overall has a positive charge.

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This creates an electromagnetic field.

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The interaction of
other charged particles,

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like negatively charged electrons

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relatively far away from the nucleus,

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with this field provide potential energy.

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You can think of this
electric potential energy

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as the same kind of concept
as a potential energy

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of a mass and a gravitational field.

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Zooming back out, each
molecule has its own

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particular configuration
of charged particles

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within the electromagnetic fields, right?

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This means it has an
associated potential energy.

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As we've seen, this
chemical potential energy

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is the result of energy stored in fields.

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Okay, so we've covered
electrical, chemical,

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thermal types of energy,

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but there's other forms out there, right?

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For instance, what about sound waves?

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Here's a speaker and an ear.

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The energy in sound waves is transferred

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through the vibrations,

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a back and forth motion
of molecules in the air.

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Another example could be
elastic potential energy

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or the energy stored in a spring.

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At the microscopic level,

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as you stretch the spring,

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see the hand stretching the spring?

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The atoms are being pulled out
of their equilibrium position

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within a solid and thus
gain potential energy

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from the electromagnetic force

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that holds the solid together.

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How neat is this?

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We can describe all these energies

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as just kinetic or potential.

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So there's one more
microscopic form of energy

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that we need to talk about,

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and it might seem a little
complicated at first.

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Let's go back to the combustion example

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we talked about earlier.

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As I said before, this process
releases radiant energy.

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We can see burning objects.

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They glow brightly.

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We can also put our hand
near the burning object.

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Don't touch it!

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And feel the radiant heat.

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This radiation that's emitted
carries energy with it.

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So how do we explain the radiant energy?

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Does it fit it into one
of these two categories,

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either kinetic or potential energy

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that we've been discussing?

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Well, it turns out it sort
of fits into both groups.

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Whoa, electromagnetic
radiation, such as light,

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can be modeled in a
couple of different ways,

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which we'll go into more
detail in another video.

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But one way to model the light

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is as a wave of electric
and magnetic fields.

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Another way to think about light

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is being made up of
particles called photons.

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In this instance, the particles
are carrying the energy.

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So with both of these models,

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radiant energy can be explained

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by the same microscopic interactions

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that cause the other forms of energy.

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In conclusion, we can see
energy at the macroscopic scale,

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like temperature or light being emitted.

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However, we must look at the microscale

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to observe the different forms of energy

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that we experience are
really just the result

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of kinetic and potential
energy of particles.

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How cool!


Energy and fields

WEBVTT
Kind: captions
Language: en

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- [Instructor] In previous
videos we have already defined

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or provided a definition for energy

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as the capacity to do work.

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We have also talked about
the notion of a field.

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We have talked about things
like an electric field

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or a gravitational field.

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And these are really mental constructs

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that we have produced to
explain force at a distance.

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For example, if I have a planet here

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and then I have some other
object here that has some mass,

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we know that these are going
to exert forces on each other,

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and actually equal and
opposite forces on each other.

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And scientists said, well,
they're not touching each other.

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How are they exerting
forces on each other?

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And so they introduced
this notion of a field

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that each of these objects produce,

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a gravitational field of sorts.

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Now Einstein came later and said,

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well, actually they're
warping space, time,

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et cetera, et cetera.

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But a field is one way to think

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about how they're able to induce a force

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so to speak in each other.

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Similarly, if you have
two electric charges,

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let's say you have two negative
point charges like that.

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We know that they push away on each other,

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that like charges repel.

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Well, they're not touching each other.

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How do they know to have
a force being applied

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to them in opposite directions?

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So once again, there's this idea

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that each of these produces a field,

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the other one is in the
other electric charges field.

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And then that field
somehow applies that force

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or makes that force
happen to the other thing.

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Notice, the field is a useful concept

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to predict what will happen

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and to quantify how it could happen.

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But it really is just something

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in our minds to make
sense of the universe.

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So with that out of the way,

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let's look at this water
wheel right over here.

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You can see that the
water comes down from here

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and then it falls.

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And as it falls, it pushes,

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it fills up these things right over here

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which then pushes it down.

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And then the whole wheel turns.

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And then that wheel could do work.

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Actually could do useful work.

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In a physics context, not all
work is necessarily useful.

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But this could actually do useful work.

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So what I wanna think about is
two different drops of water.

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I have a drop of water here,

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maybe the same drop of water.

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When it's up here versus once
it has gone all the way down

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and has been dumped into what I'm assuming

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is a stream down here.

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Now, which one has a
higher capacity to do work?

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Pause this video and think about that.

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Well, I just told you that
when the water drop is up here,

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it has the capacity as it falls

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because of the gravitational field,

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which is pulling down on it.

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And by the way, if the gravitational field

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is pulling down on the water drop,

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that water drop is also
pulling up on earth.

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But this gravitational field of earth

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is pulling down on that water drop.

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And because of that,

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if the water drop is not supported

00:03:05.570 --> 00:03:07.947
it can actually do work in this example

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on its way to being in this
position right over here.

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Now this position right over here,

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in theory, it could maybe still do work.

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Maybe there's a cliff right over here

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and it can continue to pour down.

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But the water drop up here
clearly has the capacity

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to do more work because
it has the potential work

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that it can do from
going from here to here.

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And then obviously it could then continue

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to do any work that this
position would allow it to have.

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So we would say that this water drop

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by virtue of its position,

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has a higher capacity to do
work and has more energy.

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And what is a form of that energy?

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Well, in this case, it's
gravitational potential energy.

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It's energy that is stored.

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And I put that in quotes

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because it's not like
you're going to be able

00:03:52.380 --> 00:03:54.940
to open that water drop and
all of a sudden see energy,

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but it's energy that's stored
by virtue of its position.

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Another way to think about it

00:03:59.840 --> 00:04:01.890
is instead of imagining that the energy

00:04:01.890 --> 00:04:03.340
is stored in the water drop,

00:04:03.340 --> 00:04:05.520
and it is really happening in our minds,

00:04:05.520 --> 00:04:08.770
is to say that that energy
is stored in the field.

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In this case, this gravitational field.

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Now the gravitational field
is pulling on this water drop.

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So the direction of motion

00:04:16.900 --> 00:04:19.950
would actually reduce
the energy in the field.

00:04:19.950 --> 00:04:23.550
So if we just let things happen,
earth's gravitational field

00:04:23.550 --> 00:04:25.810
is going to pull on this water drop.

00:04:25.810 --> 00:04:28.020
And actually that water drop
has a gravitational field

00:04:28.020 --> 00:04:29.480
that's going to pull up on earth,

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but as that water drop gets pulled down,

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the total amount of energy stored

00:04:34.580 --> 00:04:36.640
in the field is going to go down.

00:04:36.640 --> 00:04:37.790
Now what happened to that energy?

00:04:37.790 --> 00:04:40.280
That energy gets
transferred out of the field

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into kinetic energy of this wheel,

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which could then be
transferred into other things.


What is energy?

WEBVTT
Kind: captions
Language: en

00:00:00.120 --> 00:00:02.160
- [Instructor] Energy is a
word we hear all the time

00:00:02.160 --> 00:00:03.560
in seemingly different contexts,

00:00:03.560 --> 00:00:04.900
almost every single day.

00:00:04.900 --> 00:00:07.170
We hear about renewable
energy on the news,

00:00:07.170 --> 00:00:08.630
and particularly in the winter,

00:00:08.630 --> 00:00:10.400
we hear people talking
about their energy bills,

00:00:10.400 --> 00:00:11.500
because they're worried

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about how much it's going
to cost to heat their homes.

00:00:13.830 --> 00:00:14.950
So this brings about the question

00:00:14.950 --> 00:00:18.530
of what is energy that we
can talk about it so often

00:00:18.530 --> 00:00:20.890
and in seemingly such different ways?

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So in physics, we actually
have a specific definition

00:00:23.590 --> 00:00:25.040
of what energy is,

00:00:25.040 --> 00:00:26.470
and you'll see it's
really not that different

00:00:26.470 --> 00:00:29.060
from how we talk about energy day to day.

00:00:29.060 --> 00:00:33.130
Energy in physics is defined
as the ability to do work.

00:00:33.130 --> 00:00:35.800
We can't talk about energy
without talking about work,

00:00:35.800 --> 00:00:37.890
so we should probably
define that right now,

00:00:37.890 --> 00:00:39.550
because work is another one of these words

00:00:39.550 --> 00:00:41.730
that we use an awful lot, but once again,

00:00:41.730 --> 00:00:44.193
physics has a specific definition for it.

00:00:45.130 --> 00:00:47.010
In physics, work is performed

00:00:47.010 --> 00:00:50.120
when you apply force over a distance.

00:00:50.120 --> 00:00:52.170
We can actually write this as an equation,

00:00:52.170 --> 00:00:56.140
W equals F times d, where
W is work, F is force,

00:00:56.140 --> 00:00:58.323
and d is distance or displacement.

00:00:59.260 --> 00:01:01.130
If you've ever moved a box, a suitcase,

00:01:01.130 --> 00:01:03.780
or really any object in
your room across the floor

00:01:03.780 --> 00:01:06.590
just to get it out of your
way, you performed work.

00:01:06.590 --> 00:01:09.170
You had to apply force
to that box to move it

00:01:09.170 --> 00:01:11.490
whatever distance it took
to get out of your way.

00:01:11.490 --> 00:01:13.030
If it was a short distance,

00:01:13.030 --> 00:01:14.380
you can see from the equation,

00:01:14.380 --> 00:01:16.330
that that's going to be less work

00:01:16.330 --> 00:01:18.650
than if you have to move
it across your entire room,

00:01:18.650 --> 00:01:21.070
down the hall, into another room.

00:01:21.070 --> 00:01:23.240
And in order to perform
this work to move the box

00:01:23.240 --> 00:01:25.910
out of your way, you had
to have energy available.

00:01:25.910 --> 00:01:27.710
That energy is enabling
you to do the work,

00:01:27.710 --> 00:01:29.570
because you're going
to transfer the energy

00:01:29.570 --> 00:01:32.930
from yourself to that
box in order to move it.

00:01:32.930 --> 00:01:35.670
So, another way that we can
think about work and energy

00:01:35.670 --> 00:01:38.240
is that the change in
energy of the system,

00:01:38.240 --> 00:01:39.700
in this case, you and the box,

00:01:39.700 --> 00:01:42.250
is actually equal to the work done.

00:01:42.250 --> 00:01:43.990
When we define energy this way,

00:01:43.990 --> 00:01:46.850
it allows us to do a lot
of interesting things.

00:01:46.850 --> 00:01:49.800
We've set up a way to
measure and calculate energy,

00:01:49.800 --> 00:01:52.890
so it's actually a quantifiable property.

00:01:52.890 --> 00:01:54.870
Let's go back to the example of a box,

00:01:54.870 --> 00:01:57.480
and let's say that instead
of just trying to move a box

00:01:57.480 --> 00:01:58.940
out of your way in your room,

00:01:58.940 --> 00:02:01.010
you're actually going to pack
up everything in your room,

00:02:01.010 --> 00:02:02.120
because you're going to move

00:02:02.120 --> 00:02:03.660
to a completely different house.

00:02:03.660 --> 00:02:06.000
And now you have 10 boxes to move.

00:02:06.000 --> 00:02:09.320
We can actually calculate
the energy required

00:02:09.320 --> 00:02:12.000
to move all of those boxes.

00:02:12.000 --> 00:02:14.500
You might be saying to
yourself, "Wait a minute.

00:02:14.500 --> 00:02:16.230
I'm now moving 10 boxes.

00:02:16.230 --> 00:02:18.030
That actually sounds kind of tiring.

00:02:18.900 --> 00:02:20.150
And if I'm getting tired,

00:02:20.150 --> 00:02:22.550
does that mean I'm
actually losing energy?"

00:02:22.550 --> 00:02:25.560
It turns out that energy
is coming from somewhere,

00:02:25.560 --> 00:02:27.750
and in this case, it's
going to come from food.

00:02:27.750 --> 00:02:29.440
So as you're moving these boxes,

00:02:29.440 --> 00:02:31.310
you may find yourself getting hungry,

00:02:31.310 --> 00:02:33.090
so you should probably grab a snack,

00:02:33.090 --> 00:02:35.620
something like, I don't know, an apple,

00:02:35.620 --> 00:02:37.920
let's pretend that's
what I've drawn there,

00:02:37.920 --> 00:02:39.730
so that you can get more energy

00:02:39.730 --> 00:02:41.913
to move the rest of those 10 boxes.

00:02:43.070 --> 00:02:46.530
And you might be thinking
now, "Wait a minute.

00:02:46.530 --> 00:02:50.290
This energy coming from
food to me seems different

00:02:50.290 --> 00:02:52.970
than energy between me and moving a box."

00:02:52.970 --> 00:02:56.060
And that's because you can
actually see the box moving,

00:02:56.060 --> 00:02:58.410
which brings us to our next point,

00:02:58.410 --> 00:03:00.130
energy comes in various forms

00:03:00.130 --> 00:03:02.330
and they don't all look the same.

00:03:02.330 --> 00:03:04.740
We have equations to quantify the energy

00:03:04.740 --> 00:03:05.810
of these various forms,

00:03:05.810 --> 00:03:08.300
and we'll talk about
those in another video,

00:03:08.300 --> 00:03:10.610
but the key here is that energy

00:03:10.610 --> 00:03:12.450
can transfer between objects

00:03:12.450 --> 00:03:14.750
and it can also convert
between different forms,

00:03:14.750 --> 00:03:18.240
such as when you eat and
get energy from that apple,

00:03:18.240 --> 00:03:21.510
and then you use that
energy to move a box.

00:03:21.510 --> 00:03:25.530
So to summarize, energy
is the ability to do work.

00:03:25.530 --> 00:03:28.810
Work is done when you apply
force across a distance,

00:03:28.810 --> 00:03:31.090
and we can write that as an equation.

00:03:31.090 --> 00:03:33.010
And because we can calculate the energy

00:03:33.010 --> 00:03:35.040
of a system using equations,

00:03:35.040 --> 00:03:37.883
we now know that energy is
a quantifiable property.


Calculating gravitational potential energy

WEBVTT
Kind: captions
Language: en

00:00:01.260 --> 00:00:02.400
- [Instructor] In previous videos,

00:00:02.400 --> 00:00:05.640
we have introduced the idea of energy

00:00:05.640 --> 00:00:08.770
as the capacity to do work

00:00:08.770 --> 00:00:11.820
and we have talked about
multiple types of energies.

00:00:11.820 --> 00:00:14.830
We've talked about kinetic
energy, energy due to motion.

00:00:14.830 --> 00:00:17.330
We've talked about potential energy,

00:00:17.330 --> 00:00:21.150
which is energy by virtue of position.

00:00:21.150 --> 00:00:23.570
And when we're talking
about potential energy,

00:00:23.570 --> 00:00:27.130
we're talking about it relative
to some other position.

00:00:27.130 --> 00:00:29.150
And in particular, in this video,

00:00:29.150 --> 00:00:31.980
we're going to talk about
gravitational potential energy,

00:00:31.980 --> 00:00:34.300
which is potential energy due to position

00:00:34.300 --> 00:00:36.660
in a gravitational field.

00:00:36.660 --> 00:00:41.000
So let's say that this is
the surface of the earth.

00:00:41.000 --> 00:00:46.000
Let's say that I have a five
kilogram mass right over here,

00:00:47.650 --> 00:00:52.650
and let's say that it is 10 meters above

00:00:53.840 --> 00:00:55.300
the surface of the earth.

00:00:55.300 --> 00:00:58.780
My question to you is how
much more potential energy

00:00:58.780 --> 00:01:00.400
does it have in this position

00:01:00.400 --> 00:01:03.210
than when it is in this position,

00:01:03.210 --> 00:01:06.310
when it is sitting on
the surface of the earth,

00:01:06.310 --> 00:01:08.430
10 meters lower?

00:01:08.430 --> 00:01:10.630
Pause the video and try
to think about that.

00:01:12.610 --> 00:01:15.350
All right, now let's
work on this together.

00:01:15.350 --> 00:01:19.300
So our gravitational potential
energy is going to be equal

00:01:19.300 --> 00:01:22.950
to our mass times lowercase g,

00:01:22.950 --> 00:01:25.210
which you can view as the constant

00:01:25.210 --> 00:01:28.660
for earth's gravitational field
near the surface of earth.

00:01:28.660 --> 00:01:31.060
And the reason why I say
near the surface of earth

00:01:31.060 --> 00:01:33.550
is as you get further
and further from earth,

00:01:33.550 --> 00:01:35.330
this thing could actually change,

00:01:35.330 --> 00:01:37.030
but near the surface of the earth,

00:01:37.030 --> 00:01:39.460
we assume that it is roughly constant,

00:01:39.460 --> 00:01:43.560
and then you multiply
that times your height.

00:01:43.560 --> 00:01:46.070
So calculating this is
pretty straightforward

00:01:46.070 --> 00:01:48.270
as long as you know what g is.

00:01:48.270 --> 00:01:53.270
G, we can approximate it as
9.8 meters per second squared.

00:01:55.240 --> 00:01:57.310
So when you multiply all of this out,

00:01:57.310 --> 00:01:59.970
this is going to be equal to your mass,

00:01:59.970 --> 00:02:01.983
which is five kilograms,

00:02:03.240 --> 00:02:06.310
times the gravitational field constant,

00:02:06.310 --> 00:02:09.980
so times 9.8 meters per second squared,

00:02:14.400 --> 00:02:15.560
times your height,

00:02:15.560 --> 00:02:18.010
which in this situation is 10 meters,

00:02:18.010 --> 00:02:20.750
so times 10 meters.

00:02:20.750 --> 00:02:25.653
And so this is going to be
equal to five times 9.8 is 49,

00:02:26.530 --> 00:02:30.110
times 10 is 490.

00:02:30.110 --> 00:02:31.453
We have kilograms,

00:02:32.540 --> 00:02:34.810
and then we have meters times meters,

00:02:34.810 --> 00:02:39.280
so times meters squared
per second squared.

00:02:39.280 --> 00:02:41.160
And these might seem like strange units,

00:02:41.160 --> 00:02:42.510
but you might recognize this

00:02:42.510 --> 00:02:45.960
as also the units of force times distance,

00:02:45.960 --> 00:02:49.420
which we could also
express in terms of joules.

00:02:49.420 --> 00:02:52.340
So this is 490 joules,

00:02:52.340 --> 00:02:57.120
which is our units both for
energy and our unit for work.

00:02:57.120 --> 00:03:00.320
Now, let's make sure that
this is intuitive sense.

00:03:00.320 --> 00:03:01.680
Well, one way to think about it is

00:03:01.680 --> 00:03:05.990
how much work would it take
to go from here to here?

00:03:05.990 --> 00:03:10.380
Well, you're going to be lifting
it a distance of 10 meters,

00:03:10.380 --> 00:03:13.180
and as you're lifting it
a distance of 10 meters,

00:03:13.180 --> 00:03:15.410
what is the force you're
going to have to apply?

00:03:15.410 --> 00:03:16.640
Well, the force you're
going to have to apply

00:03:16.640 --> 00:03:18.250
is going to be the weight of the object.

00:03:18.250 --> 00:03:21.430
The weight is its mass times
the gravitational field.

00:03:21.430 --> 00:03:24.570
So in order to put it in that
position from the ground,

00:03:24.570 --> 00:03:27.320
you're going to have to do
its weight times the height,

00:03:27.320 --> 00:03:30.120
or 490 joules of work.

00:03:30.120 --> 00:03:33.930
And so you can do 490 joules
of work to get it there

00:03:33.930 --> 00:03:35.300
and then you can think about it

00:03:35.300 --> 00:03:37.830
as that energy being stored this way.

00:03:37.830 --> 00:03:39.460
And now it can then do that work.

00:03:39.460 --> 00:03:40.800
How could it do that work?

00:03:40.800 --> 00:03:42.750
Well, there's a bunch
of ways you could do it.

00:03:42.750 --> 00:03:47.750
You could have this attached
to maybe a pulley of some kind

00:03:47.850 --> 00:03:51.650
and then if it had another
weight right over here,

00:03:51.650 --> 00:03:55.420
and let's just, for simplicity,
assume it has the same mass,

00:03:55.420 --> 00:03:59.000
well, if you let this
first purple mass go,

00:03:59.000 --> 00:04:00.370
it's going to go down.

00:04:00.370 --> 00:04:02.430
And if you assume that this pulley

00:04:02.430 --> 00:04:04.010
is completely frictionless,

00:04:04.010 --> 00:04:07.130
this mass is going to
be lifted by 10 meters.

00:04:07.130 --> 00:04:09.750
And so if you have a five kilogram mass

00:04:09.750 --> 00:04:13.470
that is lifted by 10 meters in
Earth's gravitational field,

00:04:13.470 --> 00:04:15.060
near the surface of the earth,

00:04:15.060 --> 00:04:18.270
you would have just
done 490 joules of work.

00:04:18.270 --> 00:04:19.890
So hopefully this makes sense

00:04:19.890 --> 00:04:21.490
why you're just really taking the weight

00:04:21.490 --> 00:04:23.040
of the object times its height.

00:04:23.040 --> 00:04:24.700
And hopefully it also makes sense

00:04:24.700 --> 00:04:28.100
that it then has the capacity
to do that amount of work.

00:04:28.100 --> 00:04:31.953
And in this case, we said
relative to sitting on the ground.


Calculating kinetic energy

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:01.410
- [Instructor] In this video,

00:00:01.410 --> 00:00:03.420
we're gonna talk about kinetic energy

00:00:03.420 --> 00:00:06.540
and we're also gonna think
about how to calculate it.

00:00:06.540 --> 00:00:09.020
So you can already imagine
based on the word kinetic,

00:00:09.020 --> 00:00:10.780
which is referring to motion

00:00:10.780 --> 00:00:13.560
that this is the energy that an object has

00:00:13.560 --> 00:00:15.650
by virtue of its motion.

00:00:15.650 --> 00:00:17.100
And when we talk about energy,

00:00:17.100 --> 00:00:20.570
we're talking about its
capacity to do work.

00:00:20.570 --> 00:00:24.390
So just based on that early
definition of kinetic energy,

00:00:24.390 --> 00:00:26.300
which of these two running backs

00:00:26.300 --> 00:00:28.920
do you think has more kinetic energy,

00:00:28.920 --> 00:00:33.010
this gentleman on the left
whose mass is a 100 kilograms

00:00:33.010 --> 00:00:36.290
and who is traveling at a
speed of two meters per second,

00:00:36.290 --> 00:00:37.470
or the gentleman on the right,

00:00:37.470 --> 00:00:39.660
who has a mass of 25 kilograms

00:00:39.660 --> 00:00:43.120
and who's traveling with a
speed of four meters per second?

00:00:43.120 --> 00:00:45.020
Pause this video and think about that.

00:00:46.240 --> 00:00:48.550
All right, now let's
think about this together.

00:00:48.550 --> 00:00:50.530
So I'm first just gonna
give you the formula

00:00:50.530 --> 00:00:53.620
for kinetic energy, but then
we are going to derive it.

00:00:53.620 --> 00:00:56.510
So the formula for kinetic
energy is that it's equal

00:00:56.510 --> 00:00:59.480
to 1/2 times the mass of the object,

00:00:59.480 --> 00:01:02.250
times the magnitude of
its velocity squared,

00:01:02.250 --> 00:01:03.250
or another way to think about it,

00:01:03.250 --> 00:01:05.240
its speed squared.

00:01:05.240 --> 00:01:08.390
And so given this formula, pause the video

00:01:08.390 --> 00:01:10.330
and see if you can
calculate the kinetic energy

00:01:10.330 --> 00:01:11.930
for each of these running backs.

00:01:13.100 --> 00:01:15.911
All right, let's calculate
the kinetic energy

00:01:15.911 --> 00:01:18.210
for this guy on the left.

00:01:18.210 --> 00:01:22.430
It's gonna be 1/2 times his mass,

00:01:22.430 --> 00:01:27.430
which is 100 kilograms, times
the square of the speed,

00:01:28.000 --> 00:01:32.610
so times four meters
squared per second squared,

00:01:32.610 --> 00:01:35.010
have to make sure that we
square the units as well.

00:01:35.010 --> 00:01:37.570
And this is going to be
equal to 1/2 times 100

00:01:37.570 --> 00:01:42.334
is 50 times four is 200 and
then the units are kilogram

00:01:42.334 --> 00:01:45.960
meter squared per second squared.

00:01:45.960 --> 00:01:48.150
And you might already recognize
that this is the same thing

00:01:48.150 --> 00:01:52.500
as kilogram meter per
second squared times meters,

00:01:52.500 --> 00:01:56.450
or these are really the units
of force times distance,

00:01:56.450 --> 00:01:58.520
or this is the units of energy

00:01:58.520 --> 00:02:01.700
which we can write as 200 joules.

00:02:01.700 --> 00:02:04.540
Now let's do the same
thing for this running back

00:02:04.540 --> 00:02:06.330
that has less mass.

00:02:06.330 --> 00:02:10.170
Kinetic energy here is
gonna be 1/2 times the mass,

00:02:10.170 --> 00:02:14.580
25 kilograms times the
square of the speed here,

00:02:14.580 --> 00:02:19.220
so that's gonna be 16 meters
squared per second squared.

00:02:19.220 --> 00:02:20.930
And then that gets us.

00:02:20.930 --> 00:02:25.120
We're essentially gonna have
1/2 times 16 is eight times 25,

00:02:25.120 --> 00:02:27.600
200, and we get the exact same units

00:02:27.600 --> 00:02:29.960
and so we can go straight to 200 joules.

00:02:29.960 --> 00:02:31.620
So it turns out that they have

00:02:31.620 --> 00:02:33.900
the exact same kinetic energy.

00:02:33.900 --> 00:02:36.610
Even though the gentleman
on the right has one fourth

00:02:36.610 --> 00:02:39.270
the mass and only twice the speed,

00:02:39.270 --> 00:02:42.640
we see that we square
the speed right over here

00:02:42.640 --> 00:02:44.120
so that makes a huge difference.

00:02:44.120 --> 00:02:46.730
And so their energy due to their motion,

00:02:46.730 --> 00:02:50.360
they have the same capacity to do work.

00:02:50.360 --> 00:02:51.540
Now, some of you are thinking,

00:02:51.540 --> 00:02:53.970
where does this formula come from?

00:02:53.970 --> 00:02:55.930
And one way to think about work and energy

00:02:55.930 --> 00:03:00.310
is that you can use
work to transfer energy

00:03:00.310 --> 00:03:02.830
to a system or to an object somehow.

00:03:02.830 --> 00:03:05.710
And then that energy is
that object's capacity

00:03:05.710 --> 00:03:07.380
to do work again.

00:03:07.380 --> 00:03:10.710
So let's imagine some
object that has a mass m

00:03:10.710 --> 00:03:14.830
and the magnitude of its
velocity or its speed is v.

00:03:14.830 --> 00:03:17.920
So what would be the work necessary

00:03:17.920 --> 00:03:20.730
to bring that object that has mass m

00:03:20.730 --> 00:03:25.730
to a speed of v, assuming
it's starting at a standstill?

00:03:25.740 --> 00:03:27.840
Well, let's think about it a little bit.

00:03:27.840 --> 00:03:31.360
Work is equal to the magnitude of force

00:03:31.360 --> 00:03:32.720
in a certain direction,

00:03:32.720 --> 00:03:36.860
times the magnitude of the
displacement in that direction,

00:03:36.860 --> 00:03:37.810
which we could write like that.

00:03:37.810 --> 00:03:40.290
Sometimes they use s for the magnitude

00:03:40.290 --> 00:03:42.090
of displacement as well.

00:03:42.090 --> 00:03:45.130
And so what is the
force the same thing as?

00:03:45.130 --> 00:03:48.050
We know that the force is the same thing

00:03:48.050 --> 00:03:51.970
as mass times the acceleration.

00:03:51.970 --> 00:03:52.980
And we're going to assume

00:03:52.980 --> 00:03:54.500
that we have constant acceleration

00:03:54.500 --> 00:03:57.510
just so that we can simplify
our derivation here.

00:03:57.510 --> 00:03:59.960
And then what's the distance
that we're gonna travel.

00:03:59.960 --> 00:04:02.530
Well, the distance is gonna
be the average magnitude

00:04:02.530 --> 00:04:04.690
of the velocity, or we
could say the average speed,

00:04:04.690 --> 00:04:06.420
so I'll write it like this,

00:04:06.420 --> 00:04:11.420
times the time that it takes
to accelerate the object

00:04:11.420 --> 00:04:13.640
to a velocity of v.

00:04:13.640 --> 00:04:15.970
Well, how long does it take
to accelerate an object

00:04:15.970 --> 00:04:19.130
to a velocity of v if
you're accelerating it at a?

00:04:19.130 --> 00:04:22.080
Well, this is just gonna
be the velocity divided

00:04:22.080 --> 00:04:23.120
by the acceleration.

00:04:23.120 --> 00:04:23.953
Think about it.

00:04:23.953 --> 00:04:25.820
If you're going, trying
to get to a velocity

00:04:25.820 --> 00:04:28.230
of four meters per second,
and you're accelerating

00:04:28.230 --> 00:04:30.780
at two meters per second, per second,

00:04:30.780 --> 00:04:34.939
four divided by two is gonna
leave you with two seconds.

00:04:34.939 --> 00:04:37.750
And if you're starting at a speed of zero

00:04:37.750 --> 00:04:40.080
and you're going to a
magnitude of a velocity

00:04:40.080 --> 00:04:44.180
or a speed of v, and you're
assuming constant acceleration,

00:04:44.180 --> 00:04:48.870
your average velocity is
just gonna be v over two.

00:04:48.870 --> 00:04:51.710
So this is just v over two.

00:04:51.710 --> 00:04:54.990
And then we get a little bit
of a drum roll right over here.

00:04:54.990 --> 00:04:57.890
We see that acceleration
cancels with acceleration,

00:04:57.890 --> 00:05:02.890
and we are left with mass
times v squared over two,

00:05:03.460 --> 00:05:05.470
mv squared over two,

00:05:05.470 --> 00:05:08.440
which is exactly what
we had right over here.

00:05:08.440 --> 00:05:11.540
So the work necessary
to accelerate an object

00:05:11.540 --> 00:05:16.540
of mass m from zero speed to
a speed of v is exactly this.

00:05:17.490 --> 00:05:19.790
And that's how much energy is then stored

00:05:19.790 --> 00:05:22.730
in that object by virtue of its motion.

00:05:22.730 --> 00:05:24.400
And if you don't have energy loss

00:05:24.400 --> 00:05:27.313
it could in theory, do this much work.


Energy in fields

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:01.660
- [Presenter] In this
video, we're gonna talk

00:00:01.660 --> 00:00:04.290
about how energy is stored in field

00:00:04.290 --> 00:00:07.530
and in particular, how if we
change the position of things

00:00:07.530 --> 00:00:11.090
within that field, how it
might change the energy.

00:00:11.090 --> 00:00:13.060
So, just as a bit of a refresher,

00:00:13.060 --> 00:00:15.910
let's remind ourselves what energy is.

00:00:15.910 --> 00:00:20.910
It is the capacity to do work.

00:00:21.160 --> 00:00:23.330
And we've also seen that work,

00:00:23.330 --> 00:00:26.320
we can view it as equal
to the magnitude of force

00:00:26.320 --> 00:00:30.600
times the displacement in
the direction of that force.

00:00:30.600 --> 00:00:34.040
And then we can also remind
ourselves what a field is.

00:00:34.040 --> 00:00:35.810
And I'm not just talking about a big lawn

00:00:35.810 --> 00:00:37.970
or something like that, a football field.

00:00:37.970 --> 00:00:40.900
I'm talking about a general
idea in physics that's used.

00:00:40.900 --> 00:00:44.040
It's really just a concept
that allows us to predict

00:00:44.040 --> 00:00:48.680
and explain how to things that
are not touching each other

00:00:48.680 --> 00:00:49.940
are still interacting,

00:00:49.940 --> 00:00:52.640
are still able to exert
forces on each other.

00:00:52.640 --> 00:00:54.500
And in other videos, I've
also talked about that.

00:00:54.500 --> 00:00:56.670
Really nothing in this
universe is touching.

00:00:56.670 --> 00:00:59.850
We just conceptualize
that sometimes they are.

00:00:59.850 --> 00:01:01.520
But just as an example of a field,

00:01:01.520 --> 00:01:02.770
we have an electric field here.

00:01:02.770 --> 00:01:04.500
I could have done another type of field,

00:01:04.500 --> 00:01:06.520
we could have done a magnetic field,

00:01:06.520 --> 00:01:08.800
we could have done a gravitational field.

00:01:08.800 --> 00:01:11.160
Although when you study general relativity

00:01:11.160 --> 00:01:12.650
which Einstein gave us,

00:01:12.650 --> 00:01:16.090
we realize that it might
not exactly be optimal

00:01:16.090 --> 00:01:17.630
to think about it as a field.

00:01:17.630 --> 00:01:19.250
But in an electric field, right over here,

00:01:19.250 --> 00:01:21.810
we have a positive charge,
we have a negative charge.

00:01:21.810 --> 00:01:23.820
We know from experience

00:01:23.820 --> 00:01:26.420
that these two things attract each other

00:01:26.420 --> 00:01:29.610
and the convention is to
draw these field lines

00:01:29.610 --> 00:01:33.120
that go from the positive
towards the negative.

00:01:33.120 --> 00:01:37.150
Now, if we were to just let
go of these two point charges

00:01:37.150 --> 00:01:38.980
over here, what would happen?

00:01:38.980 --> 00:01:42.300
Well, we know that due to the
electric field constructed

00:01:42.300 --> 00:01:44.310
or created or that we imagined was created

00:01:44.310 --> 00:01:46.260
by this negative point charge,

00:01:46.260 --> 00:01:49.450
this positive charge would have a force

00:01:49.450 --> 00:01:51.310
acting on it towards the negative charge

00:01:51.310 --> 00:01:53.610
and vice versa due to the electric field

00:01:53.610 --> 00:01:56.370
that is created by the positive charge.

00:01:56.370 --> 00:01:59.330
The negative charge is
going to also be attracted

00:01:59.330 --> 00:02:00.170
to the positive charge.

00:02:00.170 --> 00:02:02.840
They're both going to
move towards each other.

00:02:02.840 --> 00:02:05.280
And so, when we talk
about energy in fields

00:02:05.280 --> 00:02:08.863
or energy stored in fields,
in our initial configuration,

00:02:10.582 --> 00:02:12.590
how is there energy in this field?

00:02:12.590 --> 00:02:14.820
How is their capacity to do work?

00:02:14.820 --> 00:02:16.720
Pause this video and think about that.

00:02:17.910 --> 00:02:19.100
Well, think about it this way.

00:02:19.100 --> 00:02:23.480
Imagine if each of these
charges were attached

00:02:23.480 --> 00:02:25.280
to some type of a mass,

00:02:25.280 --> 00:02:27.670
let me do this in a color
you can actually see.

00:02:27.670 --> 00:02:30.540
So, let's say that this is
towing some type of a mass

00:02:30.540 --> 00:02:35.290
and this is towing some type
of a mass right over here.

00:02:35.290 --> 00:02:38.590
Well, when you let go and
the forces are exerted

00:02:38.590 --> 00:02:40.570
on each of these point charges,

00:02:40.570 --> 00:02:42.530
assuming that the forces are large enough,

00:02:42.530 --> 00:02:45.060
they're going to be able
to pull these masses

00:02:45.060 --> 00:02:46.000
towards each other.

00:02:46.000 --> 00:02:48.790
So, there's a potential amount
of work that could be done

00:02:48.790 --> 00:02:50.300
and it would essentially keep happening

00:02:50.300 --> 00:02:52.750
until these point charges touch.

00:02:52.750 --> 00:02:55.070
And I used air quotes with my hand

00:02:55.070 --> 00:02:56.310
even though you can't see it,

00:02:56.310 --> 00:02:58.490
or until they can't get
any closer to each other

00:02:58.490 --> 00:03:01.920
or some other is keeping
them from getting any closer

00:03:01.920 --> 00:03:03.020
to each other.

00:03:03.020 --> 00:03:06.840
So now, let me think about how
could I increase the energy

00:03:06.840 --> 00:03:09.210
that is stored in this field.

00:03:09.210 --> 00:03:11.093
Pause the video and think about that.

00:03:12.750 --> 00:03:15.710
Well, what if I were to
keep the positive charge

00:03:15.710 --> 00:03:19.350
where it is, but if I were
to take the negative charge

00:03:19.350 --> 00:03:22.040
and if I were to move it
in a direction opposite

00:03:22.040 --> 00:03:25.940
from the force direction that
the field is trying to exert.

00:03:25.940 --> 00:03:27.660
So, instead of the negative charge there,

00:03:27.660 --> 00:03:30.830
what if I moved it all the way out there?

00:03:30.830 --> 00:03:34.080
Once again, let me do that in
a color you can actually see.

00:03:34.080 --> 00:03:35.580
Well, if I moved it out here

00:03:35.580 --> 00:03:39.270
and we're still towing
some type of a mass,

00:03:39.270 --> 00:03:42.680
you can see that when I moved
it against the direction

00:03:42.680 --> 00:03:46.070
that the force of the
field is trying to exert,

00:03:46.070 --> 00:03:48.300
that I've increased
the energy in the field

00:03:48.300 --> 00:03:50.410
because now I can do more work.

00:03:50.410 --> 00:03:55.410
I can drag this potential
mass over a larger distance.

00:03:55.410 --> 00:03:57.530
So, we have a general principle here.

00:03:57.530 --> 00:04:02.120
If we let these charges go in
the direction of the forces

00:04:02.120 --> 00:04:04.350
that are being exerted
on them due to the field,

00:04:04.350 --> 00:04:07.530
we're going to reduce
the energy in the field.

00:04:07.530 --> 00:04:11.430
But then if we are able to
move them against the forces

00:04:11.430 --> 00:04:13.190
of the field, and as you can imagine,

00:04:13.190 --> 00:04:14.420
we're going to have to put energy

00:04:14.420 --> 00:04:16.850
into the system to do that.

00:04:16.850 --> 00:04:20.010
But if we do that, then
we're storing more energy

00:04:20.010 --> 00:04:22.990
in this field because in that case,

00:04:22.990 --> 00:04:25.300
they're going to be further
away from each other

00:04:25.300 --> 00:04:28.410
and so they could drag their little masses

00:04:28.410 --> 00:04:30.553
that they're towing even further.


Electromagnetic radiation emission

WEBVTT
Kind: captions
Language: en

00:00:00.320 --> 00:00:03.040
- [Norm] Let me ask you a
seemingly simple question.

00:00:03.040 --> 00:00:06.060
I have a picture of fire
here, and my question is,

00:00:06.060 --> 00:00:08.310
what is fire?

00:00:08.310 --> 00:00:11.190
Well, what would you say if
I were to tell you that fire,

00:00:11.190 --> 00:00:13.560
as we see it, these flickering flames,

00:00:13.560 --> 00:00:16.050
it is nothing but hot air?

00:00:16.050 --> 00:00:17.460
And I know what you might be thinking.

00:00:17.460 --> 00:00:18.527
Hot air?

00:00:18.527 --> 00:00:20.140
"Norm, I've seen air that's hot,

00:00:20.140 --> 00:00:21.700
or I experienced air that's hot

00:00:21.700 --> 00:00:24.370
and I don't oftentimes even see the air,

00:00:24.370 --> 00:00:26.460
but here I clearly see something bright,

00:00:26.460 --> 00:00:28.070
something that's emitting light,

00:00:28.070 --> 00:00:31.350
something that's emitting
electromagnetic radiation."

00:00:31.350 --> 00:00:33.400
And then what I would say to you,

00:00:33.400 --> 00:00:34.550
if you were thinking that,

00:00:34.550 --> 00:00:38.490
is it actually turns out
that anything in our universe

00:00:38.490 --> 00:00:42.480
that has a temperature above
absolute zero, zero Kelvin,

00:00:42.480 --> 00:00:43.680
which is pretty much anything

00:00:43.680 --> 00:00:45.970
that you will ever come
across in your life,

00:00:45.970 --> 00:00:48.420
emits electromagnetic radiation.

00:00:48.420 --> 00:00:50.740
Objects with temperature
aren't the only way

00:00:50.740 --> 00:00:52.700
to create electromagnetic radiation,

00:00:52.700 --> 00:00:55.840
but it is a major way that's
happening all around us.

00:00:55.840 --> 00:00:57.960
Even if you were in a pitch-black room,

00:00:57.960 --> 00:01:01.000
you would be emitting
electromagnetic radiation.

00:01:01.000 --> 00:01:03.450
A tree outside, even
if it was dark outside,

00:01:03.450 --> 00:01:05.810
is emitting electromagnetic radiation.

00:01:05.810 --> 00:01:07.600
You might say, "Wait, but
I don't see the tree,"

00:01:07.600 --> 00:01:08.900
and that's because your eyes

00:01:08.900 --> 00:01:11.410
can only detect certain frequencies

00:01:11.410 --> 00:01:13.790
of electromagnetic radiation.

00:01:13.790 --> 00:01:16.440
If we look at this
diagram right over here,

00:01:16.440 --> 00:01:19.730
we can see how we've categorized
many of the frequencies,

00:01:19.730 --> 00:01:21.140
and you can see that up here,

00:01:21.140 --> 00:01:23.060
this is the frequency,
this is the wavelength,

00:01:23.060 --> 00:01:25.410
and these are in powers of 10.

00:01:25.410 --> 00:01:28.480
So you can really view this
as a logarithmic scale.

00:01:28.480 --> 00:01:29.530
And just over here,

00:01:29.530 --> 00:01:32.300
you can see that our
eyes can only visibly see

00:01:32.300 --> 00:01:37.300
a small section of this
logarithmic scale of frequencies.

00:01:37.480 --> 00:01:38.760
One of the things I like to wonder,

00:01:38.760 --> 00:01:40.620
if humans didn't have eyes,

00:01:40.620 --> 00:01:42.970
if we weren't able to detect
even the small segment

00:01:42.970 --> 00:01:44.590
of the electromagnetic spectrum,

00:01:44.590 --> 00:01:45.720
would we even know

00:01:45.720 --> 00:01:49.300
that something like
electromagnetic waves existed?

00:01:49.300 --> 00:01:52.160
But we can see you have
gamma rays, x-rays, UV rays,

00:01:52.160 --> 00:01:55.760
infrared rays, microwave,
FM, AM radio waves,

00:01:55.760 --> 00:01:57.570
long radio waves.

00:01:57.570 --> 00:01:59.430
In most hot air,

00:01:59.430 --> 00:02:02.570
the frequency isn't high
enough for us to see it.

00:02:02.570 --> 00:02:06.610
So most hot air is going to
be in the infrared range.

00:02:06.610 --> 00:02:10.380
Only if it gets hot enough
will we start to see it,

00:02:10.380 --> 00:02:13.080
and that's what's happening
with this fire here.

00:02:13.080 --> 00:02:15.800
And if you look closely at a fire,

00:02:15.800 --> 00:02:18.230
you might actually see that the location

00:02:18.230 --> 00:02:20.800
where the combustion
reaction is happening,

00:02:20.800 --> 00:02:22.800
that that actually might be dark.

00:02:22.800 --> 00:02:25.660
And then right above that,
you'll see some blue flame,

00:02:25.660 --> 00:02:28.220
and then you'll see,
maybe if you look closely,

00:02:28.220 --> 00:02:30.270
some green or yellow flame,

00:02:30.270 --> 00:02:32.740
and then you will see the orange flame,

00:02:32.740 --> 00:02:34.970
and then you will see the red flame.

00:02:34.970 --> 00:02:37.400
And the reason why it
might be dark right where

00:02:37.400 --> 00:02:39.180
the combustion reaction is happening

00:02:39.180 --> 00:02:43.210
is that might be very high
energy electromagnetic waves.

00:02:43.210 --> 00:02:45.880
That would be in the UV spectrum.

00:02:45.880 --> 00:02:47.930
That would be at a higher
frequency than what's visible,

00:02:47.930 --> 00:02:49.250
so to our eyes, it looks dark.

00:02:49.250 --> 00:02:52.190
And then as it cools, it goes
through the visible spectrum.

00:02:52.190 --> 00:02:54.870
And then if it cools
enough, it goes to infrared.

00:02:54.870 --> 00:02:57.060
But we human beings have
built the capability

00:02:57.060 --> 00:03:00.970
to see beyond what our
regular eyes can see.

00:03:00.970 --> 00:03:02.510
For example,

00:03:02.510 --> 00:03:05.560
these are what are often
known as thermal images,

00:03:05.560 --> 00:03:08.660
but they're really just
detecting the infrared range.

00:03:08.660 --> 00:03:10.700
So this is a picture of two dogs.

00:03:10.700 --> 00:03:12.270
It could be pitch-black outside.

00:03:12.270 --> 00:03:13.910
I mean, it could be the
middle of the night,

00:03:13.910 --> 00:03:15.760
but because they have temperature,

00:03:15.760 --> 00:03:17.980
they are releasing electromagnetic waves,

00:03:17.980 --> 00:03:18.960
which we can detect.

00:03:18.960 --> 00:03:20.440
And this over here has a scale

00:03:20.440 --> 00:03:21.850
of what the temperature must be.

00:03:21.850 --> 00:03:23.950
So you can see the eyes of the dog

00:03:23.950 --> 00:03:26.090
are the hottest part right over here.

00:03:26.090 --> 00:03:28.990
You can also see thermal
imaging of not only a hand,

00:03:28.990 --> 00:03:31.010
but after a hand has touched a wall.

00:03:31.010 --> 00:03:32.830
With our eyes, if you were to touch a wall

00:03:32.830 --> 00:03:34.250
for say 30 seconds,

00:03:34.250 --> 00:03:36.800
it doesn't look like the
wall has changed at all,

00:03:36.800 --> 00:03:38.380
but if you were to look at the infrared,

00:03:38.380 --> 00:03:40.160
you would see that you
would have heated up parts

00:03:40.160 --> 00:03:41.330
of the wall and you would be able

00:03:41.330 --> 00:03:43.350
to see the shape of the hand.

00:03:43.350 --> 00:03:45.610
And so you can imagine, we human beings,

00:03:45.610 --> 00:03:48.100
because of our ability to
detect electromagnetic waves

00:03:48.100 --> 00:03:50.250
and explore electromagnetic waves,

00:03:50.250 --> 00:03:52.360
we've been able to
leverage them more and more

00:03:52.360 --> 00:03:53.620
in our everyday lives.

00:03:53.620 --> 00:03:56.430
Thermal imaging itself
has a lot of applications.

00:03:56.430 --> 00:03:58.450
Firefighters use it to find people,

00:03:58.450 --> 00:04:01.640
or to find flames in the
middle of a lot of smoke.

00:04:01.640 --> 00:04:03.820
We have things like x-rays,

00:04:03.820 --> 00:04:05.920
which are high energy
electromagnetic waves,

00:04:05.920 --> 00:04:08.610
which we can use to see
through soft tissues.

00:04:08.610 --> 00:04:09.960
So we can see bones.

00:04:09.960 --> 00:04:11.820
This is an old image and
it looks like they're using

00:04:11.820 --> 00:04:13.580
the x-rays kind of carelessly.

00:04:13.580 --> 00:04:15.940
You don't wanna be throwing
that radiation around,

00:04:15.940 --> 00:04:16.773
but even today.

00:04:16.773 --> 00:04:18.970
I got an x-ray of my
teeth just the other day

00:04:18.970 --> 00:04:20.470
when I went to the dentist.

00:04:20.470 --> 00:04:21.960
When you talk on your cell phone,

00:04:21.960 --> 00:04:24.060
the way that your cell
phone is able to communicate

00:04:24.060 --> 00:04:26.543
is leveraging electromagnetic waves.

00:04:27.390 --> 00:04:29.180
This is another thing
that's mind blowing to me,

00:04:29.180 --> 00:04:30.750
is that my little cell phone

00:04:30.750 --> 00:04:33.020
can actually emit electromagnetic waves

00:04:33.020 --> 00:04:36.180
in the radio part of
the spectrum far enough

00:04:36.180 --> 00:04:38.080
to be received by a cell
tower that could be 10,

00:04:38.080 --> 00:04:42.750
20, and in certain cases,
30 or 40 miles away.

00:04:42.750 --> 00:04:45.990
Microwave ovens literally
released microwaves,

00:04:45.990 --> 00:04:49.240
which are absorbed by our
food, which heats up the food.

00:04:49.240 --> 00:04:51.140
And so I'll leave you there.

00:04:51.140 --> 00:04:53.400
The big picture here is
that electromagnetic waves

00:04:53.400 --> 00:04:54.730
are all around us.

00:04:54.730 --> 00:04:57.810
It's most obvious to us
in the visible spectrum,

00:04:57.810 --> 00:04:59.670
because that's what we can see.

00:04:59.670 --> 00:05:03.570
But there is a large continuum
of different frequencies

00:05:03.570 --> 00:05:05.820
that the visible is only a part of.

00:05:05.820 --> 00:05:09.620
And we human beings have
leveraged this phenomenon

00:05:09.620 --> 00:05:11.630
in all sorts of interesting ways,

00:05:11.630 --> 00:05:14.160
and I would suspect that
we're just at the beginning

00:05:14.160 --> 00:05:15.140
of this exploration.

00:05:15.140 --> 00:05:18.230
Maybe you will come up
with a new application

00:05:18.230 --> 00:05:20.163
of electromagnetic waves.


pH and solubility

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:02.270
- [Instructor] Changing
the pH of a solution

00:00:02.270 --> 00:00:06.150
can affect the solubility
of a slightly soluble salt.

00:00:06.150 --> 00:00:09.610
For example, if we took some
solid lead two fluoride,

00:00:09.610 --> 00:00:11.120
which is a white solid,

00:00:11.120 --> 00:00:13.180
and we put it in some distilled water,

00:00:13.180 --> 00:00:15.440
the solid is going to reach an equilibrium

00:00:15.440 --> 00:00:17.700
with the ions in solution.

00:00:17.700 --> 00:00:19.970
Lead two fluoride forms lead two plus ions

00:00:19.970 --> 00:00:24.160
and fluoride anions in
a one to two mole ratio.

00:00:24.160 --> 00:00:27.230
So if we have two lead two
plus ions in this diagram,

00:00:27.230 --> 00:00:30.160
we need four fluoride anions.

00:00:30.160 --> 00:00:32.270
At equilibrium, the rate of this solution

00:00:32.270 --> 00:00:34.530
is equal to the rate of precipitation,

00:00:34.530 --> 00:00:37.000
and therefore, the amount of solid

00:00:37.000 --> 00:00:41.090
and the concentration of ions
in solution remains constant.

00:00:41.090 --> 00:00:45.700
And this forms a saturated
solution of lead two fluoride.

00:00:45.700 --> 00:00:47.580
To the system at equilibrium,

00:00:47.580 --> 00:00:49.790
we're gonna add some H plus ions.

00:00:49.790 --> 00:00:51.580
So by increasing the concentration

00:00:51.580 --> 00:00:53.580
of H plus ions in solution,

00:00:53.580 --> 00:00:57.440
we're decreasing the pH of the solution.

00:00:57.440 --> 00:00:59.930
When the H plus ions are
added to the solution,

00:00:59.930 --> 00:01:01.990
most of them react with
the fluoride anions

00:01:01.990 --> 00:01:03.120
that are present.

00:01:03.120 --> 00:01:06.680
So H plus plus F minus forms HF.

00:01:06.680 --> 00:01:09.760
Comparing the first diagram
to the second diagram,

00:01:09.760 --> 00:01:12.360
I just happened to add three H plus ions,

00:01:12.360 --> 00:01:15.130
which will react with three
of the fluoride anions

00:01:15.130 --> 00:01:18.320
that are present to produce three HF.

00:01:18.320 --> 00:01:19.950
Notice how the concentration

00:01:19.950 --> 00:01:22.240
of fluoride anions in solution

00:01:22.240 --> 00:01:25.270
has decreased from the first
diagram to the second diagram,

00:01:25.270 --> 00:01:28.750
because of the addition
of the H plus ions.

00:01:28.750 --> 00:01:30.950
So the system was at equilibrium

00:01:30.950 --> 00:01:35.100
and the concentration of
fluoride anions was decreased.

00:01:35.100 --> 00:01:37.210
According to Le Chatelier's Principle,

00:01:37.210 --> 00:01:39.490
the system will shift in the direction

00:01:39.490 --> 00:01:41.460
that decreases the stress.

00:01:41.460 --> 00:01:42.910
So if the stress is decreased

00:01:42.910 --> 00:01:44.880
concentration of fluoride anions,

00:01:44.880 --> 00:01:46.870
the system will shift to the right

00:01:46.870 --> 00:01:49.990
to make more fluoride anions.

00:01:49.990 --> 00:01:51.920
And when the system shifts to the right,

00:01:51.920 --> 00:01:54.100
more lead two fluoride dissolves

00:01:54.100 --> 00:01:56.680
to increase the
concentration of Pb two plus

00:01:56.680 --> 00:01:58.710
and fluoride anion.

00:01:58.710 --> 00:02:01.060
We can see that comparing
the second diagram

00:02:01.060 --> 00:02:03.220
to the third diagram,

00:02:03.220 --> 00:02:05.850
so the amount of solid has gotten smaller,

00:02:05.850 --> 00:02:08.390
since some of that lead
two fluoride dissolved,

00:02:08.390 --> 00:02:11.550
and we've increased the
concentration of Pb two plus

00:02:11.550 --> 00:02:14.160
and F minus in solution.

00:02:14.160 --> 00:02:15.730
The solid keeps dissolving

00:02:15.730 --> 00:02:19.520
and the concentration of ions
keeps increasing in solution

00:02:19.520 --> 00:02:23.120
until the system reaches equilibrium.

00:02:23.120 --> 00:02:24.400
So for a saturated solution

00:02:24.400 --> 00:02:26.830
of lead two fluoride at equilibrium,

00:02:26.830 --> 00:02:29.830
decreasing the pH or making
the solution more acidic

00:02:29.830 --> 00:02:32.780
by increasing the
concentration of H plus ions,

00:02:32.780 --> 00:02:36.410
increases the solubility
of lead two fluoride,

00:02:36.410 --> 00:02:39.210
which is why we saw more
of the solid dissolve

00:02:39.210 --> 00:02:41.540
when the H plus ions were added.

00:02:41.540 --> 00:02:43.280
This effect of decreasing the pH

00:02:43.280 --> 00:02:46.500
and increasing the solubility
of a slightly soluble salt

00:02:46.500 --> 00:02:49.350
happens whenever the slightly soluble salt

00:02:49.350 --> 00:02:52.260
contains a basic anion.

00:02:52.260 --> 00:02:55.610
For this example, the basic
anion is the fluoride anion,

00:02:55.610 --> 00:02:58.530
which reacts with the added H plus ions.

00:02:58.530 --> 00:03:00.850
And when the basic anion reacts,

00:03:00.850 --> 00:03:04.160
that decreases the concentration
of that basic anion,

00:03:04.160 --> 00:03:07.720
which caused the equilibrium
to shift to the right.

00:03:07.720 --> 00:03:10.460
And there are many other
examples of basic anions,

00:03:10.460 --> 00:03:12.660
two more would be the hydroxide anion

00:03:12.660 --> 00:03:14.870
and the carbonate anion.

00:03:14.870 --> 00:03:17.790
And if a compound contains a basic anion,

00:03:17.790 --> 00:03:21.840
such as the hydroxide anion,
hydroxide functions as a base

00:03:21.840 --> 00:03:25.460
and reacts with H plus ions to form H2O.

00:03:25.460 --> 00:03:27.870
So therefore, the solubility of a compound

00:03:27.870 --> 00:03:31.180
containing a hydroxide ion would increase

00:03:31.180 --> 00:03:34.820
as H plus ions are added to the solution.

00:03:34.820 --> 00:03:35.910
It's also important to note

00:03:35.910 --> 00:03:38.010
for this lead two fluoride problem,

00:03:38.010 --> 00:03:42.070
if the pH is decreased at
a constant temperature,

00:03:42.070 --> 00:03:46.930
the Ksp value for PbF
two remains constant.

00:03:46.930 --> 00:03:50.220
So the molar solubility does increase,

00:03:50.220 --> 00:03:53.530
but the Ksp value remains the same.

00:03:53.530 --> 00:03:55.450
This time, instead of lead two fluoride,

00:03:55.450 --> 00:03:57.790
let's look at lead two chloride.

00:03:57.790 --> 00:04:00.380
Lead two chloride is also a white solid.

00:04:00.380 --> 00:04:02.570
So if we dissolve some in solution,

00:04:02.570 --> 00:04:04.690
eventually, we would reach an equilibrium

00:04:04.690 --> 00:04:07.550
between the solid and
the ions in solution.

00:04:07.550 --> 00:04:10.930
So this diagram here
shows a saturated solution

00:04:10.930 --> 00:04:14.620
of lead two chloride and the
system is at equilibrium.

00:04:14.620 --> 00:04:16.290
And to the system at equilibrium,

00:04:16.290 --> 00:04:21.290
we decrease the pH by adding
H plus ions to the solution.

00:04:21.490 --> 00:04:23.570
In this case, the chloride anions

00:04:23.570 --> 00:04:26.870
aren't basic enough to
react with the H plus ions.

00:04:26.870 --> 00:04:29.310
Therefore, we do not form HCl

00:04:29.310 --> 00:04:32.440
and the concentration of chloride anions

00:04:32.440 --> 00:04:36.360
remains the same as it was
in the original diagram.

00:04:36.360 --> 00:04:39.330
So if the concentration of
chloride ions remains the same

00:04:39.330 --> 00:04:41.230
and the concentration
of lead two plus ions

00:04:41.230 --> 00:04:44.810
would remain the same, the
system is still at equilibrium

00:04:44.810 --> 00:04:47.630
and decrease in the pH had no effect

00:04:47.630 --> 00:04:50.330
on the solubility of the solids.

00:04:50.330 --> 00:04:54.010
So we have the same amount
of lead two chloride solid

00:04:54.010 --> 00:04:57.050
on the bottom of the
beaker in both diagrams.

00:04:57.050 --> 00:04:59.690
So whenever an anion has
an extremely weak base,

00:04:59.690 --> 00:05:01.440
like the chloride anion,

00:05:01.440 --> 00:05:05.530
we say that this is an
anion of negligible basicity

00:05:05.530 --> 00:05:07.230
and the solubility of salts

00:05:07.230 --> 00:05:10.010
with anions of negligible basicity

00:05:10.010 --> 00:05:13.353
is unaffected by changes in pH.


The common-ion effect

WEBVTT
Kind: captions
Language: en

00:00:00.360 --> 00:00:02.140
- [Instructor] The
presence of a common ion

00:00:02.140 --> 00:00:05.040
can affect a solubility equilibrium.

00:00:05.040 --> 00:00:05.873
For example,

00:00:05.873 --> 00:00:09.530
let's say we have a saturated
solution of lead II chloride.

00:00:09.530 --> 00:00:11.950
Lead II chloride is a white solid,

00:00:11.950 --> 00:00:14.360
so here's the white solid
on the bottom of the beaker.

00:00:14.360 --> 00:00:18.100
And the solid's at equilibrium
with the ions in solution.

00:00:18.100 --> 00:00:22.210
So that would be Pb2+ and Cl-.

00:00:22.210 --> 00:00:26.890
Notice how the mole ratio is
one-to-two of Pb2+ to 2Cl-.

00:00:26.890 --> 00:00:30.590
So if we have two Pb2+
ions in our diagram,

00:00:30.590 --> 00:00:33.320
there should be twice
as many chloride anions.

00:00:33.320 --> 00:00:36.350
At equilibrium, the rate
of dissolution is equal to

00:00:36.350 --> 00:00:38.510
the rate of precipitation.

00:00:38.510 --> 00:00:41.250
Therefore, the concentration
of ions in solution

00:00:41.250 --> 00:00:43.180
remains constant.

00:00:43.180 --> 00:00:45.220
So our system is at equilibrium.

00:00:45.220 --> 00:00:48.570
And let's add some solid
potassium chloride.

00:00:48.570 --> 00:00:50.780
Potassium chloride is a soluble salt.

00:00:50.780 --> 00:00:55.780
So it will dissociate and turn
into K+ and Cl- in solution.

00:00:56.320 --> 00:00:58.650
Adding a source of chloride anion means

00:00:58.650 --> 00:01:01.360
the system is no longer at equilibrium.

00:01:01.360 --> 00:01:02.193
So let me write in here,

00:01:02.193 --> 00:01:05.950
not at equilibrium at that moment in time.

00:01:05.950 --> 00:01:07.730
So the system was at equilibrium

00:01:07.730 --> 00:01:10.320
and a stress was added to the system.

00:01:10.320 --> 00:01:13.500
In this case, the stress was
increased chloride anion.

00:01:13.500 --> 00:01:17.527
So there's an increase in
the concentration of Cl-.

00:01:18.471 --> 00:01:20.410
According to Le Chatelier's principle,

00:01:20.410 --> 00:01:21.980
the system will move in the direction

00:01:21.980 --> 00:01:23.980
that decreases the stress.

00:01:23.980 --> 00:01:25.060
So if the stress is

00:01:25.060 --> 00:01:27.810
increased concentration of chloride anion,

00:01:27.810 --> 00:01:29.610
the system will move to the left

00:01:29.610 --> 00:01:33.000
to get rid of some of
that extra chloride anion.

00:01:33.000 --> 00:01:34.720
When the system moves to the left,

00:01:34.720 --> 00:01:39.720
Pb2+ ions will combine with
chloride anions to form PbCl2.

00:01:39.747 --> 00:01:42.290
And we can see that down
here in the diagram.

00:01:42.290 --> 00:01:43.123
So imagine,

00:01:43.123 --> 00:01:47.480
say this Pb2+ ion combined
with these two chloride anions

00:01:47.480 --> 00:01:50.180
to form some more of the white solid.

00:01:50.180 --> 00:01:51.610
Looking at the third diagram,

00:01:51.610 --> 00:01:53.580
the amount of white solid has increased

00:01:53.580 --> 00:01:55.280
from the second diagram,

00:01:55.280 --> 00:01:59.859
and we've lost this Pb2+ ion
and these two chloride anions.

00:01:59.859 --> 00:02:02.450
And the amount of our precipitate PbCl2

00:02:02.450 --> 00:02:06.180
will keep forming until
equilibrium is reached.

00:02:06.180 --> 00:02:07.700
Let's just say this third diagram,

00:02:07.700 --> 00:02:10.470
it does represent the
system at equilibrium.

00:02:10.470 --> 00:02:13.410
So I'll write on here, at equilibrium.

00:02:13.410 --> 00:02:16.750
This is an example of
the common ion effect.

00:02:16.750 --> 00:02:20.310
For this problem, the common
ion is the chloride anion,

00:02:20.310 --> 00:02:22.640
because there were two sources of it.

00:02:22.640 --> 00:02:25.750
One was from the disillusion of PbCl2.

00:02:25.750 --> 00:02:28.720
If we had dissolved some solid
to make a saturated solution,

00:02:28.720 --> 00:02:32.340
the source of these chloride
anions would be from PbCl2.

00:02:32.340 --> 00:02:35.470
And the second source
is from the added KCl,

00:02:35.470 --> 00:02:38.490
which of course dissolved
to form chloride anion.

00:02:38.490 --> 00:02:42.090
So the chloride anion is the common ion.

00:02:42.090 --> 00:02:43.830
And we use Le Chatelier's principle

00:02:43.830 --> 00:02:46.360
to predict the system
will move to the left

00:02:46.360 --> 00:02:49.650
to get rid of the extra chloride anion.

00:02:49.650 --> 00:02:50.950
When the system moved to the left,

00:02:50.950 --> 00:02:53.550
we formed more of the solid PbCl2.

00:02:53.550 --> 00:02:55.830
And that's why this amount
got bigger over here.

00:02:55.830 --> 00:03:00.040
So if we compare the first
diagram with the third diagram,

00:03:00.040 --> 00:03:03.050
the first diagram has more of

00:03:03.050 --> 00:03:05.600
the lead II chloride in solution.

00:03:05.600 --> 00:03:07.830
And the third diagram has less of it.

00:03:07.830 --> 00:03:11.850
Therefore, the addition of the
common ion of chloride anion,

00:03:11.850 --> 00:03:16.650
that decreased the solubility
of lead II chloride.

00:03:16.650 --> 00:03:18.380
So the common ion effect says that

00:03:18.380 --> 00:03:21.130
the solubility of a slightly soluble salt,

00:03:21.130 --> 00:03:22.610
like lead II chloride,

00:03:22.610 --> 00:03:26.490
is decreased by the
presence of a common ion.

00:03:26.490 --> 00:03:28.360
Another way to think about this is using

00:03:28.360 --> 00:03:30.490
the reaction quotient, Q.

00:03:30.490 --> 00:03:34.140
For the diagram on the
left, we're at equilibrium.

00:03:34.140 --> 00:03:38.560
Therefore the reaction
quotient Qsp is equal to

00:03:38.560 --> 00:03:41.630
the Ksp value for lead II chloride,

00:03:41.630 --> 00:03:44.620
which means the system is at equilibrium.

00:03:44.620 --> 00:03:48.600
Adding chloride anion
increases the value for Qsp.

00:03:48.600 --> 00:03:51.790
So now Qsp is greater than Ksp

00:03:51.790 --> 00:03:54.340
and the system is not at equilibrium.

00:03:54.340 --> 00:03:56.700
In order to decrease the value for Q,

00:03:56.700 --> 00:03:59.290
the system needs to move to the left.

00:03:59.290 --> 00:04:01.920
And the system will
continue to move to the left

00:04:01.920 --> 00:04:05.890
until Qsp is equal to Ksp again

00:04:05.890 --> 00:04:08.550
and the system is at equilibrium.

00:04:08.550 --> 00:04:13.320
A shift to the left means an
increase in the amount of PbCl2

00:04:13.320 --> 00:04:18.030
which therefore decreases
the solubility of PbCl2.

00:04:18.030 --> 00:04:20.918
But it doesn't change the value for Ksp.

00:04:20.918 --> 00:04:25.918
Ksp for PbCl2 stays the same
at the same temperature.

00:04:26.530 --> 00:04:29.360
Next, let's see how the
presence of a common ion affects

00:04:29.360 --> 00:04:32.740
the molar solubility of lead II chloride.

00:04:32.740 --> 00:04:33.573
And to do that,

00:04:33.573 --> 00:04:36.100
let's calculate the molar
solubility of lead II chloride

00:04:36.100 --> 00:04:38.110
at 25 degrees Celsius

00:04:38.110 --> 00:04:43.010
in a solution that is 0.10
molar in potassium chloride.

00:04:43.010 --> 00:04:47.464
The Ksp value for lead II
chloride at 25 degrees Celsius is

00:04:47.464 --> 00:04:50.490
1.7 times 10 to the negative fifth.

00:04:50.490 --> 00:04:52.500
To help us calculate the molar solubility,

00:04:52.500 --> 00:04:53.920
we're going to use an ICE table,

00:04:53.920 --> 00:04:56.070
where I stands for the
initial concentration,

00:04:56.070 --> 00:04:57.880
C is the change in concentration,

00:04:57.880 --> 00:05:00.870
and E is the equilibrium concentration.

00:05:00.870 --> 00:05:01.750
First, let's say that

00:05:01.750 --> 00:05:04.420
none of the lead II
chloride has dissolved yet.

00:05:04.420 --> 00:05:05.350
And if that's true,

00:05:05.350 --> 00:05:09.200
the concentration of lead
II plus ions would be zero,

00:05:09.200 --> 00:05:11.890
and the concentration of chloride anions

00:05:11.890 --> 00:05:15.600
from the lead II chloride
would also be zero.

00:05:15.600 --> 00:05:18.200
However, there's another
source of chloride anions,

00:05:18.200 --> 00:05:22.320
and that's because our
solution is 0.10 molar in KCl.

00:05:22.320 --> 00:05:25.200
KCl is a soluble salt.

00:05:25.200 --> 00:05:30.190
So KCl associates completely
to turn to K+ and Cl-.

00:05:30.190 --> 00:05:34.570
Therefore, if the concentration
of KCl is 0.10 molar,

00:05:34.570 --> 00:05:38.830
that's also the concentration
of Cl- from the KCl.

00:05:38.830 --> 00:05:43.570
So we can add here plus 0.10 molar.

00:05:43.570 --> 00:05:47.000
And think about that
as being from our KCl.

00:05:47.000 --> 00:05:48.560
So there are two sources.

00:05:48.560 --> 00:05:51.340
There's going to be two sources
of chloride anions here.

00:05:51.340 --> 00:05:55.450
And so the Cl anion and is our common ion.

00:05:55.450 --> 00:05:58.570
The other source of
chloride anion is PbCl2

00:05:58.570 --> 00:05:59.780
when it dissolves.

00:05:59.780 --> 00:06:02.320
So some of the PbCl2 will dissolve,

00:06:02.320 --> 00:06:06.120
we don't know how much, so
I like to write -X in here.

00:06:06.120 --> 00:06:07.510
And if some of that dissolves,

00:06:07.510 --> 00:06:12.510
the mole ratio of PbCl2 to Pb2+
is a one-to-one mole ratio.

00:06:12.700 --> 00:06:17.700
So if we're losing X for PbCl2,
we're gaining X for Pb2+.

00:06:18.530 --> 00:06:20.100
And looking at our mole ratios,

00:06:20.100 --> 00:06:22.150
if we're gaining X for Pb2+

00:06:22.150 --> 00:06:24.860
and it's a one-to-two mole ratio,

00:06:24.860 --> 00:06:29.460
we would write in here +2X
for the chloride anion.

00:06:29.460 --> 00:06:33.120
So for the equilibrium
concentration of Pb2+,

00:06:33.120 --> 00:06:36.400
it would be zero plus X, or just X.

00:06:36.400 --> 00:06:39.590
And for the equilibrium
concentration of the chloride anion,

00:06:39.590 --> 00:06:42.830
it would be 0.10 plus 2X.

00:06:42.830 --> 00:06:47.830
So the 0.10 came from
the potassium chloride,

00:06:48.000 --> 00:06:52.350
and the 2X came from the
dissolution of lead II chloride.

00:06:52.350 --> 00:06:54.410
Next, we need to write a Ksp expression,

00:06:54.410 --> 00:06:57.200
which we can get from
the disillusion equation.

00:06:57.200 --> 00:07:02.200
So, Ksp is equal to the
concentration of lead II plus ions

00:07:02.850 --> 00:07:05.280
raised to the first power

00:07:05.280 --> 00:07:07.440
times the concentration
of chloride anions.

00:07:07.440 --> 00:07:09.550
And since there's a two as a coefficient

00:07:09.550 --> 00:07:10.690
in the balanced equation,

00:07:10.690 --> 00:07:14.020
we need to raise that
concentration to the second power.

00:07:14.020 --> 00:07:15.330
Pure solids are left out of

00:07:15.330 --> 00:07:17.080
equilibrium constant expressions.

00:07:17.080 --> 00:07:20.150
So we don't write anything for PbCl2.

00:07:20.150 --> 00:07:22.950
Next, we plug in our
equilibrium concentrations.

00:07:22.950 --> 00:07:27.100
So for lead II plus, the
equilibrium concentration is X.

00:07:27.100 --> 00:07:29.010
And for the chloride anion,

00:07:29.010 --> 00:07:32.933
the equilibrium concentration
is 0.10 plus 2X.

00:07:34.270 --> 00:07:38.860
We also need to plug in the
Ksp value for lead II chloride.

00:07:38.860 --> 00:07:41.270
Here we have the Ksp value plugged in.

00:07:41.270 --> 00:07:44.490
X and 0.10 plus 2X.

00:07:44.490 --> 00:07:49.000
And let's think about 0.10
plus 2X for a second here.

00:07:49.000 --> 00:07:50.961
With a very low value for Ksp,

00:07:50.961 --> 00:07:53.440
1.7 times 10 to the negative fifth,

00:07:53.440 --> 00:07:57.450
that means that not very much
of the PbCl2 will dissolve.

00:07:57.450 --> 00:08:00.380
And if that's true, X is
a pretty small number.

00:08:00.380 --> 00:08:04.090
And if X is a small number,
2X is also pretty small.

00:08:04.090 --> 00:08:05.960
So we're going to make an approximation

00:08:05.960 --> 00:08:09.140
and say that 0.10 plus
a pretty small number

00:08:09.140 --> 00:08:12.550
is approximately equal to just 0.10.

00:08:12.550 --> 00:08:15.130
And that's going to make
the math easier on us.

00:08:15.130 --> 00:08:18.320
So instead of writing
0.10 plus 2X squared,

00:08:18.320 --> 00:08:20.643
we just have 0.10 squared.

00:08:21.880 --> 00:08:26.450
Solving for X, we find
that X is equal to 0.0017,

00:08:27.580 --> 00:08:28.623
which we could just write as

00:08:28.623 --> 00:08:33.623
1.7 times 10 to the negative third molar.

00:08:34.240 --> 00:08:35.530
It's okay to write molar here

00:08:35.530 --> 00:08:38.010
because this X value represents

00:08:38.010 --> 00:08:42.120
the equilibrium concentration of Pb2+.

00:08:42.120 --> 00:08:45.670
And if that's the equilibrium
concentration of Pb2+,

00:08:45.670 --> 00:08:48.030
that's also the concentration
of lead to chloride

00:08:48.030 --> 00:08:48.920
that dissolved.

00:08:48.920 --> 00:08:51.290
So this number, this concentration,

00:08:51.290 --> 00:08:55.320
is the molar solubility
of lead II chloride

00:08:55.320 --> 00:08:57.160
in a solution at 25 degrees

00:08:57.160 --> 00:09:00.810
where the solution is 0.10 molar in KCl.

00:09:00.810 --> 00:09:04.040
Most textbooks leave this
-X out of their ICE tables

00:09:04.040 --> 00:09:06.810
because the concentration
of a solid doesn't change.

00:09:06.810 --> 00:09:08.250
I like to just leave it in here though

00:09:08.250 --> 00:09:10.550
to remind me that X represents

00:09:10.550 --> 00:09:14.840
the molar solubility of
the slightly soluble salt.

00:09:14.840 --> 00:09:16.010
Finally, if we'd calculate

00:09:16.010 --> 00:09:17.990
the molar solubility of lead II chloride

00:09:17.990 --> 00:09:20.620
without the presence of a common ion,

00:09:20.620 --> 00:09:23.310
this 0.10 would have been
gone from everything.

00:09:23.310 --> 00:09:25.720
And doing the math that way,
we would have found that

00:09:25.720 --> 00:09:29.150
the molar solubility at 25 degrees Celsius

00:09:29.150 --> 00:09:31.820
and using this value for the Ksp,

00:09:31.820 --> 00:09:36.820
the molar solubility
comes out to 0.016 molar.

00:09:37.720 --> 00:09:40.300
So comparing these two
smaller solubilities,

00:09:40.300 --> 00:09:43.210
0.016 molar versus 0.0017,

00:09:45.150 --> 00:09:48.120
that's approximately a factor of 10.

00:09:48.120 --> 00:09:50.980
Therefore the addition of a common ion

00:09:50.980 --> 00:09:55.980
decreased the solubility by
approximately a factor of 10.

00:09:56.980 --> 00:09:59.970
So doing the common ion
effect in a quantitative way

00:09:59.970 --> 00:10:01.750
also shows a decrease in

00:10:01.750 --> 00:10:04.280
the solubility of a slightly soluble salt

00:10:05.412 --> 00:10:07.553
because of the presence of a common ion.


Worked example: Predicting whether a precipitate forms by comparing Q and Kₛₚ

WEBVTT
Kind: captions
Language: en

00:00:00.330 --> 00:00:02.020
- [Instructor] For this problem,
our goal is to figure out

00:00:02.020 --> 00:00:04.160
whether or not a precipitate will form

00:00:04.160 --> 00:00:08.810
if we mix 0.20 liters over
4.0 times 10 to the negative

00:00:08.810 --> 00:00:12.140
third Molar solution of lead two nitrate,

00:00:12.140 --> 00:00:16.410
with 0.80 liters of an 8.0
times 10 to the negative third

00:00:16.410 --> 00:00:19.530
Molar solution of sodium sulfate.

00:00:19.530 --> 00:00:21.690
The first step is to
figure out the identity

00:00:21.690 --> 00:00:23.840
of the precipitate that might form.

00:00:23.840 --> 00:00:26.630
So we're mixing an aqueous
solution of lead two nitrate

00:00:26.630 --> 00:00:30.360
with an aqueous solution
of sodium sulfate.

00:00:30.360 --> 00:00:33.228
In the lead two nitrate
solution they're lead two plus

00:00:33.228 --> 00:00:37.046
cations and nitrate anions.

00:00:37.046 --> 00:00:39.330
In the sodium sulfate aqueous solution,

00:00:39.330 --> 00:00:43.643
there are sodium cations
and sulfate anions.

00:00:44.540 --> 00:00:48.210
So we take the cation from one
and the anion from the other.

00:00:48.210 --> 00:00:51.350
So one possible product
would be lead sulfate.

00:00:51.350 --> 00:00:55.450
So let's write on here,
PbSO4, after we cross over

00:00:55.450 --> 00:01:00.450
our charges and we take the
other cation and the other anion

00:01:01.070 --> 00:01:05.080
and so the other product
would be sodium nitrate.

00:01:05.080 --> 00:01:07.033
So we write it in here and a NaNO3.

00:01:08.170 --> 00:01:12.930
To balance the equation, we
need a two in front of NANO3.

00:01:12.930 --> 00:01:16.962
Since nitrates are soluble,
sodium nitrate is an aqueous

00:01:16.962 --> 00:01:21.962
solution and lead sulfate would
be our possible precipitate.

00:01:22.120 --> 00:01:24.130
Now that we know are possible precipitate,

00:01:24.130 --> 00:01:26.360
let's go ahead and write
a net ionic equation

00:01:26.360 --> 00:01:29.920
showing the formation of that precipitate.

00:01:29.920 --> 00:01:34.040
So lead two plus ions, would
come together with sulfate

00:01:34.040 --> 00:01:39.040
anions to form PBSO4.

00:01:39.090 --> 00:01:43.870
So PBSO4 is the possible precipitate.

00:01:43.870 --> 00:01:46.260
Since lead sulfate is
our possible precipitate,

00:01:46.260 --> 00:01:50.070
we really only care about the
concentration of lead two plus

00:01:50.070 --> 00:01:52.810
ions and sulfate anions in solution.

00:01:52.810 --> 00:01:56.610
We don't need to worry about
sodium cations or nitrate

00:01:56.610 --> 00:02:00.180
anions because those
are the spectator ions

00:02:00.180 --> 00:02:02.760
in our overall reaction.

00:02:02.760 --> 00:02:05.880
Running the overall equation,
and the net ionic equation

00:02:05.880 --> 00:02:08.470
are really optional for
a problem like this.

00:02:08.470 --> 00:02:11.350
But we really need to do
is identify the precipitate

00:02:11.350 --> 00:02:14.230
and then write out the
disillusion equation.

00:02:14.230 --> 00:02:19.230
So PBSO4 would be our
possible precipitate.

00:02:19.430 --> 00:02:24.360
And if it dissolves in water,
we would form lead two plus

00:02:24.360 --> 00:02:29.360
cations in aqueous solution,
and sulfates anions

00:02:29.530 --> 00:02:31.257
in aqueous solutions, right?

00:02:31.257 --> 00:02:33.470
aq over here.

00:02:33.470 --> 00:02:36.180
The reason why it's important
to write out the dissolution

00:02:36.180 --> 00:02:40.030
equation is because we
can write a KSP expression

00:02:40.030 --> 00:02:40.940
from it.

00:02:40.940 --> 00:02:44.250
So KSP is equal to, it
would be the concentration

00:02:44.250 --> 00:02:46.600
of lead two plus raised to the first power

00:02:46.600 --> 00:02:48.100
because we have a coefficient of one

00:02:48.100 --> 00:02:49.710
in the balanced equation,

00:02:49.710 --> 00:02:52.990
times the concentration
of sulfate also raised

00:02:52.990 --> 00:02:56.680
to the first power and
pure solids are left out

00:02:56.680 --> 00:02:58.680
of equilibrium, constant expressions.

00:02:58.680 --> 00:03:02.830
Therefore we're not going
to include lead sulfate.

00:03:02.830 --> 00:03:07.830
For lead two sulfate KSP
is equal to 6.3 times 10

00:03:09.380 --> 00:03:14.380
to the negative seven
at 25 degrees Celsius.

00:03:15.420 --> 00:03:19.310
The concentrations of lead two
plus and sulfate in the KSP

00:03:19.310 --> 00:03:23.060
expression, are
equilibrium concentrations.

00:03:23.060 --> 00:03:25.840
For our problem, we're
gonna calculate QSP,

00:03:25.840 --> 00:03:27.980
which has the same form as KSP,

00:03:27.980 --> 00:03:29.930
the differences the concentrations can be

00:03:29.930 --> 00:03:31.980
at any moment in time.

00:03:31.980 --> 00:03:34.080
And we're gonna calculate
QSP at the moment,

00:03:34.080 --> 00:03:35.960
our two solutions are mixed,

00:03:35.960 --> 00:03:40.200
and then we're going
to compare QSP to KSP.

00:03:40.200 --> 00:03:42.640
I've drawn out some diagrams
to help us understand

00:03:42.640 --> 00:03:45.720
how QSP compares to
KSP and what that means

00:03:45.720 --> 00:03:46.890
for the solution.

00:03:46.890 --> 00:03:49.020
However, these aren't perfect diagrams

00:03:49.020 --> 00:03:51.330
they're just to help get the point across.

00:03:51.330 --> 00:03:55.470
If QSP is less than KSP,
the solution is unsaturated,

00:03:55.470 --> 00:03:58.400
which means no precipitate would form.

00:03:58.400 --> 00:03:59.880
For an unsaturated solution,

00:03:59.880 --> 00:04:02.300
you can dissolve more
led two sulfate in it.

00:04:02.300 --> 00:04:05.000
So lead two sulfate as a white solid,

00:04:05.000 --> 00:04:08.130
so if we were to put a small
amount of lead two sulfate

00:04:08.130 --> 00:04:10.980
in our unsaturated
solution, it would dissolve,

00:04:10.980 --> 00:04:15.980
and it would continue to dissolve
until QSP is equal to KSP.

00:04:16.450 --> 00:04:19.760
And the system is at equilibrium.

00:04:19.760 --> 00:04:22.760
At equilibrium, the solid
is turning into the ions

00:04:22.760 --> 00:04:26.760
at the same rate, the ions are
turning back into the solid.

00:04:26.760 --> 00:04:29.780
Since the rate of dissolution
is equal to the rate

00:04:29.780 --> 00:04:32.880
of precipitation when the
system is at equilibrium,

00:04:32.880 --> 00:04:34.990
the concentrations of lead two plus ions

00:04:34.990 --> 00:04:37.070
and sulfate ions are constant,

00:04:37.070 --> 00:04:40.740
and this represents a saturated solution.

00:04:40.740 --> 00:04:43.300
And since the solution is
saturated at equilibrium,

00:04:43.300 --> 00:04:46.060
if we tried to add some
more lead two sulfate

00:04:46.060 --> 00:04:47.730
at the same temperature,

00:04:47.730 --> 00:04:49.850
we wouldn't be able to dissolve any more,

00:04:49.850 --> 00:04:52.220
we would just increase the
pile of lead two sulfate

00:04:52.220 --> 00:04:54.310
on the bottom of the beaker.

00:04:54.310 --> 00:04:58.180
That concept helps us
understand what happens when QSP

00:04:58.180 --> 00:05:00.320
is greater than KSP.

00:05:00.320 --> 00:05:04.730
When QSP is greater than KSP,
the solution is oversaturated.

00:05:04.730 --> 00:05:07.490
So it's exceeded the limit
of what can dissolve,

00:05:07.490 --> 00:05:10.640
and therefore you can imagine
some lead two plus ions

00:05:10.640 --> 00:05:15.290
combining with some sulfate
ions to form a precipitate.

00:05:15.290 --> 00:05:18.470
Therefore, when QSP is greater than KSP,

00:05:18.470 --> 00:05:20.600
a precipitate will form.

00:05:20.600 --> 00:05:23.100
The precipitate will continue to form,

00:05:23.100 --> 00:05:25.940
until QSP is equal to KSP,

00:05:25.940 --> 00:05:28.620
and the system reaches equilibrium.

00:05:28.620 --> 00:05:30.840
Next, we need to go back
to what we were given

00:05:30.840 --> 00:05:32.240
in our initial problem,

00:05:32.240 --> 00:05:34.750
when we mixed our two solutions together.

00:05:34.750 --> 00:05:37.090
Remember we only cared about
the concentration of lead

00:05:37.090 --> 00:05:39.510
two plus ions and sulfate ions.

00:05:39.510 --> 00:05:42.330
So we're gonna calculate the
concentration of those two ions

00:05:42.330 --> 00:05:45.950
at the moment in time, when
the two solutions are mixed.

00:05:45.950 --> 00:05:48.450
First let's calculate the
concentration of lead two

00:05:48.450 --> 00:05:49.790
plus ions.

00:05:49.790 --> 00:05:53.110
The original solution of lead two nitrate

00:05:53.110 --> 00:05:56.280
had a concentration of 4.0
times 10 to the negative

00:05:56.280 --> 00:05:57.610
third Molar.

00:05:57.610 --> 00:06:00.200
So molarity is equal to moles over liters.

00:06:00.200 --> 00:06:02.190
So we can plug in the concentration,

00:06:02.190 --> 00:06:04.550
and we can also plug in the
volume of that solution,

00:06:04.550 --> 00:06:08.580
which was 0.20 liters, and solve for X,

00:06:08.580 --> 00:06:13.130
X equal to 8.0 times 10 to
the negative fourth moles.

00:06:13.130 --> 00:06:14.930
That's how many moles of lead two nitrate

00:06:14.930 --> 00:06:17.870
there are and that's also
how many moles of lead two

00:06:17.870 --> 00:06:19.760
plus ions there are.

00:06:19.760 --> 00:06:22.440
Therefore to find the
concentration of lead two plus ions

00:06:22.440 --> 00:06:23.760
after the solutions are mixed,

00:06:23.760 --> 00:06:27.060
we plug in 8.0 times 10 to
the negative fourth moles,

00:06:27.060 --> 00:06:30.010
and for the volume we're
adding these two solutions

00:06:30.010 --> 00:06:32.430
together, so the total
volume of the solution

00:06:32.430 --> 00:06:34.573
is 0.20 plus 0.80.

00:06:35.534 --> 00:06:37.870
So the concentration of lead two plus ions

00:06:37.870 --> 00:06:42.400
will be equal to 8.0 times 10
to the negative fourth Molar.

00:06:42.400 --> 00:06:44.100
We can do the same type of calculation

00:06:44.100 --> 00:06:46.400
to find the concentration of sulfate ions

00:06:46.400 --> 00:06:49.140
after the two solutions have been mixed.

00:06:49.140 --> 00:06:51.560
So we take the concentration
of the original solution

00:06:51.560 --> 00:06:54.970
of sodium sulfate and plug that
into the molarity equation,

00:06:54.970 --> 00:06:59.110
plug in the volume solve for
X and 6.4 times 10 to negative

00:06:59.110 --> 00:07:02.770
third moles is how many moles
of sodium sulfate there are.

00:07:02.770 --> 00:07:05.510
That's also how many moles
of sulfate ions there are,

00:07:05.510 --> 00:07:08.930
so we plug in that number
into the concentration

00:07:08.930 --> 00:07:11.220
for sulfate, and once
again, since we're adding

00:07:11.220 --> 00:07:13.470
the two solutions together,
we divide that by the total

00:07:13.470 --> 00:07:16.430
volume to get a
concentration of sulfate ions

00:07:16.430 --> 00:07:20.220
of 6.4 times 10 to the
negative third Molar.

00:07:20.220 --> 00:07:22.850
Now that we know the concentrations
of lead two plus ions

00:07:22.850 --> 00:07:26.080
and sulfate ions, after the
two solutions have been mixed,

00:07:26.080 --> 00:07:29.930
we can plug those concentrations
into our QSP expression

00:07:29.930 --> 00:07:31.990
and solve for QSP.

00:07:31.990 --> 00:07:36.050
So at this moment in time,
QSP is equal to 5.1 times 10

00:07:36.050 --> 00:07:37.760
to the negative six.

00:07:37.760 --> 00:07:41.560
At 25 degrees Celsius, the
KSP value for lead two sulfate

00:07:41.560 --> 00:07:45.120
is equal to 6.3 times 10
to the negative seventh.

00:07:45.120 --> 00:07:48.160
QSP at this moment in time is 5.1 times 10

00:07:48.160 --> 00:07:49.690
to the negative six.

00:07:49.690 --> 00:07:54.357
Therefore QSP is greater than KSP.

00:07:55.980 --> 00:08:00.210
Since QSP is greater than
KSP, we've exceeded the limit

00:08:00.210 --> 00:08:02.930
of what can dissolve and
therefore the solution

00:08:02.930 --> 00:08:05.220
is oversaturated.

00:08:05.220 --> 00:08:09.550
So yes, a precipitate will
form and the precipitate

00:08:09.550 --> 00:08:12.190
of lead two sulfate will continue to form

00:08:12.190 --> 00:08:15.493
until QSP is equal to KSP.