Inductive patterns

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:03.060
We're asked how many toothpicks
will be needed to

00:00:03.060 --> 00:00:06.120
form the 50th figure
in this sequence?

00:00:06.120 --> 00:00:09.010
And they've drawn the first four
figures in the sequence.

00:00:09.010 --> 00:00:11.220
This is the first, the
second, the third.

00:00:11.220 --> 00:00:12.690
Now, let's see what's
happening here.

00:00:12.690 --> 00:00:16.050
So in this first figure, we have
this nice little house

00:00:16.050 --> 00:00:19.510
that they've made out of
toothpicks, and it has one,

00:00:19.510 --> 00:00:24.110
two, three, four, five,
six toothpicks.

00:00:24.110 --> 00:00:28.910
So the first figure in our
sequence has six toothpicks.

00:00:28.910 --> 00:00:32.170
Now, what happens in the
second figure here?

00:00:32.170 --> 00:00:34.010
Well, it looks just like
our first figure.

00:00:34.010 --> 00:00:38.510
We have our one, two, three,
four, five, six toothpicks,

00:00:38.510 --> 00:00:40.340
but then they add
some toothpicks.

00:00:40.340 --> 00:00:45.890
It looks like they added one,
two, three, four, five,

00:00:45.890 --> 00:00:46.650
toothpicks.

00:00:46.650 --> 00:00:50.040
So it's 6 plus 5 or
11 toothpicks.

00:00:50.040 --> 00:00:51.490
So let me write this down.

00:00:51.490 --> 00:01:00.360
It is the 6 toothpicks plus 5
more, which is equal to 11

00:01:00.360 --> 00:01:01.300
toothpicks.

00:01:01.300 --> 00:01:03.580
And then when we go to the third
figure, it looks just

00:01:03.580 --> 00:01:06.510
like the second figure, so it
has the 11 toothpicks, so the

00:01:06.510 --> 00:01:12.510
11 toothpicks are one, two,
three, four, five, six, seven,

00:01:12.510 --> 00:01:16.360
eight, nine, ten, eleven, just
like the second figure.

00:01:16.360 --> 00:01:19.970
And then they add some more.

00:01:19.970 --> 00:01:24.160
They add one, two, three,
four, five.

00:01:24.160 --> 00:01:26.810
So it looks like every time,
when you draw part of a

00:01:26.810 --> 00:01:29.560
another house, because it can
share a wall with the previous

00:01:29.560 --> 00:01:32.240
house or share a toothpick
with the previous set of

00:01:32.240 --> 00:01:34.340
houses, you add five
toothpicks.

00:01:34.340 --> 00:01:38.860
So for the third term in our
sequence, we had 11 and when

00:01:38.860 --> 00:01:42.160
we had our second term,
or our two houses, and

00:01:42.160 --> 00:01:43.940
then we add five more.

00:01:46.860 --> 00:01:53.040
So to our 50th term, so 11
plus 5 is going to be 16.

00:01:53.040 --> 00:01:58.320
And then for the fourth term,
it's going to be 16 plus 5,

00:01:58.320 --> 00:02:00.890
which is equal to 21.

00:02:00.890 --> 00:02:02.550
Now, there's a couple of
ways to think about it.

00:02:02.550 --> 00:02:06.830
You can think about however
many more you are than 1.

00:02:06.830 --> 00:02:09.780
So let's say you are in the
nth term of the sequence.

00:02:09.780 --> 00:02:15.540
If you are in the nth term,
however more you are than 1,

00:02:15.540 --> 00:02:18.280
so if you're the nth term,
you're going to be n minus 1

00:02:18.280 --> 00:02:19.790
more than 1.

00:02:19.790 --> 00:02:23.620
If that is confusing, we'll do
it with real numbers, so it

00:02:23.620 --> 00:02:25.320
gets a little bit
more tangible.

00:02:25.320 --> 00:02:34.010
So the nth term, you are n minus
1 more or greater than--

00:02:34.010 --> 00:02:38.210
I'll just say more-- than 1.

00:02:38.210 --> 00:02:41.950
For example, if n is 2,
you are 1 more than 1.

00:02:41.950 --> 00:02:46.320
If n is 3, you are 3 minus 1,
which is 2 more than 1.

00:02:46.320 --> 00:02:49.230
So however much more
you are than 1, you

00:02:49.230 --> 00:02:50.890
multiply that by 5.

00:02:50.890 --> 00:02:55.510
We're 2 more than 1, so we add
10 to the number of toothpicks

00:02:55.510 --> 00:02:56.130
we have here.

00:02:56.130 --> 00:03:00.070
We're 3 more than 1 here, so
we add 15 to the number of

00:03:00.070 --> 00:03:01.290
toothpicks we have there.

00:03:01.290 --> 00:03:05.090
So you could say that for the
nth term, the number of

00:03:05.090 --> 00:03:15.560
toothpicks is equal to the
number you're more than 1, < n

00:03:15.560 --> 00:03:19.730
minus 1 times 5.

00:03:19.730 --> 00:03:22.210
That's how much you're going
to add above and beyond the

00:03:22.210 --> 00:03:23.930
amount of toothpicks
in just the first

00:03:23.930 --> 00:03:26.880
sequence, so times 5.

00:03:26.880 --> 00:03:29.860
n minus 1 times 5 plus the
number of toothpicks that you

00:03:29.860 --> 00:03:31.840
would just have in the
first sequence or

00:03:31.840 --> 00:03:33.150
just this one house.

00:03:33.150 --> 00:03:35.850
And we already counted
that: plus 6.

00:03:35.850 --> 00:03:37.200
So that's one way to
think about it.

00:03:37.200 --> 00:03:39.560
And if this looks complicated,
you just say, well, look, if I

00:03:39.560 --> 00:03:45.060
put a 4 here, I'm 3 more than
1, so 4 minus 1 is 3, so

00:03:45.060 --> 00:03:48.810
that'll be 3 times
5, which is 15.

00:03:48.810 --> 00:03:51.335
And then you add the number
of toothpicks in 1 and

00:03:51.335 --> 00:03:52.370
then you get 6.

00:03:52.370 --> 00:03:55.060
Now another way, and many of you
all might find this easier

00:03:55.060 --> 00:04:00.870
to think about, is even in 1,
you could imagine a term

00:04:00.870 --> 00:04:02.850
here-- let me do it this way.

00:04:02.850 --> 00:04:05.170
You can imagine a term here
that they didn't draw.

00:04:05.170 --> 00:04:07.360
You can imagine a 0th term.

00:04:07.360 --> 00:04:08.360
Let me just draw it here.

00:04:08.360 --> 00:04:12.990
Imagine a 0th term, and the 0th
term would just be kind of

00:04:12.990 --> 00:04:15.640
a left wall of the house, or
in this case, the left

00:04:15.640 --> 00:04:16.839
toothpick of a house.

00:04:16.839 --> 00:04:20.130
And then the first one, you're
adding 5 toothpicks to that.

00:04:20.130 --> 00:04:22.340
In the second one, you're adding
5 toothpicks to that.

00:04:22.340 --> 00:04:24.450
And when you think about it this
way, it actually becomes

00:04:24.450 --> 00:04:26.620
a little simpler to think
in terms of n.

00:04:26.620 --> 00:04:29.530
Here, you could say, well, the
nth term-- let me do this in a

00:04:29.530 --> 00:04:31.090
different color.

00:04:31.090 --> 00:04:37.895
You could say that the nth term
is going to have-- or

00:04:37.895 --> 00:04:53.180
maybe we should say number of
toothpicks in nth figure is

00:04:53.180 --> 00:04:55.700
going to be equal to 1.

00:04:55.700 --> 00:04:59.320
So in the 0th figure, which I
just made up, you have at

00:04:59.320 --> 00:05:03.560
least 1 toothpick, and then
whatever term in the sequence

00:05:03.560 --> 00:05:06.010
you are, you multiply that times
5 and you add that to

00:05:06.010 --> 00:05:10.010
the number of toothpicks in the
0th figure, so it's 1 plus

00:05:10.010 --> 00:05:14.380
5 times n, which is actually a
simpler way to think about.

00:05:14.380 --> 00:05:17.360
The first figure is going to
be that 1 in the 0th figure

00:05:17.360 --> 00:05:19.130
plus 5: 6 toothpicks.

00:05:19.130 --> 00:05:20.640
Even in the 0th figure,
it works out.

00:05:20.640 --> 00:05:24.510
If you put a 0 here,
0 plus 1 is 1.

00:05:24.510 --> 00:05:27.670
If you put the fourth figure
here, 5 times 4 is

00:05:27.670 --> 00:05:30.160
20 plus 1 is 21.

00:05:30.160 --> 00:05:31.930
Now let's answer
their question.

00:05:31.930 --> 00:05:34.380
We need to figure out the
toothpicks in the 50th figure

00:05:34.380 --> 00:05:35.100
in the sequence.

00:05:35.100 --> 00:05:37.900
Well, we just put
50 for n here.

00:05:37.900 --> 00:05:44.840
So for the 50th figure, we
could use either formula.

00:05:44.840 --> 00:05:49.380
We have 1 plus 5 times 50.

00:05:49.380 --> 00:05:54.370
5 times 50 is 250 plus
1 is equal to 251.

00:05:54.370 --> 00:05:56.310
And now I said you could use
either formula because they

00:05:56.310 --> 00:05:59.456
should reduce to each other, if
we did our math right or if

00:05:59.456 --> 00:06:00.900
we deduced properly.

00:06:00.900 --> 00:06:03.160
So this one up here, let's just
verify this is the same

00:06:03.160 --> 00:06:04.660
thing as this over here.

00:06:04.660 --> 00:06:13.870
If we multiply 5 times n minus
1, we get 5n minus 5, right?

00:06:13.870 --> 00:06:15.290
We just distributed the 5.

00:06:15.290 --> 00:06:18.690
And then we have that plus 6.

00:06:18.690 --> 00:06:23.240
Negative 5 plus 6 is plus 1.

00:06:23.240 --> 00:06:26.740
So it's 5n plus 1
or 1 plus 5n.

00:06:26.740 --> 00:06:32.480
Either way, your 50th figure
is going to have 251.


Systems of linear inequalities word problems example

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:04.650
Luis receives a gift card
worth $25 to an online

00:00:04.650 --> 00:00:07.970
retailer that sells digital
music and games.

00:00:07.970 --> 00:00:14.490
Each song costs $0.89 and
each game costs $1.99.

00:00:14.490 --> 00:00:20.560
He wants to buy at least 15
items with this card.

00:00:20.560 --> 00:00:23.040
Set up a system of inequalities
that represents

00:00:23.040 --> 00:00:27.020
this scenario and identify the
range of possible purchases

00:00:27.020 --> 00:00:28.440
using a graph.

00:00:28.440 --> 00:00:31.320
And that's why we have some
graph paper over here.

00:00:31.320 --> 00:00:32.940
So let's define some
variables.

00:00:32.940 --> 00:00:36.490
Let's let s equal the number
of songs he buys.

00:00:39.120 --> 00:00:45.370
And then let's let g equal the
number of games that he buys.

00:00:45.370 --> 00:00:46.950
Now if we look at this
constraint right here, he

00:00:46.950 --> 00:00:51.190
wants to buy at least 15
items with this card.

00:00:51.190 --> 00:00:53.340
So the total number of items are
going to be the number of

00:00:53.340 --> 00:00:55.420
songs plus the number
of games.

00:00:55.420 --> 00:00:57.180
And that has to be
at least 15.

00:00:57.180 --> 00:01:01.600
So it has to be greater
than or equal to 15.

00:01:01.600 --> 00:01:04.390
So that's what that constraint
tells us right there.

00:01:04.390 --> 00:01:08.790
And then the other constraint is
the gift card is worth $25.

00:01:08.790 --> 00:01:11.310
So the amount that he spends on
songs plus the amount that

00:01:11.310 --> 00:01:14.810
he spends on games has to be
less than or equal to 25.

00:01:14.810 --> 00:01:17.010
So the amount that he spends on
songs are going to be the

00:01:17.010 --> 00:01:22.460
number of songs he buys times
the cost per song.

00:01:22.460 --> 00:01:27.870
Times $0.89 times-- so I will
say 0.89-- times s.

00:01:27.870 --> 00:01:31.660
That's how much he spends on
songs plus the cost per game,

00:01:31.660 --> 00:01:35.680
which is $1.99 times the
number of games.

00:01:35.680 --> 00:01:37.540
This is going to be the total
amount that he spends.

00:01:37.540 --> 00:01:44.940
And that has to be less
than or equal to 25.

00:01:44.940 --> 00:01:47.950
Now if we want to graph these,
we first have to define the

00:01:47.950 --> 00:01:50.180
axes, so let me do
that right here.

00:01:50.180 --> 00:01:52.420
And we only care about the first
quadrant because we only

00:01:52.420 --> 00:01:54.910
care about positive values for
the number of songs and the

00:01:54.910 --> 00:01:55.550
number of games.

00:01:55.550 --> 00:01:59.240
We don't talk about scenarios
where he buys a negative

00:01:59.240 --> 00:02:00.580
number of songs or games.

00:02:00.580 --> 00:02:03.610
So just the positive quadrant
right here.

00:02:03.610 --> 00:02:06.110
Let me draw the axes.

00:02:06.110 --> 00:02:10.210
So let's make the vertical axis
that I'm drawing right

00:02:10.210 --> 00:02:15.220
here, let's make that the
vertical axis and let's call

00:02:15.220 --> 00:02:18.140
that the song axis.

00:02:18.140 --> 00:02:19.980
So that's the number
of songs he buys.

00:02:19.980 --> 00:02:21.870
Let me make sure you
can see that.

00:02:21.870 --> 00:02:23.930
That is the song axis.

00:02:23.930 --> 00:02:28.070
And then let's make this, this
horizontal, that's going to be

00:02:28.070 --> 00:02:29.905
the number of games he buys.

00:02:29.905 --> 00:02:31.155
Let's bold it in.

00:02:39.320 --> 00:02:43.720
And just to make sure that we
can fit on this page-- because

00:02:43.720 --> 00:02:45.580
I have a feeling we're going
to get to reasonably large

00:02:45.580 --> 00:02:48.470
numbers-- let's make each of
these boxes equal to 2.

00:02:48.470 --> 00:02:56.710
So this would be 4, 8, 12, 16,
20, so on and so forth.

00:02:56.710 --> 00:03:02.960
And this would be 4-- this
obviously would be 0-- 4, 8,

00:03:02.960 --> 00:03:08.860
12, 16, 20, and so on.

00:03:08.860 --> 00:03:11.930
So let's see if we can graph
these two constraints.

00:03:11.930 --> 00:03:15.010
Well, this first constraint, s
plus g is going to be greater

00:03:15.010 --> 00:03:16.560
than or equal to 15.

00:03:16.560 --> 00:03:18.470
The easiest way to think about
this-- or the easiest way to

00:03:18.470 --> 00:03:20.860
graph this is to really think
about the intercepts.

00:03:20.860 --> 00:03:25.160
If g is 0, what is s?

00:03:25.160 --> 00:03:29.340
Well, s plus 0 has to be greater
than or equal to 15.

00:03:29.340 --> 00:03:35.290
So if g is 0, s is going to be
greater than or equal to 15.

00:03:35.290 --> 00:03:36.370
Let me put it this way.

00:03:36.370 --> 00:03:39.700
So if I'm going to graph
this one right here.

00:03:39.700 --> 00:03:43.710
If g is 0, s is greater
than or equal to 15.

00:03:43.710 --> 00:03:49.390
So g is 0, s, 15, let's see,
this is 12, 14, 15 is right

00:03:49.390 --> 00:03:50.380
over there.

00:03:50.380 --> 00:03:53.090
And s is going to be all of the
values equivalent to that

00:03:53.090 --> 00:03:56.170
or greater than for
g equal to 0.

00:03:56.170 --> 00:04:00.460
If s is equal to 0, g is greater
than or equal to 15.

00:04:00.460 --> 00:04:05.700
So if s is equal to 0, g is
greater than or equal to 15.

00:04:05.700 --> 00:04:08.810
So g is greater than
or equal to 15.

00:04:08.810 --> 00:04:12.740
So the boundary line, s plus g
is equal to 15, we would just

00:04:12.740 --> 00:04:14.900
have to connect these
two dots.

00:04:14.900 --> 00:04:17.649
Let me try my best to
connect these dots.

00:04:17.649 --> 00:04:19.720
So it would look something
like this.

00:04:22.400 --> 00:04:24.330
This is always the
hardest part.

00:04:24.330 --> 00:04:28.000
Let me see how well I can
connect these two dots.

00:04:28.000 --> 00:04:29.540
Nope.

00:04:29.540 --> 00:04:30.480
Let me see.

00:04:30.480 --> 00:04:32.960
I should get a line
tool for this.

00:04:32.960 --> 00:04:35.400
So that's pretty good.

00:04:35.400 --> 00:04:38.050
So that's the line s plus
g is equal to 15.

00:04:38.050 --> 00:04:41.160
And we talk about the values
greater than 15, we're going

00:04:41.160 --> 00:04:41.920
to go above the line.

00:04:41.920 --> 00:04:45.280
And you saw that when g is equal
to 0, s is greater than

00:04:45.280 --> 00:04:47.010
or equal to 15.

00:04:47.010 --> 00:04:49.070
It's all of these
values up here.

00:04:49.070 --> 00:04:53.330
And when s was 0, g was greater
than or equal to 15.

00:04:53.330 --> 00:04:57.650
So this constraint right
here is all of this.

00:04:57.650 --> 00:05:00.440
All of this area
satisfies this.

00:05:00.440 --> 00:05:03.310
All of this area-- if you pick
any coordinate here, it

00:05:03.310 --> 00:05:05.560
represents-- and really you
should think about the integer

00:05:05.560 --> 00:05:08.230
coordinates, because we're not
going to buy parts of games.

00:05:08.230 --> 00:05:10.690
But if you think about all of
the integer coordinates here,

00:05:10.690 --> 00:05:13.710
they represent combinations of
s and g, where you're buying

00:05:13.710 --> 00:05:15.270
at least 15 games.

00:05:15.270 --> 00:05:18.610
For example here, you're buying
8 games and 16 songs.

00:05:18.610 --> 00:05:19.320
That's 24.

00:05:19.320 --> 00:05:21.730
So you're definitely meeting
the first constraint.

00:05:21.730 --> 00:05:23.570
Now the second constraint.

00:05:23.570 --> 00:05:28.120
0.89s plus 1.99g is less
than or equal to 25.

00:05:28.120 --> 00:05:29.570
This is a starting point.

00:05:29.570 --> 00:05:38.270
Let's just draw the line 0.89s
plus 1.99 is equal to 25.

00:05:38.270 --> 00:05:41.660
And then we could think about
what region the less than

00:05:41.660 --> 00:05:43.000
would represent.

00:05:43.000 --> 00:05:44.890
Oh, 1.99g.

00:05:44.890 --> 00:05:46.790
And the easiest way to do this,
once again, we could do

00:05:46.790 --> 00:05:48.900
slope y-intercept all
that type of thing.

00:05:48.900 --> 00:05:50.370
But the easiest way is to
just find the s- and the

00:05:50.370 --> 00:05:51.610
g-intercepts.

00:05:51.610 --> 00:06:04.880
So if s is equal to 0 then we
have 1.99g is equal to 25 or g

00:06:04.880 --> 00:06:08.470
is equal to-- let's get a
calculator out for this.

00:06:08.470 --> 00:06:17.900
So if we take 25 divided
by 1.99, it is 12.56.

00:06:17.900 --> 00:06:26.210
g is equal to 12.56.

00:06:26.210 --> 00:06:27.970
So when s is 0, let
me plot this.

00:06:27.970 --> 00:06:32.370
When s is 0, g is 12.56.

00:06:32.370 --> 00:06:34.440
This is 12, this is 14.

00:06:34.440 --> 00:06:37.450
12.56 is going to be right
there, a little

00:06:37.450 --> 00:06:38.950
bit more than 12.

00:06:38.950 --> 00:06:40.370
That's that value there.

00:06:40.370 --> 00:06:43.500
And then let's do the same
thing if g is 0.

00:06:43.500 --> 00:06:47.700
So if g is equal to 0, then we
have-- so this term goes

00:06:47.700 --> 00:06:51.770
away-- we have 0.89s.

00:06:51.770 --> 00:06:54.640
If we use just the equality
here, the equation-- is equal

00:06:54.640 --> 00:07:00.220
to 25 or s is equal to-- get
the calculator out again.

00:07:00.220 --> 00:07:06.410
So if we take 25 divided
by 0.89, we get--

00:07:06.410 --> 00:07:09.110
it's equal to 28.08.

00:07:09.110 --> 00:07:11.180
Just a little over 28.

00:07:11.180 --> 00:07:14.670
So 28.08.

00:07:14.670 --> 00:07:19.160
So that is, g is 0, s is 28.

00:07:19.160 --> 00:07:22.890
So that is 2, 4, 24, 6, 8.

00:07:22.890 --> 00:07:23.800
A little over 28.

00:07:23.800 --> 00:07:25.600
So it's right over there.

00:07:25.600 --> 00:07:32.180
So this line, 0.89s plus 1.99g
is equal to 25 is going to go

00:07:32.180 --> 00:07:35.810
from this coordinate,
which is 0, 28.

00:07:35.810 --> 00:07:37.630
So that point right there.

00:07:37.630 --> 00:07:41.320
All the way down to
the point 12.56,0.

00:07:41.320 --> 00:07:43.420
So let me see if I
can draw that.

00:07:43.420 --> 00:07:47.130
It's going to go-- I'll draw
up one more attempt.

00:07:47.130 --> 00:07:50.560
Maybe if I start from the
bottom it'll be easier.

00:07:50.560 --> 00:07:52.220
That was a better attempt.

00:07:52.220 --> 00:07:55.100
Let me bold that in a little
bit, so you can make sure you

00:07:55.100 --> 00:07:57.510
can see it.

00:07:57.510 --> 00:08:01.390
So that line represents
this right over here.

00:08:01.390 --> 00:08:05.710
Now if we're talking about the
less than area, what would

00:08:05.710 --> 00:08:06.700
that imply?

00:08:06.700 --> 00:08:13.920
So if we think about it, when
g is equal to 0, 0.89s

00:08:13.920 --> 00:08:15.550
is less than 25.

00:08:15.550 --> 00:08:18.610
So when g is equal to 0, if we
really wanted the less than

00:08:18.610 --> 00:08:20.500
there, we could think
of it this way.

00:08:20.500 --> 00:08:23.380
It's less than instead of just
doing less than or equal to.

00:08:23.380 --> 00:08:26.630
So s is less than 28.08.

00:08:26.630 --> 00:08:30.400
So it'll be the region below.

00:08:30.400 --> 00:08:34.610
When s is 0, g-- so if we think
s is 0, if we use this

00:08:34.610 --> 00:08:38.820
original equation, 1.99g will
be less than or equal to.

00:08:38.820 --> 00:08:41.350
I use this just to plot the
graph, but if we actually care

00:08:41.350 --> 00:08:46.670
about the actual inequality, we
get 1.99g is less than 25.

00:08:46.670 --> 00:08:49.620
g would be less than
or equal to 12.56.

00:08:49.620 --> 00:08:55.390
So when s is equal to 0,
g is less than 12.56.

00:08:55.390 --> 00:08:59.950
So the area that satisfies
this second constraint is

00:08:59.950 --> 00:09:01.800
everything below this graph.

00:09:06.040 --> 00:09:09.750
Now we want the region that
satisfies both constraints.

00:09:09.750 --> 00:09:12.060
So it's going to be the overlap
of the regions that

00:09:12.060 --> 00:09:13.930
satisfy one of the two.

00:09:13.930 --> 00:09:17.060
So the overlap is going to be
this region right here.

00:09:17.060 --> 00:09:20.920
Below the orange graph and
above the blue graph,

00:09:20.920 --> 00:09:23.520
including both of them.

00:09:23.520 --> 00:09:29.220
So if you pick any combination--
so if he buys 4

00:09:29.220 --> 00:09:33.300
games and 14 songs,
that would work.

00:09:33.300 --> 00:09:37.090
Or if he bought 2 games and
16 songs, that would work.

00:09:37.090 --> 00:09:38.170
So you can kind of
get the idea.

00:09:38.170 --> 00:09:40.300
Anything in that region-- and
he can only buy integer

00:09:40.300 --> 00:09:42.780
values-- would satisfy


U03_L2_T1_we2 Representing Functions as Graphs

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:02.750
We're asked: Do the points
on the graph

00:00:02.750 --> 00:00:05.470
below represent a function?

00:00:05.470 --> 00:00:08.020
Now, before even attempting to
do this problem, let's just

00:00:08.020 --> 00:00:11.190
remind ourselves what they
mean by a function.

00:00:11.190 --> 00:00:14.490
A function literally just takes
some input, and it's

00:00:14.490 --> 00:00:17.980
usually considered x,
some number x, but

00:00:17.980 --> 00:00:19.010
it takes some input.

00:00:19.010 --> 00:00:20.530
Let me do it in a
darker color.

00:00:20.530 --> 00:00:25.450
So it takes some input, let's
call it x, and then it does

00:00:25.450 --> 00:00:28.080
something on it or it maps
it to another value.

00:00:28.080 --> 00:00:31.990
So you take your function, your
function takes x as an

00:00:31.990 --> 00:00:36.440
input and then it outputs a
unique value or it says I

00:00:36.440 --> 00:00:37.660
don't know what to do with x.

00:00:37.660 --> 00:00:41.500
If it outputs a unique value,
that value is f of x.

00:00:41.500 --> 00:00:43.680
Or another way to think about
it, maybe we could say that

00:00:43.680 --> 00:00:48.440
value is y, and you could
say that y is equal to

00:00:48.440 --> 00:00:50.180
a function of x.

00:00:50.180 --> 00:00:53.820
You give me an x and then the
function does what it needs to

00:00:53.820 --> 00:00:56.150
do on the x and then
it outputs a y.

00:00:56.150 --> 00:00:57.730
Either way to visualize it.

00:00:57.730 --> 00:01:00.290
This function either has to say
let me give you a y and

00:01:00.290 --> 00:01:02.660
one unique y, or it'll
say I'm undefined.

00:01:02.660 --> 00:01:05.129
I don't know what to
do with that x.

00:01:05.129 --> 00:01:09.860
A function cannot give you two
different y's for the same x.

00:01:09.860 --> 00:01:15.130
That would just make it hard to
specify what to map x to.

00:01:15.130 --> 00:01:17.950
So when they ask us do the
points on the graph below

00:01:17.950 --> 00:01:21.370
represent a function, we just
really have to make sure that

00:01:21.370 --> 00:01:25.470
for every x-value, there's only
one y-value that it is

00:01:25.470 --> 00:01:28.290
being mapped to, or for any
x-value, that it's undefined.

00:01:28.290 --> 00:01:32.370
For example, at 6, they have not
defined-- and let me label

00:01:32.370 --> 00:01:34.260
the axes just to be careful.

00:01:34.260 --> 00:01:35.710
This is the x-axis.

00:01:35.710 --> 00:01:40.170
This is the y or the y is
equal to f of x axis.

00:01:40.170 --> 00:01:43.270
So if you tried to put
6 into this proposed

00:01:43.270 --> 00:01:44.470
function, it's undefined.

00:01:44.470 --> 00:01:46.720
They haven't told us what
y would be equal here.

00:01:46.720 --> 00:01:48.410
That's completely cool.

00:01:48.410 --> 00:01:51.520
Over here, if you put negative
1 in this proposed function,

00:01:51.520 --> 00:01:53.250
it produces 3.

00:01:53.250 --> 00:01:54.150
That's cool.

00:01:54.150 --> 00:01:57.790
So far, this looks like it could
represent a function.

00:01:57.790 --> 00:02:02.090
If it did, just based on this
point, you would say that f of

00:02:02.090 --> 00:02:06.380
negative 1, because the input is
negative 1, is equal to 3.

00:02:06.380 --> 00:02:07.750
Cool so far.

00:02:07.750 --> 00:02:12.040
Now, when x is equal to 2-- so
for our proposed function,

00:02:12.040 --> 00:02:15.450
when you input a 2, it will
output a negative 2.

00:02:15.450 --> 00:02:16.960
Seems reasonable so far.

00:02:16.960 --> 00:02:19.590
You input a 3, it'll
output a 2.

00:02:19.590 --> 00:02:21.150
Still reasonable.

00:02:21.150 --> 00:02:25.540
Now, when x is equal to 4, if we
want this to be a function,

00:02:25.540 --> 00:02:31.095
what this graph is implying is
if you input x is equal to 4,

00:02:31.095 --> 00:02:33.840
that the value of the function,
or the proposed

00:02:33.840 --> 00:02:37.890
function, is both negative
1 and 5.

00:02:37.890 --> 00:02:43.660
So this is saying that if you
take 4 into our function, into

00:02:43.660 --> 00:02:46.440
our proposed function-- we
can't really call it a

00:02:46.440 --> 00:02:46.890
function yet.

00:02:46.890 --> 00:02:48.720
We're trying to see if we
can call it a function.

00:02:48.720 --> 00:02:52.930
So if you put into our proposed
function that it

00:02:52.930 --> 00:02:58.400
could get to negative 1 and/or
it could get to 5, this is

00:02:58.400 --> 00:02:59.230
just not allowed.

00:02:59.230 --> 00:03:02.610
It is mapping the value
4 to two values.

00:03:02.610 --> 00:03:04.190
That is not allowed
for a function.

00:03:04.190 --> 00:03:09.470
A function has to map from a
value to only one other value.

00:03:09.470 --> 00:03:13.890
So the points on the graph
below do not represent a

00:03:13.890 --> 00:03:17.090
function, so I'll
just write a no.


Finding the inequality representing the graph example

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:03.940
We're asked to graph the
inequality y is less

00:00:03.940 --> 00:00:06.920
than 3x plus 5.

00:00:06.920 --> 00:00:09.920
So if you give us any x-- and
let me label the axes here.

00:00:09.920 --> 00:00:12.170
So this is the x-axis.

00:00:12.170 --> 00:00:14.250
This is the y-axis.

00:00:14.250 --> 00:00:16.040
So this is saying you
give me an x.

00:00:16.040 --> 00:00:19.590
So let's say we take x is
equal to 1 right there.

00:00:19.590 --> 00:00:21.840
3 times 1 plus 5.

00:00:21.840 --> 00:00:23.510
So 3 times x plus 5.

00:00:23.510 --> 00:00:26.010
So 3 times 1 is 3 plus 5 is 8.

00:00:26.010 --> 00:00:30.730
So one, two, three, four,
five, six, seven, eight.

00:00:30.730 --> 00:00:33.970
This is saying that y
will be less than 8.

00:00:33.970 --> 00:00:36.810
y will be less than
3 times 1 plus 5.

00:00:36.810 --> 00:00:41.890
So the y-values that satisfy
this constraint for that x are

00:00:41.890 --> 00:00:43.850
going to be all of these
values down here.

00:00:43.850 --> 00:00:45.500
Let me do it in a
lighter color.

00:00:45.500 --> 00:00:46.820
It'll be all of these values.

00:00:46.820 --> 00:00:50.430
For x is equal to 1, it'll be
all the values down here, and

00:00:50.430 --> 00:00:53.180
it would not include
y is equal to 8.

00:00:53.180 --> 00:00:56.240
Y has to be less than 8.

00:00:56.240 --> 00:00:59.030
Now, if we kept doing that, we
would essentially just to

00:00:59.030 --> 00:01:04.530
graph the line of y is equal to
3x plus 5, but we wouldn't

00:01:04.530 --> 00:01:05.110
include it.

00:01:05.110 --> 00:01:07.520
We would just include everything
below it, just like

00:01:07.520 --> 00:01:08.700
we did right here.

00:01:08.700 --> 00:01:12.280
So we know how to graph just
y is equal to 3x plus 5.

00:01:12.280 --> 00:01:13.570
Let me write it over here.

00:01:13.570 --> 00:01:18.820
So if I were to write y is equal
to 3x plus 5, we would

00:01:18.820 --> 00:01:21.030
say, OK, 3 is the slope.

00:01:21.030 --> 00:01:26.450
Slope is equal to 3, and then
5 is the y-intercept.

00:01:26.450 --> 00:01:29.700
Now, I could just graph the
line, but because that won't

00:01:29.700 --> 00:01:33.070
be included in the y's that
satisfy this constraint, I'm

00:01:33.070 --> 00:01:35.090
going to graph it as
a dotted line.

00:01:35.090 --> 00:01:37.240
So we'll start with the
y-intercept of 5.

00:01:37.240 --> 00:01:39.540
So one, two, three,
four, five.

00:01:39.540 --> 00:01:40.900
That's the y-intercept.

00:01:40.900 --> 00:01:42.470
And the slope is 3.

00:01:42.470 --> 00:01:44.990
So if you go over to
the 1, you go up 3.

00:01:44.990 --> 00:01:48.240
So let me do that in that
darker purple color.

00:01:48.240 --> 00:01:50.750
So it'll look like this.

00:01:50.750 --> 00:01:53.660
It will look like that.

00:01:53.660 --> 00:01:54.740
That point would be on it.

00:01:54.740 --> 00:01:55.970
That point would be on it.

00:01:55.970 --> 00:01:58.880
If you go back, you're going
to go down by 3.

00:01:58.880 --> 00:02:02.190
So that point will be on it,
that point, and that point,

00:02:02.190 --> 00:02:04.530
and I'll just connect the
dots with a dotted line.

00:02:08.970 --> 00:02:12.680
That dotted line is the graph
of y is equal to 3x plus 5,

00:02:12.680 --> 00:02:14.040
but we're not going
to include it.

00:02:14.040 --> 00:02:16.480
So that's why I made it a dotted
line because we want

00:02:16.480 --> 00:02:18.060
all of the y's that are
less than that.

00:02:18.060 --> 00:02:20.930
So for any x-- so
you pick an x.

00:02:20.930 --> 00:02:22.700
Let's say x is equal
to negative 1.

00:02:22.700 --> 00:02:25.840
If you evaluate 3x plus 5 for
that x, you'd get here.

00:02:25.840 --> 00:02:27.220
But we only care about
the y's that are

00:02:27.220 --> 00:02:28.660
strictly less than that.

00:02:28.660 --> 00:02:30.220
So you don't include the line.

00:02:30.220 --> 00:02:32.110
It's everything below it.

00:02:32.110 --> 00:02:35.680
So for any x you pick, it's
going to be below that line.

00:02:35.680 --> 00:02:38.500
You take the x, go up to that
line and everything below it.

00:02:38.500 --> 00:02:41.125
So for all of the x's, it's
going to be this entire area.

00:02:44.460 --> 00:02:46.630
Let me draw it a little
bit neater than that.

00:02:46.630 --> 00:02:50.120
It's going to be this entire
area that's under the line.

00:02:50.120 --> 00:02:51.010
I'll do it in this orange.

00:02:51.010 --> 00:02:53.000
It's a little bit
easier to see.

00:02:53.000 --> 00:03:00.270
So this entire area under the
line is y is less than 3x.


U06_L1_T1_we1 Solving Systems by Graphing

WEBVTT
Kind: captions
Language: en

00:00:00.460 --> 00:00:03.790
Abby and Ben did household
chores last weekend.

00:00:03.790 --> 00:00:06.020
Together they earned $50.

00:00:06.020 --> 00:00:07.050
Let me underline that.

00:00:07.050 --> 00:00:09.680
Together they earned $50.

00:00:09.680 --> 00:00:12.740
And Abby earned $10
more than Ben.

00:00:12.740 --> 00:00:14.570
Let me underline that as well.

00:00:14.570 --> 00:00:17.930
Abby earned $10 more than Ben.

00:00:17.930 --> 00:00:20.170
How much did each earn?

00:00:20.170 --> 00:00:21.820
Now, we could just go and solve
it, but it looks like

00:00:21.820 --> 00:00:23.920
they want to ask
something else.

00:00:23.920 --> 00:00:27.900
If you were to use the graph
above, which strategy is most

00:00:27.900 --> 00:00:30.400
useful in helping you find the
answer to the problem?

00:00:30.400 --> 00:00:31.930
So we don't even have
to solve for it.

00:00:31.930 --> 00:00:35.820
They just want us to tell them
what is the best strategy for

00:00:35.820 --> 00:00:37.080
solving the problem.

00:00:37.080 --> 00:00:39.380
So the first choice they say,
finding an equation

00:00:39.380 --> 00:00:40.470
for the blue line.

00:00:40.470 --> 00:00:43.100
So let's look at this graph that
they've also given us.

00:00:43.100 --> 00:00:47.330
So the blue line here is the
graph using the information

00:00:47.330 --> 00:00:50.430
that Abby earned $10
more than Ben.

00:00:50.430 --> 00:00:51.050
That's what that says.

00:00:51.050 --> 00:00:52.290
It's written a little
bit small, but

00:00:52.290 --> 00:00:52.960
hopefully, you can see it.

00:00:52.960 --> 00:00:55.800
Abby earned $10 more than
Ben, which is this

00:00:55.800 --> 00:00:57.730
information over here.

00:00:57.730 --> 00:01:00.560
And so if you call this over
here, the B-axis for the

00:01:00.560 --> 00:01:04.900
amount Ben earned and this is
the A-axis for the amount Abby

00:01:04.900 --> 00:01:12.330
earned, the equation of this
line would be the amount Abby

00:01:12.330 --> 00:01:16.010
earned is going to be $10 more
than the amount Ben earned.

00:01:16.010 --> 00:01:18.310
So that's the equation of
that line right there.

00:01:18.310 --> 00:01:21.270
Well, that by itself isn't going
to help you figure out

00:01:21.270 --> 00:01:22.610
how much did each earn.

00:01:22.610 --> 00:01:25.390
So that by itself won't
solve the problem.

00:01:25.390 --> 00:01:27.560
Finding the red line's
y-intercept.

00:01:27.560 --> 00:01:28.540
So let's look at the red line.

00:01:28.540 --> 00:01:31.810
The red line C. is using the
information that Abby and Ben

00:01:31.810 --> 00:01:33.510
earn $50 combined.

00:01:33.510 --> 00:01:35.600
It's this information up here.

00:01:35.600 --> 00:01:39.230
And the equation of that would
be Abby's earnings plus Ben's

00:01:39.230 --> 00:01:41.980
earnings are equal to $50.

00:01:41.980 --> 00:01:44.065
If you were to just find
the y-intercept there,

00:01:44.065 --> 00:01:44.780
it's just at 50.

00:01:44.780 --> 00:01:47.370
That's really not giving you
any information in figuring

00:01:47.370 --> 00:01:49.360
out how much did they each
earn and actually

00:01:49.360 --> 00:01:50.950
solving for A and B.

00:01:50.950 --> 00:01:53.230
So B by itself won't work.

00:01:53.230 --> 00:01:56.310
Finding the lines' point
of intersection.

00:01:56.310 --> 00:01:59.140
Now, that's interesting
because the point of

00:01:59.140 --> 00:02:05.080
intersection gives you-- so let
me circle that a little

00:02:05.080 --> 00:02:05.820
bit bolder.

00:02:05.820 --> 00:02:08.590
Let me do that in orange
and a magenta color.

00:02:08.590 --> 00:02:11.850
So the point of intersection
right there, that gives us an

00:02:11.850 --> 00:02:16.140
A and B value that will satisfy
both equations.

00:02:16.140 --> 00:02:19.710
And if they're satisfying both
equations, it'll satisfy both

00:02:19.710 --> 00:02:20.960
constraints.

00:02:20.960 --> 00:02:24.990
So if we just eyeball it off
this chart, it looks like B is

00:02:24.990 --> 00:02:30.210
equal to 20 and A
is equal to 30.

00:02:30.210 --> 00:02:33.270
And if we just use these numbers
relative to this,

00:02:33.270 --> 00:02:35.000
together they earned $50.

00:02:35.000 --> 00:02:35.830
That works.

00:02:35.830 --> 00:02:39.750
If Abby earns 30 and Ben earns
20, they'll earn $50.

00:02:39.750 --> 00:02:43.550
And 30 is $10 more than 20.

00:02:43.550 --> 00:02:44.250
So this worked.

00:02:44.250 --> 00:02:46.970
By looking at the point of
intersection, we were able to

00:02:46.970 --> 00:02:49.870
figure out how much Abby
and Ben earned.

00:02:49.870 --> 00:02:51.000
So I would go with C.

00:02:51.000 --> 00:02:53.010
We don't even have to read D,
but they say, you cannot tell

00:02:53.010 --> 00:02:54.840
how much they earned because
there are two

00:02:54.840 --> 00:02:55.430
lines on the graph.

00:02:55.430 --> 00:02:57.440
No, that's complete silliness
right there.

00:02:57.440 --> 00:02:59.370
So the choice is


Absolute value equations

WEBVTT
Kind: captions
Language: en

00:00:00.790 --> 00:00:06.230
Solve the absolute value of 3x
minus 9 is equal to 0 and

00:00:06.230 --> 00:00:09.180
graph the solution
on a number line.

00:00:09.180 --> 00:00:10.380
So let me just rewrite it.

00:00:10.380 --> 00:00:15.880
We have the absolute value of
3x minus 9 is equal to 0.

00:00:15.880 --> 00:00:19.970
So if the absolute value of
something is equal to 0, what

00:00:19.970 --> 00:00:21.550
can that something be?

00:00:21.550 --> 00:00:24.120
Well the only thing that you
could take the absolute value

00:00:24.120 --> 00:00:26.830
of and get 0 is 0.

00:00:26.830 --> 00:00:28.610
So that something has to be 0.

00:00:28.610 --> 00:00:32.180
So it has to be a 0 inside of
the absolute value sign.

00:00:32.180 --> 00:00:38.500
So we know that 3x minus
9 must be equal to 0.

00:00:38.500 --> 00:00:41.530
If this was any other
non-negative value, you would

00:00:41.530 --> 00:00:42.390
have two values.

00:00:42.390 --> 00:00:45.670
If this was a positive 2, you
would say 3x minus 9 could be

00:00:45.670 --> 00:00:47.860
positive 2 or negative 2.

00:00:47.860 --> 00:00:51.030
But when you're dealing with 0,
3x minus 9 has to equal 0.

00:00:51.030 --> 00:00:53.050
That's the only way when you
take the absolute value,

00:00:53.050 --> 00:00:54.520
you're going to get 0.

00:00:54.520 --> 00:00:55.980
So then we just solve this.

00:00:55.980 --> 00:00:58.625
We add 9 to both sides
of this equation.

00:01:01.570 --> 00:01:05.200
You get 3x is equal to 9.

00:01:05.200 --> 00:01:11.140
Divide both sides by 3 and you
get x is equal to 9/3 or x is

00:01:11.140 --> 00:01:13.140
equal to 3.

00:01:13.140 --> 00:01:14.090
And you're done.

00:01:14.090 --> 00:01:15.530
And then we just do
the second part.

00:01:15.530 --> 00:01:17.790
Graph the solution
on a number line.

00:01:17.790 --> 00:01:19.400
So let's graph.

00:01:19.400 --> 00:01:20.770
We have a number line here.

00:01:20.770 --> 00:01:21.730
Let me draw one.

00:01:21.730 --> 00:01:22.950
It's a number line.

00:01:22.950 --> 00:01:24.130
I'll put some negative values.

00:01:24.130 --> 00:01:32.890
Maybe we'll start negative 2,
negative 1, 0, 1, 2, 3, 4, 5.

00:01:32.890 --> 00:01:34.190
Could keep going on.

00:01:34.190 --> 00:01:37.290
But the solution is
x is equal to 3.

00:01:39.950 --> 00:01:41.720
So just graphing that on a
number line, we just put a

00:01:41.720 --> 00:01:43.380
little dot at 3.


Stereoisomers, enantiomers, diastereomers, constitutional isomers and meso compounds

WEBVTT
Kind: captions
Language: en

00:00:00.430 --> 00:00:03.010
In this video, we're going to
look at pairs of molecules and

00:00:03.010 --> 00:00:05.910
see if they relate to each other
in any obvious way or

00:00:05.910 --> 00:00:07.820
maybe less than obvious way.

00:00:07.820 --> 00:00:10.840
So these first two right here,
they actually look like a

00:00:10.840 --> 00:00:12.260
completely different
molecules.

00:00:12.260 --> 00:00:14.110
So your gut impulse might
be to say that these are

00:00:14.110 --> 00:00:15.840
completely different
molecules.

00:00:15.840 --> 00:00:18.870
And it wouldn't be completely
off, but we look a little bit

00:00:18.870 --> 00:00:22.890
closer, you see that this guy
on the left has one, two,

00:00:22.890 --> 00:00:26.000
three, four carbons, and so does
this guy on the right.

00:00:26.000 --> 00:00:29.010
It has one, two, three,
four carbons.

00:00:29.010 --> 00:00:32.400
This guy on the left
has two, four, six,

00:00:32.400 --> 00:00:34.400
seven, eight hydrogens.

00:00:34.400 --> 00:00:38.080
This guy on the right has two,
four, six, eight hydrogens.

00:00:38.080 --> 00:00:39.680
And they both have one oxygen.

00:00:39.680 --> 00:00:42.030
So both of the molecular
formulas for both of these

00:00:42.030 --> 00:00:47.310
things are four carbons, eight
hydrogens, and one oxygen.

00:00:47.310 --> 00:00:50.510
They're both C4H8O.

00:00:50.510 --> 00:00:52.200
So they have the same
molecular formula.

00:00:52.200 --> 00:00:54.650
They're made up of the same
thing, so these are going to

00:00:54.650 --> 00:00:56.380
be isomers.

00:00:56.380 --> 00:00:57.740
They're going to be isomers,
and they're a

00:00:57.740 --> 00:00:59.460
special type of isomers.

00:00:59.460 --> 00:01:02.550
In this situation, we don't
have the same bonds.

00:01:02.550 --> 00:01:05.570
We're made up of the same
things, but the bonds, what is

00:01:05.570 --> 00:01:07.360
connected to what
is different.

00:01:07.360 --> 00:01:09.190
So we call this a constitutional
isomer.

00:01:17.640 --> 00:01:21.900
So we are essentially made up of
the same things, but we are

00:01:21.900 --> 00:01:25.200
actually two different molecule,
actually, two very

00:01:25.200 --> 00:01:26.650
different molecules here.

00:01:26.650 --> 00:01:30.180
Now let's look at this
next guy over here.

00:01:30.180 --> 00:01:34.600
So if we look at this molecule,
it does look like

00:01:34.600 --> 00:01:36.820
this carbon is chiral.

00:01:36.820 --> 00:01:38.970
It is an asymmetric carbon.

00:01:38.970 --> 00:01:42.820
It is bonded to four different
groups: fluorine, bromine,

00:01:42.820 --> 00:01:45.090
hydrogen, and then
a methyl group.

00:01:45.090 --> 00:01:46.740
And so's this one.

00:01:46.740 --> 00:01:49.200
And they're both made up
of the same things.

00:01:49.200 --> 00:01:51.450
You have the carbon-- and not
only are they made up of the

00:01:51.450 --> 00:01:53.440
same things, but the bonding
is the same.

00:01:53.440 --> 00:01:56.740
So carbon to a fluorine, carbon
to a fluorine, carbon

00:01:56.740 --> 00:01:59.730
to a bromine, carbon to a
bromine, carbon to hydrogen in

00:01:59.730 --> 00:02:02.610
both of then carbon to the
methyl group in both.

00:02:02.610 --> 00:02:05.020
But they don't look
quite the same.

00:02:05.020 --> 00:02:06.260
Are they mirror images?

00:02:06.260 --> 00:02:06.560
Well, no.

00:02:06.560 --> 00:02:09.440
This guy's mirror image would
have the fluorine popping out

00:02:09.440 --> 00:02:14.920
here, the hydrogen going back
here, and then would have the

00:02:14.920 --> 00:02:16.930
bromine pointing out here.

00:02:16.930 --> 00:02:19.600
Let's see if I can somehow get
from this guy to that guy.

00:02:19.600 --> 00:02:24.270
Let me flip this guy first. So
let me-- a good thing to do

00:02:24.270 --> 00:02:30.520
would be to just flip to see
the fastest way I could

00:02:30.520 --> 00:02:33.340
potentially get there.

00:02:33.340 --> 00:02:35.400
Let me just flip it like this.

00:02:35.400 --> 00:02:37.700
So I'm going to flip out of
the page, you can imagine.

00:02:37.700 --> 00:02:39.660
I'm going to flip
it like this.

00:02:39.660 --> 00:02:41.870
So I'm going to take this methyl
group and then put it

00:02:41.870 --> 00:02:42.810
on the right-hand side.

00:02:42.810 --> 00:02:44.430
And you can imagine, I'm going
to turn it so it would come

00:02:44.430 --> 00:02:46.770
out of the page and
then go back down.

00:02:46.770 --> 00:02:48.950
So if I did that, what
would it look like?

00:02:48.950 --> 00:02:51.130
I would have the carbon,
this carbon here.

00:02:51.130 --> 00:02:54.080
I would have the methyl group
on that side now.

00:02:54.080 --> 00:02:57.590
And then since I flipped it
over, the bromine was in the

00:02:57.590 --> 00:02:58.520
plane of the page.

00:02:58.520 --> 00:03:02.910
It'll still be in the plane of
the page, but since I flipped

00:03:02.910 --> 00:03:07.060
it over, the hydrogen, which was
in the back, will now be

00:03:07.060 --> 00:03:08.740
in the front.

00:03:08.740 --> 00:03:12.940
The hydrogen will now be in
the front and the fluorine

00:03:12.940 --> 00:03:15.620
will now be in back because
I flipped it over.

00:03:15.620 --> 00:03:20.320
So the fluorine is
now in the back.

00:03:20.320 --> 00:03:22.870
Now, how does this
compare to that?

00:03:22.870 --> 00:03:24.570
Let's see if I can somehow
get there.

00:03:24.570 --> 00:03:27.610
Well, if I take this fluorine
and I rotate it to where the

00:03:27.610 --> 00:03:30.300
hydrogen is, and I take the
hydrogen and rotate it to

00:03:30.300 --> 00:03:32.550
where-- that's all going to
happen at once-- to where the

00:03:32.550 --> 00:03:34.720
bromine is, and I take the
bromine and rotate it to where

00:03:34.720 --> 00:03:36.530
the fluorine is, I get that.

00:03:36.530 --> 00:03:41.860
So I can flip it and then I can
rotate it around this bond

00:03:41.860 --> 00:03:44.550
axis right there, and I would
get to that molecule there.

00:03:44.550 --> 00:03:46.040
So even though they look pretty
different, with the

00:03:46.040 --> 00:03:48.410
flip and a rotation, you
actually see that these are

00:03:48.410 --> 00:03:49.660
the same a molecule.

00:03:55.340 --> 00:03:56.590
Next one.

00:03:56.590 --> 00:03:58.050
So let's see, what
do we have here?

00:03:58.050 --> 00:04:00.060
Let me switch colors.

00:04:00.060 --> 00:04:02.820
So over here, this part
of both of these

00:04:02.820 --> 00:04:03.960
molecules look the same.

00:04:03.960 --> 00:04:06.380
You have the carbons
on both of them.

00:04:06.380 --> 00:04:08.570
This carbon looks like
a chiral center.

00:04:08.570 --> 00:04:12.380
It's bonded to one, two,
three different groups.

00:04:12.380 --> 00:04:14.470
You might say, oh, it's two
carbons, but this is a methyl

00:04:14.470 --> 00:04:16.829
group, and then this side has
all this business over it, so

00:04:16.829 --> 00:04:18.700
this is definitely
a chiral carbon.

00:04:18.700 --> 00:04:20.829
And over, here same thing.

00:04:20.829 --> 00:04:22.500
It's a chiral carbon.

00:04:22.500 --> 00:04:23.620
And this has the same thing.

00:04:23.620 --> 00:04:25.290
It's bonded to four
different things.

00:04:25.290 --> 00:04:28.940
So each of these molecules has
two chiral carbons, and it

00:04:28.940 --> 00:04:31.470
looks like they're made
up of the same things.

00:04:31.470 --> 00:04:36.250
And not only are they made up
of the same things, but the

00:04:36.250 --> 00:04:39.090
bonds are made in
the same way.

00:04:39.090 --> 00:04:42.830
So this carbon is bonded to a
hydrogen and a fluorine, and

00:04:42.830 --> 00:04:44.760
the two other carbons,
same thing, a

00:04:44.760 --> 00:04:46.530
hydrogen and a fluorine.

00:04:46.530 --> 00:04:48.890
Carbon, it looks like
it's a hydrogen.

00:04:48.890 --> 00:04:53.310
It's bonded to a hydrogen and a
chlorine, so it's made up of

00:04:53.310 --> 00:04:55.350
the same constituents
and they're

00:04:55.350 --> 00:04:56.410
bonded in the same way.

00:04:56.410 --> 00:05:00.630
So these look like--
but the bonding is

00:05:00.630 --> 00:05:01.820
a little bit different.

00:05:01.820 --> 00:05:04.960
Over here on this one on the
left, the hydrogen goes in the

00:05:04.960 --> 00:05:07.510
back, and over here, the
hydrogen's in the front.

00:05:07.510 --> 00:05:10.310
And over here, the chlorine's
in back, and over here, the

00:05:10.310 --> 00:05:11.560
chlorine's in front.

00:05:11.560 --> 00:05:13.290
So these look like
sterioisomers.

00:05:18.470 --> 00:05:21.630
You saw earlier in this video,
you saw structural isomers,

00:05:21.630 --> 00:05:23.290
made up of the same
things but the

00:05:23.290 --> 00:05:24.690
connections are all different.

00:05:24.690 --> 00:05:27.920
Stereoisomers, they're made
up of the same thing, the

00:05:27.920 --> 00:05:30.380
connections are the same, but
the three-dimensional

00:05:30.380 --> 00:05:32.800
configuration is a little
bit different.

00:05:32.800 --> 00:05:35.060
For example, here on this
carbon, it's connected to the

00:05:35.060 --> 00:05:37.810
same things as this carbon, but
over here, the fluorine's

00:05:37.810 --> 00:05:40.750
out front, and over here--
out here, the

00:05:40.750 --> 00:05:41.400
fluorine's out front.

00:05:41.400 --> 00:05:43.100
Over here, the fluorine's
backwards.

00:05:43.100 --> 00:05:44.540
And same thing for the
chlorine here.

00:05:44.540 --> 00:05:46.570
It's back here and
it's front here.

00:05:46.570 --> 00:05:52.770
Now, let's see if they're
related in a more nuanced way.

00:05:52.770 --> 00:05:55.780
You could imagine putting
a mirror behind.

00:05:55.780 --> 00:05:57.470
I guess the best way to
visualize it, imagine putting

00:05:57.470 --> 00:06:00.130
a mirror behind this molecule.

00:06:00.130 --> 00:06:02.940
If you put a mirror behind this
molecule, what would its

00:06:02.940 --> 00:06:04.570
reflection look like?

00:06:04.570 --> 00:06:06.940
So if you put a mirror behind
it, in the image of the

00:06:06.940 --> 00:06:10.470
mirror, this hydrogen would now,
since the mirror's behind

00:06:10.470 --> 00:06:12.750
this whole molecule, this
hydrogen is actually closer to

00:06:12.750 --> 00:06:13.450
the mirror.

00:06:13.450 --> 00:06:16.307
So then the mirror image, you
would have a hydrogen that's

00:06:16.307 --> 00:06:19.530
pointed out, and then you would
have the carbon, and

00:06:19.530 --> 00:06:22.770
then you would have the fluorine
being further away.

00:06:22.770 --> 00:06:24.930
And same thing in the
mirror image here.

00:06:24.930 --> 00:06:27.680
You would have the chlorine
coming closer since this

00:06:27.680 --> 00:06:30.270
chlorine is further back, closer
to the mirror, and then

00:06:30.270 --> 00:06:33.230
you would have the hydrogen
pointing outwards like that.

00:06:33.230 --> 00:06:36.290
And then, obviously, the rest
of the molecule would look

00:06:36.290 --> 00:06:38.790
exactly the same.

00:06:38.790 --> 00:06:42.180
And so this mirror image that I
just thought about in white

00:06:42.180 --> 00:06:45.710
is exactly what this molecule
is: hydrogen pointing out in

00:06:45.710 --> 00:06:49.800
front, hydrogen pointing
out in front.

00:06:49.800 --> 00:06:53.110
You might say, wait, this
hydrogen is on the right, this

00:06:53.110 --> 00:06:53.710
one's on the left.

00:06:53.710 --> 00:06:54.090
It doesn't matter.

00:06:54.090 --> 00:06:55.690
This is actually saying that
the hydrogen's pointing out

00:06:55.690 --> 00:06:58.040
front, the fluorine is pointing
out back, hydrogen up

00:06:58.040 --> 00:07:02.010
front, fluorine back, chlorine
out front, hydrogen back,

00:07:02.010 --> 00:07:03.930
chlorine out front,
hydrogen back.

00:07:03.930 --> 00:07:06.930
So these are actually mirror
images, but they're not the

00:07:06.930 --> 00:07:08.900
easy mirror images that we've
done in the past where the

00:07:08.900 --> 00:07:12.750
mirror was just like that
in between the two.

00:07:12.750 --> 00:07:15.260
This one is a mirror image where
you place the mirror

00:07:15.260 --> 00:07:18.300
either on top of or behind
one of the molecules.

00:07:18.300 --> 00:07:20.570
So this is a class of
stereoisomers, and we've

00:07:20.570 --> 00:07:22.130
brought up this word before.

00:07:22.130 --> 00:07:23.380
We call this enantiomers.

00:07:26.000 --> 00:07:29.030
So if each of these are an
enantiomers, I'll say they are

00:07:29.030 --> 00:07:30.830
enantiomers of each other.

00:07:30.830 --> 00:07:32.390
They're steroisomers.

00:07:32.390 --> 00:07:35.380
They're made up of the same
molecules, so that they have

00:07:35.380 --> 00:07:36.680
the same constituents.

00:07:36.680 --> 00:07:40.120
They also have the same
connections, and not only do

00:07:40.120 --> 00:07:42.090
they have the same connections,
that so far gets

00:07:42.090 --> 00:07:45.100
us a steroisomer, but they are a
special kind of stereoisomer

00:07:45.100 --> 00:07:48.450
called an enantiomer, where they
are actual mirror images

00:07:48.450 --> 00:07:50.500
of each other.

00:07:50.500 --> 00:07:54.200
Now, what is this one
over here in blue?

00:07:54.200 --> 00:07:56.330
Just like the last one, it looks
like it's made up of the

00:07:56.330 --> 00:07:57.540
same things.

00:07:57.540 --> 00:08:00.140
You have these carbons, these
carbons, these carbons and

00:08:00.140 --> 00:08:01.020
hydrogens up there.

00:08:01.020 --> 00:08:02.590
Same thing over there.

00:08:02.590 --> 00:08:05.120
You have a hydrogen, bromine,
hydrogen and a bromine,

00:08:05.120 --> 00:08:08.100
hydrogen, chlorine, hydrogen,
chlorine, hydrogen, chlorine,

00:08:08.100 --> 00:08:09.210
hydrogen, chlorine.

00:08:09.210 --> 00:08:10.500
So it's made up of
the same things.

00:08:10.500 --> 00:08:14.010
They're connected in the same
way, so they're definitely

00:08:14.010 --> 00:08:15.780
stereoisomers.

00:08:15.780 --> 00:08:17.510
Well, we have to make sure
they're not-- well, let's make

00:08:17.510 --> 00:08:19.830
sure they're not the same
molecule first. Here,

00:08:19.830 --> 00:08:21.520
hydrogen's in the front.

00:08:21.520 --> 00:08:23.770
There, hydrogen's in the back.

00:08:23.770 --> 00:08:25.600
Here, hydrogen is in the back.

00:08:25.600 --> 00:08:26.590
Here, hydrogen is
in the front.

00:08:26.590 --> 00:08:28.140
So they're not the
same molecule.

00:08:28.140 --> 00:08:30.360
They have a different
three-dimensional

00:08:30.360 --> 00:08:33.940
configuration, although their
bond connections are the same,

00:08:33.940 --> 00:08:35.190
so these are stereoisomers.

00:08:44.430 --> 00:08:46.350
Let's see if they're
enantiomers.

00:08:46.350 --> 00:08:49.410
So if we look at it like this,
you put a mirror here, you

00:08:49.410 --> 00:08:50.720
wouldn't get this
guy over here.

00:08:50.720 --> 00:08:52.770
Then you would have a chlorine
out front and a hydrogen.

00:08:52.770 --> 00:08:55.140
So you won't get it if you
get a mirror over there.

00:08:55.140 --> 00:08:58.450
But if we do the same exercise
that we did in the last pair,

00:08:58.450 --> 00:09:02.855
if you put a mirror behind this
guy, and I'm just going

00:09:02.855 --> 00:09:05.170
to focus on the stuff that's
just forward and back, because

00:09:05.170 --> 00:09:07.160
that's what's relevant
if the mirror is

00:09:07.160 --> 00:09:09.250
sitting behind the molecule.

00:09:09.250 --> 00:09:12.570
So if the mirror's sitting
behind the molecule, this

00:09:12.570 --> 00:09:15.810
bromine is actually closer to
the mirror than that hydrogen.

00:09:15.810 --> 00:09:20.680
So the bromine will now be out
front and then the hydrogen

00:09:20.680 --> 00:09:21.380
will be in back.

00:09:21.380 --> 00:09:22.930
This hydrogen will
be in the back.

00:09:22.930 --> 00:09:26.120
I'm trying to do kind of a
mirror image if it's hard to

00:09:26.120 --> 00:09:27.070
conceptualize.

00:09:27.070 --> 00:09:29.870
And then that would
all look the same.

00:09:29.870 --> 00:09:33.890
And then this chlorine will
now be out front, and this

00:09:33.890 --> 00:09:37.725
hydrogen will now be in the back
in our mirror image, if

00:09:37.725 --> 00:09:39.180
you can visualize it.

00:09:39.180 --> 00:09:40.350
And then we have another one.

00:09:40.350 --> 00:09:43.230
And this chlorine is closer to
the mirror that it's kind of

00:09:43.230 --> 00:09:44.940
been sitting on top of.

00:09:44.940 --> 00:09:47.100
So in the mirror image, it would
be pointing out, and

00:09:47.100 --> 00:09:49.690
then this hydrogen would
be pointing back.

00:09:49.690 --> 00:09:52.550
Now let's see, is our mirror
image the same as this?

00:09:52.550 --> 00:09:54.940
So the mirror image, our bromine
is pointing in the

00:09:54.940 --> 00:09:57.140
front, hydrogen in
the back there.

00:09:57.140 --> 00:10:00.690
Then we have hydrogen in-- then
in our mirror image, we

00:10:00.690 --> 00:10:02.270
have the hydrogen in back,
chlorine in front.

00:10:02.270 --> 00:10:02.770
Same there.

00:10:02.770 --> 00:10:05.460
So far, it's looking like
a mirror image.

00:10:05.460 --> 00:10:08.690
And then in this last carbon
over here, chlorine in front,

00:10:08.690 --> 00:10:10.310
hydrogen in back.

00:10:10.310 --> 00:10:12.800
But here, we have chlorine in
the back, hydrogen in front.

00:10:12.800 --> 00:10:15.750
So this part, you could
think of it this way.

00:10:15.750 --> 00:10:20.360
This is the mirror image of
this, this is the mirror image

00:10:20.360 --> 00:10:24.470
of this part, but this is not
the mirror image of that part.

00:10:24.470 --> 00:10:27.790
So when you have a stereoisomer
that is not a

00:10:27.790 --> 00:10:29.980
mirror, when you have two
stereoisomers that aren't

00:10:29.980 --> 00:10:34.330
mirror images of each other,
we call them diastereomers.

00:10:34.330 --> 00:10:35.580
I always have trouble
saying that.

00:10:35.580 --> 00:10:36.920
Let me write it.

00:10:36.920 --> 00:10:45.990
These are diastereomers, which
is essentially saying it's a

00:10:45.990 --> 00:10:48.240
stereoisomer that is
not an enantiomer.

00:10:48.240 --> 00:10:50.470
That's all it means: a
stereoisomer, not an

00:10:50.470 --> 00:10:51.090
enantiomer.

00:10:51.090 --> 00:10:52.830
A stereoisomer's either going
to be an enantiomer or a

00:10:52.830 --> 00:10:54.960
diastereomer.

00:10:54.960 --> 00:10:57.040
Now, let's do this last one.

00:10:57.040 --> 00:11:02.650
Let's see we have two-- we have
this cyclohexane ring,

00:11:02.650 --> 00:11:05.950
and they have a bromo on the
number one and the number two

00:11:05.950 --> 00:11:07.750
group, depending how
you think about it.

00:11:07.750 --> 00:11:11.510
It looks like they are mirror
images of each other.

00:11:11.510 --> 00:11:15.050
We could put a mirror right
there, and they definitely

00:11:15.050 --> 00:11:16.640
look like mirror images.

00:11:16.640 --> 00:11:18.520
And this is a chiral
carbon here.

00:11:18.520 --> 00:11:20.790
It's bonded to one carbon group
that is different than

00:11:20.790 --> 00:11:21.550
this carbon group.

00:11:21.550 --> 00:11:23.170
This carbon group
has a bromine.

00:11:23.170 --> 00:11:24.080
This carbon group doesn't.

00:11:24.080 --> 00:11:25.750
It just has a bunch of hydrogens
on it, if you kind

00:11:25.750 --> 00:11:27.210
of go in that direction.

00:11:27.210 --> 00:11:30.640
And it's hydrogen and then a
bromine, so that is chiral.

00:11:30.640 --> 00:11:33.370
And then, same argument,
that is also chiral.

00:11:33.370 --> 00:11:36.050
And obviously, this one is
chiral and that is chiral.

00:11:36.050 --> 00:11:38.880
But if you think about it, they
are mirror images of each

00:11:38.880 --> 00:11:42.370
other, and they each have
two chiral centers

00:11:42.370 --> 00:11:44.350
or two chiral carbons.

00:11:44.350 --> 00:11:46.840
But if you think about it, all
you have to do is flip this

00:11:46.840 --> 00:11:49.830
guy over and you will
get this molecule.

00:11:49.830 --> 00:11:51.970
These are the same molecules.

00:11:51.970 --> 00:11:56.380
So it is the same molecule.

00:11:56.380 --> 00:11:59.050
So this is interesting, and we
saw this when we first learned

00:11:59.050 --> 00:12:00.220
about chirality.

00:12:00.220 --> 00:12:03.350
Even though we have two chiral
centers, this is

00:12:03.350 --> 00:12:04.650
not a chiral molecule.

00:12:04.650 --> 00:12:06.690
It is the same thing as
its mirror image.

00:12:06.690 --> 00:12:10.180
It is superimposable on
its mirror image.

00:12:10.180 --> 00:12:23.410
It is superimposable on
its mirror image.

00:12:23.410 --> 00:12:27.540
So even though it has chiral
carbons in it, it is not a

00:12:27.540 --> 00:12:29.380
chiral molecule.

00:12:29.380 --> 00:12:31.530
And we call these
meso compounds.

00:12:34.700 --> 00:12:36.510
And we can point to one of them
because they really are

00:12:36.510 --> 00:12:37.660
the same compound.

00:12:37.660 --> 00:12:41.590
This is a meso compound.

00:12:41.590 --> 00:12:43.770
It has chiral centers.

00:12:43.770 --> 00:12:45.960
It has chiral carbons, I
guess you could say it.

00:12:45.960 --> 00:12:48.360
But it is not a chiral
compound.

00:12:48.360 --> 00:12:50.350
And the way to spot these fairly
straightforward is that

00:12:50.350 --> 00:12:52.500
you have chiral centers,
but there is a

00:12:52.500 --> 00:12:54.170
line of symmetry here.

00:12:54.170 --> 00:12:56.110
There's a line of symmetry
right here.

00:12:56.110 --> 00:12:59.690
These two sides of the compound
are mirror images of

00:12:59.690 --> 00:13:00.430
each other.

00:13:00.430 --> 00:13:05.190
Now, these would not be the same
molecule if I change that

00:13:05.190 --> 00:13:09.310
to a fluorine and I change
that to a fluorine.

00:13:09.310 --> 00:13:11.780
Then all of a sudden, you do
not have this symmetry.

00:13:11.780 --> 00:13:14.180
These are mirror images,
but they would not be

00:13:14.180 --> 00:13:15.060
superimposable.

00:13:15.060 --> 00:13:17.650
So if that was a fluorine,
these would actually be

00:13:17.650 --> 00:13:18.790
enantiomers.

00:13:18.790 --> 00:13:22.110
And this would not be only one
meso compound, it would be two

00:13:22.110 --> 00:13:27.860
different enantiomers, and one
of them would have an R

00:13:27.860 --> 00:13:30.340
direction and one of them would
have an S direction if

00:13:30.340 --> 00:13:33.040
we go with the naming
conventions that we learned.


R,S (Cahn-Ingold-Prelog) naming system example 2

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:04.260
Let's see if we can name this
molecule using the-- sometimes

00:00:04.260 --> 00:00:08.740
called the R-S system, or the
Cahn-Ingold-Prelog system.

00:00:08.740 --> 00:00:11.830
And the first thing to do is
just to see if there are any

00:00:11.830 --> 00:00:13.830
chiral centers in
this molecule.

00:00:13.830 --> 00:00:14.960
If there aren't, then
we don't even have

00:00:14.960 --> 00:00:16.379
to use the R-S system.

00:00:16.379 --> 00:00:17.960
We can just use our standard
nomenclature

00:00:17.960 --> 00:00:19.440
rules and we'd be done.

00:00:19.440 --> 00:00:21.760
So if we look here, this carbon
is attached to three

00:00:21.760 --> 00:00:23.230
hydrogens, so it's definitely
not attached to

00:00:23.230 --> 00:00:24.490
four different groups.

00:00:24.490 --> 00:00:27.180
Same thing about this
carbon right here.

00:00:27.180 --> 00:00:29.950
This carbon right here is
attached to a fluorine, but

00:00:29.950 --> 00:00:33.130
then it's attached to
two methyl groups.

00:00:33.130 --> 00:00:36.030
So it's the same group, so
this is also not a chiral

00:00:36.030 --> 00:00:38.480
carbon or an asymmetric
carbon.

00:00:38.480 --> 00:00:42.710
This carbon right here is
attached to a hydrogen and

00:00:42.710 --> 00:00:45.740
three other carbons, but each
of these three carbons look

00:00:45.740 --> 00:00:46.700
like different groups.

00:00:46.700 --> 00:00:49.340
This carbon is attached to two
methyls and a fluorine.

00:00:49.340 --> 00:00:51.820
This carbon is attached to two
hydrogens and a bromine.

00:00:51.820 --> 00:00:53.570
This carbon is just
a methyl group.

00:00:53.570 --> 00:00:57.110
So this right here does look
like a chiral center.

00:00:57.110 --> 00:00:58.880
It does look like a
chiral carbon, and

00:00:58.880 --> 00:01:00.250
the other ones don't.

00:01:00.250 --> 00:01:01.380
This is just a methyl group.

00:01:01.380 --> 00:01:04.200
It has three hydrogens, so
definitely not attached to

00:01:04.200 --> 00:01:05.620
four different groups.

00:01:05.620 --> 00:01:07.680
And this is attached to two
hydrogens, and those are

00:01:07.680 --> 00:01:09.960
obviously the same group,
so this is also

00:01:09.960 --> 00:01:10.890
not a chiral center.

00:01:10.890 --> 00:01:14.490
So we have one chiral
center, so the R-S

00:01:14.490 --> 00:01:16.470
naming system will apply.

00:01:16.470 --> 00:01:19.110
But a good starting point will
just be naming it using our

00:01:19.110 --> 00:01:20.550
standard nomenclature rules.

00:01:20.550 --> 00:01:24.360
And to do that we look for the
longest carbon chain here.

00:01:24.360 --> 00:01:26.970
Let's see, if we start over
here, and I don't know what

00:01:26.970 --> 00:01:30.440
direction I'm going to name it
from yet, but I just want to

00:01:30.440 --> 00:01:31.780
identify the longest chain.

00:01:31.780 --> 00:01:34.280
If we went from here, we
have one, two, three.

00:01:34.280 --> 00:01:37.090
We can either go to four or to
four there, so we definitely

00:01:37.090 --> 00:01:40.950
have four carbons, Four
carbon, longest chain.

00:01:44.530 --> 00:01:48.410
So that tells us that we will
be using the prefix but-, or

00:01:48.410 --> 00:01:51.290
it will be a butane, because
they're all single bonds here,

00:01:51.290 --> 00:01:52.830
so it is a butane.

00:01:52.830 --> 00:01:55.250
But to decide whether we branch
off, it doesn't matter

00:01:55.250 --> 00:01:58.930
whether we use this
CH3 or this CH3,

00:01:58.930 --> 00:02:00.100
they're the same group.

00:02:00.100 --> 00:02:03.750
But to decide whether we use
this part of the longest chain

00:02:03.750 --> 00:02:08.820
or we use that, we think about
the rule that the core chain

00:02:08.820 --> 00:02:12.930
to use should have as many
simple groups attached to it

00:02:12.930 --> 00:02:17.590
as possible, as opposed to
as few complex groups.

00:02:17.590 --> 00:02:21.550
So if we used this carbon as
part of our longest chain,

00:02:21.550 --> 00:02:23.590
then this will be a group that's
attached to it, which

00:02:23.590 --> 00:02:28.670
would be a bromomethyl group,
which is not as simple as

00:02:28.670 --> 00:02:29.500
maybe it could be.

00:02:29.500 --> 00:02:32.210
But if we use this carbon in our
longest chain, we'll have

00:02:32.210 --> 00:02:32.830
two groups.

00:02:32.830 --> 00:02:35.110
We'll have a bromo attached,
and we'll also

00:02:35.110 --> 00:02:36.180
have a methyl group.

00:02:36.180 --> 00:02:37.090
And that's what we want.

00:02:37.090 --> 00:02:40.630
We want more simple groups
attached to the longest chain.

00:02:40.630 --> 00:02:42.900
So what we're going to do is
we're going to use this

00:02:42.900 --> 00:02:47.400
carbon, this carbon, this
carbon, and that carbon as our

00:02:47.400 --> 00:02:48.350
longest chain.

00:02:48.350 --> 00:02:51.980
And we want to start from the
end that is closest to

00:02:51.980 --> 00:02:53.930
something being attached
to it, and that

00:02:53.930 --> 00:02:54.980
bromine is right there.

00:02:54.980 --> 00:02:57.320
So there's going to be our
number one carbon, our number

00:02:57.320 --> 00:02:59.570
two carbon, our number
three carbon, and

00:02:59.570 --> 00:03:01.120
our number four carbon.

00:03:01.120 --> 00:03:02.930
And then we can label the
different groups and then

00:03:02.930 --> 00:03:07.630
figure out what order they
should be listed in.

00:03:07.630 --> 00:03:13.620
So this is a 1-bromo and
then this will be a

00:03:13.620 --> 00:03:14.950
2-methyl right here.

00:03:19.160 --> 00:03:20.840
And then just a hydrogen.

00:03:20.840 --> 00:03:24.680
Then three we have a fluoro, so
on a carbon three, we have

00:03:24.680 --> 00:03:30.450
a fluoro, and then on carbon
three, we also have a methyl

00:03:30.450 --> 00:03:32.340
group right here, so we
also have a 3-methyl.

00:03:35.110 --> 00:03:37.720
So when we name it, we put
in alphabetical order.

00:03:37.720 --> 00:03:41.435
Bromo comes first, so this thing
right here is 1-bromo.

00:03:44.540 --> 00:03:48.380
Then alphabetically, fluoro
comes next, 1-bromo-3-fluoro.

00:03:53.260 --> 00:03:56.140
We have two methyls, so it's
going to be 2 comma

00:03:56.140 --> 00:03:57.390
3-dimethyl.

00:03:59.660 --> 00:04:02.690
And remember, the D doesn't
count in alphabetical order.

00:04:02.690 --> 00:04:11.330
Dimethylbutane, because
we have the longest

00:04:11.330 --> 00:04:12.970
chain is four carbons.

00:04:12.970 --> 00:04:14.570
Dimethylbutane.

00:04:14.570 --> 00:04:16.680
So that's just the standard
nomenclature rules.

00:04:16.680 --> 00:04:18.610
We still haven't used
the R-S system.

00:04:18.610 --> 00:04:19.790
Now we can do that.

00:04:19.790 --> 00:04:21.959
Now to think about that, we
already said that this is our

00:04:21.959 --> 00:04:25.570
chiral center, so we just have
to essentially rank the groups

00:04:25.570 --> 00:04:29.380
attached to it in order of
atomic number and then use the

00:04:29.380 --> 00:04:33.210
Cahn-Ingold-Prelog rules,
and we'll do all

00:04:33.210 --> 00:04:34.040
that in this example.

00:04:34.040 --> 00:04:36.770
So let's look at the different
groups attached to it.

00:04:36.770 --> 00:04:38.710
So when you look at it,
this guy has three

00:04:38.710 --> 00:04:40.350
carbons and a hydrogen.

00:04:40.350 --> 00:04:43.010
Carbon is definitely higher
in atomic number on

00:04:43.010 --> 00:04:43.900
the Periodic Table.

00:04:43.900 --> 00:04:45.580
It has an atomic number 6.

00:04:45.580 --> 00:04:47.160
Hydrogen is 1.

00:04:47.160 --> 00:04:48.680
You probably know
that already.

00:04:48.680 --> 00:04:51.150
So hydrogen is definitely
going to be number four.

00:04:51.150 --> 00:04:54.940
So let me put number four there
next to the hydrogen.

00:04:54.940 --> 00:04:56.560
And let me find a nice color.

00:04:56.560 --> 00:04:57.710
I'll do it in white.

00:04:57.710 --> 00:05:00.640
So hydrogen is definitely
the number four group.

00:05:00.640 --> 00:05:02.830
We have to differentiate between
this carbon group,

00:05:02.830 --> 00:05:04.870
that carbon group, and
that carbon group.

00:05:04.870 --> 00:05:07.690
And the way you do it, if
there's a tie on the three

00:05:07.690 --> 00:05:10.940
carbons, you then look at what
is attached to those carbons,

00:05:10.940 --> 00:05:13.280
and you compare the highest
thing attached to each of

00:05:13.280 --> 00:05:15.330
those carbons to the highest
things attached to the other

00:05:15.330 --> 00:05:18.760
carbons, and then you
do the same ranking.

00:05:18.760 --> 00:05:21.940
And if that's a tie, then you
keep going on and on and on.

00:05:21.940 --> 00:05:25.140
So on this carbon right here,
we have a bromine.

00:05:25.140 --> 00:05:30.390
Bromine has an atomic
number of 35, which

00:05:30.390 --> 00:05:35.410
is higher than carbon.

00:05:35.410 --> 00:05:37.940
So this guy has a bromine
attached to it.

00:05:37.940 --> 00:05:41.190
This guy only has hydrogen
attached to it.

00:05:41.190 --> 00:05:42.730
This guy has a fluorine
attached to it.

00:05:42.730 --> 00:05:44.160
That's the highest thing.

00:05:44.160 --> 00:05:48.180
So this is going to be the third
lowest, or I should say

00:05:48.180 --> 00:05:50.800
the second to lowest, because it
only has hydrogens attached

00:05:50.800 --> 00:05:52.480
to it, so that is
number three.

00:05:52.480 --> 00:05:54.430
The one has the bromine attached
to it is going to be

00:05:54.430 --> 00:05:59.020
number one, and the one that has
the fluorine attached to

00:05:59.020 --> 00:06:00.270
it is number two.

00:06:02.470 --> 00:06:04.720
And just a reminder, we were
tied with the carbon, so we

00:06:04.720 --> 00:06:07.100
have to look at the next highest
constituent, and even

00:06:07.100 --> 00:06:10.990
if this had three fluorines
attached to it, the bromine

00:06:10.990 --> 00:06:12.060
would still trump it.

00:06:12.060 --> 00:06:15.610
You compare the highest to the
highest. So now that we've

00:06:15.610 --> 00:06:18.120
done that, let me redraw this
molecule so it's a little bit

00:06:18.120 --> 00:06:19.545
easier to visualize.

00:06:19.545 --> 00:06:23.540
So I'll draw our chiral
carbon in the middle.

00:06:26.920 --> 00:06:29.440
And I'm just doing this for
visualization purposes.

00:06:29.440 --> 00:06:31.420
And right here we have
our number one group.

00:06:31.420 --> 00:06:34.010
I'll literally just call that
our number one group.

00:06:34.010 --> 00:06:37.190
So right there that is
our number one group.

00:06:37.190 --> 00:06:39.600
It's in the plane
of the screen.

00:06:39.600 --> 00:06:42.710
So I'll just call that
our number one group.

00:06:45.330 --> 00:06:49.500
Over here, also in the plane
of the screen, I have our

00:06:49.500 --> 00:06:50.750
number two group.

00:06:53.530 --> 00:06:55.210
So let me do it like that.

00:06:55.210 --> 00:07:02.260
So then you have your number
two group, just like that.

00:07:02.260 --> 00:07:04.390
And then you have your number
three group behind the

00:07:04.390 --> 00:07:06.375
molecule right now the
way it's drawn.

00:07:06.375 --> 00:07:10.200
I'll do that in magenta.

00:07:10.200 --> 00:07:11.860
So then you have your
number three group.

00:07:11.860 --> 00:07:15.490
It's behind the molecule, so
I'll draw it like this.

00:07:15.490 --> 00:07:17.930
This is our number
three group.

00:07:20.440 --> 00:07:22.480
And then we have our number
four group, which is the

00:07:22.480 --> 00:07:24.690
hydrogen pointing
out right now.

00:07:24.690 --> 00:07:26.620
And I'll just do that
in a yellow.

00:07:26.620 --> 00:07:28.910
We have our number four
group pointing out

00:07:28.910 --> 00:07:31.260
in front right now.

00:07:31.260 --> 00:07:38.480
So that is number four,
just like that.

00:07:38.480 --> 00:07:40.860
Actually, let me draw it a
little bit clearer, so it

00:07:40.860 --> 00:07:43.190
looks a little bit more like the
tripod structure that it's

00:07:43.190 --> 00:07:43.790
supposed to be.

00:07:43.790 --> 00:07:45.970
So let me redraw the
number three group.

00:07:45.970 --> 00:07:51.380
The number three group should
look like-- so this is our

00:07:51.380 --> 00:07:52.140
number three group.

00:07:52.140 --> 00:07:55.390
Let me draw it a little
bit more like this.

00:07:55.390 --> 00:07:57.080
The number three group
is behind us.

00:08:00.160 --> 00:08:02.140
And then finally, you have
your number four group in

00:08:02.140 --> 00:08:05.630
yellow, which is just a
hydrogen that's coming

00:08:05.630 --> 00:08:08.100
straight out.

00:08:08.100 --> 00:08:10.620
So that is coming straight out
of-- well, not straight out,

00:08:10.620 --> 00:08:12.240
but at an angle out
of the page.

00:08:12.240 --> 00:08:14.020
So that's our number four group,
I'll just label it

00:08:14.020 --> 00:08:14.610
number four.

00:08:14.610 --> 00:08:16.480
It really is just a hydrogen,
so I really didn't have to

00:08:16.480 --> 00:08:18.030
simplify it much there.

00:08:18.030 --> 00:08:23.120
Now by the R-S system, or by the
Cahn-Ingold-Prelog system,

00:08:23.120 --> 00:08:28.440
we want our number four group
to be the one furthest back.

00:08:28.440 --> 00:08:31.300
So we really want it where the
number three position is.

00:08:31.300 --> 00:08:33.909
And so the easiest way I can
think of doing that is you can

00:08:33.909 --> 00:08:37.720
imagine this is a tripod that's
leaning upside down.

00:08:37.720 --> 00:08:39.140
Or another way to view it
is you can view it as an

00:08:39.140 --> 00:08:42.490
umbrella, where this is the
handle of the umbrella and

00:08:42.490 --> 00:08:44.880
that's the top of the
umbrella that would

00:08:44.880 --> 00:08:46.300
block the rain, I guess.

00:08:46.300 --> 00:08:50.000
But the easiest way to get the
number four group that's

00:08:50.000 --> 00:08:53.210
actually a hydrogen in the
number three position would be

00:08:53.210 --> 00:08:55.070
to rotate it.

00:08:55.070 --> 00:08:57.580
You could imagine, rotate it
around the axis defined by the

00:08:57.580 --> 00:08:58.300
number one group.

00:08:58.300 --> 00:08:59.670
So the number one group
is just going to

00:08:59.670 --> 00:09:00.940
stay where it is.

00:09:00.940 --> 00:09:02.440
The number four is going
to rotate to the

00:09:02.440 --> 00:09:03.670
number three group.

00:09:03.670 --> 00:09:06.630
Number three is going to rotate
around to the number

00:09:06.630 --> 00:09:11.190
two group, and then the number
two group is going to rotate

00:09:11.190 --> 00:09:13.340
to where the number four
group is right now.

00:09:13.340 --> 00:09:15.330
So if we were to redraw
that, let's

00:09:15.330 --> 00:09:18.140
redraw our chiral carbon.

00:09:18.140 --> 00:09:21.220
So let me scroll over
a little bit.

00:09:21.220 --> 00:09:23.110
So we have our chiral carbon.

00:09:23.110 --> 00:09:25.430
I put the little asterisk there
to say that that's our

00:09:25.430 --> 00:09:26.630
chiral carbon.

00:09:26.630 --> 00:09:28.295
The number four group
is now behind.

00:09:28.295 --> 00:09:29.590
I'll do it with the circles.

00:09:29.590 --> 00:09:32.300
It makes it look a little bit
more like atoms. So the number

00:09:32.300 --> 00:09:35.840
four group is now behind where
the number three group used to

00:09:35.840 --> 00:09:38.230
be, so number four
is now there.

00:09:41.200 --> 00:09:42.650
Number one hasn't changed.

00:09:42.650 --> 00:09:46.030
That's kind of the axis that
we rotated around.

00:09:46.030 --> 00:09:49.270
So the number one group
has not changed.

00:09:49.270 --> 00:09:51.140
Number one is still there.

00:09:51.140 --> 00:09:55.410
Number two is now where number
four used to be, so number two

00:09:55.410 --> 00:09:56.920
is now jutting out
of the page.

00:10:05.190 --> 00:10:09.670
And then we have number three
is now where number two was.

00:10:09.670 --> 00:10:11.030
So number three is there.

00:10:14.050 --> 00:10:17.280
And now that we've put our
fourth group behind the

00:10:17.280 --> 00:10:19.630
molecule, we literally just
figure out whether we have to

00:10:19.630 --> 00:10:21.640
go clockwise or counterclockwise
to go from

00:10:21.640 --> 00:10:23.080
one, two to three.

00:10:23.080 --> 00:10:24.310
And that's pretty
straightforward.

00:10:24.310 --> 00:10:27.530
To go from one to two to
three, we have to go

00:10:27.530 --> 00:10:28.780
counterclockwise.

00:10:35.680 --> 00:10:38.520
Or another way to think of it,
we're going to the left,

00:10:38.520 --> 00:10:39.800
counterclockwise.

00:10:39.800 --> 00:10:41.510
At least on the top of
the clock, we're

00:10:41.510 --> 00:10:42.710
going to the left.

00:10:42.710 --> 00:10:46.390
And so, since we're going to
left, this is S or sinister.

00:10:46.390 --> 00:10:50.770
This is S, which stands
for sinister, which

00:10:50.770 --> 00:10:52.610
is Latin for left.

00:10:52.610 --> 00:10:53.360
So we're done.

00:10:53.360 --> 00:10:57.370
We've named it using
the R-S system.

00:10:57.370 --> 00:11:01.870
This molecule is (S)--
sinister--

00:11:01.870 --> 00:11:03.120
1-bromo-3-fluoro-2,3-di--


Cahn-Ingold-Prelog system for naming enantiomers

WEBVTT
Kind: captions
Language: en

00:00:00.820 --> 00:00:03.480
Right now, based on what we know
so far, if we wanted to

00:00:03.480 --> 00:00:07.080
name this molecule, we would
say, well, what's the longest

00:00:07.080 --> 00:00:08.450
carbon chain here?

00:00:08.450 --> 00:00:12.720
Well, we have a two-carbon
chain, and there's all single

00:00:12.720 --> 00:00:16.490
bonds, so we're dealing
with an ethane.

00:00:16.490 --> 00:00:18.440
Actually, I'll write
it all at once.

00:00:18.440 --> 00:00:21.700
And then we have on the one
carbon, we can call this the

00:00:21.700 --> 00:00:25.730
one carbon, and call this the
two carbon, we have a bromine

00:00:25.730 --> 00:00:26.780
and a fluorine.

00:00:26.780 --> 00:00:34.100
So we could call this 1-bromo,
and we're putting the bromo

00:00:34.100 --> 00:00:36.650
instead of the fluoro because
B comes before F

00:00:36.650 --> 00:00:37.640
alphabetically.

00:00:37.640 --> 00:00:46.410
1-bromo-1-fluoro, and then we're
dealing with an ethane.

00:00:46.410 --> 00:00:49.400
We have a two-carbon chain,
all single bonds,

00:00:49.400 --> 00:00:51.630
fluoroethane.

00:00:51.630 --> 00:00:54.010
That's the name of that molecule
there, just a review

00:00:54.010 --> 00:00:56.630
of some of the earlier
organic nomenclature

00:00:56.630 --> 00:00:57.940
videos we had done.

00:00:57.940 --> 00:01:00.850
Now, we know immediately, based
on the last few videos,

00:01:00.850 --> 00:01:03.920
that this is also a chiral
carbon, and if we were to take

00:01:03.920 --> 00:01:10.740
its mirror image, we would get
another enantiomer of this

00:01:10.740 --> 00:01:13.780
same molecule, or that they are
enantiomers of each other.

00:01:13.780 --> 00:01:16.710
So what is the mirror
image of this

00:01:16.710 --> 00:01:19.430
1-bromo-1-fluoroethane look like?

00:01:19.430 --> 00:01:23.380
Well, you'd have the
carbon right here.

00:01:23.380 --> 00:01:24.670
I want to get all the
colors right.

00:01:24.670 --> 00:01:28.050
You would still have the
bromine up above.

00:01:28.050 --> 00:01:31.100
You would have this methyl group
that's attached to the

00:01:31.100 --> 00:01:35.280
carbon now pointing in the
left direction, CH3.

00:01:35.280 --> 00:01:42.020
The fluorine would now still be
behind the carbon, and now

00:01:42.020 --> 00:01:44.890
the hydrogen would still pop out
of the page, but it would

00:01:44.890 --> 00:01:46.600
now pop out and to the right.

00:01:51.610 --> 00:01:53.080
That is the hydrogen.

00:01:53.080 --> 00:01:56.180
Now, based on our naming so
far, we would name this

00:01:56.180 --> 00:02:01.860
1-bromo-1-fluoroethane, and
we would also name this

00:02:01.860 --> 00:02:08.100
1-bromo-1-fluoroethane, but
these are fundamentally two

00:02:08.100 --> 00:02:09.169
different molecules.

00:02:09.169 --> 00:02:12.100
Even though they have the same
molecules in them; they have

00:02:12.100 --> 00:02:15.280
the same molecular formula;
they have the same

00:02:15.280 --> 00:02:19.640
constitution in that this
carbon is connected to a

00:02:19.640 --> 00:02:21.810
hydrogen, a fluorine, and a
bromine; this carbon is

00:02:21.810 --> 00:02:24.420
connected to the same things;
this carbon is connected to a

00:02:24.420 --> 00:02:28.440
carbon, three hydrogens; so
is this one; these are

00:02:28.440 --> 00:02:29.675
stereoisomers.

00:02:29.675 --> 00:02:32.990
These are stereoisomers, and
they're mirror images of each

00:02:32.990 --> 00:02:34.240
other, so they're enantiomers.

00:02:37.220 --> 00:02:40.500
And actually, they will, one,
polarize light differently,

00:02:40.500 --> 00:02:45.070
and they actually can often have
very different chemical

00:02:45.070 --> 00:02:47.860
properties, either in a chemical
or biological system.

00:02:47.860 --> 00:02:52.190
So it seems not good that
we have the same

00:02:52.190 --> 00:02:53.540
names for both of these.

00:02:53.540 --> 00:02:55.460
So what we're going to focus on
in this video is how do you

00:02:55.460 --> 00:02:57.860
differentiate between the two?

00:03:01.510 --> 00:03:04.460
So how do we differentiate
between the two?

00:03:04.460 --> 00:03:07.470
So the naming system we're going
to use right here is

00:03:07.470 --> 00:03:12.040
called the Cahn-Ingold-Prelog
system, but it's a different

00:03:12.040 --> 00:03:13.000
Cahn, it's not me.

00:03:13.000 --> 00:03:17.835
It's C-A-H-N instead
of K-H-A-N.

00:03:17.835 --> 00:03:26.500
Cahn-Ingold-Prelog system, and
it's a way of differentiating

00:03:26.500 --> 00:03:29.520
between this enantiomer, which
right now we would call

00:03:29.520 --> 00:03:32.110
1-bromo-1-fluoroethane,
and this enantiomer,

00:03:32.110 --> 00:03:34.820
1-bromo-1-fluoroethane.

00:03:34.820 --> 00:03:36.210
It's a pretty straightforward
thing.

00:03:36.210 --> 00:03:39.520
Really, the hardest part is to
just visualize rotating the

00:03:39.520 --> 00:03:41.560
molecules in the right way
and figuring out in which

00:03:41.560 --> 00:03:43.410
direction it's kind of--
whether it's kind of a

00:03:43.410 --> 00:03:45.010
left-handed or right-handed
molecule.

00:03:45.010 --> 00:03:46.770
We're going to take
it step by step.

00:03:46.770 --> 00:03:50.960
So the first thing you do in the
Cahn-Ingold-Prelog system

00:03:50.960 --> 00:03:56.170
is to, one, identify your
chiral molecule.

00:03:56.170 --> 00:03:57.330
Here, it's pretty obvious.

00:03:57.330 --> 00:04:00.550
It's this carbon right here.

00:04:00.550 --> 00:04:03.350
We'll just focus on this left
one, the one we started with

00:04:03.350 --> 00:04:06.430
first. It's bonded to three
different groups.

00:04:06.430 --> 00:04:09.900
And then what you want to do is
you want to rank the groups

00:04:09.900 --> 00:04:11.770
by atomic number.

00:04:11.770 --> 00:04:18.120
So if you go up here, out of
bromine, hydrogen, fluorine,

00:04:18.120 --> 00:04:21.130
and a carbon, this is what is
bonded directly to this

00:04:21.130 --> 00:04:23.900
carbon, which has the highest
atomic number?

00:04:23.900 --> 00:04:27.470
Bromine is over here-- let me
do this in a darker color.

00:04:27.470 --> 00:04:32.790
We have bromine at 35, we have
fluorine at 9, we have carbon

00:04:32.790 --> 00:04:37.250
at 6, and then we have
hydrogen at 1.

00:04:37.250 --> 00:04:40.500
So of all these, bromine is the
largest. We'll just call

00:04:40.500 --> 00:04:42.260
this number one.

00:04:42.260 --> 00:04:44.390
Then after that, we
have fluorine.

00:04:44.390 --> 00:04:46.690
That is the number two.

00:04:46.690 --> 00:04:49.810
Number three is the carbon.

00:04:49.810 --> 00:04:51.950
And then hydrogen is
the smallest, so

00:04:51.950 --> 00:04:55.450
that is number four.

00:04:55.450 --> 00:04:58.290
So now that we've numbered
them, the next step is to

00:04:58.290 --> 00:05:01.890
orient this molecule so that
the smallest atomic number

00:05:01.890 --> 00:05:04.890
group is sitting
into the page.

00:05:04.890 --> 00:05:08.060
It's sitting behind
the molecule.

00:05:08.060 --> 00:05:11.570
Right now, this hydrogen is the
smallest of all of them.

00:05:11.570 --> 00:05:13.860
Bromine's the largest, hydrogen
is the smallest, so

00:05:13.860 --> 00:05:15.970
we want to orient it behind
the molecule.

00:05:15.970 --> 00:05:17.650
The way it's drawn right
now, it's oriented in

00:05:17.650 --> 00:05:18.920
front of the molecule.

00:05:18.920 --> 00:05:21.210
So to orient it behind the
molecule, and this really is

00:05:21.210 --> 00:05:23.560
the hardest part is just to
visualize it properly.

00:05:23.560 --> 00:05:25.480
Remember, this fluorine is
behind; this is right in the

00:05:25.480 --> 00:05:27.595
plane of the paper; this is
popping out of the paper.

00:05:30.430 --> 00:05:31.920
We would want to rotate.

00:05:31.920 --> 00:05:36.820
You could imagine we'd be
rotating the molecule in this

00:05:36.820 --> 00:05:39.800
direction so that--
let me redraw it.

00:05:44.140 --> 00:05:46.090
We have the carbon here.

00:05:46.090 --> 00:05:49.060
And now since we've rotated it
like this, we've rotated it

00:05:49.060 --> 00:05:54.450
roughly 1/3 around the circle,
so it's about 120 degrees.

00:05:54.450 --> 00:05:57.220
Now, this hydrogen is where
the fluorine was.

00:06:01.430 --> 00:06:02.730
So that's where the
hydrogen is.

00:06:02.730 --> 00:06:06.340
The fluorine is now where
this methyl group is.

00:06:10.120 --> 00:06:11.960
These dotted lines show
that we're behind now.

00:06:11.960 --> 00:06:13.420
This shows that we're
in the plane.

00:06:13.420 --> 00:06:15.340
And the methyl group is now
where the hydrogen is.

00:06:15.340 --> 00:06:16.640
It's now popping out
of the page.

00:06:16.640 --> 00:06:18.370
It's going to the
left and out.

00:06:18.370 --> 00:06:24.120
So this methyl group is now
popping out of the page, out

00:06:24.120 --> 00:06:25.290
and to the left.

00:06:25.290 --> 00:06:27.300
That's where our methyl
group is.

00:06:27.300 --> 00:06:29.420
So all we've done is we've just
rotated this around about

00:06:29.420 --> 00:06:30.950
120 degrees.

00:06:30.950 --> 00:06:33.680
We've just gotten this to go
behind, and that's kind of the

00:06:33.680 --> 00:06:36.340
first step after we've
identified the chiral carbon

00:06:36.340 --> 00:06:38.380
and ranked them by
atomic number.

00:06:38.380 --> 00:06:38.760
And.
Of course.

00:06:38.760 --> 00:06:40.360
The bromine is still
going to be on top.

00:06:43.220 --> 00:06:47.020
Now, once you put the smallest
atomic number molecule in the

00:06:47.020 --> 00:06:49.430
back, then you want to
look at the rankings

00:06:49.430 --> 00:06:50.630
of one through three.

00:06:50.630 --> 00:06:52.510
And we have four
molecules here.

00:06:52.510 --> 00:06:57.040
We look at the largest, which
is bromine, number one.

00:06:57.040 --> 00:07:00.540
Then number two is fluorine,
number two, and then number

00:07:00.540 --> 00:07:01.830
three is this methyl group.

00:07:01.830 --> 00:07:04.360
That's the carbon that's bonded
to this carbon, so it's

00:07:04.360 --> 00:07:06.900
number three right there.

00:07:06.900 --> 00:07:10.660
And in the Cahn-Ingold-Prelog
system, we literally just

00:07:10.660 --> 00:07:12.640
think about what would it take
to go from number one to

00:07:12.640 --> 00:07:13.900
number two to number three?

00:07:13.900 --> 00:07:16.400
And in this case, we would
go in this direction.

00:07:16.400 --> 00:07:19.250
To go from number one to number
two to number three, we

00:07:19.250 --> 00:07:21.020
would go in the clockwise
direction.

00:07:21.020 --> 00:07:22.670
We're just ignoring the
hydrogen right now.

00:07:22.670 --> 00:07:24.200
That's just sitting behind it.

00:07:24.200 --> 00:07:26.310
That was the first step, to
orient it so it's sitting in

00:07:26.310 --> 00:07:28.040
the back, the smallest
molecule.

00:07:28.040 --> 00:07:30.590
And then the three largest
ones, you just say what

00:07:30.590 --> 00:07:32.750
direction do we have to go to
go from number one to number

00:07:32.750 --> 00:07:33.780
two to number three?

00:07:33.780 --> 00:07:37.570
In this case, we have
to go clockwise.

00:07:37.570 --> 00:07:42.180
And if we go clockwise now,
then we call this a

00:07:42.180 --> 00:07:46.210
right-handed molecule, or we use
the Latin word for right,

00:07:46.210 --> 00:07:49.410
which is rectus.

00:07:49.410 --> 00:07:54.510
And so we would call this
molecule right here not just

00:07:54.510 --> 00:08:00.700
1-bromo-1-fluoroethane, this
is R, R for rectus.

00:08:00.700 --> 00:08:03.210
Or you could even think right,
although we'll see left is

00:08:03.210 --> 00:08:05.790
used as S, which is sinister,
so the Latin is really where

00:08:05.790 --> 00:08:07.050
the R comes from.

00:08:07.050 --> 00:08:18.260
But this is
(R)-1-bromo-1-fluoroethane

00:08:18.260 --> 00:08:19.470
That's this one right here.

00:08:19.470 --> 00:08:21.910
So you might guess, well, this
must be the opposite, this

00:08:21.910 --> 00:08:23.450
must be the counterclockwise
version.

00:08:23.450 --> 00:08:24.860
We can do it really fast.

00:08:24.860 --> 00:08:26.480
So same idea.

00:08:26.480 --> 00:08:28.280
We know the largest one.

00:08:28.280 --> 00:08:29.960
Bromine is number one.

00:08:29.960 --> 00:08:32.970
That's the largest in terms
of atomic number.

00:08:32.970 --> 00:08:34.809
Fluorine is number two.

00:08:34.809 --> 00:08:36.400
Carbon is number three.

00:08:36.400 --> 00:08:38.230
Hydrogen is number four.

00:08:38.230 --> 00:08:40.830
What we want to do is put
hydrogen in the back, so what

00:08:40.830 --> 00:08:43.350
we're going to have to do is
rotate it to the back to where

00:08:43.350 --> 00:08:45.190
fluorine is right now.

00:08:45.190 --> 00:08:48.860
So if we had to redraw this
molecule right here, you'd

00:08:48.860 --> 00:08:49.890
have your carbon still.

00:08:49.890 --> 00:08:52.015
You still have your bromine
sitting on top.

00:08:52.015 --> 00:08:55.030
But we're going to put the
hydrogen now to the back, so

00:08:55.030 --> 00:08:59.120
the hydrogen is now where
the fluorine used to be.

00:08:59.120 --> 00:09:00.370
The hydrogen's there.

00:09:05.120 --> 00:09:08.310
This methyl group, this carbon
with the three hydrogens, is

00:09:08.310 --> 00:09:12.830
going to be rotated to where
the hydrogen used to be.

00:09:12.830 --> 00:09:15.060
It's now going to pop out of
the page, because we're

00:09:15.060 --> 00:09:18.710
rotating it in that direction,
so this is our methyl group

00:09:18.710 --> 00:09:19.590
right there.

00:09:19.590 --> 00:09:21.900
And then this fluorine is going
to be moved where the

00:09:21.900 --> 00:09:26.740
methyl group was, so this
fluorine will go right here.

00:09:26.740 --> 00:09:30.070
And now, using the
Cahn-Ingold-Prelog system,

00:09:30.070 --> 00:09:33.240
this is our number one, this
is our number two, just by

00:09:33.240 --> 00:09:35.800
atomic number, this
is number three.

00:09:35.800 --> 00:09:38.850
You go from number one through
number two to number three.

00:09:38.850 --> 00:09:40.620
You go in this direction.

00:09:40.620 --> 00:09:41.870
You're going counterclockwise.

00:09:45.520 --> 00:09:48.890
Or we are going to the left, or
we use the Latin word for

00:09:48.890 --> 00:09:51.890
it, which is sinister.

00:09:51.890 --> 00:09:54.420
And the word sinister comes from
the Latin word for left,

00:09:54.420 --> 00:09:57.250
so I guess right is good, and
people thought either

00:09:57.250 --> 00:09:59.100
left-handed people were bad, or
if you're not going to the

00:09:59.100 --> 00:09:59.720
right, it's bad.

00:09:59.720 --> 00:10:04.180
I don't know why sinister took
on its sinister meaning now in

00:10:04.180 --> 00:10:05.110
common language.

00:10:05.110 --> 00:10:09.400
But it's now the sinister
version of the molecule.

00:10:09.400 --> 00:10:12.700
So we would call this version,
this enantiomer of

00:10:12.700 --> 00:10:19.840
1-bromo-1-fluoroethane, we
would call this S, S for

00:10:19.840 --> 00:10:22.970
sinister, or for left, or
for counterclockwise:

00:10:22.970 --> 00:10:24.220
(S)-1-bromo-1-fluoroethane.

00:10:31.440 --> 00:10:33.330
So now we can differentiate
the names.

00:10:33.330 --> 00:10:38.180
We know that these are two
different configurations.

00:10:38.180 --> 00:10:40.540
And that's what the S and the R
tell us, that if you have to

00:10:40.540 --> 00:10:43.660
go from this to this, you would
literally have to detach

00:10:43.660 --> 00:10:45.150
and reattach different groups.

00:10:45.150 --> 00:10:46.570
You'd actually have
to break bonds.

00:10:46.570 --> 00:10:50.850
You actually have to swap two of
these groups in some way in

00:10:50.850 --> 00:10:53.470
order to get from this
enantiomer to this enantiomer.

00:10:53.470 --> 00:10:55.410
They're different
configurations, really

00:10:55.410 --> 00:10:58.270
fundamentally different
molecules, stereoisomers,

00:10:58.270 --> 00:11:00.770
enantiomers, however
you want to call them.