Dividing fractions and whole number word problems

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:01.390
- [Instructor] We are told

00:00:01.390 --> 00:00:04.820
that Billy has 1/4 of
a pound of trail mix.

00:00:04.820 --> 00:00:06.920
He wants to share it equally

00:00:06.920 --> 00:00:09.580
between himself and his brother.

00:00:09.580 --> 00:00:12.810
How much trail mix would they each get?

00:00:12.810 --> 00:00:15.950
So pause this video and
try to figure that out.

00:00:15.950 --> 00:00:18.380
All right, now let's work
through this together.

00:00:18.380 --> 00:00:22.620
So Billy starts with 1/4
of a pound of trail mix.

00:00:22.620 --> 00:00:24.970
So how can we represent 1/4?

00:00:24.970 --> 00:00:28.550
Well, if this is a whole pound,

00:00:28.550 --> 00:00:31.100
let's just imagine this
rectangle is a whole pound,

00:00:31.100 --> 00:00:33.350
I could divide it into
four equal sections.

00:00:33.350 --> 00:00:37.520
So let's see, this would be
roughly two equal sections,

00:00:37.520 --> 00:00:40.460
and then if I were to divide
each of those into two,

00:00:40.460 --> 00:00:42.903
now I have four equal sections.

00:00:44.440 --> 00:00:47.950
So Billy is starting with 1/4 of a pound.

00:00:47.950 --> 00:00:51.350
Draw a little bit, try to make
it a little bit more equal.

00:00:51.350 --> 00:00:53.570
Billy is starting with 1/4 of a pound,

00:00:53.570 --> 00:00:55.570
so let's say that is that 1/4 of a pound

00:00:55.570 --> 00:00:56.690
that he starts with.

00:00:56.690 --> 00:00:58.750
He's starting with 1/4 of a pound,

00:00:58.750 --> 00:01:00.370
and he wants to share it equally

00:01:00.370 --> 00:01:02.110
between himself and his brother.

00:01:02.110 --> 00:01:03.700
So he wants to share it equally

00:01:03.700 --> 00:01:06.300
between two people right over here.

00:01:06.300 --> 00:01:08.810
So what we wanna do is essentially say,

00:01:08.810 --> 00:01:11.200
let's start with our
total amount of trail mix,

00:01:11.200 --> 00:01:15.910
and then we're going to divide
it into two equal shares.

00:01:15.910 --> 00:01:19.100
So when they ask us how much
trail mix would they each get,

00:01:19.100 --> 00:01:20.040
we're really trying to figure out

00:01:20.040 --> 00:01:24.170
what is this 1/4 divided by two?

00:01:24.170 --> 00:01:25.498
So what would that be?

00:01:25.498 --> 00:01:27.690
Well, what if we were to take

00:01:27.690 --> 00:01:31.700
all of these four equal sections
and divide them into two?

00:01:31.700 --> 00:01:34.350
So I'll divide that one into two.

00:01:34.350 --> 00:01:36.690
I will divide this one into two.

00:01:36.690 --> 00:01:38.830
I will divide this one into two,

00:01:38.830 --> 00:01:41.670
and then I would divide this one into two.

00:01:41.670 --> 00:01:43.600
And now what are each of these sections?

00:01:43.600 --> 00:01:45.620
Well, each of these are now 1/8.

00:01:45.620 --> 00:01:47.350
That's a 1/8 right over there,

00:01:47.350 --> 00:01:49.690
the whole is divided into
eight equal sections.

00:01:49.690 --> 00:01:53.500
And so you can see, that
when you start with that 1/4,

00:01:53.500 --> 00:01:57.060
and you divide it into two equal sections,

00:01:57.060 --> 00:02:01.940
so one section and two equal
sections right over there,

00:02:01.940 --> 00:02:06.130
each of these is equal to 1/8.

00:02:06.130 --> 00:02:11.130
So 1/4 divided by two is equal to 1/8.

00:02:12.230 --> 00:02:13.643
Let's do another example.

00:02:14.578 --> 00:02:18.360
So we are told Matt is
filling containers of rice.

00:02:18.360 --> 00:02:23.360
Each container holds 1/4
of a kilogram of rice.

00:02:23.660 --> 00:02:28.240
And then they tell us if Matt
has three kilograms of rice,

00:02:28.240 --> 00:02:31.100
how many containers can he fill?

00:02:31.100 --> 00:02:32.800
So like always, pause this video,

00:02:32.800 --> 00:02:35.160
and see if you can figure that out.

00:02:35.160 --> 00:02:37.110
All right, so let's think
about what's going on.

00:02:37.110 --> 00:02:40.630
We're starting with a total
amount, three kilograms of rice,

00:02:40.630 --> 00:02:43.430
and we're trying to divide
it into equal sections.

00:02:43.430 --> 00:02:46.120
In this case we're trying to
divide it into equal sections

00:02:46.120 --> 00:02:48.400
of 1/4 of a kilogram.

00:02:48.400 --> 00:02:49.710
So we are trying to figure out

00:02:49.710 --> 00:02:54.710
what three divided by 1/4
is going to be equal to.

00:02:55.080 --> 00:02:57.510
Now to imagine that, let's
imagine three wholes,

00:02:57.510 --> 00:02:59.550
this would be three whole kilograms.

00:02:59.550 --> 00:03:04.360
So that is one whole, this is two wholes,

00:03:04.360 --> 00:03:06.450
trying to make them all the
same, but it's hand-drawn,

00:03:06.450 --> 00:03:09.610
so it's not as exact as I would like.

00:03:09.610 --> 00:03:12.400
So that's three whole kilograms here.

00:03:12.400 --> 00:03:15.300
And he wants to divide
it into sections of 1/4.

00:03:15.300 --> 00:03:17.240
So if you divide it into fourths,

00:03:17.240 --> 00:03:19.200
how many fourths are you going to have?

00:03:19.200 --> 00:03:20.540
Well, let's do that.

00:03:20.540 --> 00:03:22.700
So let's see, if we were
to divide it into halves,

00:03:22.700 --> 00:03:24.457
it would look like this.

00:03:25.960 --> 00:03:29.310
If you divide these
three wholes into halves.

00:03:29.310 --> 00:03:31.840
But then if you want to
divide it into fourths,

00:03:31.840 --> 00:03:34.450
it would look like this,

00:03:36.270 --> 00:03:38.863
I'm trying to get it as
close to equal sections.

00:03:39.770 --> 00:03:42.101
They should be exactly equal sections.

00:03:42.101 --> 00:03:45.330
So I am almost there.

00:03:45.330 --> 00:03:48.220
So there you have it.

00:03:48.220 --> 00:03:50.070
So I've just taken three wholes

00:03:50.070 --> 00:03:52.410
and I've divided it into fourths.

00:03:52.410 --> 00:03:54.440
So how many fourths are there?

00:03:54.440 --> 00:03:58.190
Well, there are one, two,
three, four, five, six,

00:03:58.190 --> 00:04:02.810
seven, eight, nine, 10, 11, 12 fourths.

00:04:02.810 --> 00:04:07.313
So three divided by 1/4 is equal to 12.

00:04:09.150 --> 00:04:10.840
And I encourage you to really think about

00:04:10.840 --> 00:04:12.770
why this is the case,

00:04:12.770 --> 00:04:14.357
that if we take a whole number like three

00:04:14.357 --> 00:04:15.850
and you divide it by 1/4,

00:04:15.850 --> 00:04:18.420
we're getting a value larger than three.

00:04:18.420 --> 00:04:21.410
And we're getting a value
that is four times three.

00:04:21.410 --> 00:04:23.543
Think about why that is the case.


Worked example: Identifying an element from its mass spectrum

WEBVTT
Kind: captions
Language: en

00:00:00.200 --> 00:00:01.360
- [Instructor] So let's say that we have

00:00:01.360 --> 00:00:03.000
some mystery substance here,

00:00:03.000 --> 00:00:04.660
and we know that it's a pure element,

00:00:04.660 --> 00:00:07.510
and we need to figure out what it is.

00:00:07.510 --> 00:00:10.040
Well, scientists have a method,

00:00:10.040 --> 00:00:11.240
and we go into the details,

00:00:11.240 --> 00:00:13.630
or more details, in other videos,

00:00:13.630 --> 00:00:18.630
called mass, sometimes it's
known as mass spectrometry

00:00:20.149 --> 00:00:21.899
or mass spectroscopy.

00:00:24.182 --> 00:00:26.860
It's a technique where you can
take a sample of a substance

00:00:26.860 --> 00:00:31.040
and think about the various atomic masses

00:00:31.040 --> 00:00:34.210
of the different isotopes
in that substance.

00:00:34.210 --> 00:00:36.230
And that's what we have right over here.

00:00:36.230 --> 00:00:38.990
They tell us the mass
spectrum for an average sample

00:00:38.990 --> 00:00:40.500
of a pure element is shown below.

00:00:40.500 --> 00:00:42.860
So let's say it's this pure element.

00:00:42.860 --> 00:00:44.360
So what this is telling us is,

00:00:44.360 --> 00:00:45.680
this looks like maybe, I don't know,

00:00:45.680 --> 00:00:50.110
let's call this 82% of our sample

00:00:50.110 --> 00:00:55.110
has an atomic mass of 88
universal atomic mass units.

00:00:55.330 --> 00:01:00.200
About, this looks like
about 7% of our sample

00:01:00.200 --> 00:01:04.460
has an atomic mass of 87
universal atomic mass units.

00:01:04.460 --> 00:01:07.390
It looks like 10% has an atomic mass

00:01:07.390 --> 00:01:09.830
of 86 universal atomic mass units,

00:01:09.830 --> 00:01:14.190
and it looks like about 1% of our sample

00:01:14.190 --> 00:01:18.140
has an atomic mass of 84
universal atomic mass units.

00:01:18.140 --> 00:01:20.260
And so from this information,

00:01:20.260 --> 00:01:23.390
we can try to estimate what
the average atomic mass

00:01:23.390 --> 00:01:25.320
of this mystery element is.

00:01:25.320 --> 00:01:30.013
We could calculate it as 0.82 times 88,

00:01:32.443 --> 00:01:35.610
plus, let's call this 7%,

00:01:35.610 --> 00:01:37.443
so 0.07 times 87,

00:01:41.329 --> 00:01:43.746
plus 10%, 0.1, times 86,

00:01:46.860 --> 00:01:48.823
plus, let's see, it should add up to 100%.

00:01:48.823 --> 00:01:50.740
This is 89,

00:01:50.740 --> 00:01:52.120
and then this gets us to 99,

00:01:52.120 --> 00:01:54.406
so then another 1%,

00:01:54.406 --> 00:01:58.270
0.01 times 84.

00:01:58.270 --> 00:02:01.410
And so if we were to do this calculation,

00:02:01.410 --> 00:02:02.750
this is our estimate

00:02:02.750 --> 00:02:05.810
of the average atomic
mass of this element.

00:02:05.810 --> 00:02:07.330
We could type this into a calculator

00:02:07.330 --> 00:02:08.410
and get some number

00:02:08.410 --> 00:02:10.940
and then look that up on a
periodic table of elements,

00:02:10.940 --> 00:02:12.870
or we could just try to estimate it.

00:02:12.870 --> 00:02:16.150
We can see that it's
going to be close to 88

00:02:16.150 --> 00:02:18.385
because that's where the
highest percentage is.

00:02:18.385 --> 00:02:20.050
When we're taking the weighted average,

00:02:20.050 --> 00:02:22.440
we have the highest
weight right over there.

00:02:22.440 --> 00:02:24.250
But these other isotopes,

00:02:24.250 --> 00:02:26.780
these other versions of the element

00:02:26.780 --> 00:02:28.270
that have a different number of neutrons,

00:02:28.270 --> 00:02:30.680
which changes its atomic mass,

00:02:30.680 --> 00:02:32.950
they're going to bring the average down.

00:02:32.950 --> 00:02:35.590
So our average atomic mass

00:02:35.590 --> 00:02:38.680
is going to be a little bit less than 88.

00:02:38.680 --> 00:02:40.980
So let's look up a
periodic table of elements.

00:02:41.960 --> 00:02:43.980
What element here has an atomic mass

00:02:43.980 --> 00:02:46.167
a little bit less than 88?

00:02:46.167 --> 00:02:48.980
Well, yttrium is 88.91,

00:02:48.980 --> 00:02:51.610
but we know it can't be that
because none of the isotopes

00:02:51.610 --> 00:02:54.110
have an atomic mass above 88.

00:02:54.110 --> 00:02:55.860
So we can rule out yttrium.

00:02:55.860 --> 00:02:57.660
Strontium is looking pretty good.

00:02:57.660 --> 00:02:58.990
It's exactly what we predicted,

00:02:58.990 --> 00:03:01.120
a little bit less than 88,

00:03:01.120 --> 00:03:03.520
and rubidium is a lot less than 88.

00:03:03.520 --> 00:03:05.500
So our, even if we were
to do the calculation,

00:03:05.500 --> 00:03:06.333
we could feel confident

00:03:06.333 --> 00:03:08.170
we're not going to be as low as rubidium.

00:03:08.170 --> 00:03:11.030
So I'm feeling very
confident just eyeballing it,

00:03:11.030 --> 00:03:11.940
just estimating,

00:03:11.940 --> 00:03:13.090
this is going to be a little bit,

00:03:13.090 --> 00:03:15.890
have an average atomic mass
a little bit less than 88,

00:03:15.890 --> 00:03:19.373
which tells me that this is strontium.


Worked example: Calculating mass percent

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:01.450
- [Instructor] So right over here,

00:00:01.450 --> 00:00:03.850
I have the molecular formula for glucose.

00:00:03.850 --> 00:00:05.950
And so let's just say that I had a sample

00:00:05.950 --> 00:00:07.660
of pure glucose right over here,

00:00:07.660 --> 00:00:09.620
this is my little pile of glucose.

00:00:09.620 --> 00:00:11.560
I'm not even gonna tell you its mass,

00:00:11.560 --> 00:00:14.220
but based on the molecular formula,

00:00:14.220 --> 00:00:17.570
can you figure out the
percentage of carbon

00:00:17.570 --> 00:00:20.170
by mass of my sample?

00:00:20.170 --> 00:00:21.580
Pause this video and think about it.

00:00:21.580 --> 00:00:24.470
And as a hint, I've given
you the average atomic masses

00:00:24.470 --> 00:00:26.173
of carbon, hydrogen, and oxygen.

00:00:27.840 --> 00:00:30.410
All right, now let's work
through this together.

00:00:30.410 --> 00:00:34.040
Now, the reason why the amount
of glucose doesn't matter

00:00:34.040 --> 00:00:35.750
is because the percent carbon by mass

00:00:35.750 --> 00:00:38.130
should be the same
regardless of the amount.

00:00:38.130 --> 00:00:39.600
But to help us think this through,

00:00:39.600 --> 00:00:41.030
we can imagine amount.

00:00:41.030 --> 00:00:44.170
Let's just assume that this is a mole,

00:00:44.170 --> 00:00:47.320
this is a mole of glucose.

00:00:47.320 --> 00:00:49.340
So one way we could think about it is,

00:00:49.340 --> 00:00:51.790
we say okay, for every mole of glucose,

00:00:51.790 --> 00:00:53.400
we have six moles of carbon.

00:00:53.400 --> 00:00:56.960
Because every glucose
molecule has six carbon atoms.

00:00:56.960 --> 00:01:01.300
So we could say, what
is going to be the mass

00:01:01.300 --> 00:01:06.190
of six moles of carbon divided by

00:01:07.360 --> 00:01:12.360
the mass of one mole of glucose?

00:01:13.890 --> 00:01:16.890
And once again, the reason
why it's six moles of carbon

00:01:16.890 --> 00:01:19.420
divided by one mole of
glucose is because this,

00:01:19.420 --> 00:01:21.660
if we assume this is a mole of glucose,

00:01:21.660 --> 00:01:23.820
every molecule of glucose has six carbons.

00:01:23.820 --> 00:01:27.170
So it's going to be six
times as many carbon atoms

00:01:27.170 --> 00:01:30.350
or six moles of carbon.

00:01:30.350 --> 00:01:32.640
Now, what is this going to be?

00:01:32.640 --> 00:01:36.570
Well, this is going to be equal to,

00:01:36.570 --> 00:01:38.350
it's going to be in our numerator,

00:01:38.350 --> 00:01:43.220
we're going to have six moles of carbon

00:01:43.220 --> 00:01:44.830
times the molar mass of carbon.

00:01:44.830 --> 00:01:46.270
Well, what's that going to be?

00:01:46.270 --> 00:01:47.103
Well, we can get that

00:01:47.103 --> 00:01:48.670
from the average atomic mass of carbon.

00:01:48.670 --> 00:01:49.830
If the average atomic mass

00:01:49.830 --> 00:01:52.700
is 12.01 universal atomic mass units,

00:01:52.700 --> 00:01:53.670
the molar mass is going to be

00:01:53.670 --> 00:01:58.670
12.01 grams per mole of carbon.

00:01:58.890 --> 00:02:03.890
So times 12.01 grams per mole of carbon.

00:02:05.940 --> 00:02:09.050
And notice the numerator
will be just left with grams.

00:02:09.050 --> 00:02:11.840
And then in the denominator,

00:02:11.840 --> 00:02:13.430
what are we going to have?

00:02:13.430 --> 00:02:15.420
Well, the mass of one mole of glucose,

00:02:15.420 --> 00:02:16.253
for every glucose molecule,

00:02:16.253 --> 00:02:19.580
we have six carbons, 12
hydrogens, and six oxygens.

00:02:19.580 --> 00:02:23.540
So it's going to be the
mass of six moles of carbon,

00:02:23.540 --> 00:02:27.230
12 moles of hydrogen,
and six moles of oxygen.

00:02:27.230 --> 00:02:29.880
So it's going to be what
we just had up here,

00:02:29.880 --> 00:02:33.370
it's going to be six moles of carbon

00:02:33.370 --> 00:02:35.340
times the molar mass of carbon,

00:02:35.340 --> 00:02:39.770
12.01 grams per mole of carbon.

00:02:39.770 --> 00:02:43.590
To that, we are going to add

00:02:43.590 --> 00:02:47.370
the mass of 12 moles of hydrogen.

00:02:47.370 --> 00:02:50.960
So 12 moles of hydrogen

00:02:50.960 --> 00:02:52.570
times the molar mass of hydrogen,

00:02:52.570 --> 00:02:57.570
which is going to be 1.008
grams per mole of hydrogen.

00:02:58.820 --> 00:03:03.290
Plus six moles of oxygen,

00:03:03.290 --> 00:03:04.980
times the molar mass of oxygen,

00:03:04.980 --> 00:03:09.980
which is going to be 16.00
grams per mole of oxygen.

00:03:11.890 --> 00:03:14.480
And the good thing is, down
here, the units cancel out,

00:03:14.480 --> 00:03:17.690
so we're left with just
grams in the denominator.

00:03:17.690 --> 00:03:18.523
And that makes sense.

00:03:18.523 --> 00:03:19.880
We're gonna end up with
grams in the numerator,

00:03:19.880 --> 00:03:21.620
grams in the denominator,
the units will cancel out,

00:03:21.620 --> 00:03:24.700
and we'll get a pure
percentage at the end.

00:03:24.700 --> 00:03:26.450
So let's see, in the numerator,

00:03:26.450 --> 00:03:28.420
six times 12.01

00:03:28.420 --> 00:03:32.840
is 72.06.

00:03:32.840 --> 00:03:35.900
And then in the denominator,

00:03:35.900 --> 00:03:37.870
I'm just going to do the
pure calculation first,

00:03:37.870 --> 00:03:40.200
and then I'm gonna worry
about significant figures.

00:03:40.200 --> 00:03:41.500
So in the denominator,

00:03:41.500 --> 00:03:46.250
we have 72.06 plus,

00:03:46.250 --> 00:03:49.447
let's see, 12 times 1.008 is 12.096,

00:03:52.710 --> 00:03:57.710
and then we have plus
six times 16 is 96.00,

00:04:01.240 --> 00:04:05.270
and this will be equal to 72,

00:04:05.270 --> 00:04:07.070
if we're just thinking
about the pure calculation,

00:04:07.070 --> 00:04:08.560
before we think about significant figures,

00:04:08.560 --> 00:04:11.690
72.06 divided by,

00:04:11.690 --> 00:04:14.070
let's see, if I add 72 to 12, I get 84,

00:04:14.070 --> 00:04:15.370
plus 96,

00:04:15.370 --> 00:04:16.850
I get 180.156.

00:04:22.520 --> 00:04:24.250
Did I do that right?

00:04:24.250 --> 00:04:25.640
If I were just to add up everything,

00:04:25.640 --> 00:04:28.340
not even think about significant figures.

00:04:28.340 --> 00:04:30.210
So we can type this into a calculator

00:04:30.210 --> 00:04:32.010
but we should remind ourselves

00:04:32.010 --> 00:04:33.560
that our final answer should have

00:04:33.560 --> 00:04:36.490
no more than four significant figures.

00:04:36.490 --> 00:04:37.890
Because even down here,

00:04:37.890 --> 00:04:40.620
if we were just doing this
blue calculation here,

00:04:40.620 --> 00:04:42.770
that should only have
four significant figures,

00:04:42.770 --> 00:04:45.060
it would have gotten us
to the hundredths place,

00:04:45.060 --> 00:04:46.620
and so when we add things together,

00:04:46.620 --> 00:04:48.650
we should get no more
than the hundredths place,

00:04:48.650 --> 00:04:50.500
but even if we rounded over there

00:04:50.500 --> 00:04:52.180
for significant figures purposes,

00:04:52.180 --> 00:04:54.410
we would still have at least four,

00:04:54.410 --> 00:04:56.070
we'd actually have five
significant figures.

00:04:56.070 --> 00:04:57.990
So this four significant figures

00:04:57.990 --> 00:05:00.530
is our significant
figures limiting factor.

00:05:00.530 --> 00:05:02.120
So we just have to calculate this

00:05:02.120 --> 00:05:05.058
and round to four significant figures.

00:05:05.058 --> 00:05:09.217
72.06 divided by 180.156

00:05:12.180 --> 00:05:13.580
is equal to,

00:05:13.580 --> 00:05:15.860
and if we round to four
significant figures,

00:05:15.860 --> 00:05:19.140
this will be .4000.

00:05:19.140 --> 00:05:20.950
So this will be, I'll say,

00:05:20.950 --> 00:05:24.800
approximately equal to 0.4000.

00:05:24.800 --> 00:05:27.560
Or we could say 40%

00:05:28.920 --> 00:05:32.600
or 40.00% carbon by mass

00:05:32.600 --> 00:05:35.640
when we round to four significant figures.

00:05:35.640 --> 00:05:36.953
And we are done.


Worked example: Calculating molar mass and number of moles

WEBVTT
Kind: captions
Language: en

00:00:00.150 --> 00:00:01.420
- [Instructor] We are asked to calculate

00:00:01.420 --> 00:00:06.420
the number of moles in a 1.52
kilogram sample of glucose.

00:00:07.070 --> 00:00:08.970
So like always, pause this video

00:00:08.970 --> 00:00:10.830
and try to figure this out on your own

00:00:10.830 --> 00:00:13.743
and this periodic table of
elements will prove useful.

00:00:14.830 --> 00:00:16.750
All right, now if we're
trying to figure out

00:00:16.750 --> 00:00:21.190
the number of moles,
remember, mole is really,

00:00:21.190 --> 00:00:23.440
you can view it as a
quantity of something.

00:00:23.440 --> 00:00:24.910
If I said a dozen of something,

00:00:24.910 --> 00:00:26.480
you'd say oh, that's 12 of that thing.

00:00:26.480 --> 00:00:28.140
If I say a mole of something,

00:00:28.140 --> 00:00:31.030
I'm saying that's Avogadro's
number of that thing.

00:00:31.030 --> 00:00:34.620
And so we have a 1.52 kilograms sample

00:00:34.620 --> 00:00:37.560
of our molecule in question, of glucose

00:00:37.560 --> 00:00:39.900
so if we can figure out the mass per mole,

00:00:39.900 --> 00:00:40.780
or another way to think about it,

00:00:40.780 --> 00:00:44.490
the molar mass of glucose,
well then we just divide

00:00:44.490 --> 00:00:47.600
the mass of our sample
by the mass per mole

00:00:47.600 --> 00:00:49.960
and we'll know how many moles we have.

00:00:49.960 --> 00:00:54.960
So what is the molar mass of glucose?

00:00:55.120 --> 00:00:56.570
Well to figure that out, and that's why

00:00:56.570 --> 00:00:58.600
this periodic table of elements is useful,

00:00:58.600 --> 00:01:00.320
we just have to figure out the molar mass

00:01:00.320 --> 00:01:02.870
of the constituent elements.

00:01:02.870 --> 00:01:05.450
So if we first look at carbon,

00:01:05.450 --> 00:01:08.790
carbon, we see from this
periodic table of elements,

00:01:08.790 --> 00:01:12.820
has a molar mass of 12.01 grams per mole.

00:01:12.820 --> 00:01:14.630
We've talked about it in other videos,

00:01:14.630 --> 00:01:18.220
you could view this 12.01
as a relative atomic mass

00:01:18.220 --> 00:01:19.480
of a carbon atom,

00:01:19.480 --> 00:01:22.270
of as the average atomic
mass of a carbon atom,

00:01:22.270 --> 00:01:24.070
or what's useful, and this is where

00:01:24.070 --> 00:01:25.800
Avogadro's Number is valuable,

00:01:25.800 --> 00:01:28.400
if you have Avogadro's Number of carbons,

00:01:28.400 --> 00:01:31.750
it is going to have a mass of 12.01 grams.

00:01:31.750 --> 00:01:36.750
So carbon has a molar mass
of 12.01 grams per mole

00:01:37.040 --> 00:01:41.230
and now we can think about
hydrogen in the same way.

00:01:41.230 --> 00:01:46.230
Hydrogen has a molar mass
of 1.008 grams per mole,

00:01:46.620 --> 00:01:49.840
008 grams per mole.

00:01:49.840 --> 00:01:53.670
And then last but not
least, we have oxygen here.

00:01:53.670 --> 00:01:56.540
Oxygen, we can see from our
periodic table of elements,

00:01:56.540 --> 00:02:01.540
it has a molar mass of
16.00 grams per mole.

00:02:01.950 --> 00:02:04.500
And so now we have all
the information we need

00:02:04.500 --> 00:02:06.550
from our periodic table of elements.

00:02:06.550 --> 00:02:09.280
So the molar mass of
glucose is going to be six

00:02:09.280 --> 00:02:11.400
times the molar mass of carbon

00:02:11.400 --> 00:02:14.250
plus 12 times the molar mass of hydrogen

00:02:14.250 --> 00:02:17.750
plus six times the molar mass of oxygen.

00:02:17.750 --> 00:02:22.750
So it's going to be six
times 12.01 grams per mole

00:02:23.780 --> 00:02:28.780
plus 12 times 1.008 grams per mole

00:02:32.680 --> 00:02:36.200
plus every molecule of
glucose has six oxygen

00:02:36.200 --> 00:02:41.200
plus six times 16.00 grams per mole.

00:02:42.680 --> 00:02:47.240
Six times 12.01

00:02:48.330 --> 00:02:52.943
plus 12 times 1.008

00:02:55.300 --> 00:03:00.300
plus six times 16

00:03:00.350 --> 00:03:03.320
is equal to, and if we're thinking

00:03:03.320 --> 00:03:05.070
about significant figures here,

00:03:05.070 --> 00:03:07.890
the molar mass of hydrogen
goes to the thousandths place

00:03:07.890 --> 00:03:10.180
but we only go to the
hundredths for carbon

00:03:10.180 --> 00:03:13.290
and for oxygen, we're adding
all of these up together

00:03:13.290 --> 00:03:15.340
so it's going to be 180.

00:03:15.340 --> 00:03:16.690
I can only go to the hundredths place

00:03:16.690 --> 00:03:20.510
for significant figures, so 180.16.

00:03:20.510 --> 00:03:25.510
So that's equal to 180.16 grams per mole.

00:03:26.350 --> 00:03:29.900
And we could say grams of glucose, C6H12O6

00:03:32.250 --> 00:03:37.250
per mole of glucose, C6H12O6

00:03:37.610 --> 00:03:40.700
and then we can use this 1.52 kilograms

00:03:40.700 --> 00:03:43.130
to figure out how many moles we have.

00:03:43.130 --> 00:03:48.130
So if we start off with
1.52 kilograms of glucose,

00:03:48.730 --> 00:03:50.903
so that's C6H12O6,

00:03:52.570 --> 00:03:54.500
well first we can convert it to grams

00:03:54.500 --> 00:03:57.400
'cause here, our molar mass
is given in terms of grams,

00:03:57.400 --> 00:03:59.860
so times, we're going to want kilograms

00:03:59.860 --> 00:04:01.640
in the denominator and
grams in the numerator,

00:04:01.640 --> 00:04:03.930
so how many grams are there per kilograms?

00:04:03.930 --> 00:04:07.520
Well, we have 1,000 grams

00:04:07.520 --> 00:04:10.390
for every one kilogram.

00:04:10.390 --> 00:04:11.960
So when you multiply these two out,

00:04:11.960 --> 00:04:14.170
this is going to give
you the number of grams

00:04:14.170 --> 00:04:17.100
we have of glucose which would be 1,520

00:04:17.100 --> 00:04:19.270
and if you have your
mass in terms of grams,

00:04:19.270 --> 00:04:22.260
you can then divide by your molar mass

00:04:22.260 --> 00:04:26.540
or you can view it as multiplying
it by the moles per gram.

00:04:26.540 --> 00:04:31.423
So for every one mole of glucose, C6H12O6,

00:04:33.840 --> 00:04:38.840
we have 180.16 grams of glucose,

00:04:40.065 --> 00:04:45.065
C6H12O6,

00:04:45.670 --> 00:04:47.840
and this is going to get us,

00:04:47.840 --> 00:04:52.840
we get 1.52 times 1,000 is equal to,

00:04:53.270 --> 00:04:56.200
this is the number of
grams of glucose we have,

00:04:56.200 --> 00:05:01.200
and then we're going to divide by 180.16,

00:05:01.200 --> 00:05:05.570
divide by 180.16,

00:05:05.570 --> 00:05:07.400
gives us this number,

00:05:07.400 --> 00:05:09.640
and let's see, if we
see significant figures,

00:05:09.640 --> 00:05:11.810
we have three significant figures here,

00:05:11.810 --> 00:05:14.440
we have five here so we wanna round it

00:05:14.440 --> 00:05:16.590
to three significant figures,

00:05:16.590 --> 00:05:19.920
so it will be 8.44 moles of glucose.

00:05:24.140 --> 00:05:28.770
So our kilograms cancel with our kilograms

00:05:28.770 --> 00:05:32.380
and then our grams of glucose

00:05:32.380 --> 00:05:35.310
cancel with our grams of glucose

00:05:35.310 --> 00:05:40.310
and we are left with
8.44 moles of glucose,

00:05:41.340 --> 00:05:43.713
moles of C6H12O6.

00:05:46.120 --> 00:05:48.083
And we are done.


How to reduce test prep anxiety: 3 tips from Sal Khan

WEBVTT
Kind: captions
Language: en

00:00:01.350 --> 00:00:03.860
- Here are my tips for reducing stress

00:00:03.860 --> 00:00:06.400
around taking important tests.

00:00:06.400 --> 00:00:10.260
Tip one, build a habit of practice.

00:00:10.260 --> 00:00:12.840
Building a habit of
practice is super valuable.

00:00:12.840 --> 00:00:15.620
I know I'm guilty myself of
sometimes I get so caught up

00:00:15.620 --> 00:00:18.380
with something, or I'm
stressed about something,

00:00:18.380 --> 00:00:20.480
that I almost freeze.

00:00:20.480 --> 00:00:22.490
But it really should be
the other way around.

00:00:22.490 --> 00:00:25.490
I try to remind myself that, Sal,

00:00:25.490 --> 00:00:28.560
if you put time in on a regular basis,

00:00:28.560 --> 00:00:31.950
if I use things like Official SAT Practice

00:00:31.950 --> 00:00:34.510
to take practice tests,
understand my strengths

00:00:34.510 --> 00:00:37.120
and weaknesses, work on
where my weaknesses are,

00:00:37.120 --> 00:00:38.770
and I do it on a regular basis,

00:00:38.770 --> 00:00:41.310
that's my best chance
of actually improving.

00:00:41.310 --> 00:00:45.200
And we have studies that show
there's a strong corelation

00:00:45.200 --> 00:00:48.710
between students who are
able to put in even six hours

00:00:48.710 --> 00:00:51.520
and growing 50% more than expected.

00:00:51.520 --> 00:00:54.270
So I really encourage you
don't get too obsessed

00:00:54.270 --> 00:00:56.810
with the outcome, but
think about what can I do

00:00:56.810 --> 00:00:58.700
on a regular basis, not all at once,

00:00:58.700 --> 00:01:00.970
not binge-practicing, but what can I do

00:01:00.970 --> 00:01:02.760
on a regular basis, day in, day out,

00:01:02.760 --> 00:01:04.350
and you'll be really impressed

00:01:04.350 --> 00:01:06.640
how much the gains will accumulate.

00:01:06.640 --> 00:01:10.310
Tip two, share your feelings.

00:01:10.310 --> 00:01:13.330
One of the things that
it's taken me many years

00:01:13.330 --> 00:01:16.880
to discover the wisdom of, and
I hope to share it with you,

00:01:16.880 --> 00:01:19.530
is whatever is going on in your life

00:01:19.530 --> 00:01:22.330
that you think is unique to you, it's not.

00:01:22.330 --> 00:01:23.930
It's probably happening in the minds

00:01:23.930 --> 00:01:25.980
of everyone else around
you, even those people

00:01:25.980 --> 00:01:27.660
who look perfect on social media

00:01:27.660 --> 00:01:29.380
and always seem to have their act together

00:01:29.380 --> 00:01:32.410
and their hair perfectly
combed and great grades,

00:01:32.410 --> 00:01:35.430
they're feeling the same
things, the same stresses,

00:01:35.430 --> 00:01:36.750
the same insecurities in their mind.

00:01:36.750 --> 00:01:39.530
They might even be feeling
far more than what you are.

00:01:39.530 --> 00:01:42.750
And so do yourself a
favor and do them a favor

00:01:42.750 --> 00:01:44.940
by being vulnerable and talking about it

00:01:44.940 --> 00:01:47.940
and talking about how you can
actually support each other.

00:01:47.940 --> 00:01:50.110
I gotta tell you, even when
I was a student like you,

00:01:50.110 --> 00:01:54.240
and even today, as I try
to navigate my own life,

00:01:54.240 --> 00:01:56.840
by being able to have a support network,

00:01:56.840 --> 00:01:58.730
people who I can commiserate with,

00:01:58.730 --> 00:02:00.750
it really helps lower the stress.

00:02:00.750 --> 00:02:02.660
And that's just gonna make
you a healthier person.

00:02:02.660 --> 00:02:05.420
But also, the more
relaxed you are entering

00:02:05.420 --> 00:02:08.090
into these tests, the better
you're going to perform.

00:02:08.090 --> 00:02:12.180
And tip three, keep a bigger perspective.

00:02:12.180 --> 00:02:15.060
One thing that some of
us adults often forget

00:02:15.060 --> 00:02:20.060
is how sometimes stressful the
stage of life you're in is.

00:02:20.810 --> 00:02:22.950
Us adults, we say, oh, I gotta pay bills.

00:02:22.950 --> 00:02:25.930
I gotta do this, I gotta pay the mortgage.

00:02:25.930 --> 00:02:28.650
But I can guess what's
going on in your mind,

00:02:28.650 --> 00:02:30.550
'cause I went through it myself.

00:02:30.550 --> 00:02:32.150
You're saying, hey, I've
gotta do really good

00:02:32.150 --> 00:02:34.490
on this test, because if
I do good on this test,

00:02:34.490 --> 00:02:36.310
then I might be able to
have that opportunity.

00:02:36.310 --> 00:02:37.750
If I do well with that opportunity,

00:02:37.750 --> 00:02:38.583
then I'll get that opportunity.

00:02:38.583 --> 00:02:40.550
And then my life will be perfect.

00:02:40.550 --> 00:02:41.830
But if I don't do well,

00:02:41.830 --> 00:02:43.850
well then that opportunity
might not happen.

00:02:43.850 --> 00:02:45.180
And then that opportunity
might not happen,

00:02:45.180 --> 00:02:47.310
and then what will I be?

00:02:47.310 --> 00:02:48.710
Who will I be?

00:02:48.710 --> 00:02:50.060
And what I'd like to tell you,

00:02:50.060 --> 00:02:53.070
and I'm literally, I'm not making this up,

00:02:53.070 --> 00:02:56.950
I have gotten rejected and
I failed at far more things

00:02:56.950 --> 00:02:58.080
than you can imagine.

00:02:58.080 --> 00:02:59.540
And even though in the moment,

00:02:59.540 --> 00:03:01.850
I sometimes thought all was lost,

00:03:01.850 --> 00:03:05.070
a week later, six months
later, a year later,

00:03:05.070 --> 00:03:07.340
I realize that actually it
wasn't that big of a deal.

00:03:07.340 --> 00:03:08.910
And in some ways it was a blessing,

00:03:08.910 --> 00:03:10.950
'cause maybe that wasn't the thing for me.

00:03:10.950 --> 00:03:14.350
And so when you go into test-prep mode,

00:03:14.350 --> 00:03:16.840
yes, of course, you wanna
do as well as you can,

00:03:16.840 --> 00:03:18.570
but that score isn't you.

00:03:18.570 --> 00:03:20.010
It doesn't define you.

00:03:20.010 --> 00:03:22.550
You are so much more than that one score.

00:03:22.550 --> 00:03:25.630
You are so much more than
what school you get into.

00:03:25.630 --> 00:03:26.880
And I'll tell you a secret.

00:03:26.880 --> 00:03:31.440
And this is after being
out in the real world

00:03:31.440 --> 00:03:33.480
for over 20 years.

00:03:33.480 --> 00:03:36.670
I've actually haven't
seen a big correlation

00:03:36.670 --> 00:03:39.510
between where someone
happened to go to school

00:03:39.510 --> 00:03:42.440
and how successful they might be.

00:03:42.440 --> 00:03:44.760
And I even did the
successful in air quotes

00:03:44.760 --> 00:03:48.490
because what society calls successful,

00:03:48.490 --> 00:03:50.960
money, fame, all of
that, I gotta tell you,

00:03:50.960 --> 00:03:53.550
also does not correlate
with real happiness.

00:03:53.550 --> 00:03:55.820
Real happiness is knowing who you are,

00:03:55.820 --> 00:03:58.830
doing what you can, but not
getting obsessed with outcomes,

00:03:58.830 --> 00:04:01.240
not coveting things, not
coveting, I must do this,

00:04:01.240 --> 00:04:02.450
I must do that.

00:04:02.450 --> 00:04:04.080
Because no matter how much money you make,

00:04:04.080 --> 00:04:06.300
or how famous or accomplished you get,

00:04:06.300 --> 00:04:08.470
if you have that mindset,
you'll never be happy.

00:04:08.470 --> 00:04:11.520
But if you say, look, I'm
gonna be my best self.

00:04:11.520 --> 00:04:14.480
I'm gonna do right by myself
and right by the world,

00:04:14.480 --> 00:04:17.900
and things will play out as they see fit,

00:04:17.900 --> 00:04:19.180
then you'll always be content.

00:04:19.180 --> 00:04:21.610
And you'll actually be far
happier than most people

00:04:21.610 --> 00:04:22.800
on this planet.

00:04:22.800 --> 00:04:24.740
So those are my tips for reducing stress

00:04:24.740 --> 00:04:27.060
as you approach these types of tests

00:04:27.060 --> 00:04:29.620
and a little bit of
general life advice too.

00:04:29.620 --> 00:04:30.690
I hope you take it to heart.

00:04:30.690 --> 00:04:32.410
Take it with a grain of salt too,

00:04:32.410 --> 00:04:35.833
but I believe that it
might be really valuable.


Course Mastery Sal (intro only)

WEBVTT
Kind: captions
Language: en

00:00:00.400 --> 00:00:03.710
- Hi teachers, this is Sal
Khan here from Khan Academy

00:00:03.710 --> 00:00:06.970
and welcome to Course Mastery.

00:00:06.970 --> 00:00:10.330
So back in 1984, famous
education researcher

00:00:10.330 --> 00:00:13.960
Benjamin Bloom published
the famous two-sigma study

00:00:13.960 --> 00:00:15.830
where he showed that a student who works

00:00:15.830 --> 00:00:18.150
in a mastery learning
framework with a tutor,

00:00:18.150 --> 00:00:22.260
one-on-one can operate two
standard deviations better.

00:00:22.260 --> 00:00:24.700
So the student who is operating
in the 50th percentile

00:00:24.700 --> 00:00:27.200
can operate well into the 90th percentile,

00:00:27.200 --> 00:00:29.650
95th, 96th percentile.

00:00:29.650 --> 00:00:31.020
You fast forward to today, there have been

00:00:31.020 --> 00:00:34.870
over 200 studies that
have backed up his claims.

00:00:34.870 --> 00:00:36.950
On top of that, you as an educator,

00:00:36.950 --> 00:00:39.110
know that your students enter your class

00:00:39.110 --> 00:00:40.830
at all different levels.

00:00:40.830 --> 00:00:43.330
You also know that
differentiation has always been

00:00:43.330 --> 00:00:46.050
considered a best practice in education.

00:00:46.050 --> 00:00:48.870
The hard part, however,
is how do you do that

00:00:48.870 --> 00:00:53.760
with 25, 30, 35 kids in the classroom?

00:00:53.760 --> 00:00:56.800
All of us at Khan
Academy, we firmly believe

00:00:56.800 --> 00:00:58.840
that if we have to pick
between an amazing teacher

00:00:58.840 --> 00:01:02.030
and an amazing technology,
we'd pick you every time,

00:01:02.030 --> 00:01:03.540
the amazing teacher.

00:01:03.540 --> 00:01:05.730
Luckily, we don't have
to make that trade-off,

00:01:05.730 --> 00:01:08.600
and so we're think about
how can we empower you,

00:01:08.600 --> 00:01:12.450
an amazing teacher, with as
powerful technology as possible?

00:01:12.450 --> 00:01:14.450
And that's what Course Mastery is.

00:01:14.450 --> 00:01:17.380
It's a way for you to set mastery goals

00:01:17.380 --> 00:01:20.440
for your students, and these
goals are fairly large goals,

00:01:20.440 --> 00:01:22.650
so that they'd be
appropriate for over a term

00:01:22.650 --> 00:01:25.300
or over a school year, and you set it once

00:01:25.300 --> 00:01:27.600
and then you can feel
confident that over the rest

00:01:27.600 --> 00:01:29.310
of the year or the rest of the term,

00:01:29.310 --> 00:01:31.490
your students have things to work on

00:01:31.490 --> 00:01:33.150
the are appropriate for them.

00:01:33.150 --> 00:01:35.300
They'll be able to learn
at their own time and pace,

00:01:35.300 --> 00:01:37.630
master concepts at
their own time and pace,

00:01:37.630 --> 00:01:39.700
consistent with Benjamin Bloom's work,

00:01:39.700 --> 00:01:42.040
and remediate their gaps as necessary.

00:01:42.040 --> 00:01:44.640
And multiple studies have
shown that when students

00:01:44.640 --> 00:01:47.530
on Khan Academy are able to
engage in mastery learning,

00:01:47.530 --> 00:01:49.220
learn at their own time and pace,

00:01:49.220 --> 00:01:51.290
for even 30 minutes or more per week.

00:01:51.290 --> 00:01:54.510
So say 45 minutes a week,
or one class period a week,

00:01:54.510 --> 00:01:56.080
they're able to accelerate their learning

00:01:56.080 --> 00:01:58.500
as measured by standardized
benchmark exams

00:01:58.500 --> 00:02:00.913
by 20 or 30%.


Mastery Learning in Mr. Vandenberg’s Class

WEBVTT
Kind: captions
Language: en

00:00:00.250 --> 00:00:03.980
- I Tim Vandenberg and I've
been teaching for 25 years,

00:00:03.980 --> 00:00:06.680
17 years in Hesperia, California,

00:00:06.680 --> 00:00:09.560
sixth grade at Carmel Elementary School.

00:00:09.560 --> 00:00:13.800
And Hesperia is a lower
socioeconomic status area,

00:00:13.800 --> 00:00:16.840
on average, especially among
our student population.

00:00:16.840 --> 00:00:19.240
100% of our students at this school

00:00:19.240 --> 00:00:21.070
are on free reduced lunch.

00:00:21.070 --> 00:00:24.250
The traditional model among most schools

00:00:24.250 --> 00:00:26.940
is just moving kids along by age,

00:00:26.940 --> 00:00:28.860
whether they've mastered
the skills or not.

00:00:28.860 --> 00:00:31.920
So by the time they come
to me in sixth grade,

00:00:31.920 --> 00:00:34.240
they've got so many gaps in their learning

00:00:34.240 --> 00:00:38.070
because they haven't mastered
the skills K through five.

00:00:38.070 --> 00:00:41.460
It's extremely difficult
for most teachers,

00:00:41.460 --> 00:00:45.080
probably all teachers
to really meet each kid

00:00:45.080 --> 00:00:47.940
at their individual mastery level.

00:00:47.940 --> 00:00:51.030
You're gonna have a third of
the class tracking with you,

00:00:51.030 --> 00:00:53.420
a third of the class
wishing you'd move faster,

00:00:53.420 --> 00:00:55.730
and a third of the class
wishing you'd reteach

00:00:55.730 --> 00:00:57.090
that a few more times.

00:00:57.090 --> 00:00:59.650
My goals as a teacher using Khan Academy

00:00:59.650 --> 00:01:02.720
is for my students to master as much

00:01:02.720 --> 00:01:06.310
of the grade level specific
skills as they can,

00:01:06.310 --> 00:01:08.040
truly master the skills.

00:01:08.040 --> 00:01:11.210
What I do is I assign to each student,

00:01:11.210 --> 00:01:13.260
the whole class, an entire unit.

00:01:13.260 --> 00:01:16.220
For example, expressions and variables.

00:01:16.220 --> 00:01:18.530
And then that next day in class,

00:01:18.530 --> 00:01:19.810
we'll have a class lecture.

00:01:19.810 --> 00:01:23.040
Students take notes in
their math portfolios,

00:01:23.040 --> 00:01:26.780
and we teach the skill of
expressions and variables.

00:01:26.780 --> 00:01:29.900
Then they dive right into Khan Academy,

00:01:29.900 --> 00:01:33.310
start the skills in that unit
and work at their own pace.

00:01:33.310 --> 00:01:34.740
And those who need extra help,

00:01:34.740 --> 00:01:37.990
they have the Khan
Academy videos and hints.

00:01:37.990 --> 00:01:39.790
And I also monitor the class.

00:01:39.790 --> 00:01:41.180
I rove around and help kids

00:01:41.180 --> 00:01:42.576
whenever they need help.

00:01:42.576 --> 00:01:43.409
(students chattering)

00:01:43.409 --> 00:01:45.810
When students master
skills on Khan Academy,

00:01:45.810 --> 00:01:47.210
they're so excited.

00:01:47.210 --> 00:01:50.051
Their self-pride and self-confidence

00:01:50.051 --> 00:01:55.051
just overflows and they start
to believe they can learn.

00:01:55.160 --> 00:01:57.760
It's so important in the learning model

00:01:57.760 --> 00:02:00.020
that students find out immediately

00:02:00.020 --> 00:02:03.230
if they are properly grasping a skill.

00:02:03.230 --> 00:02:04.670
Through Khan Academy they get

00:02:04.670 --> 00:02:08.260
that instant feedback
after every single problem.

00:02:08.260 --> 00:02:10.250
Is a correct or not correct?

00:02:10.250 --> 00:02:12.260
And if they didn't get a correct,

00:02:12.260 --> 00:02:13.940
they get to find out immediately

00:02:13.940 --> 00:02:18.110
from the hints exactly where
they might have misunderstood.

00:02:18.110 --> 00:02:19.970
It's so important for students

00:02:19.970 --> 00:02:22.080
in this day and age of technology,

00:02:22.080 --> 00:02:24.588
to learn to communicate and interact

00:02:24.588 --> 00:02:26.570
interpersonally with others.

00:02:26.570 --> 00:02:29.430
By using Khan Academy to teach students

00:02:29.430 --> 00:02:32.720
to support one another,
instead of just being locked

00:02:32.720 --> 00:02:35.460
into a computer screen,
they're actually interacting

00:02:35.460 --> 00:02:38.230
with their neighbors,
their friends in class.

00:02:38.230 --> 00:02:41.810
They learn to interact
with others in all of life.

00:02:41.810 --> 00:02:44.590
So as many good teachers love to do,

00:02:44.590 --> 00:02:48.730
they take their top successful students

00:02:48.730 --> 00:02:50.880
and spread them out in the class

00:02:50.880 --> 00:02:52.820
and give them two elbow buddies,

00:02:52.820 --> 00:02:54.120
one on each side of them.

00:02:54.120 --> 00:02:56.410
I'm monitoring, I'm encouraging first,

00:02:56.410 --> 00:02:57.650
students to help each other.

00:02:57.650 --> 00:03:01.620
It's so much better when
students help each other first,

00:03:01.620 --> 00:03:04.460
because then they become so
much more self-sufficient,

00:03:04.460 --> 00:03:07.000
self-motivated, self-rewarded.

00:03:07.000 --> 00:03:10.140
Plus, those peer helpers feel so special

00:03:10.140 --> 00:03:11.186
as they reward their friends

00:03:11.186 --> 00:03:13.300
with the help that they give.

00:03:13.300 --> 00:03:14.630
That really makes it possible

00:03:14.630 --> 00:03:18.780
to promote and increase
teacher to student interaction,

00:03:18.780 --> 00:03:21.080
because now the teacher
is spending their time

00:03:21.080 --> 00:03:23.720
where students really truly need the help,

00:03:23.720 --> 00:03:26.000
on 32 or more different levels

00:03:26.000 --> 00:03:28.230
in a class of that many students.

00:03:28.230 --> 00:03:30.170
I don't have one math class.

00:03:30.170 --> 00:03:33.120
I have 32 math classes.

00:03:33.120 --> 00:03:36.640
Every single student is
working at their own pace.

00:03:36.640 --> 00:03:39.100
Now I can meet students where they're at,

00:03:39.100 --> 00:03:41.310
instead of where the
middle of the class is at.

00:03:41.310 --> 00:03:44.600
Because the Khan Academy
grade level skills

00:03:44.600 --> 00:03:49.420
are so well aligned with the
Common Core standards for math,

00:03:49.420 --> 00:03:53.200
I can trust that if my
students master those skills

00:03:53.200 --> 00:03:56.720
before the state test, they
will do amazingly well.

00:03:56.720 --> 00:03:58.800
And they have for years now.

00:03:58.800 --> 00:04:00.410
After class, I always make sure

00:04:00.410 --> 00:04:04.330
to look at the data progress reports

00:04:04.330 --> 00:04:05.710
on the teacher dashboard.

00:04:05.710 --> 00:04:07.960
That really helps me
know who is succeeding

00:04:07.960 --> 00:04:11.140
and who is really struggling
and needs extra help.

00:04:11.140 --> 00:04:14.660
And then I set my pace and remediation

00:04:14.660 --> 00:04:17.490
and instructional support accordingly.

00:04:17.490 --> 00:04:21.250
There is no way I could have
known to that great detail,

00:04:21.250 --> 00:04:22.530
who is really getting it

00:04:22.530 --> 00:04:25.507
and who's not without
the help of Khan Academy.

00:04:25.507 --> 00:04:26.340
- [Students] Yes!

00:04:26.340 --> 00:04:28.030
- I love being a teacher because I love it

00:04:28.030 --> 00:04:31.090
when kids learn to love learning,

00:04:31.090 --> 00:04:32.730
and when they love learning,

00:04:32.730 --> 00:04:35.310
they don't need me for
the rest of their life.

00:04:35.310 --> 00:04:37.300
So as they grow up and become adults

00:04:37.300 --> 00:04:38.930
pursuing their own interests,

00:04:38.930 --> 00:04:40.880
they've learned how to learn on their own

00:04:40.880 --> 00:04:43.023
and they have a passion and desire to.


Continuity and change in American society, 1754-1800

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:04.670
- [Instructor] In 1819, American
author Washington Irving

00:00:04.670 --> 00:00:09.450
published a short story about
a man named Rip Van Winkle.

00:00:09.450 --> 00:00:12.130
In the story, Rip lived
in a sleepy village

00:00:12.130 --> 00:00:14.080
in the Catskill Mountains of New York,

00:00:14.080 --> 00:00:16.980
where he spent his days hanging
around the local tavern,

00:00:16.980 --> 00:00:19.720
the King George, and avoiding his wife

00:00:19.720 --> 00:00:22.350
any time she asked him to
do some work on their farm.

00:00:22.350 --> 00:00:25.190
One evening, Rip was
walking in the mountains

00:00:25.190 --> 00:00:28.250
when he came upon a strange group of men

00:00:28.250 --> 00:00:29.910
who gave him some liquor to drink.

00:00:29.910 --> 00:00:33.320
He fell asleep, and when we
woke up the next morning,

00:00:33.320 --> 00:00:35.110
he went back into town and found

00:00:35.110 --> 00:00:37.380
that everything had changed.

00:00:37.380 --> 00:00:40.860
Instead of a sleepy village,
there was a bustling town,

00:00:40.860 --> 00:00:42.730
and the inhabitants all seemed

00:00:42.730 --> 00:00:45.700
to be loudly debating over an election.

00:00:45.700 --> 00:00:49.000
One person wanted to know if
Rip favored the Federalists

00:00:49.000 --> 00:00:52.080
or the Republicans, groups
that he had never heard of.

00:00:52.080 --> 00:00:54.850
The King George Tavern had
transformed into something

00:00:54.850 --> 00:00:58.300
called the General Washington
Tavern, and outside it,

00:00:58.300 --> 00:01:02.080
someone had put up an
unfamiliar flag bearing stars

00:01:02.080 --> 00:01:03.160
and stripes.

00:01:03.160 --> 00:01:06.120
Gradually, Rip realized that
he had been asleep not just

00:01:06.120 --> 00:01:09.250
for one night, but for 20
years, and that he had slept

00:01:09.250 --> 00:01:11.400
through the entire American Revolution.

00:01:11.400 --> 00:01:14.010
Now, this is just a story,
and it's a pretty fun one,

00:01:14.010 --> 00:01:15.330
I can't do it justice here,

00:01:15.330 --> 00:01:17.410
but I highly recommend you read it.

00:01:17.410 --> 00:01:19.870
But this story reveals a lot about

00:01:19.870 --> 00:01:24.210
how Americans thought about
the amount of social change

00:01:24.210 --> 00:01:26.700
that accompanied the American Revolution.

00:01:26.700 --> 00:01:29.310
If you, like Rip Van Winkle,

00:01:29.310 --> 00:01:31.430
fell asleep in the British colonies

00:01:31.430 --> 00:01:34.210
and woke up in the United States,

00:01:34.210 --> 00:01:36.850
which aspects of life
would be familiar to you

00:01:36.850 --> 00:01:38.970
and which would be completely alien?

00:01:38.970 --> 00:01:41.640
In other words, how much
did the American Revolution

00:01:41.640 --> 00:01:43.390
really affect society?

00:01:43.390 --> 00:01:46.780
If we set out to answer
this question as historians,

00:01:46.780 --> 00:01:49.210
what we're really doing is exercising

00:01:49.210 --> 00:01:53.930
the historical thinking skill
of continuity and change.

00:01:53.930 --> 00:01:56.710
What changed and what stayed the same

00:01:56.710 --> 00:01:59.950
from before the Revolution to after it?

00:01:59.950 --> 00:02:03.310
We know that the Revolution
changed the political status

00:02:03.310 --> 00:02:05.640
of the British colonies in North America,

00:02:05.640 --> 00:02:07.890
which went from being
part of the British Empire

00:02:07.890 --> 00:02:10.130
to being an independent nation,

00:02:10.130 --> 00:02:12.630
but how big of a deal was that, really?

00:02:12.630 --> 00:02:15.710
Was it not much more than
erasing British colonies

00:02:15.710 --> 00:02:18.970
from the map and writing
in United States instead,

00:02:18.970 --> 00:02:22.760
or did I actually lead to
far-reaching changes in

00:02:22.760 --> 00:02:24.430
how people lived?

00:02:24.430 --> 00:02:26.190
If we're trying to answer this question,

00:02:26.190 --> 00:02:29.530
we really only have three options.

00:02:29.530 --> 00:02:32.370
First, things changed a lot.

00:02:32.370 --> 00:02:33.850
There was a great deal of change,

00:02:33.850 --> 00:02:36.040
and things were very
different after the Revolution

00:02:36.040 --> 00:02:38.010
compared to beforehand.

00:02:38.010 --> 00:02:41.380
Second, things didn't change much at all.

00:02:41.380 --> 00:02:44.150
The Revolution was a
revolution in name only,

00:02:44.150 --> 00:02:47.070
and most things were the same afterwards.

00:02:47.070 --> 00:02:49.950
Or third, some things changed

00:02:49.950 --> 00:02:52.120
but other things stayed the same.

00:02:52.120 --> 00:02:53.960
When we're asking what changed

00:02:53.960 --> 00:02:56.250
and what stayed the same over time,

00:02:56.250 --> 00:02:59.110
we need to be consistent
about the aspects of society

00:02:59.110 --> 00:03:03.010
that we choose so that we're
comparing apples to apples.

00:03:03.010 --> 00:03:05.280
So, let's decide which aspects we're going

00:03:05.280 --> 00:03:07.130
to compare over time.

00:03:07.130 --> 00:03:08.820
There are a lot that we could choose from,

00:03:08.820 --> 00:03:13.050
religion, slavery, gender roles,

00:03:13.050 --> 00:03:17.110
class and social structures,
political institutions.

00:03:17.110 --> 00:03:19.300
It's a little like a choose
your own adventure book

00:03:19.300 --> 00:03:20.540
for historians.

00:03:20.540 --> 00:03:24.550
All right, I'm gonna choose
political institutions,

00:03:24.550 --> 00:03:27.960
social structures, and gender roles.

00:03:27.960 --> 00:03:29.740
Why am I choosing these?

00:03:29.740 --> 00:03:31.550
Well, I guess that I'm interested in

00:03:31.550 --> 00:03:34.300
how the ideas of the Revolution,

00:03:34.300 --> 00:03:36.010
that all men are created equal

00:03:36.010 --> 00:03:38.880
and that government should
represent the will of the people,

00:03:38.880 --> 00:03:40.470
played out in reality.

00:03:40.470 --> 00:03:43.090
Did the Revolution really
lead to more equality

00:03:43.090 --> 00:03:44.590
for men or for women?

00:03:44.590 --> 00:03:47.000
Did government really
become more democratic?

00:03:47.000 --> 00:03:50.090
So, let's pretend that
we're Rip Van Winkle,

00:03:50.090 --> 00:03:53.530
taking a gander at the
society around us before

00:03:53.530 --> 00:03:55.130
and after the Revolution.

00:03:55.130 --> 00:03:57.470
I'm not gonna go into a
whole lot of detail here,

00:03:57.470 --> 00:03:59.450
but if there's anything
you're not familiar with,

00:03:59.450 --> 00:04:01.640
just jot it down and
then you can look it up

00:04:01.640 --> 00:04:02.830
when you have a chance.

00:04:02.830 --> 00:04:07.000
So, what were political
institutions, social structures,

00:04:07.000 --> 00:04:09.490
and gender roles like
before the Revolution?

00:04:09.490 --> 00:04:12.650
Well, first of all, there
were 13 separate colonies,

00:04:12.650 --> 00:04:14.560
not just one single nation.

00:04:14.560 --> 00:04:17.720
The colonies were ruled
by a hereditary monarch,

00:04:17.720 --> 00:04:20.950
the King of England, and they
had virtual representation

00:04:20.950 --> 00:04:21.830
in Parliament.

00:04:21.830 --> 00:04:24.640
Colonists considered themselves Englishmen

00:04:24.640 --> 00:04:27.200
who were entitled to the
rights of Englishmen.

00:04:27.200 --> 00:04:29.440
Colonies had property requirements

00:04:29.440 --> 00:04:33.310
and usually also religious
requirements for voters.

00:04:33.310 --> 00:04:35.130
Economically, things weren't too bad

00:04:35.130 --> 00:04:37.580
for your average white
colonist in the North,

00:04:37.580 --> 00:04:39.940
although by the eve of the Revolution,

00:04:39.940 --> 00:04:42.120
there was a growing number of poor people

00:04:42.120 --> 00:04:43.630
as land become scarcer.

00:04:43.630 --> 00:04:47.030
American colonists were
generally better off

00:04:47.030 --> 00:04:49.040
than the working class back in Britain.

00:04:49.040 --> 00:04:53.100
In the South, however, the
planter aristocracy ruled,

00:04:53.100 --> 00:04:56.300
with a handful of wealthy
white slave owners

00:04:56.300 --> 00:04:59.010
dominating society and politics.

00:04:59.010 --> 00:05:01.110
White indentured servants still existed

00:05:01.110 --> 00:05:03.120
in both the North and the South,

00:05:03.120 --> 00:05:05.960
although the practice was
becoming a little less common.

00:05:05.960 --> 00:05:10.010
Most African Americans,
excepting a few free people

00:05:10.010 --> 00:05:12.600
of color in the North, were enslaved

00:05:12.600 --> 00:05:16.510
and had no hope of social
mobility, save for running away.

00:05:16.510 --> 00:05:19.630
Indigenous people were taking advantage

00:05:19.630 --> 00:05:23.030
of the dueling empires
of Britain and France

00:05:23.030 --> 00:05:25.760
as best they could, but
after the Seven Years' War,

00:05:25.760 --> 00:05:28.210
the departure of France
meant that they were dealing

00:05:28.210 --> 00:05:29.550
with Britain alone.

00:05:29.550 --> 00:05:32.410
The British government tired
to prevent more conflict

00:05:32.410 --> 00:05:35.100
between white settlers
and indigenous people

00:05:35.100 --> 00:05:38.510
with the Proclamation of 1763,

00:05:38.510 --> 00:05:42.010
which stipulated that the
colonists could not expand west

00:05:42.010 --> 00:05:43.970
past the Appalachian Mountains.

00:05:43.970 --> 00:05:47.690
Gender roles in the American
colonies mimicked those

00:05:47.690 --> 00:05:49.800
of British society pretty closely.

00:05:49.800 --> 00:05:51.960
White men did farm labor.

00:05:51.960 --> 00:05:54.690
Women cared for the home and children.

00:05:54.690 --> 00:05:58.630
A woman had no political or legal identity

00:05:58.630 --> 00:06:01.960
apart from her husband in a
practice called coverture,

00:06:01.960 --> 00:06:04.850
so a married woman couldn't
own property or vote.

00:06:04.850 --> 00:06:09.527
Both enslaved men and enslaved
women worked in the fields.

00:06:09.527 --> 00:06:11.930
(yawns)

00:06:11.930 --> 00:06:14.000
All this history has tired me out.

00:06:14.000 --> 00:06:15.520
Let's take a little rest and come back

00:06:15.520 --> 00:06:16.723
to our chart in a minute.

00:06:16.723 --> 00:06:19.008
(crickets chirping)

00:06:19.008 --> 00:06:20.410
Ah, that was a nice nap.

00:06:20.410 --> 00:06:21.500
Hang on, what year is it?

00:06:21.500 --> 00:06:23.710
Did we sleep through the
whole American Revolution?

00:06:23.710 --> 00:06:25.610
Yikes, let's finish this chart quickly.

00:06:25.610 --> 00:06:28.320
How different were political institutions,

00:06:28.320 --> 00:06:31.930
social structures, and gender
roles after the Revolution?

00:06:31.930 --> 00:06:35.040
In terms of politics, things had changed.

00:06:35.040 --> 00:06:38.180
Instead of 13 separate
colonies ruled by a king

00:06:38.180 --> 00:06:40.730
and Parliament, there was one nation ruled

00:06:40.730 --> 00:06:42.660
by a three-branch government,

00:06:42.660 --> 00:06:45.930
where citizens were directly
represented in Congress.

00:06:45.930 --> 00:06:48.250
Instead of the rights of Englishmen,

00:06:48.250 --> 00:06:52.510
people appealed to Enlightenment
ideas of natural rights,

00:06:52.510 --> 00:06:55.090
with protections from government tyranny

00:06:55.090 --> 00:06:57.710
enshrined in a Bill of Rights.

00:06:57.710 --> 00:07:01.500
Many states reduced or eliminated property

00:07:01.500 --> 00:07:03.630
and religious requirements for voting,

00:07:03.630 --> 00:07:06.130
expanding the electorate among white men.

00:07:06.130 --> 00:07:08.920
Overall, social structures
were pretty similar,

00:07:08.920 --> 00:07:11.140
with the exception that the institution

00:07:11.140 --> 00:07:14.690
of slavery was being phased
out in northern states,

00:07:14.690 --> 00:07:18.180
and the indentured servitude
of whites was being phased out

00:07:18.180 --> 00:07:19.210
pretty much everywhere.

00:07:19.210 --> 00:07:21.490
In the South, slavery continued.

00:07:21.490 --> 00:07:24.520
For indigenous people,
American independence meant

00:07:24.520 --> 00:07:28.060
that that Proclamation line
was no longer being enforced

00:07:28.060 --> 00:07:30.830
and white settlers saw western lands

00:07:30.830 --> 00:07:33.950
as one of the prizes of
victory in the Revolution.

00:07:33.950 --> 00:07:37.880
Gender roles also looked pretty
similar to before the war.

00:07:37.880 --> 00:07:41.930
Coverture remained, and men
and women continued working

00:07:41.930 --> 00:07:45.210
at the same tasks that they
had prior to independence.

00:07:45.210 --> 00:07:49.320
One minor difference was
the elevation in the status

00:07:49.320 --> 00:07:52.940
of white women, who earned
respect for their contributions

00:07:52.940 --> 00:07:55.400
to the war effort as Daughters of Liberty.

00:07:55.400 --> 00:07:57.500
After the Revolution, they took up roles

00:07:57.500 --> 00:08:01.410
as Republican mothers who
instilled civic virtue

00:08:01.410 --> 00:08:04.690
in their sons and also
required more education

00:08:04.690 --> 00:08:08.050
in order to properly
inculcate those values.

00:08:08.050 --> 00:08:11.230
So, what do we make of these
changes in continuities?

00:08:11.230 --> 00:08:13.340
The biggest area of change was going from

00:08:13.340 --> 00:08:15.740
hereditary monarchy to democracy,

00:08:15.740 --> 00:08:17.420
expanding the vote for white men.

00:08:17.420 --> 00:08:21.500
The ideas of liberty and
equality had some impact

00:08:21.500 --> 00:08:23.740
on social structures and gender roles,

00:08:23.740 --> 00:08:27.370
leading to the gradual abolition
of slavery in the North

00:08:27.370 --> 00:08:29.340
and some new opportunities for women.

00:08:29.340 --> 00:08:31.670
If I were to answer our question

00:08:31.670 --> 00:08:34.170
with one of those three options,

00:08:34.170 --> 00:08:38.810
I'd say some things changed and
some things stayed the same.

00:08:38.810 --> 00:08:41.400
The Revolution changed
the rhetoric of rights

00:08:41.400 --> 00:08:43.700
and expanded democracy for white men

00:08:43.700 --> 00:08:46.870
but didn't have much of a
positive impact on the lives

00:08:46.870 --> 00:08:50.140
of women, enslaved people,
or indigenous people.

00:08:50.140 --> 00:08:52.900
Now, you could choose
totally different aspects

00:08:52.900 --> 00:08:54.810
of society to look at and come up

00:08:54.810 --> 00:08:56.850
with a completely different take than me.

00:08:56.850 --> 00:08:59.570
This is what being a
historian is all about.

00:08:59.570 --> 00:09:01.860
If we take care to select aspects

00:09:01.860 --> 00:09:04.760
of society to compare across time,

00:09:04.760 --> 00:09:07.500
we can answer some tough questions about

00:09:07.500 --> 00:09:09.340
how society changed.

00:09:09.340 --> 00:09:10.173
Sleep tight.


The mole and Avogadro's number

WEBVTT
Kind: captions
Language: en

00:00:00.800 --> 00:00:01.660
- [Instructor] In a previous video,

00:00:01.660 --> 00:00:06.660
we introduced ourselves to the
idea of average atomic mass,

00:00:06.940 --> 00:00:09.900
which we began to realize
could be a very useful way

00:00:09.900 --> 00:00:13.080
of thinking about a
mass at an atomic level,

00:00:13.080 --> 00:00:15.370
or at a molecular level.

00:00:15.370 --> 00:00:16.930
But, what we're gonna do in this video

00:00:16.930 --> 00:00:19.950
is connect it to the masses
that we might actually see

00:00:19.950 --> 00:00:20.783
in a chemistry lab.

00:00:20.783 --> 00:00:23.610
You're very unlikely to just
be dealing with one atom,

00:00:23.610 --> 00:00:26.110
or just a few atoms, or
just a few molecules.

00:00:26.110 --> 00:00:28.560
You're more likely to
deal with several grams

00:00:28.560 --> 00:00:30.360
of an actual substance.

00:00:30.360 --> 00:00:33.840
So, how do we go from the
masses at an atomic scale

00:00:33.840 --> 00:00:38.840
to the masses, masses of samples

00:00:39.110 --> 00:00:41.690
that you see in an actual chemistry lab,

00:00:41.690 --> 00:00:45.610
or in, I guess you could
say, r-scale of the world.

00:00:45.610 --> 00:00:47.550
Well, the chemistry
community has come up with

00:00:47.550 --> 00:00:49.060
a useful tool.

00:00:49.060 --> 00:00:51.360
They said, all right, let's
think about a given element.

00:00:51.360 --> 00:00:52.330
So, say, lithium.

00:00:52.330 --> 00:00:55.683
We know its average atomic mass is 6.94,

00:00:55.683 --> 00:01:00.683
6.94 unified atomic mass units
per atom, atom of lithium.

00:01:05.180 --> 00:01:09.370
What if there were a certain
number of atoms of lithium

00:01:09.370 --> 00:01:12.370
such that if I have that number,

00:01:12.370 --> 00:01:17.370
so times certain, certain number of atoms,

00:01:19.210 --> 00:01:23.093
then I will actually
end up with 6.94 grams,

00:01:25.900 --> 00:01:28.700
grams of lithium.

00:01:28.700 --> 00:01:32.017
And, this number of atoms is 6.02214076

00:01:36.600 --> 00:01:40.840
times 10 to the 23rd power.

00:01:40.840 --> 00:01:44.920
So, if you have a sample with
this number of lithium atoms,

00:01:44.920 --> 00:01:49.170
that sample is going to
have a mass of 6.94 grams.

00:01:49.170 --> 00:01:51.160
Whatever its average atomic mass is

00:01:51.160 --> 00:01:53.470
in terms of unified atomic mass units,

00:01:53.470 --> 00:01:56.870
if you have that number of the atom,

00:01:56.870 --> 00:02:01.870
you will have a mass of that
same number in terms of grams.

00:02:02.420 --> 00:02:05.840
Now, you might be saying, is
there a name for this number,

00:02:05.840 --> 00:02:07.670
and there is indeed a name,

00:02:07.670 --> 00:02:10.070
and it is called Avogadro's number,

00:02:10.070 --> 00:02:14.690
named in honor of the early
19th century Italian chemist,

00:02:14.690 --> 00:02:16.390
Amedeo Avogadro.

00:02:16.390 --> 00:02:20.030
And, in most contexts,
because you're not normally

00:02:20.030 --> 00:02:23.220
dealing with data with this
many significant digits,

00:02:23.220 --> 00:02:25.280
we will usually approximate it as

00:02:25.280 --> 00:02:30.280
6.022 times 10 to the 23rd power.

00:02:30.860 --> 00:02:33.950
Now, there's another word
that it's very useful

00:02:33.950 --> 00:02:36.440
to familiarize yourself with in chemistry,

00:02:36.440 --> 00:02:40.360
and that's the idea of a mole.

00:02:40.360 --> 00:02:42.900
Now, what is a mole?

00:02:42.900 --> 00:02:44.800
It is not a little mark on your cheek.

00:02:44.800 --> 00:02:46.340
It is not a burrowing animal.

00:02:46.340 --> 00:02:48.220
Actually, it is both of those things,

00:02:48.220 --> 00:02:49.960
but, in a chemistry context,

00:02:49.960 --> 00:02:54.690
a mole is just saying you
have this much of something.

00:02:54.690 --> 00:02:57.300
The word mole was first
used by the German chemist

00:02:57.300 --> 00:03:00.870
Wilhelm Ostwald at the
end of the 19th century,

00:03:00.870 --> 00:03:02.170
and he came up with the word

00:03:02.170 --> 00:03:05.030
because of its relation to molecule.

00:03:05.030 --> 00:03:06.760
Now, what does that mean?

00:03:06.760 --> 00:03:09.280
Well, think about the word dozen.

00:03:09.280 --> 00:03:12.300
If I say I've got a dozen of eggs,

00:03:12.300 --> 00:03:14.680
how many eggs do I have?

00:03:14.680 --> 00:03:16.370
Well, if I have a dozen of eggs,

00:03:16.370 --> 00:03:18.570
that means I have 12 eggs.

00:03:18.570 --> 00:03:22.240
So, if I say I have a
mole of lithium atoms,

00:03:22.240 --> 00:03:24.800
how many lithium atoms do I have?

00:03:24.800 --> 00:03:27.770
That means that I have 6.02214076

00:03:29.690 --> 00:03:33.250
times 10 the to 23rd lithium atoms.

00:03:33.250 --> 00:03:36.510
Exact same idea, it's just
that Avogadro's number

00:03:36.510 --> 00:03:40.103
is much hairier of a number than a dozen.

00:03:40.940 --> 00:03:45.230
So, let's use our new
found powers of the mole

00:03:45.230 --> 00:03:49.380
and Avogadro's number to start
doing some useful things.

00:03:49.380 --> 00:03:53.010
Let's say that someone were
to walk up to you and say,

00:03:53.010 --> 00:03:58.010
hey, you, I have a 15.4
milligram sample of germanium.

00:04:02.120 --> 00:04:07.120
How many atoms of germanium
am I dealing with?

00:04:08.050 --> 00:04:10.300
Pause this video and
try to think about that.

00:04:11.780 --> 00:04:13.520
So, let me clear out some space

00:04:13.520 --> 00:04:16.423
the periodic table of
elements was taking up.

00:04:17.490 --> 00:04:19.100
All right, so we started off

00:04:19.100 --> 00:04:24.100
with 15.4 milligrams of germanium.

00:04:24.690 --> 00:04:26.800
The first step might be
hey, let's convert this

00:04:26.800 --> 00:04:29.210
to grams of germanium.

00:04:29.210 --> 00:04:32.460
And so, we can do a little
bit of dimensional analysis.

00:04:32.460 --> 00:04:34.040
We can just multiply this,

00:04:34.040 --> 00:04:37.370
for every one gram of germanium

00:04:37.370 --> 00:04:41.130
that is equivalent to 1,000 milligrams,

00:04:41.130 --> 00:04:42.950
milligrams of germanium.

00:04:42.950 --> 00:04:46.010
And so, if you essentially
multiply by one thousandth

00:04:46.010 --> 00:04:50.750
or divide by 1,000, we're gonna
get the grams of germanium.

00:04:50.750 --> 00:04:52.720
And, you can see that in
the dimensional analysis

00:04:52.720 --> 00:04:54.960
by seeing that that is going
to cancel out with that

00:04:54.960 --> 00:04:58.020
leaving us with just
the grams of germanium.

00:04:58.020 --> 00:05:01.130
And, now that we have an
expression for grams of germanium,

00:05:01.130 --> 00:05:03.350
we can think about moles of germanium.

00:05:03.350 --> 00:05:05.350
So, how do we do that?

00:05:05.350 --> 00:05:07.940
Well, we're going to
multiply by some quantity,

00:05:07.940 --> 00:05:09.710
and in the denominator we're going to want

00:05:09.710 --> 00:05:12.920
grams of germanium for the
dimensional analysis to work out,

00:05:12.920 --> 00:05:16.190
grams of germanium, and
in the numerator we want

00:05:16.190 --> 00:05:21.190
the new expression to be in
terms of moles of germanium.

00:05:21.300 --> 00:05:24.270
So, one mole of germanium is equal to

00:05:24.270 --> 00:05:26.990
how many grams of germanium?

00:05:26.990 --> 00:05:28.650
Well, we see it right over here.

00:05:28.650 --> 00:05:33.650
Germanium's molar mass
is 72.63 grams per mole.

00:05:33.780 --> 00:05:38.780
So, for every mole, we have
72.63 grams of germanium.

00:05:40.660 --> 00:05:42.780
And, you can see that the units work out.

00:05:42.780 --> 00:05:44.820
These grams of germanium
are going to cancel

00:05:44.820 --> 00:05:46.350
with the grams of germanium

00:05:46.350 --> 00:05:50.080
just leaving us with moles of germanium.

00:05:50.080 --> 00:05:51.590
In an actual chemistry practice,

00:05:51.590 --> 00:05:53.710
finding out the moles of a substance

00:05:53.710 --> 00:05:56.440
might actually be the most useful thing,

00:05:56.440 --> 00:05:59.280
but if you wanted to find out
the actual atoms of germanium

00:05:59.280 --> 00:06:01.710
that we're dealing with,
we will just multiply by

00:06:01.710 --> 00:06:03.670
the number of atoms you have per mole.

00:06:03.670 --> 00:06:06.430
And, this is going to
be true for any element.

00:06:06.430 --> 00:06:10.710
For every mole, you have
Avogadro's number of atoms.

00:06:10.710 --> 00:06:12.550
And, we're going to approximate that as

00:06:12.550 --> 00:06:17.550
6.022 times 10 to the 23rd
atoms, atoms of germanium,

00:06:20.620 --> 00:06:25.620
for every one mole, mole of germanium.

00:06:27.040 --> 00:06:29.370
And so, just to review what we just did,

00:06:29.370 --> 00:06:31.230
we had milligrams of germanium.

00:06:31.230 --> 00:06:32.820
You multiply these two together,

00:06:32.820 --> 00:06:34.910
you'll have grams of
germanium, which makes sense,

00:06:34.910 --> 00:06:37.120
you're essentially just dividing by 1,000.

00:06:37.120 --> 00:06:39.570
If you were to multiply
your grams of germanium

00:06:39.570 --> 00:06:42.100
times the moles per gram,

00:06:42.100 --> 00:06:43.480
which is really just the reciprocal

00:06:43.480 --> 00:06:45.110
of this molar mass we got here,

00:06:45.110 --> 00:06:47.360
and just to make sure
where it makes sense,

00:06:47.360 --> 00:06:50.330
the units work out nice with
the dimensional analysis,

00:06:50.330 --> 00:06:53.370
this right over here tells you your moles,

00:06:53.370 --> 00:06:55.940
moles of germanium.

00:06:55.940 --> 00:06:57.410
And then, if you take your moles

00:06:57.410 --> 00:07:00.050
and then you multiply
it by Avogadro's number,

00:07:00.050 --> 00:07:02.020
it tells you how many
atoms of germanium we have,

00:07:02.020 --> 00:07:02.853
and that makes sense.

00:07:02.853 --> 00:07:04.950
If I told you I had a certain
number of dozen of eggs,

00:07:04.950 --> 00:07:06.470
if I wanted to know how many eggs that is

00:07:06.470 --> 00:07:08.480
I would multiply by 12.

00:07:08.480 --> 00:07:13.480
So, this whole expression
is the number of atoms,

00:07:13.900 --> 00:07:16.960
atoms of germanium.

00:07:16.960 --> 00:07:21.490
So, we have 15.4 milligrams.

00:07:21.490 --> 00:07:23.510
If we wanna figure out
how many grams we have,

00:07:23.510 --> 00:07:25.190
we then divide by 1,000,

00:07:25.190 --> 00:07:26.910
that's what our dimensional
analysis tells us,

00:07:26.910 --> 00:07:28.810
and it also makes logical sense,

00:07:28.810 --> 00:07:30.650
divided by 1,000.

00:07:30.650 --> 00:07:33.600
So, this is how many grams we have.

00:07:33.600 --> 00:07:35.690
And then, if we wanna
figure out how many moles,

00:07:35.690 --> 00:07:38.290
and it's going to be a
small fraction of a mole

00:07:38.290 --> 00:07:41.790
because a mole is 72.63 grams per mole,

00:07:41.790 --> 00:07:44.230
we have a small fraction of a gram,

00:07:44.230 --> 00:07:46.320
much less 72.63 grams.

00:07:46.320 --> 00:07:48.070
And so, we saw from our analysis

00:07:48.070 --> 00:07:49.160
to figure out the number of moles,

00:07:49.160 --> 00:07:52.430
we're now going to
essentially divide by 72.63,

00:07:52.430 --> 00:07:57.430
so divided by 72.63 is equal to,

00:07:57.810 --> 00:08:01.200
this is the number of
moles of germanium we have.

00:08:01.200 --> 00:08:03.260
And, if we wanna figure
out the number of atoms

00:08:03.260 --> 00:08:05.100
of germanium, we'll then multiply that

00:08:05.100 --> 00:08:06.640
times Avogadro's number.

00:08:06.640 --> 00:08:11.640
So, times 6.022 times 10 to the 23rd,

00:08:12.270 --> 00:08:15.900
and this EE button means times-10-to-the,

00:08:15.900 --> 00:08:19.750
EE 23rd power, so that's how
you do it on a calculator.

00:08:19.750 --> 00:08:24.260
And then, that gives us this many atoms.

00:08:24.260 --> 00:08:27.670
And, let's see, just to get
our significant digits here,

00:08:27.670 --> 00:08:29.960
our significant figures,
out of all of the things

00:08:29.960 --> 00:08:33.290
we multiplied, see we had
four significant digits here,

00:08:33.290 --> 00:08:34.370
four significant digits here,

00:08:34.370 --> 00:08:36.010
but we only had three over here,

00:08:36.010 --> 00:08:38.140
so I'm going to round to
three significant digits.

00:08:38.140 --> 00:08:43.140
So, I'll go to 1.28 times
10 to the 20th atoms.

00:08:43.860 --> 00:08:46.270
So, we have approximately

00:08:46.270 --> 00:08:51.270
1.28 times 10 to the
20th atoms of germanium,

00:08:54.690 --> 00:08:55.643
which is a lot.


Average atomic mass

WEBVTT
Kind: captions
Language: en

00:00:00.890 --> 00:00:02.300
- [Instructor] The thing
that I've always found

00:00:02.300 --> 00:00:04.300
amazing about chemistry,

00:00:04.300 --> 00:00:06.390
it's an entire field of science

00:00:06.390 --> 00:00:09.130
that we as human beings have developed

00:00:09.130 --> 00:00:11.950
to actually understand what is happening

00:00:11.950 --> 00:00:15.340
in an almost unimaginably small scale.

00:00:15.340 --> 00:00:17.970
In particular we're gonna be
thinking about the atomic,

00:00:17.970 --> 00:00:20.930
and even the subatomic scale.

00:00:20.930 --> 00:00:24.920
And by looking at that scale
we can then begin to understand

00:00:24.920 --> 00:00:26.890
the universe in which we live in,

00:00:26.890 --> 00:00:28.280
the scale in which we live in,

00:00:28.280 --> 00:00:32.160
and even be able to make
predictions about what will happen,

00:00:32.160 --> 00:00:37.030
and make things that are
useful for human beings.

00:00:37.030 --> 00:00:40.700
So if we're going to operate
at this small of a scale,

00:00:40.700 --> 00:00:42.580
and we're gonna appreciate
in a few seconds

00:00:42.580 --> 00:00:45.000
how small of a scale it is,

00:00:45.000 --> 00:00:48.010
we're going to have to have
some units of measurement.

00:00:48.010 --> 00:00:51.960
And this video is going to focus on mass.

00:00:51.960 --> 00:00:55.670
How do we measure mass
at such a small scale?

00:00:55.670 --> 00:00:58.290
Well to do that the chemistry community

00:00:58.290 --> 00:01:02.380
has historically used something
called an atomic mass unit.

00:01:02.380 --> 00:01:07.380
I'll write it here,
atomic, atomic mass unit,

00:01:08.900 --> 00:01:12.560
and it's historically denoted as AMU.

00:01:12.560 --> 00:01:14.260
And more recently,

00:01:14.260 --> 00:01:15.710
the more modern version of this

00:01:15.710 --> 00:01:18.000
is the unified atomic mass unit,

00:01:18.000 --> 00:01:22.890
that is denoted by just
a U instead of an AMU.

00:01:22.890 --> 00:01:25.210
So how does a unified atomic mass unit

00:01:25.210 --> 00:01:26.910
connect to our units of mass

00:01:26.910 --> 00:01:28.570
that we might use on a larger scale

00:01:28.570 --> 00:01:31.740
like, say, grams or kilograms.

00:01:31.740 --> 00:01:36.733
Well, the unified atomic
mass unit is defined as

00:01:36.733 --> 00:01:41.733
1.660540 times 10

00:01:42.560 --> 00:01:47.400
to the negative 27 kilograms.

00:01:47.400 --> 00:01:50.360
So when you see something like this,

00:01:50.360 --> 00:01:52.010
you might have a few reactions.

00:01:52.010 --> 00:01:55.220
Your first reaction, which would
be an appropriate reaction,

00:01:55.220 --> 00:02:00.220
is that wow, 10 to the negative
27 power is very small.

00:02:00.710 --> 00:02:02.340
To appreciate it you could write it out,

00:02:02.340 --> 00:02:06.020
it would be zero point and then 26 zeros

00:02:06.020 --> 00:02:08.720
and then you would have one
six six zero five four zero.

00:02:08.720 --> 00:02:11.920
So very, very, very small,
really unimaginably small.

00:02:11.920 --> 00:02:15.700
We can only try to abstract it
with things like mathematics.

00:02:15.700 --> 00:02:16.860
The other thing you might appreciate

00:02:16.860 --> 00:02:19.940
is this feels like a bit
of a hairy number here,

00:02:19.940 --> 00:02:24.940
1.660540, why did they define it that way?

00:02:25.940 --> 00:02:28.300
And the answer to your question is,

00:02:28.300 --> 00:02:31.180
this definition makes it a lot cleaner

00:02:31.180 --> 00:02:34.660
when we think about the
mass of whether it's an atom

00:02:34.660 --> 00:02:39.240
or the constituents of an atom
like a proton or a neutron.

00:02:39.240 --> 00:02:42.750
Roughly speaking the mass of a proton

00:02:43.720 --> 00:02:48.350
is approximately one
unified atomic mass unit.

00:02:48.350 --> 00:02:50.136
The mass of a neutron

00:02:50.136 --> 00:02:55.136
is approximately one
unified atomic mass unit.

00:02:55.350 --> 00:02:56.880
It actually turns out that a proton's

00:02:56.880 --> 00:02:58.560
a little bit more than one,

00:02:58.560 --> 00:03:03.560
it's about 1.007 atomic mass units,

00:03:03.570 --> 00:03:05.290
but it's approximately one.

00:03:05.290 --> 00:03:07.070
And the neutron is
actually a little bit more

00:03:07.070 --> 00:03:08.330
than even a proton,

00:03:08.330 --> 00:03:13.330
it's 1.008 approximately
unified atomic mass units.

00:03:14.640 --> 00:03:16.950
Now an electron's mass
is actually far smaller

00:03:16.950 --> 00:03:17.900
than either of these,

00:03:17.900 --> 00:03:19.810
it's actually almost one two thousandth

00:03:19.810 --> 00:03:21.260
of a proton or a neutron,

00:03:21.260 --> 00:03:23.080
and so you can imagine an atom

00:03:23.080 --> 00:03:24.390
which is made up of protons

00:03:24.390 --> 00:03:27.050
and usually neutrons
and electrons as well,

00:03:27.050 --> 00:03:29.340
the mass is mainly going to be

00:03:29.340 --> 00:03:31.770
the protons and neutrons in the nucleus.

00:03:31.770 --> 00:03:34.190
And so if you know the number of protons

00:03:34.190 --> 00:03:35.840
and neutrons in the nucleus,

00:03:35.840 --> 00:03:37.500
you're going to have a pretty good sense

00:03:37.500 --> 00:03:39.780
of its atomic mass.

00:03:39.780 --> 00:03:41.720
And you can see that indicated

00:03:41.720 --> 00:03:46.080
on a periodic table of
elements which we have here.

00:03:46.080 --> 00:03:48.300
And we will study the
periodic table of elements

00:03:48.300 --> 00:03:51.100
in a lot more detail in other videos.

00:03:51.100 --> 00:03:53.070
But you can see a couple
of interesting elements.

00:03:53.070 --> 00:03:54.990
One, you have the abbreviation
of a given element,

00:03:54.990 --> 00:03:56.578
H represents hydrogen.

00:03:56.578 --> 00:03:58.830
The number on top on this periodic table,

00:03:58.830 --> 00:04:00.110
that's the atomic number,

00:04:00.110 --> 00:04:02.660
and that tells you how
many protons it has.

00:04:02.660 --> 00:04:06.370
And an element is defined
by the number of protons.

00:04:06.370 --> 00:04:10.260
So any atom that has exactly
one proton in its nucleus

00:04:10.260 --> 00:04:13.070
is going to be hydrogen by definition.

00:04:13.070 --> 00:04:16.720
Any atom that has exactly 20 protons

00:04:16.720 --> 00:04:20.590
in its nucleus is going to
be calcium by definition.

00:04:20.590 --> 00:04:23.760
Any atom that has exactly
36 protons in its nucleus

00:04:23.760 --> 00:04:27.620
is going to be krypton by definition.

00:04:27.620 --> 00:04:31.960
So what would you expect the
mass of a hydrogen atom to be?

00:04:31.960 --> 00:04:34.070
Pause this video and think about it.

00:04:34.070 --> 00:04:36.520
Well we know that all hydrogen atoms

00:04:36.520 --> 00:04:39.840
by definition have one proton,

00:04:39.840 --> 00:04:40.710
but it actually turns out

00:04:40.710 --> 00:04:42.640
there's different versions of hydrogen

00:04:42.640 --> 00:04:45.460
that can have different
numbers of neutrons.

00:04:45.460 --> 00:04:47.350
Most of the hydrogen in the universe

00:04:47.350 --> 00:04:51.430
actually has zero neutrons, zero neutrons.

00:04:51.430 --> 00:04:55.800
There are versions that
have one or two neutrons,

00:04:55.800 --> 00:05:00.800
but most, 99.98% roughly,
of hydrogen in the universe

00:05:01.686 --> 00:05:04.150
has one proton, zero neutrons,

00:05:04.150 --> 00:05:05.850
and if it's a neutral hydrogen

00:05:05.850 --> 00:05:08.010
it's going to have one electron.

00:05:08.010 --> 00:05:11.050
And when we talk about
versions of a given element

00:05:11.050 --> 00:05:14.100
there's a fancy word for
it, they're called isotopes.

00:05:14.100 --> 00:05:15.370
And the different isotopes,

00:05:15.370 --> 00:05:17.090
they'll all have the
same number of protons

00:05:17.090 --> 00:05:18.960
'cause they're talking
about the same element,

00:05:18.960 --> 00:05:22.130
but they'll have different
numbers of neutrons.

00:05:22.130 --> 00:05:26.270
And so if this is the most
common form of hydrogen.

00:05:26.270 --> 00:05:28.520
What do you think its mass is going to be?

00:05:28.520 --> 00:05:30.760
Well its mass is going to
be essentially the mass

00:05:30.760 --> 00:05:32.520
of a proton plus an electron,

00:05:32.520 --> 00:05:35.140
and roughly speaking it's going
to be the mass of a proton

00:05:35.140 --> 00:05:36.120
'cause the mass of a proton's

00:05:36.120 --> 00:05:38.460
going to be so much larger
than the mass of an electron.

00:05:38.460 --> 00:05:40.020
And so you would expect

00:05:40.020 --> 00:05:45.020
that its mass is approximately
one unified atomic mass unit.

00:05:45.770 --> 00:05:47.510
Now if you were to precisely look at

00:05:47.510 --> 00:05:51.370
the mass of a proton and a electron,

00:05:51.370 --> 00:05:53.730
if you add them together,
you actually get something

00:05:53.730 --> 00:05:57.490
that's a little bit closer to 1.008.

00:05:57.490 --> 00:05:59.030
And you actually see that

00:05:59.030 --> 00:06:02.400
right over here on the
periodic table of elements.

00:06:02.400 --> 00:06:06.530
Now this number, although
it is pretty close

00:06:06.530 --> 00:06:09.660
to the mass of the version of hydrogen

00:06:09.660 --> 00:06:11.190
that I just described,

00:06:11.190 --> 00:06:12.995
it's actually a weighted average

00:06:12.995 --> 00:06:16.010
of the various versions of hydrogen.

00:06:16.010 --> 00:06:17.480
It's just close to this version

00:06:17.480 --> 00:06:20.550
because this version
represents most of the hydrogen

00:06:20.550 --> 00:06:23.350
that we actually see around us.

00:06:23.350 --> 00:06:27.120
If for example you had two
versions of an element,

00:06:27.120 --> 00:06:28.620
some hypothetical element,

00:06:28.620 --> 00:06:31.800
and let's say that 80% of the element

00:06:31.800 --> 00:06:34.130
that we see is version one

00:06:34.130 --> 00:06:35.970
and version one has a mass

00:06:35.970 --> 00:06:38.400
of let's call it five atomic mass units,

00:06:38.400 --> 00:06:41.970
and then version two,
it's the remainder, 20%,

00:06:41.970 --> 00:06:43.710
of what we observe of that element,

00:06:43.710 --> 00:06:47.650
it has an atomic mass of
six atomic mass units.

00:06:47.650 --> 00:06:49.370
You would get a weighted average here

00:06:49.370 --> 00:06:53.410
of 5.2 unified atomic mass units.

00:06:53.410 --> 00:06:57.800
And that's actually how
these numbers are calculated.

00:06:57.800 --> 00:07:02.020
They are not just the mass
of one type of that element,

00:07:02.020 --> 00:07:03.860
they're a weighted average mass

00:07:03.860 --> 00:07:06.670
of the various isotopes,
of the various types.

00:07:06.670 --> 00:07:10.270
And so this number on a
periodic table of elements

00:07:10.270 --> 00:07:14.340
is known as the average atomic mass,

00:07:14.340 --> 00:07:19.293
average, average atomic atomic mass.

00:07:21.470 --> 00:07:23.320
Now in older chemistry books,

00:07:23.320 --> 00:07:24.290
and this is actually the case

00:07:24.290 --> 00:07:25.740
when I first learned chemistry,

00:07:25.740 --> 00:07:28.320
they call this number atomic weight.

00:07:28.320 --> 00:07:29.940
And I've always complained about it

00:07:29.940 --> 00:07:32.270
because it's really talking
about mass and not weight.

00:07:32.270 --> 00:07:33.160
If you don't know the difference

00:07:33.160 --> 00:07:35.240
you'll learn that at
some point in the future,

00:07:35.240 --> 00:07:39.010
and it's really talking
about average atomic mass.

00:07:39.010 --> 00:07:40.610
Now I'll give you one little detail

00:07:40.610 --> 00:07:41.960
that might be useful to you.

00:07:41.960 --> 00:07:45.370
Sometimes you'll hear something
called relative atomic mass.

00:07:45.370 --> 00:07:47.940
It actually turns out this
periodic table of elements,

00:07:47.940 --> 00:07:49.740
because it does not write a little U

00:07:49.740 --> 00:07:51.260
after each of these numbers,

00:07:51.260 --> 00:07:53.620
it's essentially these
number are unitless,

00:07:53.620 --> 00:07:56.370
so it's really talking
about relative atomic mass.

00:07:56.370 --> 00:07:59.900
So it's saying, hey on
average, for example,

00:07:59.900 --> 00:08:01.959
the mass of a carbon atom

00:08:01.959 --> 00:08:04.533
is going to be roughly 12 times that of,

00:08:04.533 --> 00:08:08.540
on average, the mass of a hydrogen atom.

00:08:08.540 --> 00:08:10.567
If they put the units here,

00:08:10.567 --> 00:08:14.460
then that would actually
truly be average atomic mass.

00:08:14.460 --> 00:08:17.160
But for our purposes,
as we go into chemistry,

00:08:17.160 --> 00:08:18.930
you can look at these numbers,

00:08:18.930 --> 00:08:23.430
and say okay, if oxygen has
a relative atomic mass of 16,

00:08:23.430 --> 00:08:25.180
it's average atomic mass

00:08:25.180 --> 00:08:30.050
is going to be 16 unified
atomic mass units.

00:08:30.050 --> 00:08:32.280
And as we will see in the future,

00:08:32.280 --> 00:08:34.870
this understanding of average atomic mass

00:08:34.870 --> 00:08:37.603
will prove to be very, very useful.


Subtracting fractions with unlike denominators introduction

WEBVTT
Kind: captions
Language: en

00:00:00.120 --> 00:00:01.370
- [Instructor] Let's say
we wanted to figure out

00:00:01.370 --> 00:00:05.750
what one half minus one third is equal to.

00:00:05.750 --> 00:00:08.980
And we can visualize
each of these fractions.

00:00:08.980 --> 00:00:13.140
One half could look like
that where if I take a whole

00:00:13.140 --> 00:00:15.590
and if I divide it into
two equal sections,

00:00:15.590 --> 00:00:18.500
one of those two equal
sections would be a half

00:00:18.500 --> 00:00:20.260
and you see that shaded in green here.

00:00:20.260 --> 00:00:23.440
And then from that, we're
trying to subtract a third

00:00:23.440 --> 00:00:25.880
and we can visualize a third this way.

00:00:25.880 --> 00:00:27.900
That if this whole thing is a whole,

00:00:27.900 --> 00:00:29.620
I divide it into three equal sections

00:00:29.620 --> 00:00:33.460
and one of those three
equal sections is a third.

00:00:33.460 --> 00:00:36.920
So what we wanna do is
take away this gray box

00:00:36.920 --> 00:00:39.490
from this green box and figure out

00:00:39.490 --> 00:00:42.930
how we can mathematically
say what is left over.

00:00:42.930 --> 00:00:46.170
So pause this video and see
if you can have a go at this.

00:00:46.170 --> 00:00:48.910
And I'll give you a
hint, it will be useful

00:00:48.910 --> 00:00:51.990
to be able to represent
your halves and thirds

00:00:51.990 --> 00:00:54.313
in terms of a different denominator.

00:00:55.810 --> 00:00:59.170
All right, now let's work
through this together.

00:00:59.170 --> 00:01:01.970
So the way that we can approach this is

00:01:01.970 --> 00:01:04.210
to get a common denominator.

00:01:04.210 --> 00:01:06.230
If I can express both fractions

00:01:06.230 --> 00:01:07.983
in terms of the same denominator,

00:01:07.983 --> 00:01:10.720
it's going to be a lot easier to subtract.

00:01:10.720 --> 00:01:13.420
And the common denominator
that's most useful

00:01:13.420 --> 00:01:16.510
is to find the least common denominator.

00:01:16.510 --> 00:01:17.820
And the smallest number

00:01:17.820 --> 00:01:20.310
that is both a multiple of two and three

00:01:20.310 --> 00:01:22.850
is actually two times three, or six.

00:01:22.850 --> 00:01:25.160
So what if we were to
write each of these numbers

00:01:25.160 --> 00:01:27.500
in terms of sixths.

00:01:27.500 --> 00:01:31.235
So how can we rewrite one
half in terms of sixths?

00:01:31.235 --> 00:01:33.390
I always have trouble saying that.

00:01:33.390 --> 00:01:36.630
Well if I start with one
half and if I multiply

00:01:36.630 --> 00:01:38.430
the denominator by three,

00:01:38.430 --> 00:01:40.050
that's going to get us to sixths

00:01:40.050 --> 00:01:42.060
and so I don't change the
value of the fraction.

00:01:42.060 --> 00:01:44.430
I need to multiply the
numerator by three as well.

00:01:44.430 --> 00:01:46.260
As long as I multiply both the numerator

00:01:46.260 --> 00:01:48.410
and the denominator by the same thing.

00:01:48.410 --> 00:01:51.360
Well, then that's still
going to be equal to one half

00:01:51.360 --> 00:01:54.950
and you can visualize
what that looks like.

00:01:54.950 --> 00:01:58.380
If you take each of
these two equal sections

00:01:58.380 --> 00:02:01.320
and turn them into three equal sections,

00:02:01.320 --> 00:02:03.530
well then you're gonna have
a total of six equal sections

00:02:03.530 --> 00:02:04.750
or sixths.

00:02:04.750 --> 00:02:06.430
Two times three in the denominator

00:02:06.430 --> 00:02:08.440
and the part that was shaded in in green

00:02:08.440 --> 00:02:09.820
which was just one of those sections

00:02:09.820 --> 00:02:12.680
is now three times as many sections.

00:02:12.680 --> 00:02:17.680
So your one half is now
equal to three over six.

00:02:19.120 --> 00:02:21.630
And we can do the same thing over here.

00:02:21.630 --> 00:02:23.660
If we start with one third

00:02:23.660 --> 00:02:25.861
how do we express it in terms of sixths?

00:02:25.861 --> 00:02:30.830
Well to go from three to six
I would multiply it by two,

00:02:30.830 --> 00:02:33.320
and so I also wanna do
that in the numerator

00:02:33.320 --> 00:02:35.470
so that I don't change
the value of the fraction

00:02:35.470 --> 00:02:37.690
and we can visualize that.

00:02:37.690 --> 00:02:39.885
Notice, if you take all three sections

00:02:39.885 --> 00:02:43.420
and you turn each of
them into two sections

00:02:43.420 --> 00:02:45.610
you now have six equal sections.

00:02:45.610 --> 00:02:47.820
So you are now dealing with sixths,

00:02:47.820 --> 00:02:50.020
and that one section before

00:02:50.020 --> 00:02:52.660
is now going to become two sections.

00:02:52.660 --> 00:02:56.350
So this is now going to
be equal to two sixths.

00:02:56.350 --> 00:02:59.460
So we can actually rewrite things as

00:02:59.460 --> 00:03:01.600
this is the same thing as

00:03:01.600 --> 00:03:06.600
three sixths minus, minus two sixths.

00:03:07.940 --> 00:03:10.710
And what do you think that is going to be?

00:03:10.710 --> 00:03:13.180
Well if I have three of something

00:03:13.180 --> 00:03:14.580
and I subtract two of them away

00:03:14.580 --> 00:03:17.103
I'm going to be left with
one of that something.

00:03:17.103 --> 00:03:21.120
So I'm going to be left
with one sixth in this case.

00:03:21.120 --> 00:03:23.800
And we can visualize it just the way

00:03:23.800 --> 00:03:25.520
we visualized everything else.

00:03:25.520 --> 00:03:27.790
If you take two of these gray bars

00:03:27.790 --> 00:03:30.880
or two of these sections
from these three sections

00:03:30.880 --> 00:03:32.690
you're just going to be
left with one of them.

00:03:32.690 --> 00:03:35.153
This is one of the six equal sections.


Worked example: Determining an empirical formula from percent composition data

WEBVTT
Kind: captions
Language: en

00:00:00.940 --> 00:00:01.940
- [Instructor] Let's say that we have

00:00:01.940 --> 00:00:04.770
some type of a container that has

00:00:04.770 --> 00:00:08.410
some type of mystery molecule in it.

00:00:08.410 --> 00:00:10.350
So that's my mystery molecule there,

00:00:10.350 --> 00:00:12.930
and we're able to measure the composition

00:00:12.930 --> 00:00:15.510
of the mystery molecule by mass.

00:00:15.510 --> 00:00:20.510
We're able to see that it
is 73% by mass mercury,

00:00:21.800 --> 00:00:25.933
and by mass it is 27% chlorine,

00:00:27.710 --> 00:00:30.970
so the remainder is chlorine by mass.

00:00:30.970 --> 00:00:33.910
So pause this video and
see if you can come up with

00:00:36.263 --> 00:00:38.170
what is likely the empirical formula

00:00:38.170 --> 00:00:42.150
for our mystery molecule in here,

00:00:42.150 --> 00:00:43.550
and as a little bit of a hint,

00:00:43.550 --> 00:00:46.313
a periodic table of
elements might be useful.

00:00:47.350 --> 00:00:50.890
All right, now let's work
through this together,

00:00:50.890 --> 00:00:53.550
and to help us make things
a little bit more tangible,

00:00:53.550 --> 00:00:57.100
I'm just going to assume a
mass for this entire bag.

00:00:57.100 --> 00:01:00.910
Let's just assume it is,

00:01:00.910 --> 00:01:03.250
or this entire container is 100 grams.

00:01:03.250 --> 00:01:05.860
I could have assumed
1,000 grams or 5 grams,

00:01:05.860 --> 00:01:08.130
but 100 grams will make the math easy

00:01:08.130 --> 00:01:09.840
because our whole goal is to say, hey,

00:01:09.840 --> 00:01:13.020
what's the ratio between
the number of moles we have

00:01:13.020 --> 00:01:15.810
of mercury and the number of
the moles we have of chlorine

00:01:15.810 --> 00:01:19.180
and then that will inform
the likely empirical formula.

00:01:19.180 --> 00:01:22.480
So if we assume 100 grams,
well then we are dealing with

00:01:22.480 --> 00:01:27.480
a situation that our mercury,
we have 73 grams of mercury,

00:01:29.300 --> 00:01:31.890
and we can figure out
how many moles this is

00:01:31.890 --> 00:01:35.410
by looking at the average
atomic mass of mercury.

00:01:35.410 --> 00:01:38.610
That's why that periodic
table of elements is useful.

00:01:38.610 --> 00:01:43.610
We see that one mole of mercury
is 200.59 grams on average,

00:01:44.460 --> 00:01:46.420
so we could multiply this times

00:01:46.420 --> 00:01:51.420
one over 200.59 moles per gram.

00:01:55.440 --> 00:01:59.060
So when we multiply this out,
the grams will cancel out

00:01:59.060 --> 00:02:00.300
and we're just going to be left with

00:02:00.300 --> 00:02:02.750
a certain number of moles.

00:02:02.750 --> 00:02:05.750
So I'll take 73 and we're just
going to divide it by 200.59,

00:02:07.802 --> 00:02:10.140
divided by 200.59

00:02:11.700 --> 00:02:16.700
is going to be equal to
0.36, and I'll just say 0.36

00:02:17.110 --> 00:02:18.250
because this is going to be a little bit

00:02:18.250 --> 00:02:20.820
of an estimation game,
and significant digits,

00:02:20.820 --> 00:02:22.160
I only have two significant digits

00:02:22.160 --> 00:02:27.160
on the original mass of
mercury, so 0.36 moles, roughly.

00:02:29.240 --> 00:02:31.100
I'll even say roughly right over there,

00:02:31.100 --> 00:02:33.810
and I can do the same thing with chlorine.

00:02:33.810 --> 00:02:37.990
Chlorine, if I have 27% by mass,

00:02:37.990 --> 00:02:42.000
27% of 100, which I'm
assuming, is 27 grams.

00:02:42.000 --> 00:02:45.710
And then how many grams per mole?

00:02:45.710 --> 00:02:48.290
If I have one mole for chlorine,

00:02:48.290 --> 00:02:53.290
on average on earth the average
atomic mass is 35.45 grams.

00:02:54.490 --> 00:02:58.120
And so this is going to
approximate how many moles

00:02:58.120 --> 00:03:00.130
because the grams are going to cancel out,

00:03:00.130 --> 00:03:02.534
and it makes sense that
this is going to be

00:03:02.534 --> 00:03:07.200
a fraction of a mole because
27 grams is less than 35.45.

00:03:07.200 --> 00:03:12.200
We take 27 divided by 35.45.

00:03:13.000 --> 00:03:17.933
It gets us to 0.76, roughly, 0.76.

00:03:19.990 --> 00:03:22.660
And remember, we're talking about moles.

00:03:22.660 --> 00:03:25.020
This is how many moles
of chlorine we have,

00:03:25.020 --> 00:03:28.150
or this is how many moles
of mercury, that's a number.

00:03:28.150 --> 00:03:31.080
You can view that as the
number of atoms of mercury

00:03:31.080 --> 00:03:33.630
or the number of atoms of chlorine.

00:03:33.630 --> 00:03:37.890
Moles are just the quantity
specified by Avogadro's number,

00:03:37.890 --> 00:03:42.467
so this is 0.76 times Avogadro's
number of chlorine atoms.

00:03:46.040 --> 00:03:48.170
So what's the ratio here?

00:03:48.170 --> 00:03:51.200
Well, it looks like for
every one mercury atom,

00:03:51.200 --> 00:03:53.450
there is roughly two chlorine atoms.

00:03:53.450 --> 00:03:58.260
If I take two times 0.36, it is 0.72,

00:03:58.260 --> 00:04:00.540
which is roughly close, it's not exact,

00:04:00.540 --> 00:04:02.800
but when you're doing this
type of empirical analysis,

00:04:02.800 --> 00:04:04.320
you're not going to get exact results,

00:04:04.320 --> 00:04:07.290
and it's best to assume the simplest ratio

00:04:07.290 --> 00:04:09.340
that gets you pretty close.

00:04:09.340 --> 00:04:12.020
So if we assume a ratio
of two chlorine atoms

00:04:12.020 --> 00:04:13.890
for every one mercury atom,

00:04:13.890 --> 00:04:16.580
the likely empirical formula is

00:04:16.580 --> 00:04:21.450
for every mercury atom we
will have two chlorines.

00:04:21.450 --> 00:04:24.340
And so this could be the
likely empirical formula.

00:04:24.340 --> 00:04:26.000
The name of this molecule happens to be

00:04:26.000 --> 00:04:28.170
mercury two chloride,
and I won't go in depth

00:04:28.170 --> 00:04:30.810
why it's called mercury two chloride,

00:04:30.810 --> 00:04:33.963
but that's actually what we
likely had in our container.