Worked example: Analyzing the purity of a mixture

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:02.440
- [Instructor] We're
told, you have a solid

00:00:02.440 --> 00:00:05.330
that you know is mostly sodium chloride,

00:00:05.330 --> 00:00:08.460
you suspect that it
might have or it may have

00:00:08.460 --> 00:00:11.660
some sodium iodide, potassium chloride

00:00:11.660 --> 00:00:14.290
or lithium chloride as well.

00:00:14.290 --> 00:00:17.110
When you analyze a sample
you see that it contains

00:00:17.110 --> 00:00:20.150
73% chlorine by mass.

00:00:20.150 --> 00:00:22.870
Is the sample pure sodium chloride?

00:00:22.870 --> 00:00:27.270
If not, what else does
it likely have in it?

00:00:27.270 --> 00:00:29.930
So pause this video and see
if you can figure that out

00:00:29.930 --> 00:00:33.440
and it will likely be useful
to have a period table handy

00:00:33.440 --> 00:00:34.333
to do it.

00:00:35.650 --> 00:00:38.030
All right, so the way we're
going to approach it is

00:00:38.030 --> 00:00:39.950
we're gonna think about
each of these compounds

00:00:39.950 --> 00:00:43.630
and try to figure out the
percent chlorine by mass.

00:00:43.630 --> 00:00:45.820
And to do that, we have to think about

00:00:45.820 --> 00:00:50.350
the molar masses of the
various constituent atoms

00:00:50.350 --> 00:00:52.410
or the various constituent elements

00:00:52.410 --> 00:00:55.210
that make up those compounds.

00:00:55.210 --> 00:00:57.270
And to figure out the
molar mass for each element

00:00:57.270 --> 00:00:59.560
I just have to look at
its average atomic mass

00:00:59.560 --> 00:01:01.600
and say, okay I'm going to have that many

00:01:01.600 --> 00:01:06.410
grams per mole, if I
have a mole of that atom.

00:01:06.410 --> 00:01:08.140
Sodium,

00:01:08.140 --> 00:01:10.220
chlorine,

00:01:10.220 --> 00:01:11.720
iodine,

00:01:11.720 --> 00:01:13.150
potassium,

00:01:13.150 --> 00:01:15.220
and lithium.

00:01:15.220 --> 00:01:19.243
And the sodium's average
atomic mass is 22.99,

00:01:20.750 --> 00:01:25.750
chlorine is 35.45,

00:01:26.020 --> 00:01:27.060
iodine

00:01:27.060 --> 00:01:27.893
is

00:01:27.893 --> 00:01:31.860
126.90,

00:01:31.860 --> 00:01:35.460
potassium is 39.10,

00:01:35.460 --> 00:01:40.460
and lithium is 6.94.

00:01:40.500 --> 00:01:44.400
And so now I can remove my
period table of elements.

00:01:44.400 --> 00:01:47.200
And so let's first think
about sodium chloride.

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So,

00:01:48.130 --> 00:01:50.900
percent chlorine...

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Actually let me make a little table here,

00:01:52.190 --> 00:01:54.520
I think that will be the
most useful thing to do.

00:01:54.520 --> 00:01:59.400
So here I will put the various compounds.

00:01:59.400 --> 00:02:00.900
Compound.

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And here I will put the percent

00:02:03.420 --> 00:02:04.670
Cl

00:02:04.670 --> 00:02:06.160
by mass.

00:02:06.160 --> 00:02:07.000
By

00:02:07.000 --> 00:02:07.970
mass.

00:02:07.970 --> 00:02:10.460
So first we can think
about sodium chloride

00:02:10.460 --> 00:02:11.950
and I'll do all of these
in a different color

00:02:11.950 --> 00:02:13.760
just to make things interesting.

00:02:13.760 --> 00:02:15.860
So sodium chloride.

00:02:15.860 --> 00:02:20.040
So chlorine's molar mass is 35.45

00:02:20.040 --> 00:02:21.950
grams per mole.

00:02:21.950 --> 00:02:25.210
And then we need to divide
that by the molar mass

00:02:25.210 --> 00:02:27.400
of the entire compound.

00:02:27.400 --> 00:02:29.410
So that's going to be
the molar mass of sodium

00:02:29.410 --> 00:02:32.070
at 22.99 grams per mole.

00:02:32.070 --> 00:02:34.410
Plus the molar mass of chlorine again

00:02:34.410 --> 00:02:36.430
at 35.45

00:02:36.430 --> 00:02:37.910
grams per mole.

00:02:37.910 --> 00:02:41.480
So we have 35.45

00:02:41.480 --> 00:02:44.220
divided by, open parentheses,

00:02:44.220 --> 00:02:47.600
22.99

00:02:47.600 --> 00:02:50.950
plus 35.45,

00:02:50.950 --> 00:02:52.360
close the parentheses.

00:02:52.360 --> 00:02:53.870
Then I get it equal.

00:02:53.870 --> 00:02:57.150
So it looks like it's
a little bit over 60%.

00:02:57.150 --> 00:02:59.450
And that's actually
enough for us to go on,

00:02:59.450 --> 00:03:03.610
because if this si approximately 61%

00:03:03.610 --> 00:03:06.690
we see that's that a
very different than 73%.

00:03:06.690 --> 00:03:09.390
So already it's very clear
that to the first question,

00:03:09.390 --> 00:03:11.400
is the sample pure sodium chloride?

00:03:11.400 --> 00:03:14.540
No it's not, cause it has
a different percentage

00:03:14.540 --> 00:03:17.410
of chlorine by mass than
pure sodium chloride would.

00:03:17.410 --> 00:03:20.720
This would be what pure sodium
chloride would look like.

00:03:20.720 --> 00:03:23.740
So it must have been
mixed in with something

00:03:23.740 --> 00:03:28.540
that has a higher percentage
of chlorine by mass.

00:03:28.540 --> 00:03:30.610
So let's look at the other candidates.

00:03:30.610 --> 00:03:32.710
So we can look at

00:03:32.710 --> 00:03:35.200
sodium iodide.

00:03:35.200 --> 00:03:37.810
So sodium iodide.

00:03:37.810 --> 00:03:41.120
What's its percent chlorine
by mass going to be?

00:03:41.120 --> 00:03:43.670
Well this has no chlorine by mass,

00:03:43.670 --> 00:03:45.330
so this is zero.

00:03:45.330 --> 00:03:50.320
So if you had sodium iodide
mixed in with sodium chloride,

00:03:50.320 --> 00:03:53.760
that would reduce the average.

00:03:53.760 --> 00:03:56.820
That would reduce the
percent chlorine by mass.

00:03:56.820 --> 00:03:58.170
It wouldn't increase it.

00:03:58.170 --> 00:04:01.710
So we already can rule out this character.

00:04:01.710 --> 00:04:03.020
Let's look at the next candidate.

00:04:03.020 --> 00:04:04.480
Potassium chloride.

00:04:04.480 --> 00:04:05.550
I'll write that right over here.

00:04:05.550 --> 00:04:08.700
Potassium chloride.

00:04:08.700 --> 00:04:11.100
And so its percent chlorine would be

00:04:11.100 --> 00:04:15.230
the molar mass of chlorine, 35.45

00:04:15.230 --> 00:04:18.880
divided by the molar mass
of the entire compound.

00:04:18.880 --> 00:04:23.220
And so that would be the molar
mass of potassium, 39.10.

00:04:23.220 --> 00:04:27.440
Plus the molar mass of chlorine, 35.45.

00:04:27.440 --> 00:04:29.800
And we could try to calculate this,

00:04:29.800 --> 00:04:32.330
but even when you look at
the numbers you can see that

00:04:32.330 --> 00:04:35.590
the denominator here, this
denominator right over here

00:04:35.590 --> 00:04:38.587
is bigger than what we
had for sodium chloride.

00:04:38.587 --> 00:04:39.970
And we have the same numerator.

00:04:39.970 --> 00:04:43.130
So if the denominator is bigger,
that means we're going to

00:04:43.130 --> 00:04:45.600
get a lower value than 61%.

00:04:45.600 --> 00:04:47.873
This is less than 61%.

00:04:48.780 --> 00:04:53.300
And since this has a lower
percent chlorine by mass,

00:04:53.300 --> 00:04:57.170
if it was mixed in, it
would average down from 61%.

00:04:57.170 --> 00:05:00.590
It wouldn't go up to 73%, so we can rule

00:05:00.590 --> 00:05:02.050
that one out as well.

00:05:02.050 --> 00:05:04.040
And now let's look at this last candidate

00:05:04.040 --> 00:05:05.980
and I'm feeling good
about it because something

00:05:05.980 --> 00:05:07.190
got mixed in.

00:05:07.190 --> 00:05:09.320
So let's look at lithium,

00:05:09.320 --> 00:05:11.410
lithium chloride.

00:05:11.410 --> 00:05:13.880
What is its percent chlorine by mass?

00:05:13.880 --> 00:05:17.510
Well it's going to be the
molar mass of chlorine, 35.45.

00:05:17.510 --> 00:05:20.140
Divided by the molar mass
of the entire compound,

00:05:20.140 --> 00:05:22.020
and I'll just write chlorine's molar mass.

00:05:22.020 --> 00:05:24.350
And then I'm gonna add that
to the molar mass of lithium

00:05:24.350 --> 00:05:28.630
which is actually quite
low, 6.94 grams per mole.

00:05:28.630 --> 00:05:30.730
So once again, when we
compare to sodium chloride,

00:05:30.730 --> 00:05:32.650
we have the same numerator.

00:05:32.650 --> 00:05:34.500
We have the same numerator
but we clearly have

00:05:34.500 --> 00:05:35.780
a smaller denominator.

00:05:35.780 --> 00:05:37.980
This value is smaller than this value

00:05:37.980 --> 00:05:39.610
and the other number is the same.

00:05:39.610 --> 00:05:42.150
So this has a smaller denominator,

00:05:42.150 --> 00:05:45.460
which means that the whole
value is going to be larger.

00:05:45.460 --> 00:05:49.460
This is going to be greater than 61%.

00:05:49.460 --> 00:05:52.190
We take 35.45,

00:05:52.190 --> 00:05:54.483
divided by, open parentheses,

00:05:54.483 --> 00:05:57.220
6.94

00:05:57.220 --> 00:06:00.380
plus 35.45,

00:06:00.380 --> 00:06:01.600
close parentheses,

00:06:01.600 --> 00:06:03.160
is equal to

00:06:03.160 --> 00:06:06.560
it's roughly 84% chlorine by mass.

00:06:06.560 --> 00:06:07.770
So this thing

00:06:07.770 --> 00:06:11.840
is approximately 84% chlorine by mass.

00:06:11.840 --> 00:06:13.490
So that does the trick.

00:06:13.490 --> 00:06:16.020
If you had some lithium chloride mixed in

00:06:16.020 --> 00:06:17.580
with your sodium chloride,

00:06:17.580 --> 00:06:20.680
it could increase or it would increase

00:06:20.680 --> 00:06:24.560
the percent chlorine by mass above 61%.

00:06:24.560 --> 00:06:26.750
And actually based on these values,

00:06:26.750 --> 00:06:28.390
based on the 61%,

00:06:28.390 --> 00:06:29.770
the 84%

00:06:29.770 --> 00:06:31.230
and the 73%,

00:06:31.230 --> 00:06:32.400
you could actually figure out

00:06:32.400 --> 00:06:35.560
what percent is your
sample of sodium chloride

00:06:35.560 --> 00:06:37.760
and lithium chloride if you assume

00:06:37.760 --> 00:06:39.560
those are the only two things in it.


Valence electrons

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:01.443
- [Instructor] We are now going

00:00:01.443 --> 00:00:04.490
to talk about valence electrons,

00:00:04.490 --> 00:00:08.320
and non-valence electrons, which
are known as core electrons

00:00:08.320 --> 00:00:10.870
and so one question that you
might have been asking yourself

00:00:10.870 --> 00:00:11.980
this whole time that we've been

00:00:11.980 --> 00:00:15.760
looking at electron configurations
is, what is the point?

00:00:15.760 --> 00:00:18.090
And the point of electron
configurations is,

00:00:18.090 --> 00:00:19.570
is they can give us insights

00:00:19.570 --> 00:00:22.360
as to how a given atom
or how a given element

00:00:22.360 --> 00:00:25.400
is likely to react with other atoms.

00:00:25.400 --> 00:00:27.150
And so just to make that point,

00:00:27.150 --> 00:00:28.790
or make it a little bit clearer,

00:00:28.790 --> 00:00:30.830
let's look at the electron configuration

00:00:30.830 --> 00:00:33.760
of an element that we'll
see a lot of in chemistry,

00:00:33.760 --> 00:00:35.100
of oxygen.

00:00:35.100 --> 00:00:37.790
So oxygen's electron
configuration is what?

00:00:37.790 --> 00:00:40.233
Pause this video and see if
you can work through that.

00:00:41.160 --> 00:00:43.430
Well, in a neutral oxygen atom,

00:00:43.430 --> 00:00:46.420
you have eight protons
and eight electrons,

00:00:46.420 --> 00:00:50.770
so first you're gonna fill the one shell,

00:00:50.770 --> 00:00:54.470
then you are going to start
filling the second shell,

00:00:54.470 --> 00:00:57.770
so you're gonna go 2s2,
so I have four right now,

00:00:57.770 --> 00:00:59.060
I have to have four more,

00:00:59.060 --> 00:01:01.443
so then you're going to have 2p4.

00:01:02.570 --> 00:01:04.940
And then notice, if I add
up all the electrons here,

00:01:04.940 --> 00:01:07.340
I have exactly eight electrons.

00:01:07.340 --> 00:01:10.680
Now if I'm thinking about
how might oxygen react,

00:01:10.680 --> 00:01:14.690
it's interesting to look at
the outer oxygen electrons.

00:01:14.690 --> 00:01:18.490
The electrons that are
in the outermost shell.

00:01:18.490 --> 00:01:22.230
So the outermost shell is being
described right over here,

00:01:22.230 --> 00:01:23.510
this second shell.

00:01:23.510 --> 00:01:26.020
So how many electrons are
in the outermost shell?

00:01:26.020 --> 00:01:27.870
You have six electrons here.

00:01:27.870 --> 00:01:32.870
So oxygen has six valence,
valence electrons.

00:01:34.330 --> 00:01:36.340
And how many core electrons does it have?

00:01:36.340 --> 00:01:39.060
And the core electrons
generally aren't reactive,

00:01:39.060 --> 00:01:41.630
or aren't involved as much in reactions?

00:01:41.630 --> 00:01:46.630
It has two core, two core electrons.

00:01:46.910 --> 00:01:50.650
Now, why is six valence
electrons interesting?

00:01:50.650 --> 00:01:52.830
Well, atoms tend to be more stable

00:01:52.830 --> 00:01:54.960
when they have a filled outer shell,

00:01:54.960 --> 00:01:58.940
or in most examples, at
least a filled SNP subshells

00:01:58.940 --> 00:02:00.500
in their outer shell.

00:02:00.500 --> 00:02:02.930
And so in this situation, you say, okay,

00:02:02.930 --> 00:02:05.000
oxygen has six valence electrons,

00:02:05.000 --> 00:02:07.890
and oftentimes that's drawn
with a Lewis structure,

00:02:07.890 --> 00:02:09.700
and it might look something like this,

00:02:09.700 --> 00:02:13.820
where oxygen has one, two, three, four,

00:02:13.820 --> 00:02:16.440
five, six valence electrons,

00:02:16.440 --> 00:02:19.190
and you might say, hey, it would be nice

00:02:19.190 --> 00:02:23.000
if oxygen somehow were able
to share, or get ahold of,

00:02:23.000 --> 00:02:24.460
two more electrons,

00:02:24.460 --> 00:02:26.590
because then that outermost shell

00:02:26.590 --> 00:02:29.910
will have a full number
of eight electrons.

00:02:29.910 --> 00:02:34.570
The 2s and the 2p would be
filled then, we would have 2p6.

00:02:34.570 --> 00:02:35.790
And so you'd say, alright,

00:02:35.790 --> 00:02:39.060
well maybe they can grab those
electrons from something else

00:02:39.060 --> 00:02:40.940
and that's actually what
oxygen does a lot of,

00:02:40.940 --> 00:02:43.760
it grabs electrons from other things.

00:02:43.760 --> 00:02:46.320
You can look at something like calcium.

00:02:46.320 --> 00:02:48.190
Pause this video, think
about what the electron

00:02:48.190 --> 00:02:49.650
configuration of calcium is,

00:02:49.650 --> 00:02:52.960
and then think about how
calcium is likely to react

00:02:52.960 --> 00:02:55.730
given that atoms tend to be more stable

00:02:55.730 --> 00:02:57.930
when they have a full outer shell,

00:02:57.930 --> 00:03:01.933
where both their S and P
subshells are completely filled.

00:03:02.950 --> 00:03:05.060
Well, calcium's electron configuration,

00:03:05.060 --> 00:03:08.190
I could do it in noble gas
notation or configuration,

00:03:08.190 --> 00:03:10.710
it'd have the electron
configuration of argon,

00:03:10.710 --> 00:03:13.540
and one of the reasons why
the noble gases are so stable

00:03:13.540 --> 00:03:15.910
is that they have a completely full shell.

00:03:15.910 --> 00:03:20.120
Argon for example has a
completely full first shell,

00:03:20.120 --> 00:03:24.000
second shell, and third shell,
and then to build calcium,

00:03:24.000 --> 00:03:27.990
will then have two electrons
in that fourth shell,

00:03:27.990 --> 00:03:30.183
so it is argon and then 4s2.

00:03:32.320 --> 00:03:35.550
So how many valence
electrons does calcium have?

00:03:35.550 --> 00:03:36.680
Well, you could see it right over there,

00:03:36.680 --> 00:03:40.980
it has two valence electrons.

00:03:40.980 --> 00:03:42.460
What about its core electrons?

00:03:42.460 --> 00:03:45.560
Well, a neutral calcium atom
would have 20 electrons,

00:03:45.560 --> 00:03:46.870
'cause it has 20 protons,

00:03:46.870 --> 00:03:51.780
so it would have 18 core electrons.

00:03:51.780 --> 00:03:55.210
Electrons that are less likely to react.

00:03:55.210 --> 00:03:57.170
And so you can say, what's the easiest way

00:03:57.170 --> 00:04:00.950
for calcium to get to a full outer shell?

00:04:00.950 --> 00:04:03.110
Well, instead of trying
to gain six electrons,

00:04:03.110 --> 00:04:06.430
it might be a lot easier to
just lose these two electrons.

00:04:06.430 --> 00:04:08.760
It is actually the case that many times,

00:04:08.760 --> 00:04:12.880
calcium will lose electrons,
and become ionized,

00:04:12.880 --> 00:04:14.910
will get a positive charge.

00:04:14.910 --> 00:04:16.760
So the big picture here is,

00:04:16.760 --> 00:04:19.580
one of the values of
electron configuration

00:04:19.580 --> 00:04:21.960
is to think about which of your electrons

00:04:21.960 --> 00:04:23.970
are most likely to react.

00:04:23.970 --> 00:04:26.170
Those are your valence electrons.

00:04:26.170 --> 00:04:28.680
In most cases, your valence electrons

00:04:28.680 --> 00:04:31.330
are going to be your outermost electrons.

00:04:31.330 --> 00:04:32.470
They're going to be the electrons

00:04:32.470 --> 00:04:34.430
in that outermost shell.

00:04:34.430 --> 00:04:37.140
Generally speaking, if
you're talking about elements

00:04:37.140 --> 00:04:40.690
that are in the S block or the P block,

00:04:40.690 --> 00:04:43.550
you can think about how many
valence electrons they have

00:04:43.550 --> 00:04:45.460
just based on what column they're in.

00:04:45.460 --> 00:04:48.910
This column right over here
has one valence electron.

00:04:48.910 --> 00:04:51.610
This column over here has
two valence electrons.

00:04:51.610 --> 00:04:54.420
This column out here has
three valence electrons,

00:04:54.420 --> 00:04:56.990
four valence electrons,
five valence electrons,

00:04:56.990 --> 00:05:00.300
six valence electrons, and
seven valence electrons.

00:05:00.300 --> 00:05:03.760
The noble gases here,
they are very unreactive,

00:05:03.760 --> 00:05:04.640
so one way to think about it

00:05:04.640 --> 00:05:06.640
is they are very very very stable,

00:05:06.640 --> 00:05:09.313
they have filled their outer shell.


Shells, subshells, and orbitals

WEBVTT
Kind: captions
Language: en

00:00:01.250 --> 00:00:02.914
- [Instructor] We've
learned in other videos

00:00:02.914 --> 00:00:05.210
that the atom is in fact made up

00:00:05.210 --> 00:00:07.730
of even smaller constituent particles

00:00:07.730 --> 00:00:08.780
which is pretty amazing

00:00:08.780 --> 00:00:11.590
because atoms are already
unimaginably small.

00:00:11.590 --> 00:00:14.600
And those particles are the protons

00:00:14.600 --> 00:00:16.980
which have positive charge,

00:00:16.980 --> 00:00:21.980
you have your neutrons
which have neutral charge

00:00:22.220 --> 00:00:23.710
or no charge

00:00:23.710 --> 00:00:28.710
and then you have your electrons
which have negative charge.

00:00:30.410 --> 00:00:33.320
Now, the big question
physicist and chemists

00:00:33.320 --> 00:00:35.430
were facing over a hundred years ago

00:00:35.430 --> 00:00:37.600
is how are these things configure

00:00:37.600 --> 00:00:39.692
and they realized that the positive charge

00:00:39.692 --> 00:00:41.790
is concentrated at the center of the atom.

00:00:41.790 --> 00:00:44.287
In fact, most of the mass
which is made up of the protons

00:00:44.287 --> 00:00:47.470
and the neutrons is
concentrated at the center

00:00:47.470 --> 00:00:50.840
and so the early model
for how an atom worked

00:00:50.840 --> 00:00:54.580
was maybe you have your protons
and neutrons in the center

00:00:54.580 --> 00:00:56.300
so let's say, we're talking
about a helium atom.

00:00:56.300 --> 00:01:00.750
A helium atom has two
protons in the nucleus

00:01:00.750 --> 00:01:05.320
and a typical helium atom
would have two neutrons as well

00:01:05.320 --> 00:01:07.700
so the nucleus might
look something like that.

00:01:07.700 --> 00:01:09.387
And early physicists and chemists said,

00:01:09.387 --> 00:01:12.007
"All right, well, if the
protons have a positive charge,

00:01:12.007 --> 00:01:13.487
"electrons have a negative charge,

00:01:13.487 --> 00:01:14.806
"so they'll be attracted to each other."

00:01:14.806 --> 00:01:18.320
Opposite signs, opposite charges attract.

00:01:18.320 --> 00:01:20.341
The same charge repels each other.

00:01:20.341 --> 00:01:24.556
So maybe the electron
which has a negative charge

00:01:24.556 --> 00:01:28.260
orbits around the nucleus
the way that a planet

00:01:28.260 --> 00:01:30.150
would orbit around its star.

00:01:30.150 --> 00:01:32.610
So, maybe it orbits something like this.

00:01:32.610 --> 00:01:34.480
So maybe one electron has an orbit

00:01:34.480 --> 00:01:38.290
that looks something like that,
and then another electron,

00:01:38.290 --> 00:01:39.603
if we were talking about
a neutral helium atom

00:01:39.603 --> 00:01:42.690
will have two electrons and two protons,

00:01:42.690 --> 00:01:47.320
well maybe, the other one
orbits something like this.

00:01:47.320 --> 00:01:49.240
I'm trying to just draw an elliptic

00:01:49.240 --> 00:01:51.510
or a circular looking orbit.

00:01:51.510 --> 00:01:56.147
And so this is the idea that
the electrons are in orbits.

00:01:57.570 --> 00:02:00.890
Now, it turns out that this
is not exactly the case.

00:02:00.890 --> 00:02:04.700
Electrons are not in these
well-defined circular

00:02:04.700 --> 00:02:06.490
or elliptical orbits.

00:02:06.490 --> 00:02:08.790
In fact, at any given point in time,

00:02:08.790 --> 00:02:10.610
it's not necessarily exactly right there,

00:02:10.610 --> 00:02:12.660
it could be there but there's
some probability it's here,

00:02:12.660 --> 00:02:13.770
there's some probability that it's there,

00:02:13.770 --> 00:02:14.746
there's some probability
that it's there's,

00:02:14.746 --> 00:02:16.620
some probability that it's over there.

00:02:16.620 --> 00:02:21.620
And so to describe where
electrons are likely to be found,

00:02:21.840 --> 00:02:26.840
physicist and chemists introduced
to the idea of an orbital

00:02:27.200 --> 00:02:29.310
and the best way to think about orbitals

00:02:29.310 --> 00:02:31.420
is to think about a hydrogen atom

00:02:31.420 --> 00:02:33.770
and actually the map for orbitals,

00:02:33.770 --> 00:02:35.730
it's hydrogen as the simplest atom

00:02:35.730 --> 00:02:38.590
and so the map for orbitals
has been best completed

00:02:38.590 --> 00:02:40.780
for the hydrogen atom.

00:02:40.780 --> 00:02:43.610
So then a hydrogen atom
especially the typical isotope

00:02:43.610 --> 00:02:44.852
of hydrogen found on Earth,

00:02:44.852 --> 00:02:46.830
the nucleus actually has no neutrons.

00:02:46.830 --> 00:02:49.702
You just have a single
proton at the center.

00:02:49.702 --> 00:02:52.265
And if you have a neutral hydrogen atom,

00:02:52.265 --> 00:02:57.160
that one electron,
instead of being in orbit

00:02:57.160 --> 00:03:00.420
around that one proton like that,

00:03:00.420 --> 00:03:02.047
we can really just think
about the probabilities

00:03:02.047 --> 00:03:03.650
of where it might be.

00:03:03.650 --> 00:03:06.930
It could be here, it could
be here at any given moment,

00:03:06.930 --> 00:03:08.430
it could be there at any given moment,

00:03:08.430 --> 00:03:10.314
it could be off the screen at some moment

00:03:10.314 --> 00:03:12.140
but it's more likely to be

00:03:12.140 --> 00:03:15.510
in certain regions of space
around the nucleus and others.

00:03:15.510 --> 00:03:18.514
And we can visualize where
it's most likely to be

00:03:18.514 --> 00:03:22.050
by saying, "All right, it
looks like 90% of the time,

00:03:22.050 --> 00:03:27.050
"it's in a sphere that
looks something like that."

00:03:28.290 --> 00:03:30.330
But once again, it could be here,

00:03:30.330 --> 00:03:31.230
it could be there, it could be there,

00:03:31.230 --> 00:03:33.340
could be there, could be
there, could be out here,

00:03:33.340 --> 00:03:34.870
it could be anywhere.

00:03:34.870 --> 00:03:37.790
We're just saying where it
happens to be 90% of the time.

00:03:37.790 --> 00:03:39.710
That's the visualization.

00:03:39.710 --> 00:03:41.290
Now, an interesting question is

00:03:41.290 --> 00:03:43.920
what if you were to give that electron

00:03:43.920 --> 00:03:45.625
a little bit more energy?

00:03:45.625 --> 00:03:47.340
Well, what does energy mean?

00:03:47.340 --> 00:03:49.340
Well, if you think about planets or rocket

00:03:49.340 --> 00:03:50.838
or satellite orbiting around,

00:03:50.838 --> 00:03:53.270
if you were to give it a
little bit more energy,

00:03:53.270 --> 00:03:54.860
if you ere to give it a little bit push,

00:03:54.860 --> 00:03:57.650
it could have a larger orbit,

00:03:57.650 --> 00:03:59.840
it would look something like that.

00:03:59.840 --> 00:04:01.580
But quantum mechanics

00:04:01.580 --> 00:04:04.260
isn't about things happening gradually.

00:04:04.260 --> 00:04:06.360
Sometimes people think quantum means small

00:04:06.360 --> 00:04:07.250
or something like that.

00:04:07.250 --> 00:04:08.510
No, it really means

00:04:08.510 --> 00:04:10.810
that you're talking
about discreet packets.

00:04:10.810 --> 00:04:13.800
So in quantum physics, quantum chemistry,

00:04:13.800 --> 00:04:18.290
if you add a certain amount
of energy to an electron,

00:04:18.290 --> 00:04:21.260
instead of having a 90%
chance of being found

00:04:21.260 --> 00:04:25.500
in this first shell,
this first energy level,

00:04:25.500 --> 00:04:26.880
it could then be found,

00:04:26.880 --> 00:04:29.500
it would then jump into
the next energy level

00:04:29.500 --> 00:04:30.900
or the next shell.

00:04:30.900 --> 00:04:33.844
And so now, it might be
more of, 90% of the time,

00:04:33.844 --> 00:04:38.000
it's going to be found in
this shell right over here.

00:04:38.000 --> 00:04:40.490
And then if you were to give
it the right boost of energy,

00:04:40.490 --> 00:04:41.900
once again, just a little bit won't do,

00:04:41.900 --> 00:04:42.733
you have to give it enough

00:04:42.733 --> 00:04:45.010
so then it jumps into
the next energy level,

00:04:45.010 --> 00:04:47.450
then it might form this weird patterns

00:04:47.450 --> 00:04:49.761
that looks kinda like dumbbells
where 90% of the time,

00:04:49.761 --> 00:04:53.440
it's kind of you can view
it as it's on the orbital

00:04:53.440 --> 00:04:55.695
that looks kind of like
that dumbbell shape.

00:04:55.695 --> 00:04:58.680
I just did in kind of
the horizontal direction.

00:04:58.680 --> 00:04:59.790
You can have it in a vertical direction.

00:04:59.790 --> 00:05:03.330
You could also have it on the
in-out direction of this page.

00:05:03.330 --> 00:05:05.820
And if you were wondering where
did these shapes come from

00:05:05.820 --> 00:05:07.510
and if you keep adding
more and more energy,

00:05:07.510 --> 00:05:10.160
you get these more and more
exotic shapes for orbitals,

00:05:10.160 --> 00:05:11.870
think about standing waves.

00:05:11.870 --> 00:05:13.880
That's my best hint I can give you

00:05:13.880 --> 00:05:16.090
that the quantum level,
actually at all levels,

00:05:16.090 --> 00:05:17.700
but especially at the quantum level,

00:05:17.700 --> 00:05:20.101
you see things like
electrons have both particle

00:05:20.101 --> 00:05:22.680
and wave-like properties.

00:05:22.680 --> 00:05:25.019
Imagine something like a standing wave

00:05:25.019 --> 00:05:27.387
where if I were to just take a rope

00:05:27.387 --> 00:05:29.870
and if I were to just shake it,

00:05:29.870 --> 00:05:32.410
I might get standing
waves that look like that.

00:05:32.410 --> 00:05:35.105
If I were to take a
some type of a membrane

00:05:35.105 --> 00:05:37.960
in two dimensions and if
I were to push on one side

00:05:37.960 --> 00:05:39.846
right here if I were to drum on that,

00:05:39.846 --> 00:05:42.550
you might get, so this part dips down,

00:05:42.550 --> 00:05:44.490
and then that part dips up.

00:05:44.490 --> 00:05:46.850
And so when you get to three dimensions,

00:05:46.850 --> 00:05:49.090
you end up getting this dumbbell shape

00:05:49.090 --> 00:05:49.980
when you add more energy

00:05:49.980 --> 00:05:52.560
and then you get more and
more and more exotic shapes,

00:05:52.560 --> 00:05:55.330
just to imagine what some of
the first orbitals look like

00:05:55.330 --> 00:05:58.312
rendered by a computer,
you see it right over here.

00:05:58.312 --> 00:06:00.969
So if you have your
lowest energy electron,

00:06:00.969 --> 00:06:05.050
you are in what is called
an S-orbital right over here

00:06:05.050 --> 00:06:08.530
and this one we would call 1s

00:06:08.530 --> 00:06:10.960
'cause it is at the first shell,

00:06:10.960 --> 00:06:13.524
the one closest to the nucleus.

00:06:13.524 --> 00:06:15.556
If you give even more energy,

00:06:15.556 --> 00:06:20.113
then that electron might jump
into the second energy level

00:06:20.113 --> 00:06:24.320
or the second shell and the
orbital in that second shell

00:06:24.320 --> 00:06:25.420
which would be the default

00:06:25.420 --> 00:06:27.461
if it's the lowest energy
in the second shell

00:06:27.461 --> 00:06:30.060
would be the 2s orbital.

00:06:30.060 --> 00:06:32.640
Once again, you have
this spherical orbital,

00:06:32.640 --> 00:06:35.180
it's just a little, it's more
likely to be found further out

00:06:35.180 --> 00:06:37.650
than the one, it was
just in the one shell.

00:06:37.650 --> 00:06:40.400
Once again, if you add even more energy,

00:06:40.400 --> 00:06:42.588
you'll fall, you'll still
be in the second shell

00:06:42.588 --> 00:06:45.664
but you will be into one of these orbitals

00:06:45.664 --> 00:06:47.420
that have higher energies

00:06:47.420 --> 00:06:49.930
so you could view this as the 2p orbital

00:06:49.930 --> 00:06:53.760
that is in the x-dimension.

00:06:53.760 --> 00:06:57.920
This could be the 2p orbital
that is in the y-dimension

00:06:57.920 --> 00:06:59.714
as some people call that 2px.

00:06:59.714 --> 00:07:00.547
Some people would call that 2py.

00:07:02.120 --> 00:07:04.360
This you could view as
the in and out of the page

00:07:04.360 --> 00:07:06.860
so you could view that as the z-dimension.

00:07:06.860 --> 00:07:10.100
So that is 2pz and the
orbitals keep going.

00:07:10.100 --> 00:07:13.500
There is a d-orbital once
you get to the third shell.

00:07:13.500 --> 00:07:16.960
Once you get to the fourth
shell, there is an f-orbital.

00:07:16.960 --> 00:07:19.480
All we've talked about
right now is an hydrogen.

00:07:19.480 --> 00:07:22.152
If you keep giving more
energy to that one electron,

00:07:22.152 --> 00:07:23.630
what happens to it?

00:07:23.630 --> 00:07:26.139
What is the shape of the probabilities

00:07:26.139 --> 00:07:29.090
of where it might be into
two-dimensional space?

00:07:29.090 --> 00:07:31.490
As you can imagine, if
you have two electrons,

00:07:31.490 --> 00:07:33.140
it's not exactly the same

00:07:33.140 --> 00:07:35.290
but this is pretty good approximation.

00:07:35.290 --> 00:07:39.330
You can actually put two
electrons in this 1s orbital

00:07:39.330 --> 00:07:41.104
but after that, you can
imagine the electrons

00:07:41.104 --> 00:07:42.490
are repelling each other.

00:07:42.490 --> 00:07:43.999
So another electron doesn't wanna go there

00:07:43.999 --> 00:07:46.656
so the third electron that you add

00:07:46.656 --> 00:07:49.730
is going to end up in the 2s orbital.

00:07:49.730 --> 00:07:51.830
It's gonna be at that higher energy level

00:07:51.830 --> 00:07:53.330
and then that can fit two.

00:07:53.330 --> 00:07:54.831
So you can fit up to four electrons

00:07:54.831 --> 00:07:57.090
between the 1s and the 2s.

00:07:57.090 --> 00:07:58.790
And then the fifth one
is going to have to go

00:07:58.790 --> 00:08:01.270
into one of these p-orbitals.

00:08:01.270 --> 00:08:03.477
Now, one last point, just
to make sure you understand

00:08:03.477 --> 00:08:07.038
the terminology of orbitals and shells.

00:08:07.038 --> 00:08:11.040
So first of all, you
have this idea of shells

00:08:11.040 --> 00:08:14.540
and sometimes the word shell
will be used interchangeably

00:08:14.540 --> 00:08:18.710
with energy level, energy levels.

00:08:18.710 --> 00:08:20.580
And so in this diagram

00:08:20.580 --> 00:08:22.170
or this a visualization right over here,

00:08:22.170 --> 00:08:24.400
I've depicted the one shell

00:08:24.400 --> 00:08:26.710
and then I've also
depicted the two shells.

00:08:26.710 --> 00:08:28.736
So this is a shell right over here.

00:08:28.736 --> 00:08:31.722
This is another shell.

00:08:31.722 --> 00:08:36.300
Now, you'll also hear the
term, subshell, subshell,

00:08:38.180 --> 00:08:41.920
or sometimes people will say sublevels

00:08:41.920 --> 00:08:46.300
and that's where they're
talking about s or p or d

00:08:46.300 --> 00:08:49.560
and eventually f so if I circle this,

00:08:49.560 --> 00:08:51.270
I'm talking about that first shell.

00:08:51.270 --> 00:08:55.050
Now, the first shell only
contains one subshell

00:08:55.050 --> 00:09:00.050
and that's the 1s subshell
and the 1s subshell

00:09:00.247 --> 00:09:03.380
only has one orbital.

00:09:03.380 --> 00:09:06.430
Once again, the 1s orbital.

00:09:06.430 --> 00:09:09.150
So for the first shell,
the shell, the subshell,

00:09:09.150 --> 00:09:11.770
the orbital is all
referring to the same thing,

00:09:11.770 --> 00:09:13.050
but as we get to the second shell,

00:09:13.050 --> 00:09:14.040
it's a little bit different.

00:09:14.040 --> 00:09:15.875
If we're talking about the subshells,

00:09:15.875 --> 00:09:20.875
in the second shell, there's
s and p so this is a subshell,

00:09:21.080 --> 00:09:24.570
and then this is another
subshell right over here.

00:09:24.570 --> 00:09:28.810
There's actually three
orbitals in the p-subshell.

00:09:28.810 --> 00:09:29.900
So I'll leave you there.

00:09:29.900 --> 00:09:33.420
In the next video, we'll
actually look at various atoms

00:09:33.420 --> 00:09:35.500
and think about their
electron configurations.

00:09:35.500 --> 00:09:36.940
Where do their electrons sit?

00:09:36.940 --> 00:09:39.433
In which of these shells,
subshells, and orbitals?


Introduction to electron configurations

WEBVTT
Kind: captions
Language: en

00:00:00.820 --> 00:00:01.840
- [Instructor] In a previous video,

00:00:01.840 --> 00:00:03.590
we've introduced ourselves

00:00:03.590 --> 00:00:05.360
to the idea of an orbital,

00:00:05.360 --> 00:00:08.400
that electrons don't just orbit a nucleus

00:00:08.400 --> 00:00:10.780
the way that a planet might orbit a star,

00:00:10.780 --> 00:00:12.710
but really, in order to describe

00:00:12.710 --> 00:00:15.350
where an electron is at
any given point in time,

00:00:15.350 --> 00:00:17.040
we're really thinking about probabilities,

00:00:17.040 --> 00:00:18.470
where it's more likely to be found

00:00:18.470 --> 00:00:19.950
and less likely to be found.

00:00:19.950 --> 00:00:22.450
And an orbital is a description of that,

00:00:22.450 --> 00:00:25.410
where is it more or
less likely to be found.

00:00:25.410 --> 00:00:29.040
And this diagram shows
us the types of orbitals

00:00:29.040 --> 00:00:31.830
which can be found in
the various subshells

00:00:31.830 --> 00:00:33.810
which are found in the various shells.

00:00:33.810 --> 00:00:35.260
So you have the s subshell,

00:00:35.260 --> 00:00:38.030
the p subshell that has three
different orbitals in it,

00:00:38.030 --> 00:00:42.370
you have the d subshell
that has one, two, three,

00:00:42.370 --> 00:00:44.930
four, five different orbitals in it.

00:00:44.930 --> 00:00:49.090
And then you have the f subshells.

00:00:49.090 --> 00:00:51.680
Now each orbital can fit two electrons.

00:00:51.680 --> 00:00:53.390
So if you're thinking about the subshell,

00:00:53.390 --> 00:00:56.840
the s subshell could fit two electrons,

00:00:56.840 --> 00:01:00.590
the p subshell can fit six electrons,

00:01:00.590 --> 00:01:04.500
the d subshell can fit 10 electrons,

00:01:04.500 --> 00:01:09.160
and the f subshell can fit 14 electrons,

00:01:09.160 --> 00:01:11.380
two per orbital.

00:01:11.380 --> 00:01:13.150
Now the goal of this video is to think

00:01:13.150 --> 00:01:16.600
about electron configurations
for particular atoms.

00:01:16.600 --> 00:01:18.880
And to help us with that, we will look

00:01:18.880 --> 00:01:22.230
at a periodic table of elements.

00:01:22.230 --> 00:01:23.760
And so first, let's just think

00:01:23.760 --> 00:01:27.050
about the electron configuration
of the simplest element.

00:01:27.050 --> 00:01:29.480
If we're talking about
a neutral hydrogen atom,

00:01:29.480 --> 00:01:32.170
a neutral hydrogen atom, it
has an atomic number of one

00:01:32.170 --> 00:01:34.100
which tells us it has one proton,

00:01:34.100 --> 00:01:37.080
and if it's neutral, that
means it has one electron.

00:01:37.080 --> 00:01:39.340
Now where would that one electron be?

00:01:39.340 --> 00:01:42.220
Well it would be in
the lowest energy level

00:01:42.220 --> 00:01:46.010
or the first shell, and that first shell

00:01:46.010 --> 00:01:48.520
has only one subshell in it.

00:01:48.520 --> 00:01:50.800
It only has one type of orbital.

00:01:50.800 --> 00:01:54.750
It only has an s subshell,
and so that one electron

00:01:54.750 --> 00:01:58.240
in that neutral hydrogen
atom would go over there.

00:01:58.240 --> 00:02:01.260
So we would say its
electron configuration 1s1,

00:02:01.260 --> 00:02:03.270
in the first shell which is made only

00:02:03.270 --> 00:02:06.490
of an s subshell, it has one electron.

00:02:06.490 --> 00:02:08.290
Now what happens if we go to helium?

00:02:09.190 --> 00:02:11.430
Well, a neutral helium atom

00:02:11.430 --> 00:02:13.260
is going to have two electrons.

00:02:13.260 --> 00:02:16.770
So instead of just having one
electron in that first shell,

00:02:16.770 --> 00:02:17.980
we can fit up to two there.

00:02:17.980 --> 00:02:22.490
So its electron
configuration would be 1s2.

00:02:22.490 --> 00:02:23.670
Now what do you think is going to happen

00:02:23.670 --> 00:02:25.283
when we go to lithium?

00:02:26.170 --> 00:02:27.770
Well lithium, a neutral lithium

00:02:27.770 --> 00:02:30.060
will have three electrons in it,

00:02:30.060 --> 00:02:32.830
so the first two could go
to the first energy level,

00:02:32.830 --> 00:02:36.290
the first shell, so the
first two will go 1s2,

00:02:36.290 --> 00:02:37.980
and then the third electron is going

00:02:37.980 --> 00:02:40.410
to go into the second shell,

00:02:40.410 --> 00:02:42.720
and the subshell that
it's going to fill first

00:02:42.720 --> 00:02:44.470
is the s subshell.

00:02:44.470 --> 00:02:46.630
So then it'll go to the second shell

00:02:46.630 --> 00:02:49.400
and start filling up the s subshell.

00:02:49.400 --> 00:02:52.020
So notice, two electrons
in the first shell

00:02:52.020 --> 00:02:54.830
and one electron in the second shell.

00:02:54.830 --> 00:02:56.203
Now what about beryllium?

00:02:57.280 --> 00:02:59.030
Well, that's gonna look a lot like lithium

00:02:59.030 --> 00:03:01.230
but now it has four electrons.

00:03:01.230 --> 00:03:04.283
So two of them are going to
go into the first shell, 1s2,

00:03:05.165 --> 00:03:08.160
and then the next two are
going to fill up the s subshell

00:03:08.160 --> 00:03:09.500
in the second shell.

00:03:09.500 --> 00:03:11.350
I know it's a bit of a mouthful, 2s2.

00:03:12.840 --> 00:03:16.430
Notice, we have four total electrons

00:03:16.430 --> 00:03:19.620
which would be the case in
a neutral beryllium atom.

00:03:19.620 --> 00:03:21.180
But what about boron?

00:03:21.180 --> 00:03:23.150
Boron gets interesting.

00:03:23.150 --> 00:03:25.760
A neutral boron would have five electrons.

00:03:25.760 --> 00:03:30.760
So the first two we're going
to fill the first shell, 1s2,

00:03:31.040 --> 00:03:32.860
now the second two are then going to go

00:03:32.860 --> 00:03:37.200
to the second shell and
fill up the s subshell 2s2,

00:03:37.200 --> 00:03:41.050
and then we're going to start
filling up the p subshell.

00:03:41.050 --> 00:03:45.830
So let's see, we have one
more electron so we go 2p1.

00:03:45.830 --> 00:03:47.530
So we're going to have one electron

00:03:47.530 --> 00:03:50.200
in one of these p orbitals.

00:03:50.200 --> 00:03:53.440
And then what happens
when we go to carbon?

00:03:53.440 --> 00:03:55.480
Well it's going to look a lot like boron

00:03:55.480 --> 00:03:57.700
but now we have one more
electron to deal with

00:03:57.700 --> 00:03:59.200
if we have a neutral carbon atom,

00:03:59.200 --> 00:04:00.800
it's going to have six electrons.

00:04:00.800 --> 00:04:03.550
So then an extra electron is once again

00:04:03.550 --> 00:04:06.220
going to fall into the p subshell

00:04:06.220 --> 00:04:11.220
in the second shell because
that can fit six electrons.

00:04:11.380 --> 00:04:14.850
So we're going to fill the
first shell with two electrons

00:04:14.850 --> 00:04:17.480
then the 2s subshell with two electrons,

00:04:17.480 --> 00:04:19.150
and then we have two more electrons

00:04:19.150 --> 00:04:20.683
for the 2p subshell.

00:04:22.890 --> 00:04:26.160
Now you can imagine as we get
to larger and larger atoms

00:04:26.160 --> 00:04:27.800
with more and more electrons,

00:04:27.800 --> 00:04:29.890
this can get quite complex.

00:04:29.890 --> 00:04:32.570
So one notation folks often use

00:04:32.570 --> 00:04:35.130
is noble gas configuration

00:04:35.130 --> 00:04:37.210
where instead of saying,
okay, this is carbon,

00:04:37.210 --> 00:04:38.330
they could say that, hey look,

00:04:38.330 --> 00:04:41.010
carbon is going to have
the electron configuration

00:04:41.010 --> 00:04:43.210
of helium, remember, the noble gasses

00:04:43.210 --> 00:04:45.740
are these Group 8
elements right over here,

00:04:45.740 --> 00:04:49.430
so it's going to have the
electron configuration of helium

00:04:49.430 --> 00:04:51.990
which tells us this right over here,

00:04:51.990 --> 00:04:56.902
and then from that, we're
going to also have 2s2,

00:04:56.902 --> 00:04:59.960
2s2, and then 2p2.

00:04:59.960 --> 00:05:02.770
You could just take helium's
electron configuration

00:05:02.770 --> 00:05:04.830
right over here and put it right over here

00:05:04.830 --> 00:05:07.353
and you would get exactly
what we wrote before.


Worked example: Calculating the mass of a substance in a mixture

WEBVTT
Kind: captions
Language: en

00:00:00.310 --> 00:00:04.610
- [Instructor] We're
told that a 0.450 gram

00:00:04.610 --> 00:00:09.610
potassium supplement contains
22% potassium by mass.

00:00:11.570 --> 00:00:14.196
The potassium is present in the supplement

00:00:14.196 --> 00:00:18.730
as potassium chloride,
which has a molar mass

00:00:18.730 --> 00:00:23.540
of 74.55 grams per mole.

00:00:23.540 --> 00:00:26.409
How many grams of
potassium chloride are in

00:00:26.409 --> 00:00:28.560
the potassium supplement?

00:00:28.560 --> 00:00:30.670
So pause this video and
see if you can figure that

00:00:30.670 --> 00:00:33.560
on your own, and I will give you a hint.

00:00:33.560 --> 00:00:35.490
You might need a periodic table,

00:00:35.490 --> 00:00:37.420
so I'll give you one right over there.

00:00:37.420 --> 00:00:39.150
All right, now let's work
through this together.

00:00:39.150 --> 00:00:42.080
So they already give us the molar mass

00:00:42.080 --> 00:00:44.600
of potassium chloride,

00:00:44.600 --> 00:00:46.780
but it'll be useful for us to know

00:00:46.780 --> 00:00:50.440
the molar mass of potassium itself.

00:00:50.440 --> 00:00:51.970
And we can see it's 39.10.

00:00:53.043 --> 00:00:53.876
So for potassium, it is 39.10.

00:00:57.480 --> 00:00:59.470
That's its average atomic mass,

00:00:59.470 --> 00:01:03.631
but you could also view
it as 39.10 grams per mole

00:01:03.631 --> 00:01:06.960
of potassium, could write it like that.

00:01:06.960 --> 00:01:09.510
And that is, I think, all we will need

00:01:09.510 --> 00:01:11.860
the periodic table of elements for.

00:01:11.860 --> 00:01:14.544
And so, how do we think
about how many grams

00:01:14.544 --> 00:01:18.678
of potassium chloride are
in the potassium supplement?

00:01:18.678 --> 00:01:20.297
Well what I could do is, I could say,

00:01:20.297 --> 00:01:22.590
"All right, what's the total
mass of my supplement,"

00:01:22.590 --> 00:01:25.510
and multiply it by 22% to figure out

00:01:25.510 --> 00:01:28.770
what is the mass of potassium I have.

00:01:28.770 --> 00:01:30.130
So let me figure that out.

00:01:30.130 --> 00:01:34.160
So mass of potassium,

00:01:34.160 --> 00:01:39.060
that is going to be my 0.450 grams

00:01:39.060 --> 00:01:43.700
times 22%, which is going to be equal to,

00:01:43.700 --> 00:01:45.440
I'll get my calculator out,

00:01:45.440 --> 00:01:50.440
0.450 times 22%, or .22,

00:01:51.510 --> 00:01:55.249
is equal to 0.099.

00:01:55.249 --> 00:01:59.140
0.099.

00:01:59.140 --> 00:02:02.760
So that's how many grams
of potassium I have.

00:02:02.760 --> 00:02:04.940
And now I can use that to figure out

00:02:04.940 --> 00:02:07.350
how many moles of potassium I have.

00:02:07.350 --> 00:02:09.530
And if I know how many
moles of potassium I have,

00:02:09.530 --> 00:02:12.810
all the potassium is present
as potassium chloride.

00:02:12.810 --> 00:02:14.380
Because then I'll have
the same number of moles

00:02:14.380 --> 00:02:16.611
of potassium chloride, and
then I could figure out,

00:02:16.611 --> 00:02:18.515
well, based on.

00:02:18.515 --> 00:02:21.400
And if I know the number of
moles of potassium chloride,

00:02:21.400 --> 00:02:24.030
well then I know the mass
of potassium chloride,

00:02:24.030 --> 00:02:25.550
because they give us the molar mass.

00:02:25.550 --> 00:02:27.300
So let's do that.

00:02:27.300 --> 00:02:31.703
So we have 0.099

00:02:32.770 --> 00:02:35.620
grams of potassium.

00:02:35.620 --> 00:02:38.920
And I wanna figure out how
many moles of potassium I have.

00:02:38.920 --> 00:02:41.430
So I'm gonna multiply that times,

00:02:41.430 --> 00:02:45.540
one mole of potassium

00:02:45.540 --> 00:02:49.400
has a mass of how many grams of potassium?

00:02:49.400 --> 00:02:51.780
And we can see it right over there.

00:02:51.780 --> 00:02:54.780
It's 39.10 grams per mole.

00:02:54.780 --> 00:02:57.143
So 39.10.

00:02:58.260 --> 00:03:01.300
One mole is equivalent to 39.10 grams,

00:03:01.300 --> 00:03:02.910
if we're dealing with potassium.

00:03:02.910 --> 00:03:06.318
So this calculation will
tell me moles of potassium.

00:03:06.318 --> 00:03:10.340
Now, I have exactly one potassium atom

00:03:10.340 --> 00:03:13.530
for every potassium chloride molecule.

00:03:13.530 --> 00:03:15.380
And so, whatever this number is,

00:03:15.380 --> 00:03:17.260
I'm gonna have the same number of moles

00:03:17.260 --> 00:03:18.600
of potassium chloride,

00:03:18.600 --> 00:03:20.930
but just to make that clear,
I will write this down.

00:03:20.930 --> 00:03:23.860
I have one mole

00:03:23.860 --> 00:03:28.795
of potassium chloride for every one

00:03:28.795 --> 00:03:32.630
mole of potassium.

00:03:32.630 --> 00:03:35.280
And you could already see how
the units will cancel out.

00:03:35.280 --> 00:03:36.968
That will cancel with that.

00:03:36.968 --> 00:03:39.080
That will cancel with that.

00:03:39.080 --> 00:03:41.430
And so, this calculation
is going to tell me

00:03:41.430 --> 00:03:43.630
moles of potassium chloride,

00:03:43.630 --> 00:03:46.030
but I wanna know the mass
of potassium chloride.

00:03:46.030 --> 00:03:50.130
So then I will multiply
this by the molar mass,

00:03:50.130 --> 00:03:52.640
times 74, and I'm gonna
do this in another color,

00:03:52.640 --> 00:03:57.640
just makes it look nice, 74.55 grams

00:03:58.750 --> 00:04:01.420
of potassium chloride

00:04:01.420 --> 00:04:04.880
for every mole

00:04:04.880 --> 00:04:07.240
of potassium chloride.

00:04:07.240 --> 00:04:09.860
And so then, this will cancel with this,

00:04:09.860 --> 00:04:11.450
and this will tell me how many grams

00:04:11.450 --> 00:04:14.330
of potassium chloride I actually have.

00:04:14.330 --> 00:04:16.220
So let's get the calculator out again.

00:04:16.220 --> 00:04:17.630
So I have 0.099

00:04:19.340 --> 00:04:21.730
divided by 39.10,

00:04:21.730 --> 00:04:26.020
divided by 39.10,

00:04:26.020 --> 00:04:29.380
times one, times 74.55,

00:04:29.380 --> 00:04:34.380
times 74.55, is going to be equal to that.

00:04:35.350 --> 00:04:38.480
And then let me think about
my significant figures

00:04:38.480 --> 00:04:40.328
or my significant digits here.

00:04:40.328 --> 00:04:43.570
So let's see, out of all
of the information I used,

00:04:43.570 --> 00:04:46.365
I have three significant figures here,

00:04:46.365 --> 00:04:49.662
I have three here, I have four here,

00:04:49.662 --> 00:04:52.100
I have four here.

00:04:52.100 --> 00:04:54.400
So I'm multiplying a bunch
of things and dividing,

00:04:54.400 --> 00:04:55.670
so I have to take the minimum number

00:04:55.670 --> 00:04:58.110
of significant figures, which is three.

00:04:58.110 --> 00:05:00.150
So I will round to three
significant figures,

00:05:00.150 --> 00:05:04.036
which is 0.189 grams.

00:05:04.036 --> 00:05:06.334
So this is,

00:05:06.334 --> 00:05:08.320
let me do this in a new color,

00:05:08.320 --> 00:05:13.320
0.189 grams of potassium chloride,

00:05:14.580 --> 00:05:17.420
which is exactly what they are asking us.

00:05:17.420 --> 00:05:19.693
And we are done.


Worked example: Determining an empirical formula from combustion data

WEBVTT
Kind: captions
Language: en

00:00:00.200 --> 00:00:02.870
- [Instructor] We are told
that a sample of a compound

00:00:02.870 --> 00:00:07.190
containing only carbon and hydrogen atoms

00:00:07.190 --> 00:00:09.890
is completely combusted,

00:00:09.890 --> 00:00:13.580
producing 5.65 grams of carbon dioxide

00:00:13.580 --> 00:00:17.290
and 3.47 grams of H2O or water.

00:00:17.290 --> 00:00:20.290
What is the empirical
formula of the compound?

00:00:20.290 --> 00:00:21.260
So pause this video

00:00:21.260 --> 00:00:23.860
and see if you can work through that.

00:00:23.860 --> 00:00:26.260
All right, now let's just try
to make sure we understand

00:00:26.260 --> 00:00:27.700
what's going on.

00:00:27.700 --> 00:00:29.710
They say that I have
some mystery compound.

00:00:29.710 --> 00:00:31.820
It only contains carbon and hydrogen,

00:00:31.820 --> 00:00:33.610
so it's going to have
some number of carbon,

00:00:33.610 --> 00:00:34.860
I'll call that x.

00:00:34.860 --> 00:00:39.160
Some number of hydrogens,
I'll call that y.

00:00:39.160 --> 00:00:42.800
We're going to put it in the
presence of molecular oxygen

00:00:42.800 --> 00:00:44.560
and it's going to combust

00:00:44.560 --> 00:00:46.220
and after it's combusted,

00:00:46.220 --> 00:00:51.220
I'm going to end up with some
carbon dioxide and some water.

00:00:51.480 --> 00:00:53.240
And what I just drew here,

00:00:53.240 --> 00:00:55.940
this is a chemical reaction
that I'm describing.

00:00:55.940 --> 00:00:57.330
I haven't balanced it.

00:00:57.330 --> 00:00:59.650
I could try to, even with the x's and y's,

00:00:59.650 --> 00:01:01.400
but that's not the point of this video.

00:01:01.400 --> 00:01:04.430
The point of this video is
they tell us how many grams

00:01:04.430 --> 00:01:06.310
of the carbon dioxide we have

00:01:06.310 --> 00:01:08.680
and how many grams of the water we have,

00:01:08.680 --> 00:01:10.890
they tells us that right over there.

00:01:10.890 --> 00:01:13.310
And so what we need to
do is say, all right,

00:01:13.310 --> 00:01:16.100
from that, we can figure
out how many moles

00:01:16.100 --> 00:01:18.520
of carbon dioxide we have,

00:01:18.520 --> 00:01:21.380
how many moles of water we have,

00:01:21.380 --> 00:01:24.350
and from that, we can
figure out how many moles

00:01:24.350 --> 00:01:25.930
of carbon did we start with

00:01:25.930 --> 00:01:28.450
and how many moles of
hydrogen did we start with?

00:01:28.450 --> 00:01:30.230
And if we look at those ratios,

00:01:30.230 --> 00:01:32.780
then we can come up with
the empirical formula

00:01:32.780 --> 00:01:34.320
of the compound.

00:01:34.320 --> 00:01:37.020
So just to start, because
I'm going to be thinking

00:01:37.020 --> 00:01:40.010
about molar moles and molar masses

00:01:40.010 --> 00:01:43.410
and the mass of a mole
of a molecule or an atom,

00:01:43.410 --> 00:01:46.510
let's just get the average atomic mass

00:01:46.510 --> 00:01:50.570
for carbon, hydrogen, and
oxygen for us to work with.

00:01:50.570 --> 00:01:53.740
So I'll get out our handy periodic table.

00:01:53.740 --> 00:01:57.523
We can see hydrogen has an
average atomic mass of 1.008.

00:01:59.070 --> 00:02:00.960
Let me write that down.

00:02:00.960 --> 00:02:05.473
So we have hydrogen is at 1.008,

00:02:07.500 --> 00:02:10.850
and then we have carbon,

00:02:10.850 --> 00:02:15.313
and carbon is at 12.01.

00:02:17.410 --> 00:02:22.083
So carbon is at 12.01,

00:02:23.375 --> 00:02:24.380
and we could also think about them

00:02:24.380 --> 00:02:26.630
in terms of molar masses.

00:02:26.630 --> 00:02:30.160
We could say this is gram per mole,

00:02:30.160 --> 00:02:32.650
grams per mole,

00:02:32.650 --> 00:02:35.430
and then last, but not
least, we have oxygen

00:02:35.430 --> 00:02:40.430
and then oxygen is at
16.00 grams per mole.

00:02:41.130 --> 00:02:44.090
It's the average atomic mass,

00:02:44.090 --> 00:02:46.590
but whether we can think
of that as molar mass,

00:02:46.590 --> 00:02:49.100
that number is molar mass.

00:02:49.100 --> 00:02:50.880
So oxygen

00:02:52.190 --> 00:02:57.190
is at 16.00 grams per mole.

00:02:59.190 --> 00:03:01.370
And so now we can try to figure out

00:03:01.370 --> 00:03:06.370
how many moles of C in
the product do we have?

00:03:08.150 --> 00:03:10.930
So we can see that all of
the carbon in the product

00:03:10.930 --> 00:03:14.274
is in the carbon dioxide
that's in the product,

00:03:14.274 --> 00:03:19.067
and so we have 5.65 grams of CO2.

00:03:20.490 --> 00:03:23.700
We can think about how
many moles of CO2 that is,

00:03:23.700 --> 00:03:27.270
so times one mole

00:03:27.270 --> 00:03:32.270
of CO2 for every how many grams of CO2.

00:03:34.580 --> 00:03:36.900
Well, we just have to think about,

00:03:36.900 --> 00:03:39.002
actually, let me just
put it right over here.

00:03:39.002 --> 00:03:39.835
CO2,

00:03:41.550 --> 00:03:43.090
you're going to have, let's see,

00:03:43.090 --> 00:03:44.420
you have one carbon

00:03:44.420 --> 00:03:46.860
and two oxygens.

00:03:46.860 --> 00:03:51.860
So it is going to be
12.01 plus two times 16.

00:03:53.110 --> 00:03:58.110
Two times 16.00 grams per mole,

00:03:59.470 --> 00:04:00.330
and so let's see.

00:04:00.330 --> 00:04:03.000
This would get us to, this is 32

00:04:03.000 --> 00:04:06.340
plus 12.01, so that is 44.01.

00:04:06.340 --> 00:04:07.790
And that's grams per mole,

00:04:07.790 --> 00:04:09.150
but now we're thinking
about moles per gram,

00:04:09.150 --> 00:04:14.150
so it's going to be one over 44.01

00:04:14.730 --> 00:04:16.820
and so if we did just this,

00:04:16.820 --> 00:04:20.020
the grams of CO2 would
cancel the grams of CO2

00:04:20.020 --> 00:04:22.440
and this would give us moles of CO2,

00:04:22.440 --> 00:04:25.360
but I care about moles
of carbon in the product.

00:04:25.360 --> 00:04:27.520
So how many moles of carbon are there

00:04:27.520 --> 00:04:30.310
for every mole of CO2?

00:04:30.310 --> 00:04:35.310
Well we know that we
have one mole of carbon

00:04:35.750 --> 00:04:40.750
for every one mole of CO2.

00:04:41.100 --> 00:04:45.110
Every carbon dioxide molecule
has one carbon in it,

00:04:45.110 --> 00:04:48.320
and so what is this going to get us?

00:04:48.320 --> 00:04:52.640
So we have 5.65

00:04:52.640 --> 00:04:57.310
divided by, divided by 44.01,

00:04:57.310 --> 00:05:00.060
and then times one, so I don't
have to do anything there.

00:05:00.060 --> 00:05:04.210
That is equal to, I'll round
it to three digits here,

00:05:04.210 --> 00:05:06.043
so 0.128,

00:05:07.500 --> 00:05:10.930
so this is 0.128

00:05:10.930 --> 00:05:13.550
and my units here are, let's see.

00:05:13.550 --> 00:05:14.760
The grams of carbon dioxide

00:05:14.760 --> 00:05:16.170
cancel the grams of carbon dioxide.

00:05:16.170 --> 00:05:18.410
The moles of carbon
dioxide cancel the moles

00:05:18.410 --> 00:05:19.600
of carbon dioxide,

00:05:19.600 --> 00:05:21.670
so I am exactly where I want to be.

00:05:21.670 --> 00:05:25.400
This is how many moles
of carbon that I have.

00:05:25.400 --> 00:05:27.460
And you can do the dimensional analysis,

00:05:27.460 --> 00:05:30.060
but it also makes
intuitive sense, hopefully.

00:05:30.060 --> 00:05:32.850
If this is how many grams
of carbon dioxide we have

00:05:32.850 --> 00:05:35.910
and a mole of carbon dioxide
is going to have a mass

00:05:35.910 --> 00:05:38.030
of 44.01 grams,

00:05:38.030 --> 00:05:41.320
well then 5.65 over this
is going to tell us how,

00:05:41.320 --> 00:05:44.720
what fraction of a mole
we have of carbon dioxide

00:05:44.720 --> 00:05:47.550
and then whatever that
number of moles we have

00:05:47.550 --> 00:05:48.860
of carbon dioxide is gonna be the same

00:05:48.860 --> 00:05:50.550
as the moles of carbon,

00:05:50.550 --> 00:05:53.710
'cause we have one atom of carbon

00:05:53.710 --> 00:05:55.800
for every carbon dioxide molecule,

00:05:55.800 --> 00:05:56.950
so that all makes sense.

00:05:56.950 --> 00:06:00.090
And now let's do the same for hydrogen.

00:06:00.090 --> 00:06:03.550
So let's think about moles of hydrogen

00:06:03.550 --> 00:06:05.140
in the product,

00:06:05.140 --> 00:06:07.030
and it's going to be the same exercise.

00:06:07.030 --> 00:06:08.670
And if you're so inspired

00:06:08.670 --> 00:06:10.010
and you didn't calculate
it in the beginning,

00:06:10.010 --> 00:06:13.330
I encourage you to try to
do this part on your own.

00:06:13.330 --> 00:06:17.080
All right, so all of the
hydrogen is in the water,

00:06:17.080 --> 00:06:19.480
so and we know that we
have, in our product,

00:06:19.480 --> 00:06:21.920
3.47 grams of water.

00:06:21.920 --> 00:06:26.530
3.47 grams of H2O,

00:06:26.530 --> 00:06:29.640
and now let's think about how
many moles of H2O that is.

00:06:29.640 --> 00:06:31.250
So that's going to be, let's see,

00:06:31.250 --> 00:06:34.170
every one mole of H2O

00:06:35.060 --> 00:06:39.400
is going to have a mass
of how many grams of H2O?

00:06:39.400 --> 00:06:40.960
And we could do that up here.

00:06:40.960 --> 00:06:43.210
H2O, it's going to be,

00:06:43.210 --> 00:06:44.930
we have two hydrogens,

00:06:44.930 --> 00:06:48.740
so it's going to be two times 1.008

00:06:48.740 --> 00:06:52.310
plus the mass, the average atomic mass

00:06:52.310 --> 00:06:55.760
of the oxygen is going to be plus 16,

00:06:55.760 --> 00:06:57.330
but we can also view that as

00:06:57.330 --> 00:06:59.030
what would be the mass in grams,

00:06:59.030 --> 00:07:00.280
if you had a mole of it?

00:07:00.280 --> 00:07:03.280
And so this is going to
be in grams per mole,

00:07:03.280 --> 00:07:04.770
and so this is going to be, let's see,

00:07:04.770 --> 00:07:06.280
two times 1.008.

00:07:06.280 --> 00:07:08.623
This part over here is 2.016,

00:07:10.390 --> 00:07:11.680
and then you add 16 to it.

00:07:11.680 --> 00:07:12.880
It's going to be 18.016.

00:07:14.711 --> 00:07:17.070
18.016,

00:07:17.070 --> 00:07:19.580
and then if I just calculated this,

00:07:19.580 --> 00:07:22.710
this would give me how
many moles of water I have

00:07:22.710 --> 00:07:24.140
in my product,

00:07:24.140 --> 00:07:26.780
but I care about moles of hydrogen.

00:07:26.780 --> 00:07:29.560
And so how many moles
of hydrogen do I have

00:07:29.560 --> 00:07:33.260
for every mole of water?

00:07:33.260 --> 00:07:36.410
So for how many moles of hydrogen

00:07:36.410 --> 00:07:38.853
for every mole of water?

00:07:39.730 --> 00:07:42.520
Well I'm going to have
two moles of hydrogen

00:07:42.520 --> 00:07:44.990
for every mole of water

00:07:44.990 --> 00:07:47.020
because in each water molecule,

00:07:47.020 --> 00:07:48.500
I have two hydrogens.

00:07:48.500 --> 00:07:50.317
And so that's going to
cancel out with that

00:07:50.317 --> 00:07:52.540
and we're just going to be
left with moles of hydrogen.

00:07:52.540 --> 00:07:56.300
And so this is going to be equal to,

00:07:56.300 --> 00:08:01.300
I'll take my 3.47 grams of water,

00:08:01.660 --> 00:08:03.970
divide it by the,

00:08:03.970 --> 00:08:08.100
how much, how many grams a mole of water,

00:08:08.100 --> 00:08:09.260
what its mass would be,

00:08:09.260 --> 00:08:11.417
so divided by 18.016.

00:08:15.760 --> 00:08:19.510
This is how many moles of water I have.

00:08:19.510 --> 00:08:20.480
Now for every,

00:08:20.480 --> 00:08:23.440
for every molecule of
water, I have two hydrogens,

00:08:23.440 --> 00:08:25.770
so then I will multiply by two.

00:08:25.770 --> 00:08:29.260
Times two is equal to zero point,

00:08:29.260 --> 00:08:31.270
I'll just round three
digits right over here.

00:08:31.270 --> 00:08:32.693
0.385.

00:08:34.020 --> 00:08:39.020
0.385 moles of hydrogen.

00:08:39.640 --> 00:08:43.250
So now we know the
number of hydrogen atoms.

00:08:43.250 --> 00:08:45.420
We know the number of carbon atoms,

00:08:45.420 --> 00:08:48.220
and to figure out the empirical
formula of the compound,

00:08:48.220 --> 00:08:50.240
we can think about the
ratio between the two,

00:08:50.240 --> 00:08:55.240
so I'm gonna find the ratio
of hydrogens to carbons.

00:08:56.200 --> 00:08:58.970
And that is going to be equal to,

00:08:58.970 --> 00:09:03.970
I have 0.385 moles of hydrogen

00:09:04.100 --> 00:09:06.430
over, over

00:09:07.860 --> 00:09:10.540
0.128 moles of carbon.

00:09:10.540 --> 00:09:12.940
0.128 moles of carbon,

00:09:12.940 --> 00:09:14.750
and what is this equal to?

00:09:14.750 --> 00:09:16.740
And it looks like it's
going to be roughly three,

00:09:16.740 --> 00:09:18.670
but let me verify that.

00:09:18.670 --> 00:09:20.050
In my head, that seems so,

00:09:20.050 --> 00:09:22.670
I already have the hydrogen there,

00:09:22.670 --> 00:09:27.670
and so if I divide it by 0.128,

00:09:28.030 --> 00:09:30.960
I get, yep, pretty close to three.

00:09:30.960 --> 00:09:32.750
Now actually, I think if I, yep,

00:09:32.750 --> 00:09:35.550
pretty close to three, so there you go.

00:09:35.550 --> 00:09:38.880
This is approximately three,

00:09:38.880 --> 00:09:41.800
and so I can, with pretty good confidence,

00:09:41.800 --> 00:09:43.830
this was very close to three.

00:09:43.830 --> 00:09:45.540
I could say for every carbon,

00:09:45.540 --> 00:09:48.630
I have three hydrogens
in my original compound,

00:09:48.630 --> 00:09:50.150
in this thing right over here.

00:09:50.150 --> 00:09:53.060
So the empirical formula
of our original compound

00:09:53.060 --> 00:09:54.780
for every one carbon,

00:09:54.780 --> 00:09:57.200
I have three hydrogens.

00:09:57.200 --> 00:09:59.770
So CH3,

00:09:59.770 --> 00:10:01.543
and we are done.


Example comparing mass percentages of element in comounds

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:02.740
- [Instructor] So we have
four different compounds here,

00:00:02.740 --> 00:00:05.030
and we also have their molar masses

00:00:05.030 --> 00:00:06.770
and what I would like you to do

00:00:06.770 --> 00:00:10.860
is think about which of these
compounds has the highest,

00:00:10.860 --> 00:00:15.720
highest percentage of sulfur by mass.

00:00:18.140 --> 00:00:21.910
So pause this video and see
if you can figure that out.

00:00:21.910 --> 00:00:25.060
All right, now one way to approach this

00:00:25.060 --> 00:00:29.030
is to say for each of these compounds,

00:00:29.030 --> 00:00:31.640
so if we say per mole

00:00:32.830 --> 00:00:35.610
of each compound,

00:00:35.610 --> 00:00:37.213
of each compound,

00:00:38.150 --> 00:00:41.850
we could figure out how
many grams, I would say

00:00:41.850 --> 00:00:43.520
what is the mass,

00:00:43.520 --> 00:00:46.870
what is the mass of sulfur

00:00:46.870 --> 00:00:50.210
divided by the total mass of the compound?

00:00:50.210 --> 00:00:54.080
Total, total mass of the compound.

00:00:54.080 --> 00:00:55.840
Now the mass of sulfur,

00:00:55.840 --> 00:00:59.780
we can see that for a mole
of each of these compounds,

00:00:59.780 --> 00:01:02.750
you have exactly one mole of sulfur.

00:01:02.750 --> 00:01:03.990
In all of these formulas,

00:01:03.990 --> 00:01:06.180
you see exactly one sulfur.

00:01:06.180 --> 00:01:07.870
So in all of these situations,

00:01:07.870 --> 00:01:11.560
the mass of sulfur is
going to be the same.

00:01:11.560 --> 00:01:13.700
This is going to be the same,

00:01:13.700 --> 00:01:17.430
same for all compounds.

00:01:17.430 --> 00:01:19.790
It wouldn't be the same for all compounds

00:01:19.790 --> 00:01:21.400
if some of them had two sulfurs

00:01:21.400 --> 00:01:22.410
or some of them had three

00:01:22.410 --> 00:01:23.690
or maybe some of them had none,

00:01:23.690 --> 00:01:25.350
but all of them have one sulfur,

00:01:25.350 --> 00:01:27.840
so for a mole of each of these compounds,

00:01:27.840 --> 00:01:29.950
you're going to have a mole of sulfur,

00:01:29.950 --> 00:01:33.200
and so they're going to have
the same mass of sulfur.

00:01:33.200 --> 00:01:35.310
We could take out a periodic table

00:01:35.310 --> 00:01:37.100
and we could look it up
and we could say, oh, look.

00:01:37.100 --> 00:01:40.130
The average atomic mass of sulfur is 32.06

00:01:40.130 --> 00:01:41.970
and so if I had a mole of it,

00:01:41.970 --> 00:01:44.150
it would be 32.06 grams,

00:01:44.150 --> 00:01:47.730
so we could put the 32.06
grams up here, if we like.

00:01:47.730 --> 00:01:52.360
This would be 32.06 grams

00:01:52.360 --> 00:01:54.300
in all of these cases 'cause once again,

00:01:54.300 --> 00:01:55.830
if you have a mole of
each of these compounds,

00:01:55.830 --> 00:01:56.980
you're going to have a mole of sulfur

00:01:56.980 --> 00:01:59.540
because you only see one sulfur in these,

00:01:59.540 --> 00:02:01.500
in each of these formulas,

00:02:01.500 --> 00:02:04.040
but the big picture is
in all of the cases,

00:02:04.040 --> 00:02:05.940
I'm gonna have the same
value in the numerator,

00:02:05.940 --> 00:02:08.830
so I want to have the highest percentage,

00:02:08.830 --> 00:02:12.810
I would want to minimize the
value in the denominator.

00:02:12.810 --> 00:02:14.410
So I would really want to see which one

00:02:14.410 --> 00:02:16.270
would have the lowest denominator,

00:02:16.270 --> 00:02:18.340
or which one would have the lowest mass

00:02:18.340 --> 00:02:19.580
for a mole of the molecules

00:02:19.580 --> 00:02:20.800
or another way of thinking about it,

00:02:20.800 --> 00:02:23.680
which of them will have
the lowest molar mass?

00:02:23.680 --> 00:02:25.720
And you could see very clearly

00:02:25.720 --> 00:02:27.730
that this compound right over here

00:02:27.730 --> 00:02:30.750
has the lower, lowest molar mass.

00:02:30.750 --> 00:02:32.060
So we're done.

00:02:32.060 --> 00:02:35.600
This has the highest
percentage of sulfur by mass

00:02:35.600 --> 00:02:38.170
because per mole, it has
the same mass of sulfur

00:02:38.170 --> 00:02:39.310
as everything else,

00:02:39.310 --> 00:02:41.776
but it has the lowest total mass,

00:02:41.776 --> 00:02:43.840
so it's gonna have the
highest percentage of sulfur.

00:02:43.840 --> 00:02:44.980
So a quick way to do it,

00:02:44.980 --> 00:02:47.200
we just looked at the lowest molar mass.

00:02:47.200 --> 00:02:49.760
You could have gone and taken 32.06

00:02:49.760 --> 00:02:51.220
and divided by each of these values

00:02:51.220 --> 00:02:52.070
and figured out a percentage.

00:02:52.070 --> 00:02:53.890
Well, they're not asking us
to figure out the percentage.

00:02:53.890 --> 00:02:56.180
They're saying which one
has the highest percentage?

00:02:56.180 --> 00:02:59.253
And that would be this second
compound right over there.


Effects of transatlantic voyages, 1492-1607

WEBVTT
Kind: captions
Language: en

00:00:00.150 --> 00:00:01.530
- [Instructor] When Christopher Columbus

00:00:01.530 --> 00:00:03.420
first arrived in the Americas,

00:00:03.420 --> 00:00:05.900
he had no way of knowing that he had

00:00:05.900 --> 00:00:08.220
set off a complex chain of events

00:00:08.220 --> 00:00:09.440
that would lead to everything

00:00:09.440 --> 00:00:13.000
from humanity's largest
demographic disaster,

00:00:13.000 --> 00:00:16.780
to the founding of a new
nation nearly 300 years later,

00:00:16.780 --> 00:00:19.800
to you watching a video about the history

00:00:19.800 --> 00:00:22.530
of that nation right at this very moment.

00:00:22.530 --> 00:00:23.890
It's strange, right?

00:00:23.890 --> 00:00:26.400
Columbus's voyages to the New World

00:00:26.400 --> 00:00:30.000
and those of the navigators and
settlers who came after him,

00:00:30.000 --> 00:00:32.330
changed the worlds to an extent

00:00:32.330 --> 00:00:34.930
rarely seen in human history.

00:00:34.930 --> 00:00:37.510
Let's briefly review the effects

00:00:37.510 --> 00:00:40.420
of these transatlantic voyages on Europe,

00:00:40.420 --> 00:00:45.420
Africa, and the Americas
between 1492 and 1607,

00:00:45.460 --> 00:00:47.700
the period between first contact

00:00:47.700 --> 00:00:50.840
and the establishment
of the first permanent

00:00:50.840 --> 00:00:53.910
English settlement in the
Americas at Jamestown.

00:00:53.910 --> 00:00:56.640
So you might call this the pre-British era

00:00:56.640 --> 00:00:58.740
of colonization in the Americas.

00:00:58.740 --> 00:01:01.470
So what changes did these voyages cause?

00:01:01.470 --> 00:01:03.860
Well, there were demographic changes,

00:01:03.860 --> 00:01:05.940
and by demographic I mean shifts

00:01:05.940 --> 00:01:08.370
in the structure of populations.

00:01:08.370 --> 00:01:10.990
The indigenous populations of the Americas

00:01:10.990 --> 00:01:13.970
faced a catastrophic decline in numbers

00:01:13.970 --> 00:01:17.160
as a result of diseases
carried by Europeans.

00:01:17.160 --> 00:01:20.570
On the flip side, the
populations of Africa and Europe

00:01:20.570 --> 00:01:23.670
grew with the introduction
of nutritious foods

00:01:23.670 --> 00:01:26.730
found in the Americas
like potatoes and corn.

00:01:26.730 --> 00:01:30.880
Contact also led to the
creation of new cultural groups,

00:01:30.880 --> 00:01:34.270
as indigenous people,
Europeans, and Africans

00:01:34.270 --> 00:01:36.880
mixed in the New World
and had children together.

00:01:36.880 --> 00:01:40.660
The transatlantic voyages
also led to economic changes,

00:01:40.660 --> 00:01:44.080
including shifts in the
systems of money and labor.

00:01:44.080 --> 00:01:49.050
Spain extracted gold and silver
from the New World by force,

00:01:49.050 --> 00:01:51.720
compelling indigenous
people and then later

00:01:51.720 --> 00:01:54.680
enslaved Africans to labor in mines.

00:01:54.680 --> 00:01:56.810
These riches flooded into Europe

00:01:56.810 --> 00:01:59.150
and caused a huge increase in prices,

00:01:59.150 --> 00:02:00.960
which may have led to the development

00:02:00.960 --> 00:02:03.080
of banking and capitalism there.

00:02:03.080 --> 00:02:06.730
And European demand for
laborers in New World mines

00:02:06.730 --> 00:02:10.680
and plantations led to the
expansion of the slave trade,

00:02:10.680 --> 00:02:12.340
resulting in the forced migration

00:02:12.340 --> 00:02:15.150
of millions of African
people to the Americas.

00:02:15.150 --> 00:02:17.910
Columbus's discovery also fostered

00:02:17.910 --> 00:02:20.330
political changes in
Europe and the New World,

00:02:20.330 --> 00:02:21.960
as other European countries wanted

00:02:21.960 --> 00:02:23.590
to claim colonies of their own.

00:02:23.590 --> 00:02:26.560
And the power structure
among indigenous nations

00:02:26.560 --> 00:02:30.320
changed, too, with the
addition of European allies

00:02:30.320 --> 00:02:33.500
and the destruction of large
portions of the population,

00:02:33.500 --> 00:02:37.140
leading to the downfall of
powerful empires like the Aztecs.

00:02:37.140 --> 00:02:39.540
The cultures of indigenous people changed,

00:02:39.540 --> 00:02:42.340
as Europeans introduced new material goods

00:02:42.340 --> 00:02:44.440
and animals into their environment.

00:02:44.440 --> 00:02:47.410
For example, the Spanish
brought horses to North America,

00:02:47.410 --> 00:02:49.700
changing the society of plains people,

00:02:49.700 --> 00:02:53.610
who could now hunt and follow
herds of bison on horseback.

00:02:53.610 --> 00:02:57.330
And new religious practices
also emerged in the Americas,

00:02:57.330 --> 00:03:00.520
as indigenous peoples
combined their own beliefs

00:03:00.520 --> 00:03:02.830
with those of Catholicism.

00:03:02.830 --> 00:03:06.140
By examining the effects
of transatlantic voyages,

00:03:06.140 --> 00:03:08.010
what we're really doing is practicing

00:03:08.010 --> 00:03:10.120
the skill of causation.

00:03:10.120 --> 00:03:11.810
This is probably the most important

00:03:11.810 --> 00:03:13.760
skill in the historian's toolbox.

00:03:13.760 --> 00:03:15.510
Understanding and arguing about

00:03:15.510 --> 00:03:17.780
what caused an event to happen,

00:03:17.780 --> 00:03:22.120
or what consequences an event
had on society later on.

00:03:22.120 --> 00:03:24.330
Now this seems pretty straightforward.

00:03:24.330 --> 00:03:27.650
For example, a cause and
effect statement might be,

00:03:27.650 --> 00:03:31.690
I slept through my alarm this
morning, so I missed the bus.

00:03:31.690 --> 00:03:33.690
Cause: oversleeping.

00:03:33.690 --> 00:03:36.040
Effect: missed bus.

00:03:36.040 --> 00:03:39.690
Notice that the effect has
to happen after the cause.

00:03:39.690 --> 00:03:42.220
Missing the bus didn't
cause me to oversleep.

00:03:42.220 --> 00:03:44.430
So until we invent the time machine,

00:03:44.430 --> 00:03:48.320
effects must happen later than causes.

00:03:48.320 --> 00:03:51.460
But there can be a few
pitfalls to watch out for

00:03:51.460 --> 00:03:54.340
when we try to determine
causes and effects.

00:03:54.340 --> 00:03:58.240
First, not everything has
just one cause and one effect.

00:03:58.240 --> 00:04:00.920
For example, maybe I
slept through my alarm

00:04:00.920 --> 00:04:04.440
because I stayed up too
late last night watching TV.

00:04:04.440 --> 00:04:07.050
That's another cause for missing the bus.

00:04:07.050 --> 00:04:09.340
And there could be more than one effect

00:04:09.340 --> 00:04:10.980
of sleeping through the alarm,

00:04:10.980 --> 00:04:12.750
not just missing the bus,

00:04:12.750 --> 00:04:15.530
but also missing my test in first period.

00:04:15.530 --> 00:04:18.780
Which was the most important
cause of missing the bus,

00:04:18.780 --> 00:04:21.470
oversleeping or watching too much TV?

00:04:21.470 --> 00:04:24.000
And which was the more important effect

00:04:24.000 --> 00:04:25.450
of sleeping through my alarm,

00:04:25.450 --> 00:04:28.220
missing the bus or missing the test?

00:04:28.220 --> 00:04:31.370
These kinds of questions are
what historians argue about.

00:04:31.370 --> 00:04:35.460
Which was the most important
cause of Atlantic exploration,

00:04:35.460 --> 00:04:37.890
competition between European countries,

00:04:37.890 --> 00:04:41.340
or the desire to convert
new people to Catholicism?

00:04:41.340 --> 00:04:44.420
Another potential pitfall
is one you might have seen

00:04:44.420 --> 00:04:47.180
in a science class or in statistics,

00:04:47.180 --> 00:04:51.530
which is correlation
does not imply causation.

00:04:51.530 --> 00:04:55.310
In other words, two events
aren't necessarily related

00:04:55.310 --> 00:04:59.480
just because they happened
close together in time or space.

00:04:59.480 --> 00:05:03.320
For example, although epidemic
diseases led to the deaths

00:05:03.320 --> 00:05:06.050
of indigenous people in the New World

00:05:06.050 --> 00:05:10.230
at the same time that the
discovery of new foodstuffs

00:05:10.230 --> 00:05:12.800
increased the population
of Europe and Africa,

00:05:12.800 --> 00:05:15.390
the introduction of diseases didn't cause

00:05:15.390 --> 00:05:17.450
those populations to increase.

00:05:17.450 --> 00:05:20.900
Those were just two things
that happened simultaneously.

00:05:20.900 --> 00:05:23.500
One way you can check whether one event

00:05:23.500 --> 00:05:25.520
was caused by an earlier one,

00:05:25.520 --> 00:05:29.450
is to ask whether event
B would have happened

00:05:29.450 --> 00:05:31.880
whether or not event A happened.

00:05:31.880 --> 00:05:34.010
The populations of Europe and Africa

00:05:34.010 --> 00:05:36.590
would likely have
increased with the addition

00:05:36.590 --> 00:05:38.550
of those new foods even if there

00:05:38.550 --> 00:05:41.250
hadn't been any epidemic diseases at all.

00:05:41.250 --> 00:05:43.720
The last thing that we
wanna take into account

00:05:43.720 --> 00:05:45.640
while we're thinking about causation,

00:05:45.640 --> 00:05:47.630
is the difference between short

00:05:47.630 --> 00:05:50.110
and long-term effects of an event.

00:05:50.110 --> 00:05:52.220
Missing my first period test might

00:05:52.220 --> 00:05:54.510
be a short-term effect of oversleeping,

00:05:54.510 --> 00:05:57.710
but failing the class
because I missed tests

00:05:57.710 --> 00:05:59.870
would be a long-term effect.

00:05:59.870 --> 00:06:01.570
And maybe because I failed that test

00:06:01.570 --> 00:06:04.750
I ended up focusing on a
different subject in school,

00:06:04.750 --> 00:06:06.620
and heading into a different career.

00:06:06.620 --> 00:06:08.950
That would be a really long-term effect.

00:06:08.950 --> 00:06:12.140
Think about the effects
of transatlantic voyages

00:06:12.140 --> 00:06:13.570
that we've discussed,

00:06:13.570 --> 00:06:15.290
and see if you can categorize them

00:06:15.290 --> 00:06:18.520
into short-term effects
and long-term effects.

00:06:18.520 --> 00:06:22.650
You might find that some
things fit into both categories

00:06:22.650 --> 00:06:25.330
as processes that started immediately

00:06:25.330 --> 00:06:27.930
but then went on for a long time,

00:06:27.930 --> 00:06:30.750
like the epidemic
diseases that immediately

00:06:30.750 --> 00:06:32.430
affected indigenous people,

00:06:32.430 --> 00:06:36.030
but then continued to reshape
the demographic composition

00:06:36.030 --> 00:06:38.770
of the Americas for hundreds of years.

00:06:38.770 --> 00:06:41.770
So let's recap what we've
learned about causation.

00:06:41.770 --> 00:06:44.870
First, historians argue about causation

00:06:44.870 --> 00:06:48.820
as they try to pin down the
reason an event happened.

00:06:48.820 --> 00:06:53.110
Second, causes must happen before effects.

00:06:53.110 --> 00:06:57.200
Third, a single event might
have more than one cause

00:06:57.200 --> 00:06:58.840
or more than one effect,

00:06:58.840 --> 00:07:01.100
and some causes and effects may be

00:07:01.100 --> 00:07:02.930
more important than others.

00:07:02.930 --> 00:07:05.710
Fourth, events that
happened near to each other

00:07:05.710 --> 00:07:09.640
in time or space, aren't
necessarily related

00:07:09.640 --> 00:07:11.970
by a cause and effect relationship.

00:07:11.970 --> 00:07:13.280
Coincidences happen.

00:07:13.280 --> 00:07:16.290
And lastly, causes may have both short

00:07:16.290 --> 00:07:19.730
and long-term effects, immediate results,

00:07:19.730 --> 00:07:21.410
and downstream impacts that go

00:07:21.410 --> 00:07:23.553
far beyond the time in question.


Equivalent fractions on number lines

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:02.100
- [Instructor] So they are telling us that

00:00:02.100 --> 00:00:04.980
r fifths is equal to eight tenths

00:00:04.980 --> 00:00:08.410
and we need to figure out
what is r going to be equal to

00:00:08.410 --> 00:00:10.720
and they help us out with this number line

00:00:10.720 --> 00:00:12.970
where they've put eight
tenths on the number line.

00:00:12.970 --> 00:00:15.910
That makes sense because
to go from zero to one,

00:00:15.910 --> 00:00:19.900
they've split it into
one, two, three, four,

00:00:19.900 --> 00:00:24.900
five, six, seven, eight,
nine, ten equal jumps

00:00:25.520 --> 00:00:28.540
and at this point, we have
gone eight of those ten

00:00:28.540 --> 00:00:32.110
equal jumps between zero and
one so that is eight tenths

00:00:32.110 --> 00:00:35.230
and they've also labeled one fifth for us

00:00:35.230 --> 00:00:37.835
and one way to think about it is

00:00:37.835 --> 00:00:39.530
if we look at these bold lines,

00:00:39.530 --> 00:00:40.570
zero,

00:00:40.570 --> 00:00:41.880
one,

00:00:41.880 --> 00:00:42.880
two,

00:00:42.880 --> 00:00:43.960
three,

00:00:43.960 --> 00:00:45.020
four,

00:00:45.020 --> 00:00:45.940
five,

00:00:45.940 --> 00:00:49.370
if you just look at the purple,
we have five equal jumps.

00:00:49.370 --> 00:00:52.730
So each of those jumps are a fifth

00:00:52.730 --> 00:00:54.930
and so it makes sense that our first jump

00:00:54.930 --> 00:00:56.750
right over here gets us to one fifth

00:00:56.750 --> 00:00:57.583
and you can see that

00:00:57.583 --> 00:01:00.320
that is equivalent to two of the tenths.

00:01:00.320 --> 00:01:03.890
I'll just write that up here
so we can see that equivalence.

00:01:03.890 --> 00:01:06.310
One fifth is equal to two tenths

00:01:06.310 --> 00:01:09.480
but how many fifths is
equal to eight tenths?

00:01:09.480 --> 00:01:11.913
Pause this video and try to figure it out.

00:01:13.440 --> 00:01:16.940
All right, well this is one fifth.

00:01:16.940 --> 00:01:20.730
If we do one more jump of a
fifth, that would be two fifths.

00:01:20.730 --> 00:01:22.480
Then if we go another fifth,

00:01:22.480 --> 00:01:24.160
that will get us to three fifths

00:01:24.160 --> 00:01:25.810
and then if we go another fifth,

00:01:25.810 --> 00:01:28.210
that will get us to four fifths

00:01:28.210 --> 00:01:31.520
which we see is exactly
equivalent to eight tenths

00:01:31.520 --> 00:01:34.470
and that makes sense
because we also saw that

00:01:34.470 --> 00:01:38.040
every fifth is equivalent to two tenths.

00:01:38.040 --> 00:01:40.000
So four fifths is going to be equivalent

00:01:40.000 --> 00:01:41.610
to eight of those tenths.

00:01:41.610 --> 00:01:43.680
We see that very clearly right over here

00:01:43.680 --> 00:01:46.220
and so r is equal to four.

00:01:46.220 --> 00:01:47.690
Four fifths is equal to eight tenths.

00:01:47.690 --> 00:01:49.640
So r is equal to four.

00:01:49.640 --> 00:01:50.943
Let's do another example.

00:01:52.100 --> 00:01:55.120
What fraction is equivalent to point A?

00:01:55.120 --> 00:01:57.870
So pause this video and see
if you can figure that out.

00:01:58.800 --> 00:02:02.000
All right, so let's figure
out where point A is.

00:02:02.000 --> 00:02:04.230
So to go from zero to one,

00:02:04.230 --> 00:02:09.230
we have one, two, three,
four, five, six equal jumps.

00:02:10.530 --> 00:02:12.700
So each of these jumps are a sixth.

00:02:12.700 --> 00:02:16.340
So going from zero, one jump
will get us to one sixth,

00:02:16.340 --> 00:02:19.300
then two sixths, then three sixths,

00:02:19.300 --> 00:02:23.280
then four sixths, then five sixths

00:02:23.280 --> 00:02:26.990
and so can we see four
sixths in the choices?

00:02:26.990 --> 00:02:28.950
No I do not see four sixths.

00:02:28.950 --> 00:02:32.720
So we have to find an equivalent
fraction to four sixths.

00:02:32.720 --> 00:02:34.440
So we could go choice by choice.

00:02:34.440 --> 00:02:36.810
The first choice has five sixths.

00:02:36.810 --> 00:02:39.380
Well we very clearly see that five sixths

00:02:39.380 --> 00:02:40.960
would be here on the number line

00:02:40.960 --> 00:02:43.450
which is clearly a different
place than four sixths.

00:02:43.450 --> 00:02:46.150
So we could rule out this first choice

00:02:46.150 --> 00:02:48.300
but what about these other ones?

00:02:48.300 --> 00:02:49.980
Let's see, let's see
how we can think about.

00:02:49.980 --> 00:02:53.690
Four fifths versus four sixths.

00:02:53.690 --> 00:02:55.450
Could those be equivalent?

00:02:55.450 --> 00:02:59.760
If I have four out of five
versus four out of six,

00:02:59.760 --> 00:03:01.520
that's not feeling too good

00:03:01.520 --> 00:03:05.060
so I'm gonna put like a
curly line through it.

00:03:05.060 --> 00:03:06.630
That's not feeling right,
that if I could have

00:03:06.630 --> 00:03:10.490
four out of five equal jumps
or five equal sections,

00:03:10.490 --> 00:03:11.323
that that would be the same

00:03:11.323 --> 00:03:12.810
as four out of six equal sections.

00:03:12.810 --> 00:03:14.760
If I divided it into six equal sections,

00:03:14.760 --> 00:03:16.300
each of those sections are
going to be a little bit

00:03:16.300 --> 00:03:19.200
smaller than if I divided
into five equal sections.

00:03:19.200 --> 00:03:20.520
So if I have four of each,

00:03:20.520 --> 00:03:21.740
they're going to be a different value.

00:03:21.740 --> 00:03:23.010
Actually when I talk it out like that,

00:03:23.010 --> 00:03:26.100
I feel even more confident
that I could rule this one out.

00:03:26.100 --> 00:03:28.750
Now what about six fourths?

00:03:28.750 --> 00:03:29.620
Well one way to think about it

00:03:29.620 --> 00:03:32.080
is four fourths would be equal to one.

00:03:32.080 --> 00:03:34.680
So six fourths is going to be beyond one.

00:03:34.680 --> 00:03:36.890
So it's definitely not
going to be where A is,

00:03:36.890 --> 00:03:38.710
so I could rule that one out

00:03:38.710 --> 00:03:41.160
and we could say oh, well
maybe it's just going to be D

00:03:41.160 --> 00:03:43.000
but let's make sure that this makes sense.

00:03:43.000 --> 00:03:46.790
Two thirds, what does
two thirds look like?

00:03:46.790 --> 00:03:50.220
Well let me try to divide
this part of the number line

00:03:50.220 --> 00:03:54.730
from zero to one into thirds,
into three equal sections.

00:03:54.730 --> 00:03:57.150
So I have zero there

00:03:57.150 --> 00:03:59.760
and then that could be one third,

00:03:59.760 --> 00:04:02.190
two thirds and then three thirds.

00:04:02.190 --> 00:04:03.710
That looks like three equal sections.

00:04:03.710 --> 00:04:06.170
So this is one third,

00:04:06.170 --> 00:04:09.600
this is two thirds, I'm
making another jump of a third

00:04:09.600 --> 00:04:12.580
and then when I get to one,
of course that is three thirds

00:04:12.580 --> 00:04:14.500
or we could have said six sixths

00:04:14.500 --> 00:04:15.920
and so point A,

00:04:15.920 --> 00:04:18.220
which is right over here
I'm writing over it,

00:04:18.220 --> 00:04:21.140
that is indeed equal to two thirds.

00:04:21.140 --> 00:04:25.040
You can see each jump of a
third is equal to two sixths.

00:04:25.040 --> 00:04:28.690
So it makes sense that four
sixths is equal to two thirds

00:04:28.690 --> 00:04:31.350
or that two thirds is equal to four sixths

00:04:31.350 --> 00:04:32.913
so I like this one.


Comparing fractions word problems

WEBVTT
Kind: captions
Language: en

00:00:00.290 --> 00:00:02.320
- [Instructor] We're told
that Katie made a table

00:00:02.320 --> 00:00:06.020
to show how much time she
spent on homework last week,

00:00:06.020 --> 00:00:08.010
and so we can see the different subjects

00:00:08.010 --> 00:00:10.930
and then how much she
spent in terms of hours.

00:00:10.930 --> 00:00:12.860
So in math, she spent 3/4 of an hour,

00:00:12.860 --> 00:00:14.790
reading, 7/8 of an hour,

00:00:14.790 --> 00:00:17.070
writing, 3/6 of an hour,

00:00:17.070 --> 00:00:19.400
and then science, 5/10 of an hour.

00:00:19.400 --> 00:00:21.430
And then they ask us on which activities

00:00:21.430 --> 00:00:26.010
did Katie spend more than 2/3 of an hour?

00:00:26.010 --> 00:00:28.903
So pause this video and see
if you can figure that out.

00:00:30.050 --> 00:00:32.680
All right, so we essentially
have to figure out

00:00:32.680 --> 00:00:37.620
which of these fractions are
greater than 2/3 of an hour?

00:00:37.620 --> 00:00:39.020
Which are greater than 2/3?

00:00:39.020 --> 00:00:41.530
And this is all in terms of hours.

00:00:41.530 --> 00:00:44.580
So first let's just think
about representing 2/3,

00:00:44.580 --> 00:00:46.130
so let me do it like this,

00:00:46.130 --> 00:00:47.190
and I'm going to hand draw it

00:00:47.190 --> 00:00:49.130
so it's not going to be perfect.

00:00:49.130 --> 00:00:52.770
But if this is a whole right over here,

00:00:52.770 --> 00:00:55.150
I could split it into
three equal sections,

00:00:55.150 --> 00:00:56.630
so I'm gonna try to do that.

00:00:56.630 --> 00:00:59.220
Let me see, does that look about right?

00:00:59.220 --> 00:01:00.440
So three equal sections,

00:01:00.440 --> 00:01:03.540
so that would be 1/3 that would be 1/3,

00:01:03.540 --> 00:01:04.870
and then that would be 1/3,

00:01:04.870 --> 00:01:08.380
and then 2/3 would be two of them,

00:01:08.380 --> 00:01:09.640
so I'll pick these first two.

00:01:09.640 --> 00:01:11.140
Well, it doesn't have
to be those first two,

00:01:11.140 --> 00:01:14.003
so that's 1/3 and then 2/3.

00:01:15.070 --> 00:01:17.150
So let's see if we can
draw a similar visual

00:01:17.150 --> 00:01:18.860
for each of these.

00:01:18.860 --> 00:01:21.660
So what about 3/4?

00:01:21.660 --> 00:01:22.720
So once again,

00:01:22.720 --> 00:01:25.930
let's make this a whole.

00:01:25.930 --> 00:01:27.720
And now if I want to
think in terms of fourths,

00:01:27.720 --> 00:01:29.580
I have to divide it into
four equal sections,

00:01:29.580 --> 00:01:30.776
so let's see.

00:01:30.776 --> 00:01:32.970
If I divide it, that will
be two equal sections,

00:01:32.970 --> 00:01:34.590
and then I can divide each of those

00:01:34.590 --> 00:01:37.530
into two equal sections, so let's see.

00:01:37.530 --> 00:01:39.320
Maybe something like this,

00:01:39.320 --> 00:01:42.050
and then like this.

00:01:42.050 --> 00:01:45.050
So it's hand drawn, but these
are four equal sections,

00:01:45.050 --> 00:01:46.870
and so this would be a fourth,

00:01:46.870 --> 00:01:49.180
that would be a fourth,
and that would be a fourth,

00:01:49.180 --> 00:01:50.013
and that would be a fourth.

00:01:50.013 --> 00:01:51.560
4/4 make a whole,

00:01:51.560 --> 00:01:54.880
so three of those fourths would be one,

00:01:54.880 --> 00:01:57.220
two, and then three.

00:01:57.220 --> 00:01:59.820
And so you can see, and
I've drawn it pretty close.

00:01:59.820 --> 00:02:02.040
It's not perfect 'cause it's hand drawn,

00:02:02.040 --> 00:02:06.930
but you can see that 3/4 is
more of a whole than 2/3.

00:02:06.930 --> 00:02:08.800
It's greater than 2/3.

00:02:08.800 --> 00:02:12.450
So Katie spent more than
2/3 of an hour on math

00:02:12.450 --> 00:02:14.810
because 3/4 is greater than 2/3,

00:02:14.810 --> 00:02:16.870
so I like this one right over there.

00:02:16.870 --> 00:02:18.840
I'll just put a square
or circle around the ones

00:02:18.840 --> 00:02:20.110
that she spent that extra time on

00:02:20.110 --> 00:02:23.430
or the more, the greater
than 2/3 of an hour on.

00:02:23.430 --> 00:02:26.008
And I'll think about reading, 7/8.

00:02:26.008 --> 00:02:28.570
So to compare that, I will, once again,

00:02:28.570 --> 00:02:29.963
make a whole here,

00:02:30.860 --> 00:02:33.050
and then I want to think about 7/8,

00:02:33.050 --> 00:02:35.300
so I'm gonna split into
eight equal sections.

00:02:35.300 --> 00:02:38.050
So let's see, that will split
into two equal sections,

00:02:38.050 --> 00:02:42.730
and then, then I can go
to four equal sections,

00:02:42.730 --> 00:02:45.690
and then if I split
each of those into two,

00:02:45.690 --> 00:02:48.080
this would be eight equal sections,

00:02:48.080 --> 00:02:52.960
so it may look something like this.

00:02:52.960 --> 00:02:56.750
Not perfect, but I think
it will get the job done.

00:02:56.750 --> 00:02:58.620
So each of these are 1/8,

00:02:58.620 --> 00:03:03.620
so 7/8 are going to be one, two, three,

00:03:03.850 --> 00:03:08.850
four, five, six, and 7/8.

00:03:08.860 --> 00:03:10.060
Clearly, once again,

00:03:10.060 --> 00:03:12.940
greater than our 2/3
that we have in purple.

00:03:12.940 --> 00:03:17.250
So she spent more than
2/3 of an hour on reading.

00:03:17.250 --> 00:03:18.310
Now what about writing?

00:03:18.310 --> 00:03:22.160
3/6, what would that look like?

00:03:22.160 --> 00:03:25.470
Well, I'll do another one right over here.

00:03:25.470 --> 00:03:27.970
So if that is a whole,

00:03:27.970 --> 00:03:29.480
well, actually let me
split it to thirds first,

00:03:29.480 --> 00:03:31.300
since we already have a
bit of a reference there.

00:03:31.300 --> 00:03:33.640
We can look up there and we can see.

00:03:33.640 --> 00:03:35.970
Those are thirds and if we
split each of those into two,

00:03:35.970 --> 00:03:37.440
we're going to have sixths,

00:03:37.440 --> 00:03:40.200
'cause we'll have six equal sections.

00:03:40.200 --> 00:03:43.733
So it would look something like that,

00:03:44.670 --> 00:03:47.000
and then three of those six,

00:03:47.000 --> 00:03:51.040
well, that's one, two, and three.

00:03:51.040 --> 00:03:54.160
So we can see that 3/6 is less than 2/3

00:03:54.160 --> 00:03:55.910
so I'm not gonna circle that one.

00:03:55.910 --> 00:03:58.590
She didn't spend more than
2/3 of an hour on writing,

00:03:58.590 --> 00:04:01.970
and then last, but not least, science.

00:04:01.970 --> 00:04:03.660
5/10.

00:04:03.660 --> 00:04:04.910
Well once again,

00:04:04.910 --> 00:04:08.240
we could make a whole here,

00:04:08.240 --> 00:04:09.230
and let's see.

00:04:09.230 --> 00:04:11.250
I want to do into 10 equal sections,

00:04:11.250 --> 00:04:13.760
so that's two equal sections,

00:04:13.760 --> 00:04:16.149
and each of these, I can do
into five equal sections.

00:04:16.149 --> 00:04:16.982
Let's see.

00:04:16.982 --> 00:04:20.940
One, two, three,

00:04:20.940 --> 00:04:24.570
four, five, I can do a
little bit neater than that,

00:04:24.570 --> 00:04:27.540
three, four and five,

00:04:27.540 --> 00:04:29.853
and then one,

00:04:31.010 --> 00:04:33.403
two, three,

00:04:34.440 --> 00:04:36.820
four and five.

00:04:36.820 --> 00:04:38.120
I can make it a little bit neater,

00:04:38.120 --> 00:04:39.210
but I think this will get us

00:04:39.210 --> 00:04:40.840
to where we need to get to.

00:04:40.840 --> 00:04:42.020
So these are each 1/10.

00:04:42.020 --> 00:04:44.190
I could write 1/10, 1/10,

00:04:44.190 --> 00:04:45.570
I could do that for all 10 of these,

00:04:45.570 --> 00:04:47.620
but we care about five of these tenths,

00:04:47.620 --> 00:04:50.120
so one, two,

00:04:50.120 --> 00:04:54.180
three, four, five of those tenths.

00:04:54.180 --> 00:04:57.280
And notice, 5/10 is the
exact same thing as 3/6,

00:04:57.280 --> 00:05:00.450
and like 3/6, it is less than 2/3.

00:05:00.450 --> 00:05:02.820
So which activities did
Katie spend more than 2/3

00:05:02.820 --> 00:05:04.482
of an hour on?

00:05:04.482 --> 00:05:05.782
Clearly, math and reading.