Reaction coupling to create glucose 6 phosphate

WEBVTT
Kind: captions
Language: en

00:00:00.697 --> 00:00:03.148
- [Voiceover] It's super
valuable in biological systems

00:00:03.148 --> 00:00:05.226
to be able to take a glucose molecule

00:00:05.226 --> 00:00:06.677
and to phosphorylate it.

00:00:06.677 --> 00:00:08.325
So let's start with a glucose molecule

00:00:08.325 --> 00:00:10.419
and phosphorylate it, and the reason why

00:00:10.419 --> 00:00:12.497
is once you have this phosphate group--

00:00:12.497 --> 00:00:15.039
let me make sure I put that
charge right over there.

00:00:15.039 --> 00:00:17.396
Once you have this phosphate group,

00:00:17.396 --> 00:00:18.778
or once you have this negative charge

00:00:18.778 --> 00:00:20.693
on this glucose six phosphate,

00:00:20.693 --> 00:00:22.829
it becomes much harder
for it to leave the cell.

00:00:22.829 --> 00:00:25.720
The cell wants to hog as many
glucose molecules as it can.

00:00:25.720 --> 00:00:27.032
When the glucose isn't charged,

00:00:27.032 --> 00:00:29.272
it's able to pass through
the cellular membrane,

00:00:29.272 --> 00:00:30.909
but then once it becomes phosphorylated,

00:00:30.909 --> 00:00:32.534
it's going to stay in the cell.

00:00:32.534 --> 00:00:34.659
And glucose six phosphate right over here,

00:00:34.659 --> 00:00:36.737
this is a very important input

00:00:36.737 --> 00:00:40.951
to a whole series of
processes inside of cells.

00:00:40.951 --> 00:00:44.956
Now unfortunately, this reaction

00:00:44.956 --> 00:00:47.011
of taking glucose and phosphorylating it,

00:00:47.011 --> 00:00:49.611
it requires energy, it's endergonic,

00:00:49.611 --> 00:00:51.527
it's not going to happen spontaneously.

00:00:51.527 --> 00:00:54.174
It has a positive delta-G.

00:00:54.174 --> 00:00:57.830
It is ender, ender,

00:00:57.830 --> 00:00:59.850
it is endergonic.

00:00:59.850 --> 00:01:02.096
And so you can imagine
what we're going to need

00:01:02.096 --> 00:01:03.187
to make it happen.

00:01:03.187 --> 00:01:06.321
We're going to have to use the
energy currency of the cell,

00:01:06.321 --> 00:01:08.539
our good friend ATP.

00:01:08.539 --> 00:01:10.617
And the way that we're going
to make this reaction happen

00:01:10.617 --> 00:01:12.997
is we're going to couple
what's essentially,

00:01:12.997 --> 00:01:14.924
you could view it as a hydrolysis of ATP,

00:01:14.924 --> 00:01:16.839
although we won't have
exactly a water molecule

00:01:16.839 --> 00:01:18.035
in the mechanism,

00:01:18.035 --> 00:01:20.566
but what's functionally
the hydrolysis of ATP

00:01:20.566 --> 00:01:22.400
into ADP and a phosphate group.

00:01:22.400 --> 00:01:24.524
Which is very energetically favorable.

00:01:24.524 --> 00:01:25.999
It is exergonic,

00:01:25.999 --> 00:01:27.798
it would happen spontaneously

00:01:27.798 --> 00:01:29.307
under the right conditions.

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It won't just always happen

00:01:30.480 --> 00:01:32.059
inside of an solution,

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it needs a little bit of
activation energy or an enzyme

00:01:34.505 --> 00:01:36.305
to lower the activation energy,

00:01:36.305 --> 00:01:38.905
but the net reaction, it is exergonic.

00:01:38.905 --> 00:01:41.587
So what we can do is we can
couple these two reactions.

00:01:41.587 --> 00:01:44.524
And so when we couple the two reactions,

00:01:44.524 --> 00:01:45.998
when we couple the two reactions,

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we have ATP,

00:01:48.755 --> 00:01:50.883
ATP plus glucose,

00:01:51.588 --> 00:01:53.732
plus glucose,

00:01:55.374 --> 00:01:56.303
reacting,

00:01:56.303 --> 00:01:58.195
and we use an enzyme,

00:01:58.195 --> 00:02:00.378
the general term for it is hexokinase,

00:02:00.378 --> 00:02:03.872
to facilitate this reaction,
to lower the activation energy,

00:02:03.872 --> 00:02:06.542
it's going to yield, it's going to yield

00:02:06.542 --> 00:02:10.512
glucose six phosphate, glucose,

00:02:10.512 --> 00:02:14.753
glucose-6-phosphate,

00:02:15.449 --> 00:02:16.535
phosphate,

00:02:17.992 --> 00:02:20.266
and ADP.

00:02:21.014 --> 00:02:23.725
And ADP.

00:02:24.311 --> 00:02:26.157
A-D-P.

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Now what's the delta-G for
this reaction going to be?

00:02:28.618 --> 00:02:30.290
Well it's a coupled
reaction, you can view it

00:02:30.290 --> 00:02:32.774
as a combination of these two reactions,

00:02:32.774 --> 00:02:34.481
and so roughly speaking you can say,

00:02:34.481 --> 00:02:36.419
well, let's just add the delta-G's.

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So if you add the delta-G's here,

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you're going to get,

00:02:39.519 --> 00:02:40.901
if you add this negative delta-G,

00:02:40.901 --> 00:02:43.454
this exergonic and this positive delta-G,

00:02:43.454 --> 00:02:47.471
you're gonna get -30.5 plus 13.8,

00:02:47.471 --> 00:02:51.952
that's going to be -16.7 kilojules,

00:02:51.952 --> 00:02:54.019
kilojules per mol.

00:02:54.019 --> 00:02:57.339
And so this coupled reaction
is going to be exergonic.

00:02:57.339 --> 00:02:59.150
Not quite as exergonic as hydrolysis,

00:02:59.150 --> 00:03:01.379
because now you're gonna be
using some of that energy,

00:03:01.379 --> 00:03:03.317
but this can happen spontaneously,

00:03:03.317 --> 00:03:05.709
especially if you can lower
the activation energy enough

00:03:05.709 --> 00:03:07.276
for it to happen.

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And so let's now look at the mechanism

00:03:09.470 --> 00:03:10.573
of how it happens.

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Now without an enzyme, without an enzyme,

00:03:13.232 --> 00:03:15.774
the way that this reaction needs to occur

00:03:15.774 --> 00:03:18.537
is that you have an electron,

00:03:18.537 --> 00:03:20.336
you have an electron pair right over here

00:03:20.336 --> 00:03:21.927
on this hydroxyl group,

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and it needs to do what's
called a nucleophilic attack

00:03:24.957 --> 00:03:28.312
on this phosphorous right over here.

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But without an enzyme, it's
gonna be very hard for it to do.

00:03:30.831 --> 00:03:32.746
It's gonna have a high activation energy

00:03:32.746 --> 00:03:34.755
because it's going to be
impaired by all of this

00:03:34.755 --> 00:03:37.785
negative charge from these
oxygens right over here.

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You can imagine, electrons don't like

00:03:39.108 --> 00:03:40.455
going through a lot of negative charge,

00:03:40.455 --> 00:03:42.312
they're repulsed by negative charge.

00:03:42.312 --> 00:03:43.972
So we're gonna need an enzyme

00:03:43.972 --> 00:03:45.690
to help facilitate this reaction,

00:03:45.690 --> 00:03:50.206
to help lower the energy
to actually start it.

00:03:50.206 --> 00:03:52.969
Essentially get these
electrons out of the way.

00:03:52.969 --> 00:03:54.513
And the enzyme, or the general term

00:03:54.513 --> 00:03:57.949
for the enzymes that do
this, is called hexokinase.

00:03:57.949 --> 00:04:00.461
And hexokinase, let me write this down.

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Hexokinase.

00:04:04.831 --> 00:04:07.791
And the way it does it
is it provides ions to,

00:04:07.791 --> 00:04:09.126
one way to think about it is to

00:04:09.126 --> 00:04:11.669
keep these electrons over here busy.

00:04:11.669 --> 00:04:14.188
And in particular, it has a magnesium ion,

00:04:14.188 --> 00:04:16.510
a magnesium ion,

00:04:16.510 --> 00:04:17.764
right over here,

00:04:17.764 --> 00:04:20.631
and this is bound to the
rest of the hexokinase.

00:04:20.631 --> 00:04:22.407
Remember, this is all
happening in three dimensions,

00:04:22.407 --> 00:04:24.891
So the hexokinase is
kinda wrapping around it,

00:04:24.891 --> 00:04:27.411
so these can keep these electrons busy,

00:04:27.411 --> 00:04:29.965
there's other ions on the hexokinase

00:04:29.965 --> 00:04:31.567
that can keep these electrons busy,

00:04:31.567 --> 00:04:34.666
other positive ions keep
these electrons busy.

00:04:34.666 --> 00:04:36.524
And so these electrons can sneak in

00:04:36.524 --> 00:04:38.706
and do the nucleophilic attack.

00:04:38.706 --> 00:04:40.146
Remember, when we talk about enzymes

00:04:40.146 --> 00:04:42.584
these are these protein, these protein,

00:04:42.584 --> 00:04:45.811
let me do the same color that
I wrote the hexokinase in.

00:04:45.811 --> 00:04:49.410
These are these complex protein structures

00:04:49.410 --> 00:04:51.906
right over here, just like this,

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and so you might have the magnesium ion,

00:04:54.587 --> 00:04:57.082
and let me do that in that purple color.

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Just right over there, and then
maybe the glucose molecule,

00:05:02.520 --> 00:05:06.433
the glucose molecule gets
bound right over here,

00:05:06.433 --> 00:05:08.371
and then maybe you have your ATP,

00:05:08.371 --> 00:05:10.739
it gets bound right, right over here,

00:05:10.739 --> 00:05:12.829
and I'm obviously, I'm just kind of

00:05:12.829 --> 00:05:14.454
giving you an example,

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this isn't exactly what's happening.

00:05:16.196 --> 00:05:19.794
But by essentially wrapping
it with this positive charge,

00:05:19.794 --> 00:05:21.849
it's able to pull the electrons away

00:05:21.849 --> 00:05:24.276
to help facilitate this
nucleophilic attack

00:05:24.276 --> 00:05:27.433
that needs to happen for
the reaction to proceed.

00:05:27.433 --> 00:05:28.873
And so this bond right over here

00:05:28.873 --> 00:05:32.251
between this oxygen and this phosphorous,

00:05:32.251 --> 00:05:34.236
that is going to be,

00:05:34.236 --> 00:05:37.556
that is going to be this
bond right over here,

00:05:37.556 --> 00:05:42.262
and as this happens, then this character,

00:05:42.838 --> 00:05:46.342
then these two electrons can
be taken by this character,

00:05:46.342 --> 00:05:48.919
and so this oxygen

00:05:48.919 --> 00:05:50.672
is this oxygen right over here,

00:05:50.672 --> 00:05:53.110
and now has a negative charge.

00:05:53.110 --> 00:05:54.596
And so what we've just resulted with

00:05:54.596 --> 00:05:58.137
is glucose-6-phosphate and ADP.

00:05:58.137 --> 00:05:59.715
And ADP.

00:05:59.715 --> 00:06:01.677
And it's energetically favorable,

00:06:01.677 --> 00:06:02.734
it's exergonic.

00:06:02.734 --> 00:06:03.871
It's going to happen,

00:06:03.871 --> 00:06:05.299
assuming that you have the enzyme there

00:06:05.299 --> 00:06:08.074
to help distract these electrons,

00:06:08.074 --> 00:06:09.955
lowering the activation energy.

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And I know what you're thinking,

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we had this hydrogen right over here,

00:06:12.950 --> 00:06:15.596
so this hydrogen should
be right over here still,

00:06:15.596 --> 00:06:17.152
and then another water molecule could come

00:06:17.152 --> 00:06:20.356
and nab the proton, the hydrogen proton,

00:06:20.356 --> 00:06:22.016
and so you're left once again

00:06:22.016 --> 00:06:25.058
with just the glucose-6-phosphate.

00:06:25.058 --> 00:06:26.811
So this, hopefully this gives you a sense

00:06:26.811 --> 00:06:28.808
of how reaction coupling occurs,

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and also a sense of how
ATP is actually useful.

00:06:32.476 --> 00:06:33.730
When I first learned about ATP, I'm like,

00:06:33.730 --> 00:06:34.775
okay, fine,

00:06:34.775 --> 00:06:36.416
it's, you know, it really wants to let go

00:06:36.416 --> 00:06:39.365
of this phosphate group,
it's energetically favorable,

00:06:39.365 --> 00:06:41.698
but how is that actually used to,

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to drive things, to actually do,

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to do things in the system

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that might not be energetically favorable.

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And hopefully this gives you
a sense of how it's done,

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and also the importance of an enzyme

00:06:54.836 --> 00:06:57.048
in facilitating it.


Endergonic, exergonic, exothermic, and endothermic reactions

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:02.030
- [Voiceover] So we have some words here

00:00:02.030 --> 00:00:03.680
that relate the different reactions

00:00:03.680 --> 00:00:05.520
and whether they absorb or release

00:00:05.520 --> 00:00:07.150
different types of energy.

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So the first word here, exothermic.

00:00:09.750 --> 00:00:13.190
Exothermic the root of the word is therm

00:00:13.190 --> 00:00:16.430
which relates to heat
and these word indeed

00:00:16.430 --> 00:00:19.180
means a reaction that releases heat.

00:00:21.230 --> 00:00:25.140
Releases, it releases heat.

00:00:25.140 --> 00:00:27.420
And one way to think about
it if you're thinking about

00:00:27.420 --> 00:00:29.920
constant pressures or change in enthalpy

00:00:29.920 --> 00:00:32.940
it can be viewed as your,

00:00:32.940 --> 00:00:35.350
how much heat you absorb or release.

00:00:35.350 --> 00:00:39.220
So a negative change in enthalpy

00:00:39.220 --> 00:00:40.720
means that you're releasing heat.

00:00:40.720 --> 00:00:43.550
One way to think of, if you
view enthalpy as heat content

00:00:43.550 --> 00:00:47.160
you have less heat content
after the reaction than before

00:00:47.160 --> 00:00:48.880
it was meant you release heat.

00:00:48.880 --> 00:00:51.210
Which means you're change
in enthalpy is going to be

00:00:51.210 --> 00:00:55.150
less than zero so these
all mean the same thing.

00:00:55.150 --> 00:00:57.130
Well, this is true.

00:00:57.130 --> 00:00:58.420
You're releasing heat.

00:00:58.420 --> 00:01:00.950
This is a same thing as
releasing heat if you talk about

00:01:00.950 --> 00:01:02.680
constant pressure.

00:01:02.680 --> 00:01:05.400
Constant pressure which is a reasonable

00:01:05.400 --> 00:01:07.950
assumption if you're doing
something in a beaker

00:01:07.950 --> 00:01:11.110
that's open to the air
or if you're thinking

00:01:11.110 --> 00:01:13.750
about a lot of different
biological systems.

00:01:13.750 --> 00:01:16.220
Now based on that logic what
do you think this word means,

00:01:16.220 --> 00:01:17.620
endothermic.

00:01:17.620 --> 00:01:21.730
Well endothermic, therm

00:01:21.730 --> 00:01:24.890
same root and now your prefix is endo

00:01:24.890 --> 00:01:28.010
so this is a process that absorbs heat.

00:01:28.010 --> 00:01:31.970
Absorbs heat.

00:01:31.970 --> 00:01:33.850
Or if you're thinking
of a constant pressure,

00:01:33.850 --> 00:01:36.080
you can say your enthalpy
after the reaction

00:01:36.080 --> 00:01:38.760
is gonna be higher than the
enthalpy before the reaction.

00:01:38.760 --> 00:01:42.720
So your delta H is going to be

00:01:42.720 --> 00:01:45.920
greater than zero.

00:01:45.920 --> 00:01:47.670
All right, fair enough.

00:01:47.670 --> 00:01:49.850
Now let's look at these
two characters over here.

00:01:49.850 --> 00:01:52.090
Exergonic and endergonic

00:01:52.090 --> 00:01:55.450
so exergonic the root here is ergon

00:01:55.450 --> 00:01:57.600
and you might not be as familiar with that

00:01:57.600 --> 00:01:59.610
as you are with therm
but you might have heard

00:01:59.610 --> 00:02:00.960
the word ergonomic.

00:02:00.960 --> 00:02:02.620
Say, hey that's a nice ergonomic desk.

00:02:02.620 --> 00:02:04.250
That means it's a desk
that's good to do work at

00:02:04.250 --> 00:02:06.090
or it's a nice ergonomic chair.

00:02:06.090 --> 00:02:09.690
An ergon does indeed come
from the Greek for work.

00:02:09.690 --> 00:02:12.900
And so exergonic is a reaction
that releases work energy

00:02:12.900 --> 00:02:15.000
or at least that's what the word implies.

00:02:15.000 --> 00:02:19.370
Releases, let me do
that in the same color.

00:02:19.370 --> 00:02:22.060
This is something that is going to

00:02:22.060 --> 00:02:26.940
release work

00:02:26.940 --> 00:02:30.420
energy.

00:02:30.420 --> 00:02:32.950
And endergonic, same logic,

00:02:32.950 --> 00:02:34.520
well that's gonna be
something based on just

00:02:34.520 --> 00:02:37.220
the way the word is setup
that absorbs work energy

00:02:37.220 --> 00:02:42.000
or uses work

00:02:42.660 --> 00:02:43.790
energy.

00:02:43.790 --> 00:02:47.350
Now one of our variables

00:02:47.350 --> 00:02:50.290
or properties that we can
use to think about energy

00:02:50.290 --> 00:02:53.520
that can be used for
work is Gibbs free energy

00:02:53.520 --> 00:02:55.950
and the formula for Gibbs free energy,

00:02:55.950 --> 00:02:58.050
if we're thinking about constant
pressure and temperature,

00:02:58.050 --> 00:02:59.510
so let me write that down.

00:02:59.510 --> 00:03:04.090
So if we're talking
about constant pressure

00:03:06.000 --> 00:03:10.390
and temperature then the formula

00:03:10.390 --> 00:03:12.390
for Gibbs free energy or
you can even view this

00:03:12.390 --> 00:03:14.820
as a definition of Gibbs free energy.

00:03:14.820 --> 00:03:16.820
The change in Gibbs free energy,

00:03:16.820 --> 00:03:18.520
let me do this in another color.

00:03:18.520 --> 00:03:22.940
The change in Gibbs
free energy is equal to

00:03:22.940 --> 00:03:27.940
our change in enthalpy

00:03:27.970 --> 00:03:32.960
minus, use in the different color.

00:03:32.960 --> 00:03:37.960
Minus our temperature

00:03:37.960 --> 00:03:39.990
times our change in entropy

00:03:39.990 --> 00:03:42.310
and if this looks
completely foreign to you,

00:03:42.310 --> 00:03:43.920
I encourage you to watch the video

00:03:43.920 --> 00:03:46.350
on Gibbs free energy but the reason why

00:03:46.350 --> 00:03:48.640
this is related to energy for work

00:03:48.640 --> 00:03:50.640
is okay, look I have my,

00:03:50.640 --> 00:03:53.120
whether I'm absorbing
or I'm releasing heat

00:03:53.120 --> 00:03:56.450
and I'm subtracting out entropy
which is kind of the energy

00:03:56.450 --> 00:03:58.790
that is going to the
disorder of the universe

00:03:58.790 --> 00:04:01.870
and what's left over is the
energy that I can do for work.

00:04:01.870 --> 00:04:03.580
That's one way to think about it.

00:04:03.580 --> 00:04:06.520
So you can see that
this relates work energy

00:04:06.520 --> 00:04:09.770
to change in enthalpy right over here.

00:04:09.770 --> 00:04:13.530
So exergonic, something that releases

00:04:13.530 --> 00:04:16.090
work energy could say
that has less work energy

00:04:16.090 --> 00:04:18.040
after the reaction than before it,

00:04:18.040 --> 00:04:20.490
your delta G is going
to be less than zero.

00:04:20.490 --> 00:04:22.260
So let me write that down.

00:04:22.260 --> 00:04:27.220
So here our delta G is
going to be less than zero

00:04:27.220 --> 00:04:29.270
and these things, these
are reactions that release

00:04:29.270 --> 00:04:30.670
work energy, we've seen it

00:04:30.670 --> 00:04:31.980
in the video on Gibss free energy.

00:04:31.980 --> 00:04:34.480
We consider this to be spontaneous.

00:04:34.480 --> 00:04:37.010
Spontaneous.

00:04:37.010 --> 00:04:39.370
These are going to move forward.

00:04:39.370 --> 00:04:43.390
So these over here, the ones
that absorb work energy,

00:04:43.390 --> 00:04:45.130
well they're gonna have more work energy

00:04:45.130 --> 00:04:47.720
in the system than before is
one way to think about it.

00:04:47.720 --> 00:04:50.760
So your delta G

00:04:50.760 --> 00:04:52.700
is going to be greater than zero

00:04:52.700 --> 00:04:55.020
and we say these are not spontaneous.

00:04:55.020 --> 00:05:00.020
So these are not spontaneous.

00:05:00.020 --> 00:05:02.090
Now that we have the
definitions out of the way

00:05:02.090 --> 00:05:04.510
and we have a way to
relate these variables,

00:05:04.510 --> 00:05:06.490
let's look at these
different scenarios of things

00:05:06.490 --> 00:05:08.470
that are exothermic and exergonic

00:05:08.470 --> 00:05:10.720
or exothermic and endergonic and see why

00:05:10.720 --> 00:05:12.690
they make an intuitive sense.

00:05:12.690 --> 00:05:16.050
So in this first reaction
it's exothermic, our delta H

00:05:16.050 --> 00:05:17.380
is less than zero.

00:05:17.380 --> 00:05:19.770
That means it has less
enthalpy after the reaction

00:05:19.770 --> 00:05:21.710
than before which means it released heat

00:05:21.710 --> 00:05:25.150
and so you can see here,
this heat is being released.

00:05:25.150 --> 00:05:26.890
And where did that energy come from?

00:05:26.890 --> 00:05:28.820
Well when it bonds

00:05:28.820 --> 00:05:31.020
in this new configurations on a net basis

00:05:31.020 --> 00:05:33.450
the electrons are able to
go to lower energy states

00:05:33.450 --> 00:05:35.270
and release that energy.

00:05:35.270 --> 00:05:37.790
And heat, if you're thinking
about in a microscopic scale

00:05:37.790 --> 00:05:39.723
it's something that's
raising your temperature

00:05:39.723 --> 00:05:42.200
at least locally which it
means just about transferring

00:05:42.200 --> 00:05:45.720
kinetic energy to these
microscopic molecules.

00:05:45.720 --> 00:05:47.150
Remember when you're talking
about heat or temperature

00:05:47.150 --> 00:05:48.870
you're thinking about
these macro variables

00:05:48.870 --> 00:05:50.060
but on a microscopic variable,

00:05:50.060 --> 00:05:52.720
you're talking about kinetic
energies and potential energies

00:05:52.720 --> 00:05:53.720
and things like that.

00:05:53.720 --> 00:05:55.331
So what's happening is these electrons

00:05:55.331 --> 00:05:57.650
or when they get into a new configuration

00:05:57.650 --> 00:05:59.750
and they're going to release energy

00:05:59.750 --> 00:06:04.210
and that can be transferred
to the individual molecules.

00:06:04.210 --> 00:06:06.750
So you see here, we've released energy

00:06:06.750 --> 00:06:09.420
and we also have an increase in entropy.

00:06:09.420 --> 00:06:11.440
We have more entropy after the reaction

00:06:11.440 --> 00:06:12.420
than before the reaction.

00:06:12.420 --> 00:06:15.320
We have more objects right over here,

00:06:15.320 --> 00:06:17.760
there's more states in which
they could actually be in

00:06:17.760 --> 00:06:19.920
and they're actually moving faster.

00:06:19.920 --> 00:06:22.210
So this one, we see if you just apply,

00:06:22.210 --> 00:06:24.120
if you apply the formula over here

00:06:24.120 --> 00:06:26.090
this is gonna be less than zero.

00:06:26.090 --> 00:06:28.770
This over here, delta S is
going to be greater than zero.

00:06:28.770 --> 00:06:30.870
The temperature, that's
gonna be absolute temperature

00:06:30.870 --> 00:06:33.320
in terms of Kelvin so it's
always going to be positive

00:06:33.320 --> 00:06:36.190
and so this whole term
is going to be positive

00:06:36.190 --> 00:06:38.630
so you're gonna have a
negative, minus a positive

00:06:38.630 --> 00:06:39.750
it's going to be negative.

00:06:39.750 --> 00:06:42.730
So our delta G

00:06:42.730 --> 00:06:45.150
is going to be less than zero and we see

00:06:45.150 --> 00:06:46.060
that this is spontaneous.

00:06:46.060 --> 00:06:47.700
This is going to move
forward and it makes sense,

00:06:47.700 --> 00:06:49.920
it releases energy, the electrons like it.

00:06:49.920 --> 00:06:52.010
It creates a more disordered state.

00:06:52.010 --> 00:06:53.470
Another way to think
about it is think about

00:06:53.470 --> 00:06:55.500
trying to do the reaction the other way,

00:06:55.500 --> 00:06:58.060
you're gonna have to get some
energy for those electrons

00:06:58.060 --> 00:07:00.450
to get into a higher
energy state when they form

00:07:00.450 --> 00:07:01.600
these new bonds your gonna have to get

00:07:01.600 --> 00:07:04.040
these four constituents
together in the exact right way.

00:07:04.040 --> 00:07:07.120
That seems a lot less likely to happen

00:07:07.120 --> 00:07:10.750
than going in from the left to the right.

00:07:10.750 --> 00:07:13.490
Now let's think about
something that absorbs heat

00:07:13.490 --> 00:07:15.290
and this one's a little
bit counter intuitive.

00:07:15.290 --> 00:07:19.020
It absorbs heat but it's
still going to be spontaneous.

00:07:19.020 --> 00:07:21.360
It's still going to be exergonic.

00:07:21.360 --> 00:07:22.920
It's still going to happen.

00:07:22.920 --> 00:07:25.190
So delta H is greater than zero

00:07:25.190 --> 00:07:27.160
so it absorbs heat to happen.

00:07:27.160 --> 00:07:28.630
So I have these two molecules

00:07:28.630 --> 00:07:31.790
with these different constituents,
they are about to collide

00:07:31.790 --> 00:07:33.260
and we're saying that
the temperature is high.

00:07:33.260 --> 00:07:36.140
If the temperature is low,
this might not be spontaneous

00:07:36.140 --> 00:07:38.320
but if the temperature is
high enough it will be.

00:07:38.320 --> 00:07:40.580
So the temperature high
in a microscopic basis,

00:07:40.580 --> 00:07:41.790
you're saying, okay these
things just have them,

00:07:41.790 --> 00:07:43.190
really high kinetic energy,

00:07:43.190 --> 00:07:46.090
they're going to ram into
each other really fast

00:07:46.090 --> 00:07:47.990
and they're gonna ram
into each other so fast

00:07:47.990 --> 00:07:50.290
that they can form all
these other constituents.

00:07:50.290 --> 00:07:53.410
So you have the net entropy,

00:07:53.410 --> 00:07:56.360
you have the net entropy has increased.

00:07:56.360 --> 00:07:58.800
Even though over here our electrons

00:07:58.800 --> 00:08:01.250
are in a higher energy state
to form this configuration

00:08:01.250 --> 00:08:03.320
so it had to absorb heat,

00:08:03.320 --> 00:08:05.920
so it had to absorb heat energy.

00:08:05.920 --> 00:08:08.820
So we could say heat but
heat on a microscopic level,

00:08:08.820 --> 00:08:11.720
we're just talking about
kind of kinetic energy

00:08:11.720 --> 00:08:13.530
of these molecules.

00:08:13.530 --> 00:08:17.450
So it have to absorb it but
where did that energy come from?

00:08:17.450 --> 00:08:20.190
Well, it came from the kinetic
energy of the molecules.

00:08:20.190 --> 00:08:22.650
They might had a certain
kinetic energy before

00:08:22.650 --> 00:08:24.250
but then some of that gets lost

00:08:24.250 --> 00:08:26.150
so when they all get banged up

00:08:26.150 --> 00:08:27.950
into their different configurations.

00:08:27.950 --> 00:08:29.490
If you're saying, well
I still don't get this.

00:08:29.490 --> 00:08:31.390
Think about trying to do
this reaction the other way.

00:08:31.390 --> 00:08:33.990
Try to get these four
constituents in the right time,

00:08:33.990 --> 00:08:35.890
all together, even though
if they're happening,

00:08:35.890 --> 00:08:38.390
if they're put together at the right way

00:08:38.390 --> 00:08:41.320
their electrons could configure
in a way to release energy

00:08:41.320 --> 00:08:42.810
but this is super high temperature.

00:08:42.810 --> 00:08:44.480
This is a really, really chaotic system.

00:08:44.480 --> 00:08:45.980
It's not gonna go from right to left,

00:08:45.980 --> 00:08:47.230
it's gonna go from left to right.

00:08:47.230 --> 00:08:48.870
When it's really chaotic,
things are banging

00:08:48.870 --> 00:08:50.860
each other really fast,
you're more likely to go

00:08:50.860 --> 00:08:53.730
on a direction of higher entropy.

00:08:53.730 --> 00:08:55.630
So now let's look at,

00:08:55.630 --> 00:08:59.500
and so this is spontaneous
even though it absorbs heat.

00:08:59.500 --> 00:09:02.050
If you're not draining
the heat away locally,

00:09:02.050 --> 00:09:04.890
your temperature at least
around these molecules

00:09:04.890 --> 00:09:06.150
it will go down.

00:09:06.150 --> 00:09:08.450
But as source we're assuming
constant temperature

00:09:08.450 --> 00:09:10.780
for this so you can assume
that in a macro level

00:09:10.780 --> 00:09:12.633
that temperature dissipates
and gets absorbed

00:09:12.633 --> 00:09:14.670
outside of the system somehow.

00:09:14.670 --> 00:09:16.620
Now, let's look at this configuration.

00:09:16.620 --> 00:09:19.650
It's exothermic so delta
H is less than zero,

00:09:19.650 --> 00:09:21.240
less enthalpy after the
reaction than before

00:09:21.240 --> 00:09:25.100
so it's releasing heat
but it's not spontaneous.

00:09:25.100 --> 00:09:28.290
And it's not spontaneous
because it's reducing

00:09:28.290 --> 00:09:29.630
the entropy in the world.

00:09:29.630 --> 00:09:31.850
It's reducing the entropy in the world

00:09:31.850 --> 00:09:35.480
and the entropy matters because
our temperature is high.

00:09:35.480 --> 00:09:38.620
One way to look at this equation
is entropy doesn't matter

00:09:38.620 --> 00:09:39.590
when temperature is low.

00:09:39.590 --> 00:09:41.950
Temperature is really scaling your entropy

00:09:41.950 --> 00:09:45.220
but when temperature is high,
entropy start to take over.

00:09:45.220 --> 00:09:47.500
This variable starts to matter a lot.

00:09:47.500 --> 00:09:50.820
So over here, because entropy is negative,

00:09:50.820 --> 00:09:53.750
this isn't gonna, this thing's
not gonna actually happen.

00:09:53.750 --> 00:09:56.090
So if these things were
coming together very slowly,

00:09:56.090 --> 00:09:58.640
their electrons could
configure in just the right way

00:09:58.640 --> 00:10:00.230
so that they can get
to a lower energy state

00:10:00.230 --> 00:10:01.263
and release energy.

00:10:01.263 --> 00:10:03.700
But they're buzzing
pass each other so fast

00:10:03.700 --> 00:10:05.550
that they're not gonna
have a chance to do that.

00:10:05.550 --> 00:10:08.190
If you think about it the
other way, this reaction

00:10:08.190 --> 00:10:09.540
is much more likely to happen.

00:10:09.540 --> 00:10:12.020
If you have a bunch of
this diatomic molecules

00:10:12.020 --> 00:10:14.190
running around, they're gonna
bump into each other so fast

00:10:14.190 --> 00:10:17.570
that they're gonna knock
the constituents off of

00:10:17.570 --> 00:10:21.080
these diatomic molecules or at
least the way it's depicted,

00:10:21.080 --> 00:10:23.060
it kinda looks like a diatomic molecule.

00:10:23.060 --> 00:10:25.350
And they might absorb some
of that kinetic energy

00:10:25.350 --> 00:10:27.750
in doing it, in order
to go from right to left

00:10:27.750 --> 00:10:29.690
but that's more likely to happen.

00:10:29.690 --> 00:10:32.150
So from left to right not spontaneous

00:10:32.150 --> 00:10:35.250
because entropy really matters
at this high temperature.

00:10:35.250 --> 00:10:37.440
Then finally, and this
one's pretty intuitive

00:10:37.440 --> 00:10:41.890
something that needs heat,
something that needs heat energy

00:10:41.890 --> 00:10:44.000
and has a reduction in entropy

00:10:44.000 --> 00:10:46.550
that's definitely not
going to be spontaneous.

00:10:46.550 --> 00:10:50.070
So this is greater than
zero, this is less than zero

00:10:50.070 --> 00:10:51.990
but then you're subtracting
it so this whole thing

00:10:51.990 --> 00:10:54.070
is greater than zero, this delta G

00:10:54.070 --> 00:10:55.990
is going to be greater than zero.

00:10:55.990 --> 00:10:58.920
Delta, let me do that in a green color.

00:10:58.920 --> 00:11:02.790
This delta G is going
to be greater than zero

00:11:02.790 --> 00:11:05.520
and it makes sense that you
have these two molecules

00:11:05.520 --> 00:11:07.720
that you have to get together
in just the right way.

00:11:07.720 --> 00:11:11.290
They need heat in order to
proceed with this reaction

00:11:11.290 --> 00:11:14.510
to kind of excite, to excite the electrons

00:11:14.510 --> 00:11:15.940
to higher energy state to get into this,

00:11:15.940 --> 00:11:17.880
I guess you could say less stable bond.

00:11:17.880 --> 00:11:19.390
Why would they do that?

00:11:19.390 --> 00:11:21.620
The reaction is much more
likely to go in this way

00:11:21.620 --> 00:11:23.130
or if you had a bunch of these molecules

00:11:23.130 --> 00:11:24.560
they're all knocking into each other,

00:11:24.560 --> 00:11:26.050
they get into a more stable configuration

00:11:26.050 --> 00:11:28.830
and there's more entropy
when they split up

00:11:28.830 --> 00:11:30.950
than when they actually stay together.

00:11:30.950 --> 00:11:32.510
So delta G greater than zero.

00:11:32.510 --> 00:11:35.430
This is endergonic and endothermic

00:11:35.430 --> 00:11:38.120
and of course, this one was
delta G greater than zero.

00:11:38.120 --> 00:11:40.240
Even though this would release energy

00:11:40.240 --> 00:11:42.550
that the things that's so
chaotic they're not gonna have

00:11:42.550 --> 00:11:44.550
a chance to do that and
you're much more likely to go

00:11:44.550 --> 00:11:47.190
in the direction of maximizing entropy

00:11:47.190 --> 00:11:50.550
and so this one also is not spontaneous.


Gibbs free energy and spontaneous reactions

WEBVTT
Kind: captions
Language: en

00:00:00.166 --> 00:00:02.546
- [Voiceover] We're going
to explore Gibbs Free Energy

00:00:02.546 --> 00:00:03.347
a little bit in this video.

00:00:03.347 --> 00:00:05.669
And, in particular, its
usefulness in determining

00:00:05.669 --> 00:00:08.826
whether a reaction is going
to be spontaneous or not,

00:00:08.826 --> 00:00:12.449
which is super useful in
chemistry and biology.

00:00:12.449 --> 00:00:16.047
And, it was defined by
Josiah Willard Gibbs.

00:00:16.047 --> 00:00:18.717
And, what we see here, we
see this famous formula

00:00:18.717 --> 00:00:20.668
which is going to help
us predict spontaneity.

00:00:20.668 --> 00:00:24.301
And, it says that the
change in Gibbs Free Energy

00:00:24.301 --> 00:00:28.480
is equal to the change, and
this 'H' here is enthalpy.

00:00:28.480 --> 00:00:30.848
So, this is a change in enthalpy

00:00:30.848 --> 00:00:32.751
which you could view as heat content,

00:00:32.751 --> 00:00:34.748
especially because this formula applies

00:00:34.748 --> 00:00:37.406
if we're dealing with constant
pressure and temperature.

00:00:37.406 --> 00:00:39.555
So, that's a change in enthaply

00:00:39.555 --> 00:00:44.036
minus temperature times change in entropy,

00:00:44.036 --> 00:00:45.928
change in entropy.

00:00:45.928 --> 00:00:48.063
So, 'S' is entropy and it seems

00:00:48.063 --> 00:00:52.370
like this bizarre formula that's
hard to really understand.

00:00:52.370 --> 00:00:55.226
But, as we'll see, it makes
a lot of intuitive sense.

00:00:55.226 --> 00:00:58.373
Now, Gibbs Free, Gibbs,
Josiah Willard Gibbs,

00:00:58.373 --> 00:01:00.044
he defined this to think about, well,

00:01:00.044 --> 00:01:02.681
how much enthalpy is going to be useful

00:01:02.681 --> 00:01:03.853
for actually doing work?

00:01:03.853 --> 00:01:06.223
How much is free to do useful things?

00:01:06.223 --> 00:01:07.744
But, in this video, we're
gonna think about it

00:01:07.744 --> 00:01:11.331
in the context of how we can
use change in Gibbs Free Energy

00:01:11.331 --> 00:01:13.724
to predict whether a reaction is going

00:01:13.724 --> 00:01:15.627
to spontaneously happen,

00:01:15.627 --> 00:01:17.230
whether it's going to be spontaneous.

00:01:17.230 --> 00:01:19.355
And, to get straight to the punch line,

00:01:19.355 --> 00:01:23.755
if Delta G is less than zero,

00:01:23.755 --> 00:01:26.889
our reaction is going to be spontaneous.

00:01:26.889 --> 00:01:29.791
It's going to be spontaneous.

00:01:29.791 --> 00:01:31.277
It's going to happen,

00:01:31.277 --> 00:01:32.753
assuming that things are able to interact

00:01:32.753 --> 00:01:33.947
in the right way.

00:01:33.947 --> 00:01:37.314
It's going to be spontaneous.

00:01:37.314 --> 00:01:40.890
Now, let's think a little bit
about why that makes sense.

00:01:40.890 --> 00:01:43.432
If this expression over here is negative,

00:01:43.432 --> 00:01:46.288
our reaction is going to be spontaneous.

00:01:46.288 --> 00:01:48.470
So, let's think about all
of the different scenarios.

00:01:48.470 --> 00:01:49.991
So, in this scenario over here,

00:01:49.991 --> 00:01:54.565
if our change in enthalpy
is less than zero,

00:01:54.565 --> 00:01:56.365
and our entropy increases,

00:01:56.365 --> 00:01:58.187
our enthalpy decreases.

00:01:58.187 --> 00:01:59.685
So, this means we're going to release,

00:01:59.685 --> 00:02:01.774
we're going to release energy here.

00:02:01.774 --> 00:02:03.353
We're gonna release enthalpy.

00:02:03.353 --> 00:02:04.909
And, you could think about this as,

00:02:04.909 --> 00:02:07.231
so let's see, we're gonna release energy.

00:02:07.231 --> 00:02:09.193
So, release.

00:02:09.193 --> 00:02:10.284
I'll just draw it.

00:02:10.284 --> 00:02:12.385
This is a release of enthalpy over here.

00:02:12.385 --> 00:02:15.043
I end up with less enthalpy
than I started with.

00:02:15.043 --> 00:02:16.506
But, entropy increases.

00:02:16.506 --> 00:02:18.352
Disorder increases the number of states

00:02:18.352 --> 00:02:20.546
that my system can take on increases.

00:02:20.546 --> 00:02:22.330
Well, this makes a lot of sense.

00:02:22.330 --> 00:02:23.082
This makes a lot of sense

00:02:23.082 --> 00:02:24.602
that this is going to
happen spontaneously,

00:02:24.602 --> 00:02:26.679
regardless of what the temperature is.

00:02:26.679 --> 00:02:28.457
I have these two molecules.

00:02:28.457 --> 00:02:31.057
They are about to bump into each other.

00:02:31.057 --> 00:02:32.593
And, when they get close to each other,

00:02:32.593 --> 00:02:34.660
their electrons may be, say hey,

00:02:34.660 --> 00:02:36.413
"Wait, there's a better configuration here

00:02:36.413 --> 00:02:38.213
"where we can go into lower energy states,

00:02:38.213 --> 00:02:39.653
"where we can release energy

00:02:39.653 --> 00:02:40.814
"and in doing so,

00:02:40.814 --> 00:02:44.214
"these different
constituents can part ways."

00:02:44.214 --> 00:02:45.956
And so, you actually
have more constituents.

00:02:45.956 --> 00:02:46.815
They've parted ways.

00:02:46.815 --> 00:02:47.779
You've had energy released.

00:02:47.779 --> 00:02:48.917
Entropy increases.

00:02:48.917 --> 00:02:51.215
And, makes a lot of sense
that this is a natural thing

00:02:51.215 --> 00:02:53.514
that would actually occur.

00:02:53.514 --> 00:02:55.695
This over here, this is spontaneous.

00:02:55.695 --> 00:02:59.493
Delta G is, not just Delta,

00:02:59.493 --> 00:03:02.314
Delta G is less than zero.

00:03:02.314 --> 00:03:03.532
So, this one over here,

00:03:03.532 --> 00:03:05.216
I'm gonna make all the spontaneous ones,

00:03:05.216 --> 00:03:08.873
I'm gonna square them
off in this green color.

00:03:08.873 --> 00:03:11.450
Now, what about this one down here?

00:03:11.450 --> 00:03:15.629
This one down here, Delta
H is greater than zero.

00:03:15.629 --> 00:03:19.656
So, your enthalpy for this
reaction needs to increase,

00:03:19.656 --> 00:03:22.316
and your entropy is going to decrease.

00:03:22.316 --> 00:03:25.171
So, that's, you know, you
can imagine these two atoms,

00:03:25.171 --> 00:03:27.214
or maybe these molecules
that get close to each other,

00:03:27.214 --> 00:03:28.955
but their electrons say, "Hey, no, no."

00:03:28.955 --> 00:03:30.035
In order for us to bond,

00:03:30.035 --> 00:03:31.870
we would have to get to
a higher energy state.

00:03:31.870 --> 00:03:33.831
We would require some energy,

00:03:33.831 --> 00:03:36.270
and the disorder is going to go down.

00:03:36.270 --> 00:03:37.652
This isn't going to happen.

00:03:37.652 --> 00:03:39.767
And so, of course, and
this is a combination,

00:03:39.767 --> 00:03:41.946
if Delta H is greater than zero,

00:03:41.946 --> 00:03:43.246
and if this is less than zero,

00:03:43.246 --> 00:03:45.545
than this entire term
is gonna be positive.

00:03:45.545 --> 00:03:47.727
And so, Delta G is going
to be greater than zero.

00:03:47.727 --> 00:03:51.269
So, here, Delta G is going
to be greater than zero.

00:03:51.269 --> 00:03:52.951
And, hopefully, it makes
some intuitive sense

00:03:52.951 --> 00:03:55.505
that this is not going to be spontaneous.

00:03:55.505 --> 00:03:59.708
So, this one, this one does not happen.

00:03:59.708 --> 00:04:02.389
Now, over here, we have some permutations

00:04:02.389 --> 00:04:04.270
of Delta H's and Delta S's,

00:04:04.270 --> 00:04:07.033
and whether they're spontaneous
depends on the temperature.

00:04:07.033 --> 00:04:08.972
So, over here, if we are dealing,

00:04:08.972 --> 00:04:12.048
our Delta H is less than zero.

00:04:12.048 --> 00:04:15.229
So, we're going to have
a release of energy here,

00:04:15.229 --> 00:04:17.191
but our entropy decreases.

00:04:17.191 --> 00:04:18.387
What's gonna happen?

00:04:18.387 --> 00:04:19.849
Well, if the temperature is low,

00:04:19.849 --> 00:04:22.461
these things will be able to
gently get close to each other,

00:04:22.461 --> 00:04:25.364
and their electrons are
going to be able to interact.

00:04:25.364 --> 00:04:27.047
Maybe they get to a lower energy state,

00:04:27.047 --> 00:04:29.067
and they can release energy.

00:04:29.067 --> 00:04:31.041
They're releasing energy,

00:04:31.041 --> 00:04:33.247
and the electrons will
spontaneously do this.

00:04:33.247 --> 00:04:34.906
But, the entropy has gone down.

00:04:34.906 --> 00:04:36.230
But, this can actually happen,

00:04:36.230 --> 00:04:37.531
because the temperature,

00:04:37.531 --> 00:04:40.107
the temperature here is low.

00:04:40.107 --> 00:04:40.943
And, some of you might be saying,

00:04:40.943 --> 00:04:42.023
"Wait, doesn't that violate

00:04:42.023 --> 00:04:43.927
"The Second Law of Thermodynamics?"

00:04:43.927 --> 00:04:45.424
And, you have to remember,

00:04:45.424 --> 00:04:48.326
the entropy, if you're just
thinking about this part

00:04:48.326 --> 00:04:50.520
of the system, yes that goes down.

00:04:50.520 --> 00:04:53.167
But, you have heat being released.

00:04:53.167 --> 00:04:56.487
And, that heat is going to
make, is going to add entropy

00:04:56.487 --> 00:04:58.507
to the rest of the system.

00:04:58.507 --> 00:05:02.222
So, still, The Second Law
of Thermodynamics holds

00:05:02.222 --> 00:05:04.990
that the entropy of the
universe is going to increase,

00:05:04.990 --> 00:05:07.081
because of this released heat.

00:05:07.081 --> 00:05:08.404
But, if you just look at
the constituents here,

00:05:08.404 --> 00:05:09.983
the entropy went down.

00:05:09.983 --> 00:05:13.465
So, this is going to be,
this right over here is going

00:05:13.465 --> 00:05:15.462
to be spontaneous as well.

00:05:15.462 --> 00:05:17.703
And, we're always wanting
to back to the formula.

00:05:17.703 --> 00:05:21.847
If this is negative and this is negative,

00:05:21.847 --> 00:05:24.402
well, this is going to be a positive term.

00:05:24.402 --> 00:05:25.783
But, if 'T' low enough,

00:05:25.783 --> 00:05:27.583
this term isn't going to matter.

00:05:27.583 --> 00:05:29.781
'T' is, you confuse it as the
weighing factor on entropy.

00:05:29.781 --> 00:05:32.969
So, if 'T' is low, the entropy
doesn't matter as much.

00:05:32.969 --> 00:05:34.861
Then, enthalpy really takes over.

00:05:34.861 --> 00:05:36.800
So, in this situation, Delta G,

00:05:36.800 --> 00:05:38.059
we're assuming 'T' is low enough

00:05:38.059 --> 00:05:41.478
to make Delta G negative.

00:05:41.478 --> 00:05:43.800
And, this is going to be spontaneous.

00:05:43.800 --> 00:05:45.378
Now, if you took that same scenario,

00:05:45.378 --> 00:05:47.073
but you had a high temperature,

00:05:47.073 --> 00:05:49.207
well now, you have these
same two molecules.

00:05:49.207 --> 00:05:50.553
Let's say that these are the molecules,

00:05:50.553 --> 00:05:53.966
maybe this is, this one's the
purple one right over here.

00:05:53.966 --> 00:05:55.615
You have the same two molecules here.

00:05:55.615 --> 00:05:58.366
Hey, they could get to a more kind of a,

00:05:58.366 --> 00:05:59.991
they could release energy.

00:05:59.991 --> 00:06:02.685
But over here, you're saying,

00:06:02.685 --> 00:06:04.190
"Well, look, they could."

00:06:04.190 --> 00:06:07.010
The change in enthalpy is negative.

00:06:07.010 --> 00:06:09.250
But, they're buzzing past each other

00:06:09.250 --> 00:06:11.015
so fast that they're
not gonna have a chance.

00:06:11.015 --> 00:06:12.054
Their electrons aren't gonna have a chance

00:06:12.054 --> 00:06:13.773
to actually interact in the right way

00:06:13.773 --> 00:06:15.896
for the reaction to actually go on.

00:06:15.896 --> 00:06:18.568
And so, this is a situation
where it won't be spontaneous,

00:06:18.568 --> 00:06:20.601
because they're just gonna
buzz past each other.

00:06:20.601 --> 00:06:23.444
They're not gonna have a
chance to interact properly.

00:06:23.444 --> 00:06:25.825
And so, you can imagine if 'T' is high,

00:06:25.825 --> 00:06:28.483
if 'T' is high, this term's
going to matter a lot.

00:06:28.483 --> 00:06:31.442
And, so the fact that entropy is negative

00:06:31.442 --> 00:06:33.870
is gonna make this whole thing positive.

00:06:33.870 --> 00:06:35.506
And, this is gonna be more positive

00:06:35.506 --> 00:06:37.085
than this is going to be negative.

00:06:37.085 --> 00:06:39.082
So, this is a situation where our Delta G

00:06:39.082 --> 00:06:41.230
is greater than zero.

00:06:41.230 --> 00:06:42.785
So, once again, not spontaneous.

00:06:42.785 --> 00:06:44.608
And, everything I'm doing
is just to get an intuition

00:06:44.608 --> 00:06:47.858
for why this formula for
Gibbs Free Energy makes sense.

00:06:47.858 --> 00:06:49.727
And, remember, this is true
under constant pressure

00:06:49.727 --> 00:06:50.680
and temperature.

00:06:50.680 --> 00:06:52.723
But, those are reasonable assumptions

00:06:52.723 --> 00:06:53.988
if we're dealing with, you know,

00:06:53.988 --> 00:06:55.241
things in a test tube,

00:06:55.241 --> 00:06:58.736
or if we're dealing with a
lot of biological systems.

00:06:58.736 --> 00:07:00.058
Now, let's go over here.

00:07:00.058 --> 00:07:03.519
So, our enthalpy,

00:07:03.519 --> 00:07:05.679
our change in enthalpy is positive.

00:07:05.679 --> 00:07:10.489
And, our entropy would
increase if these react,

00:07:10.489 --> 00:07:12.400
but our temperature is low.

00:07:12.400 --> 00:07:15.059
So, if these reacted,
maybe they would bust apart

00:07:15.059 --> 00:07:16.080
and do something,

00:07:16.080 --> 00:07:17.707
they would do something like this.

00:07:17.707 --> 00:07:20.039
But, they're not going to do that,

00:07:20.039 --> 00:07:22.606
because when these things
bump into each other,

00:07:22.606 --> 00:07:24.718
they're like, "Hey, you know
all of our electrons are nice.

00:07:24.718 --> 00:07:27.317
"There are nice little
stable configurations here.

00:07:27.317 --> 00:07:28.815
"I don't see any reason to react."

00:07:28.815 --> 00:07:29.674
Even though, if we did react,

00:07:29.674 --> 00:07:31.208
we were able to increase the entropy.

00:07:31.208 --> 00:07:33.145
Hey, no reason to react here.

00:07:33.145 --> 00:07:35.525
And, if you look at these
different variables,

00:07:35.525 --> 00:07:39.439
if this is positive,
even if this is positive,

00:07:39.439 --> 00:07:41.507
if 'T' is low, this isn't going to be able

00:07:41.507 --> 00:07:42.860
to overwhelm that.

00:07:42.860 --> 00:07:46.273
And so, you have a Delta G
that is greater than zero,

00:07:46.273 --> 00:07:47.909
not spontaneous.

00:07:47.909 --> 00:07:49.976
If you took the same scenario,

00:07:49.976 --> 00:07:52.471
and you said, "Okay, let's
up the temperature here.

00:07:52.471 --> 00:07:54.300
"Let's up the average kinetic energy."

00:07:54.300 --> 00:07:55.463
None of these things are going to be able

00:07:55.463 --> 00:07:57.564
to slam into each other.

00:07:57.564 --> 00:08:00.478
And, even though, even
though the electrons

00:08:00.478 --> 00:08:02.579
would essentially require some energy

00:08:02.579 --> 00:08:05.029
to get, to really form these bonds,

00:08:05.029 --> 00:08:08.024
this can happen because you have all

00:08:08.024 --> 00:08:09.823
of this disorder being created.

00:08:09.823 --> 00:08:11.298
You have these more states.

00:08:11.298 --> 00:08:12.957
And, it's less likely to go the other way,

00:08:12.957 --> 00:08:14.397
because, well, what are the odds

00:08:14.397 --> 00:08:16.046
of these things just getting together

00:08:16.046 --> 00:08:17.566
in the exact right configuration

00:08:17.566 --> 00:08:21.362
to get back into these, this
lower number of molecules.

00:08:21.362 --> 00:08:23.197
And, once again, you look
at these variables here.

00:08:23.197 --> 00:08:25.797
Even if Delta H is greater than zero,

00:08:25.797 --> 00:08:27.376
even if this is positive,

00:08:27.376 --> 00:08:29.024
if Delta S is greater than zero

00:08:29.024 --> 00:08:30.220
and 'T' is high,

00:08:30.220 --> 00:08:31.962
this thing is going to become,

00:08:31.962 --> 00:08:33.621
especially with the negative sign here,

00:08:33.621 --> 00:08:35.897
this is going to overwhelm the enthalpy,

00:08:35.897 --> 00:08:37.371
and the change in enthalpy,

00:08:37.371 --> 00:08:39.275
and make the whole expression negative.

00:08:39.275 --> 00:08:43.199
So, over here, Delta G is
going to be less than zero.

00:08:43.199 --> 00:08:46.345
And, this is going to be spontaneous.

00:08:46.345 --> 00:08:47.854
Hopefully, this gives you some intuition

00:08:47.854 --> 00:08:50.455
for the formula for Gibbs Free Energy.

00:08:50.455 --> 00:08:52.521
And, once again, you have to caveat it.

00:08:52.521 --> 00:08:55.980
It's under, it assumes constant
pressure and temperature.

00:08:55.980 --> 00:08:58.302
But, it is useful for thinking

00:08:58.302 --> 00:09:00.055
about whether a reaction is spontaneous.

00:09:00.055 --> 00:09:03.213
And, as you look at biological
or chemical systems,

00:09:03.213 --> 00:09:05.558
you'll see that Delta
G's for the reactions.

00:09:05.558 --> 00:09:07.706
And so, you'll say, "Oh,
it's a negative Delta G?

00:09:07.706 --> 00:09:09.180
"That's going to be a
spontaneous reaction.

00:09:09.180 --> 00:09:10.736
"It's a zero Delta G.

00:09:10.736 --> 00:09:12.117
"That's gonna be an equilibrium."

00:09:12.117 --> 00:09:14.190
Or, you could say, "That's
a positive Delta G.

00:09:14.190 --> 00:09:16.310
"That's not going to be spontaneous."


Why heat increases entropy

WEBVTT
Kind: captions
Language: en

00:00:00.170 --> 00:00:01.865
- [Voiceover] In the
video on the second law

00:00:01.865 --> 00:00:04.210
of thermodynamics I talk
about how the entropy

00:00:04.210 --> 00:00:06.868
of the universe is constantly increasing,

00:00:06.868 --> 00:00:09.318
that it's not going to decrease.

00:00:09.318 --> 00:00:12.261
And another way of thinking
about it is that the energy in

00:00:12.261 --> 00:00:15.971
the universe, more and more of
it is going towards entropy,

00:00:15.971 --> 00:00:18.227
it's becoming less and less useful.

00:00:18.227 --> 00:00:21.150
And the argument that I
use, even in our every day,

00:00:21.150 --> 00:00:23.408
I talk about hey, while I'm
making this video, my body's

00:00:23.408 --> 00:00:26.963
generating heat, and that
heat is leading to entropy,

00:00:26.963 --> 00:00:30.056
it's leading to more
entropy in the universe.

00:00:30.056 --> 00:00:34.682
And a reasonable question is,
how does heat lead to entropy?

00:00:34.682 --> 00:00:39.027
Remember heat is a
transfer of thermal energy,

00:00:39.027 --> 00:00:41.867
and entropy, this is
a state of the system,

00:00:41.867 --> 00:00:43.236
it's the number of,

00:00:43.236 --> 00:00:46.518
it's the amount of disorder
we have, it's the number

00:00:46.518 --> 00:00:49.598
of states that a system
could actually take on.

00:00:49.598 --> 00:00:52.436
So let's have an example here,
let's assume that this is an

00:00:52.436 --> 00:00:55.950
ideal, closed system, this
little white square here.

00:00:55.950 --> 00:00:59.104
And these molecules are bouncing
around at some temperature,

00:00:59.104 --> 00:01:01.182
so they have some average
kinetic energy, each molecule

00:01:01.182 --> 00:01:03.803
will be doing different things,
and I always draw it as this

00:01:03.803 --> 00:01:06.956
translational kinetic energy,
but they could be rotating

00:01:06.956 --> 00:01:09.790
and oscillating, and doing
all sorts of other things.

00:01:09.790 --> 00:01:12.584
So they could be doing
other things as well,

00:01:12.584 --> 00:01:14.724
but the translational kinetic
energy is a little bit

00:01:14.724 --> 00:01:17.463
easier to actually visualize.

00:01:17.463 --> 00:01:20.756
But now let's transfer
some heat into the system.

00:01:20.756 --> 00:01:25.214
So we have a transfer of thermal
energy, which we call heat,

00:01:25.214 --> 00:01:28.480
let me pick a color for
that, I will use orange,

00:01:28.480 --> 00:01:31.171
and we use the letter Q to denote heat.

00:01:31.171 --> 00:01:33.085
So we have a heat
transfer coming into this,

00:01:33.085 --> 00:01:36.089
and then because of this, the
temperature of this system

00:01:36.089 --> 00:01:39.488
goes up, the average
kinetic energy goes up,

00:01:39.488 --> 00:01:43.339
these things start bouncing
around with more momentum,

00:01:43.339 --> 00:01:45.124
with more velocity.

00:01:45.124 --> 00:01:46.932
So why does this system have entropy?

00:01:46.932 --> 00:01:48.597
You might say, well
look, you know there's,

00:01:48.597 --> 00:01:50.286
they have the same number of molecules,

00:01:50.286 --> 00:01:53.184
I have the same amount of volume,

00:01:53.184 --> 00:01:55.380
I'm looking at a
two-dimensional, looks like area,

00:01:55.380 --> 00:01:56.975
but we could imagine the
same amount of volume

00:01:56.975 --> 00:01:58.873
that it's filling up, it
feels like there's the same

00:01:58.873 --> 00:02:01.491
number of places that the
actual molecules could be.

00:02:01.491 --> 00:02:05.346
But our state is not
dictated purely by position,

00:02:05.346 --> 00:02:08.045
not purely by where the
different things are.

00:02:08.045 --> 00:02:10.597
The state is everything
about the system that

00:02:10.597 --> 00:02:12.334
you could use to predict
what's going to happen

00:02:12.334 --> 00:02:14.772
next to the system, so
the state also includes

00:02:14.772 --> 00:02:17.932
the various velocities of these particles.

00:02:17.932 --> 00:02:19.592
So when you have a higher temperature,

00:02:19.592 --> 00:02:22.472
you have a larger number
of potential velocities

00:02:22.472 --> 00:02:25.223
that you might be able
to actually take on.

00:02:25.223 --> 00:02:27.647
And also when you have
this higher kinetic energy,

00:02:27.647 --> 00:02:31.792
remember all of these molecules,
at the end of the day,

00:02:31.792 --> 00:02:35.641
they're made up of atoms that have nuclei

00:02:35.641 --> 00:02:37.971
and they have electrons
buzzing around them.

00:02:37.971 --> 00:02:40.369
And as they, if they don't
have much kinetic energy,

00:02:40.369 --> 00:02:42.141
they might not be able to get too close.

00:02:42.141 --> 00:02:44.963
So let's say this is the
outer electrons of one,

00:02:44.963 --> 00:02:47.318
I'll just say atom, and
let's say that this is

00:02:47.318 --> 00:02:49.936
another one right over here.

00:02:49.936 --> 00:02:52.505
If they're going with only
a reasonable kinetic energy,

00:02:52.505 --> 00:02:54.598
if they go with a
reasonable kinetic energy,

00:02:54.598 --> 00:02:56.804
they might be able to get, maybe they're

00:02:56.804 --> 00:02:58.591
going to be able to get that close.

00:02:58.591 --> 00:03:01.805
But if they were running, if
they were hitting each other

00:03:01.805 --> 00:03:04.268
much faster, they might be able
to get a little bit closer,

00:03:04.268 --> 00:03:07.718
they might kind of smush into each other,

00:03:07.718 --> 00:03:10.127
if you imagine kind of two
balls hitting each other

00:03:10.127 --> 00:03:13.031
much faster, they're going
to push on each other

00:03:13.031 --> 00:03:15.052
a little bit harder, and
so there's actually more

00:03:15.052 --> 00:03:16.932
possible states you can take on

00:03:16.932 --> 00:03:19.013
when you have higher kinetic energy.

00:03:19.013 --> 00:03:21.771
So this is, these things came in really,

00:03:21.771 --> 00:03:23.859
really fast and smushed into each other,

00:03:23.859 --> 00:03:25.292
while these were nice and polite,

00:03:25.292 --> 00:03:28.502
and came it at a nice gentle velocity.

00:03:28.502 --> 00:03:31.552
So you could actually even
have more positional states,

00:03:31.552 --> 00:03:35.449
more different configurations
in three-dimensional space.

00:03:35.449 --> 00:03:39.906
So that's why heat is
actually leading to entropy.

00:03:39.906 --> 00:03:41.895
Now I know what some
of you might be saying,

00:03:41.895 --> 00:03:45.603
well heat doesn't only
cause disorder, in fact,

00:03:45.603 --> 00:03:48.230
heat can be used to do work.

00:03:48.230 --> 00:03:50.002
In fact, that's the whole basis, in fact,

00:03:50.002 --> 00:03:51.658
a lot of the basis of the
Industrial Revolution,

00:03:51.658 --> 00:03:53.209
steam engines, combustion engines,

00:03:53.209 --> 00:03:55.766
the combustion engine in
your car that uses heat,

00:03:55.766 --> 00:03:58.449
uses a combustion reaction to expand,

00:03:58.449 --> 00:04:02.803
to push up a piston, which
is used to do actual work.

00:04:02.803 --> 00:04:05.965
And that is, of course, true.

00:04:05.965 --> 00:04:08.778
And over here we have an
example of that happening.

00:04:08.778 --> 00:04:12.504
So I have some molecules
in here buzzing around

00:04:12.504 --> 00:04:15.183
with some temperature, and
then I'm going to apply,

00:04:15.183 --> 00:04:17.610
I'm going to add some heat to the system.

00:04:17.610 --> 00:04:21.992
So let's add some heat to the system.

00:04:21.992 --> 00:04:25.628
And in this system, I don't
have just a closed boundary,

00:04:25.628 --> 00:04:27.642
these things start buzzing around more,

00:04:27.642 --> 00:04:29.906
they can take on more states
and all of that type of thing,

00:04:29.906 --> 00:04:32.658
but they can also use
to expand the container.

00:04:32.658 --> 00:04:35.538
So what we see happening here
is they push this piston,

00:04:35.538 --> 00:04:38.610
they push this piston open,
you actually have work,

00:04:38.610 --> 00:04:41.351
let me do work in a different color.

00:04:41.351 --> 00:04:44.229
You actually have work being done.

00:04:44.229 --> 00:04:47.138
I'll do it smaller.

00:04:47.138 --> 00:04:49.973
You actually have some work being done,

00:04:49.973 --> 00:04:51.214
and how is that work being done?

00:04:51.214 --> 00:04:52.887
Well as these things bounce around,

00:04:52.887 --> 00:04:55.543
we're talking about a lot of molecules,

00:04:55.543 --> 00:04:57.026
every now and then one of these molecules

00:04:57.026 --> 00:04:59.217
is going to bump there
and then bounce off,

00:04:59.217 --> 00:05:01.541
but that's going to provide
some force for a very small

00:05:01.541 --> 00:05:04.267
amount of time, that's going
to push it up a little bit

00:05:04.267 --> 00:05:06.089
and but you have so
many of these molecules,

00:05:06.089 --> 00:05:08.202
I've only drawn a handful
of them, but in any

00:05:08.202 --> 00:05:10.632
real thermodynamic system,
you're going to be talking

00:05:10.632 --> 00:05:13.197
about many millions and
millions and millions,

00:05:13.197 --> 00:05:15.656
you're talking about things on the,

00:05:15.656 --> 00:05:19.144
multiples of Avogadro's
number, number of molecules.

00:05:19.144 --> 00:05:21.076
And so at any given moment,
a lot of them are going to

00:05:21.076 --> 00:05:22.947
be bouncing right off this
thing, and they're going to be

00:05:22.947 --> 00:05:24.711
doing work, they're going to be pushing,

00:05:24.711 --> 00:05:27.608
they're going to be displacing
this piston in the direction

00:05:27.608 --> 00:05:29.801
of the force, or part, a
component of their force is going

00:05:29.801 --> 00:05:33.955
to be pushing this piston
actually up, and doing work.

00:05:33.955 --> 00:05:37.966
But no heat-based, I guess you could say,

00:05:37.966 --> 00:05:41.109
system or engine can be 100% efficient.

00:05:41.109 --> 00:05:43.954
So some of this can be used to do work,

00:05:43.954 --> 00:05:47.164
but a lot of it is going to
be used to add to the disorder

00:05:47.164 --> 00:05:50.364
of the system, to increase
the number of states

00:05:50.364 --> 00:05:52.170
that the system could take on.

00:05:52.170 --> 00:05:54.627
One way to think about it,
and this has always helped me,

00:05:54.627 --> 00:05:57.506
is heat is transfer of thermal energy,

00:05:57.506 --> 00:05:59.480
that happens at the
boundary of the system,

00:05:59.480 --> 00:06:01.407
this heat could be you
know, maybe there's a,

00:06:01.407 --> 00:06:03.966
maybe there's a flame down here,

00:06:03.966 --> 00:06:05.685
and at the boundaries this
thing might be able to,

00:06:05.685 --> 00:06:08.035
if this wasn't a fully-closed
system, it could release heat

00:06:08.035 --> 00:06:09.899
at the boundaries of the system.

00:06:09.899 --> 00:06:13.598
But within the system, the
heat is just leading the

00:06:13.598 --> 00:06:17.299
increased thermal energy is
just leading to more entropy.

00:06:17.299 --> 00:06:19.871
Now work also happens at
the boundary of the system,

00:06:19.871 --> 00:06:22.509
so up here, there's probably
some heat being released,

00:06:22.509 --> 00:06:24.768
but it's also able to do work.

00:06:24.768 --> 00:06:26.802
So heat and work, these
are happening at the

00:06:26.802 --> 00:06:29.710
boundaries of the system,
but a lot of that energy

00:06:29.710 --> 00:06:32.484
goes into the inside of the
system, and that is just,

00:06:32.484 --> 00:06:34.619
things are just gonna, you
know, it's like a big mosh pit,

00:06:34.619 --> 00:06:36.632
these things are going to run
into each other much faster,

00:06:36.632 --> 00:06:38.818
and way more states
that they could take on.

00:06:38.818 --> 00:06:40.874
And so that's why, when
I talk about you know,

00:06:40.874 --> 00:06:42.798
if I move around and I'm
walking on the floor,

00:06:42.798 --> 00:06:44.933
just the friction of the carpet
is going to generate heat.

00:06:44.933 --> 00:06:47.126
That's going to contribute
to entropy in the universe.

00:06:47.126 --> 00:06:50.097
Just me existing, the
cellular processes in my body

00:06:50.097 --> 00:06:53.089
that generate heat, it
increases the entropy of the

00:06:53.089 --> 00:06:55.419
universe that makes the
total energy of the universe

00:06:55.419 --> 00:06:58.699
less useful, that's why it's happening.


Comparing areas and perimeters of rectangles

WEBVTT
Kind: captions
Language: en

00:00:00.750 --> 00:00:02.660
So I have this yellow
rectangle here,

00:00:02.660 --> 00:00:04.830
and we know two things
about this yellow rectangle.

00:00:04.830 --> 00:00:07.450
We know that it
has a length of 10,

00:00:07.450 --> 00:00:10.650
that the length of this
side right over here is 10.

00:00:10.650 --> 00:00:13.370
And we also know that
this yellow rectangle

00:00:13.370 --> 00:00:16.690
has an area of 60
square units, whatever

00:00:16.690 --> 00:00:19.580
units we're
measuring this 10 in.

00:00:19.580 --> 00:00:23.480
So what I want you to do
is now pause this video,

00:00:23.480 --> 00:00:25.240
and based on the
information given

00:00:25.240 --> 00:00:27.370
on these other rectangles--
so in some of them

00:00:27.370 --> 00:00:29.860
we give you two of their
dimensions, in some of them

00:00:29.860 --> 00:00:32.009
we give you something
like the perimeter

00:00:32.009 --> 00:00:34.970
and one of the dimensions--
I want you to pause the video

00:00:34.970 --> 00:00:38.090
and think about which of these
rectangles, if any of them,

00:00:38.090 --> 00:00:42.390
have either the same area
or the same perimeter

00:00:42.390 --> 00:00:44.630
as this yellow rectangle.

00:00:44.630 --> 00:00:47.630
So pause the video right now.

00:00:47.630 --> 00:00:50.030
Well, the best way to
figure out which of these

00:00:50.030 --> 00:00:53.560
have the same area or perimeter
as this original yellow

00:00:53.560 --> 00:00:56.130
rectangle is to just figure
out the area and the perimeter

00:00:56.130 --> 00:00:58.720
for all of these rectangles
and see which ones of them

00:00:58.720 --> 00:01:00.230
are equivalent.

00:01:00.230 --> 00:01:01.990
So we already know
the area for this one,

00:01:01.990 --> 00:01:03.830
but we don't know its perimeter.

00:01:03.830 --> 00:01:05.245
So how do we figure that out?

00:01:05.245 --> 00:01:06.620
Well, to figure
out perimeter, we

00:01:06.620 --> 00:01:09.350
would need to know the
lengths of all the sides.

00:01:09.350 --> 00:01:14.030
Well, if the area is 60 square
units, that means the length

00:01:14.030 --> 00:01:20.850
times the width is equal to
60, that 10 times this width

00:01:20.850 --> 00:01:23.080
right over here is
going to be equal to 60.

00:01:23.080 --> 00:01:26.540
So 10 times what is equal to 60?

00:01:26.540 --> 00:01:29.840
Well, 10 times 6 is equal to 60.

00:01:29.840 --> 00:01:33.530
10 times 6 is equal
to 60 square units.

00:01:33.530 --> 00:01:36.720
10 units times 6 units is
equal to 60 square units.

00:01:36.720 --> 00:01:37.220
Fair enough.

00:01:37.220 --> 00:01:39.870
So how do we figure
out the perimeter now?

00:01:39.870 --> 00:01:41.170
Well, this is a rectangle.

00:01:41.170 --> 00:01:42.790
So we know if this
length is 10, then

00:01:42.790 --> 00:01:44.680
this length must also be 10.

00:01:44.680 --> 00:01:48.274
And if this width is 6, then
this width must be 6 as well.

00:01:48.274 --> 00:01:49.940
And now we can figure
out the perimeter.

00:01:49.940 --> 00:01:53.717
It's 10 plus 10 plus
6 plus 6, which is 32.

00:01:53.717 --> 00:01:54.800
So let me write that down.

00:01:54.800 --> 00:01:59.090
The perimeter of our
original yellow rectangle

00:01:59.090 --> 00:02:01.980
is equal to 32.

00:02:01.980 --> 00:02:04.180
Now let's go on to each
of these other rectangles

00:02:04.180 --> 00:02:06.530
and figure out what their
perimeters and the areas are.

00:02:06.530 --> 00:02:09.720
We already know the perimeter
for this purple or mauve

00:02:09.720 --> 00:02:12.110
rectangle, but we need
to figure out its area.

00:02:12.110 --> 00:02:14.430
In order to figure out
its area, we can't just

00:02:14.430 --> 00:02:16.790
rely on this one dimension
just on its width.

00:02:16.790 --> 00:02:19.390
We have to figure out
its length as well.

00:02:19.390 --> 00:02:21.510
So how do we figure that out?

00:02:21.510 --> 00:02:23.980
Well, one way to realize
it is that the perimeter

00:02:23.980 --> 00:02:27.370
is the distance all the
way around the rectangle.

00:02:27.370 --> 00:02:30.430
So what would be the distance
halfway around the rectangle?

00:02:30.430 --> 00:02:31.760
So let me see if I can draw it.

00:02:31.760 --> 00:02:35.970
What would be the distance
of this side, our length,

00:02:35.970 --> 00:02:38.440
plus this side?

00:02:38.440 --> 00:02:40.520
Well, it would be
half the perimeter.

00:02:40.520 --> 00:02:44.090
5 plus something is going to
be equal to half the perimeter.

00:02:44.090 --> 00:02:45.890
Remember, the perimeter
is all four sides.

00:02:45.890 --> 00:02:47.530
If we just took these
two sides, which

00:02:47.530 --> 00:02:49.340
would be half the perimeter.

00:02:49.340 --> 00:02:51.420
So, these two sides
must be equal to,

00:02:51.420 --> 00:02:54.240
when you take their sum,
must be equal to 17,

00:02:54.240 --> 00:02:55.180
half the perimeter.

00:02:55.180 --> 00:02:58.960
So 5 plus what is equal to 17?

00:02:58.960 --> 00:03:01.970
5 plus this question
mark is equal to 17.

00:03:01.970 --> 00:03:05.100
Well, 5 plus 12 is equal to 17.

00:03:05.100 --> 00:03:06.150
And you can verify this.

00:03:06.150 --> 00:03:09.810
12 plus 5 is 17, and
then that times 2

00:03:09.810 --> 00:03:12.450
gets us the perimeter of 34.

00:03:12.450 --> 00:03:15.530
Now, given that, what is
the area of this figure?

00:03:15.530 --> 00:03:18.240
Well, the area's going to
be 12 units times 5 units

00:03:18.240 --> 00:03:21.180
to get 60 square units.

00:03:21.180 --> 00:03:24.070
Area is equal to 60.

00:03:24.070 --> 00:03:26.280
So this one right over
here has the same area,

00:03:26.280 --> 00:03:27.600
different perimeter.

00:03:27.600 --> 00:03:32.530
Same area as the original yellow
rectangle, different area.

00:03:32.530 --> 00:03:33.770
Now let's go over here.

00:03:33.770 --> 00:03:35.710
So this is not just a rectangle.

00:03:35.710 --> 00:03:37.290
This is also a
square, because I have

00:03:37.290 --> 00:03:40.040
the same length
and the same width.

00:03:40.040 --> 00:03:41.929
So what's the area here?

00:03:41.929 --> 00:03:43.720
Well, for the area, I
just have to multiply

00:03:43.720 --> 00:03:44.844
the length times the width.

00:03:44.844 --> 00:03:48.970
8 units times 8 units
is 64 square units.

00:03:48.970 --> 00:03:50.390
And what is the perimeter here?

00:03:54.010 --> 00:03:56.930
Well, these two sides are going
to make up half the perimeter.

00:03:56.930 --> 00:03:58.596
If I wanted to figure
out the whole one,

00:03:58.596 --> 00:04:00.790
I know this is also
8 and this is also 8.

00:04:00.790 --> 00:04:03.300
So the perimeter is 8 times 4.

00:04:03.300 --> 00:04:07.660
8 times 4 sides,
which is equal to 32.

00:04:07.660 --> 00:04:10.240
So this square right over
here has a different area,

00:04:10.240 --> 00:04:15.704
but it has the same perimeter
as our original yellow square.

00:04:15.704 --> 00:04:17.120
Now let's move
onto this blue one.

00:04:17.120 --> 00:04:18.279
What's the area?

00:04:18.279 --> 00:04:20.000
And you're probably
getting used to this.

00:04:20.000 --> 00:04:25.400
15 units times 4 units is
going to be 60 square units.

00:04:25.400 --> 00:04:27.260
And what's the perimeter?

00:04:27.260 --> 00:04:29.010
What's the perimeter?

00:04:29.010 --> 00:04:30.590
Well, it's going
to be 4 plus 15,

00:04:30.590 --> 00:04:32.160
and whatever that is times 2.

00:04:32.160 --> 00:04:34.800
4 plus 15 is 19.

00:04:34.800 --> 00:04:39.210
And then 19 times 2 is 38.

00:04:39.210 --> 00:04:42.470
So this one right here
has the same area,

00:04:42.470 --> 00:04:45.570
different perimeter
as our original.

00:04:45.570 --> 00:04:49.440
Now, finally, here in
purple, what is the area?

00:04:49.440 --> 00:04:54.920
The area is 10 times 20,
which is equal to 200.

00:04:54.920 --> 00:04:57.590
So if it's 10, say, well,
10 units times 20 units

00:04:57.590 --> 00:05:00.250
is 200 square units.

00:05:00.250 --> 00:05:02.890
And what is the perimeter?

00:05:02.890 --> 00:05:04.860
What is the perimeter?

00:05:04.860 --> 00:05:08.550
Well, 10 plus 20 is 30, but
I've just considered only two

00:05:08.550 --> 00:05:10.330
of the sides right here.

00:05:10.330 --> 00:05:11.910
That's only half way around.

00:05:11.910 --> 00:05:15.940
So 10 plus 20 is
30 times 2 is 60.

00:05:15.940 --> 00:05:16.950
So let's see.

00:05:16.950 --> 00:05:19.457
This has a different
area, and it also

00:05:19.457 --> 00:05:20.540
has a different perimeter.

00:05:20.540 --> 00:05:23.760
This one's perimeter looks
just like the same number.

00:05:23.760 --> 00:05:25.469
It's 60, as is the
area here, but that's

00:05:25.469 --> 00:05:26.510
not what we're comparing.

00:05:26.510 --> 00:05:28.670
We have a different
perimeter and different area.

00:05:28.670 --> 00:05:33.194
So neither of these are the
same as our original rectangle.


Number properties terminology 1

WEBVTT
Kind: captions
Language: en

00:00:01.070 --> 00:00:05.310
a plus b times open
parentheses c plus d is

00:00:05.310 --> 00:00:10.120
equal to a plus bc plus
bd represents which

00:00:10.120 --> 00:00:12.656
of the following properties?

00:00:12.656 --> 00:00:15.030
So to get from the left-hand
side to the right-hand side,

00:00:15.030 --> 00:00:17.490
it looks like what they did
is they multiplied the b times

00:00:17.490 --> 00:00:18.400
the c plus d.

00:00:18.400 --> 00:00:20.732
In fact, they
distributed the b. b

00:00:20.732 --> 00:00:25.680
times c plus d is b
times c, plus b times d.

00:00:25.680 --> 00:00:28.910
So this is clearly the
distributive property.

00:00:28.910 --> 00:00:30.550
Let's do another one.

00:00:30.550 --> 00:00:34.000
4 plus open parentheses
10 plus 6, they're saying,

00:00:34.000 --> 00:00:37.144
is the same thing as 4
plus 10 first, plus 6.

00:00:37.144 --> 00:00:39.560
So on the left-hand side, we're
doing the 10 plus 6 first,

00:00:39.560 --> 00:00:40.920
and then we're adding the 4.

00:00:40.920 --> 00:00:43.296
On the right-hand side, we're
adding the 4 plus 10 first,

00:00:43.296 --> 00:00:44.461
and then we're adding the 6.

00:00:44.461 --> 00:00:46.380
And we're saying they're
equal to each other.

00:00:46.380 --> 00:00:49.084
It doesn't matter how we
associate these numbers.

00:00:49.084 --> 00:00:51.000
Here we're associating
the 10 and the 6 first,

00:00:51.000 --> 00:00:52.224
and then we're adding the 4.

00:00:52.224 --> 00:00:54.140
Here we're associating
the 4 and the 10 first,

00:00:54.140 --> 00:00:55.590
and then we're adding the 6.

00:00:55.590 --> 00:00:57.905
So this is the associative
property for addition.

00:01:00.940 --> 00:01:02.990
Let's do several more.

00:01:02.990 --> 00:01:06.300
a plus b is equal to b
plus a represents which

00:01:06.300 --> 00:01:07.697
of the following properties?

00:01:07.697 --> 00:01:09.530
So it doesn't matter
which order I'm adding.

00:01:09.530 --> 00:01:12.150
It doesn't matter if I
do a plus b or b plus a.

00:01:12.150 --> 00:01:15.431
This is the
commutative property.

00:01:15.431 --> 00:01:17.360
Do another one.

00:01:17.360 --> 00:01:19.450
Which one of the
equations on the right

00:01:19.450 --> 00:01:21.830
represents the associative
property of addition?

00:01:21.830 --> 00:01:23.750
So remember,
associative property--

00:01:23.750 --> 00:01:25.960
we're talking about
it doesn't matter

00:01:25.960 --> 00:01:27.567
how we associate the numbers.

00:01:27.567 --> 00:01:29.900
So we might do the operation
on two of the numbers first

00:01:29.900 --> 00:01:33.480
and then on the third, or on
maybe two of the other numbers

00:01:33.480 --> 00:01:35.100
and then on the one
that's left over.

00:01:35.100 --> 00:01:37.910
So let's see what over
here looks like that.

00:01:37.910 --> 00:01:40.810
So this right over here, this
is the commutative property.

00:01:40.810 --> 00:01:43.280
This right over here is
the distributive property.

00:01:43.280 --> 00:01:45.700
This one right over here--
on the left-hand side,

00:01:45.700 --> 00:01:47.450
we add b plus c first.

00:01:47.450 --> 00:01:49.625
On the right-hand side,
we add a plus b first.

00:01:49.625 --> 00:01:51.500
And these two things
are equal to each other.

00:01:51.500 --> 00:01:53.400
It doesn't matter
how we associate it,

00:01:53.400 --> 00:01:56.080
if we associate b plus c
first or a plus b first.

00:01:56.080 --> 00:02:00.030
So this is the associative
property of addition.

00:02:00.030 --> 00:02:03.140
Let's do-- which one of
the equations on the right

00:02:03.140 --> 00:02:04.660
represents the
distributive property

00:02:04.660 --> 00:02:07.700
of addition over multiplication?

00:02:07.700 --> 00:02:08.460
So let's see.

00:02:08.460 --> 00:02:11.140
This first one, they're just
changing the associations.

00:02:11.140 --> 00:02:13.260
Here, this is commutative,
this last one.

00:02:13.260 --> 00:02:15.705
Here, they're actually
distributing the b

00:02:15.705 --> 00:02:17.090
over the c plus d.

00:02:17.090 --> 00:02:21.260
So b times c plus d is the
same thing as bc plus bd.

00:02:21.260 --> 00:02:23.424
So it's that one
right over there.

00:02:23.424 --> 00:02:24.590
Maybe do a few more of this.

00:02:24.590 --> 00:02:25.870
This is a lot of fun.

00:02:25.870 --> 00:02:28.910
a plus b plus c is equal
to a plus b plus c,

00:02:28.910 --> 00:02:31.820
so this once again, they're
re-associating the numbers.

00:02:31.820 --> 00:02:34.360
But it doesn't matter which
order we associate them in.

00:02:34.360 --> 00:02:39.596
So this is the
associative property.

00:02:39.596 --> 00:02:41.220
Which one of the
equations on the right

00:02:41.220 --> 00:02:44.020
represents the commutative
property of addition?

00:02:44.020 --> 00:02:46.930
So commutative-- we don't
care about the order

00:02:46.930 --> 00:02:48.700
in which we're
doing the operation.

00:02:48.700 --> 00:02:51.460
So a plus b is
equal to b plus a.

00:02:54.385 --> 00:02:56.010
Which one of the
equations on the right

00:02:56.010 --> 00:02:58.099
represents the commutative
property of addition?

00:02:58.099 --> 00:02:59.640
Well, that's what
they just asked us.

00:02:59.640 --> 00:03:02.940
a plus b is equal to b plus a.

00:03:02.940 --> 00:03:04.920
And we are done.


Properties of numbers 1

WEBVTT
Kind: captions
Language: en

00:00:00.810 --> 00:00:04.200
What number could
replace this weird circle

00:00:04.200 --> 00:00:06.946
with an x symbol
looking thing below?

00:00:06.946 --> 00:00:08.570
And over here, they
have this equation.

00:00:08.570 --> 00:00:12.430
They say 8 plus 4 is equal
to 4 plus weird circle

00:00:12.430 --> 00:00:14.240
with the x thing.

00:00:14.240 --> 00:00:17.270
And what they're really
wanting us to appreciate

00:00:17.270 --> 00:00:22.530
is that, look, 8 plus 4 is the
exact same thing as 4 plus 8.

00:00:22.530 --> 00:00:24.390
That's the commutative
law of addition,

00:00:24.390 --> 00:00:27.230
which is just a very fancy way
of saying that, well, 8 plus 4

00:00:27.230 --> 00:00:28.870
is the same thing as 4 plus 8.

00:00:28.870 --> 00:00:31.640
It doesn't matter which number
comes before the addition sign

00:00:31.640 --> 00:00:33.530
and which one comes after.

00:00:33.530 --> 00:00:36.770
So 8 plus 4 is the
same thing as 4 plus 8.

00:00:36.770 --> 00:00:41.135
This little thing could be
replaced by the number 8.

00:00:41.135 --> 00:00:42.010
Let's do another one.

00:00:45.220 --> 00:00:48.120
What number could replace
this little-- looks

00:00:48.120 --> 00:00:50.650
almost like a cross--
below, or it looks almost

00:00:50.650 --> 00:00:51.940
like a dagger or something.

00:00:51.940 --> 00:00:56.210
10 plus 4 in parentheses
plus 3, and then they

00:00:56.210 --> 00:00:59.470
have something plus 4 plus 3.

00:00:59.470 --> 00:01:01.930
So it looks like
they're wanting us

00:01:01.930 --> 00:01:03.590
to realize that
it doesn't matter

00:01:03.590 --> 00:01:05.950
if we do the 10 plus
4 first or whether we

00:01:05.950 --> 00:01:07.970
do the 4 plus 3 first.

00:01:07.970 --> 00:01:10.730
So if we just took this
statement right over here

00:01:10.730 --> 00:01:12.340
and changed the
parentheses so that we

00:01:12.340 --> 00:01:15.117
add the 4 plus 3 first--
so they're doing here--

00:01:15.117 --> 00:01:16.950
this number right over
here could be the 10.

00:01:19.772 --> 00:01:21.980
And this right over here is
just the associative law,

00:01:21.980 --> 00:01:23.938
or the associative law
of addition, or the fact

00:01:23.938 --> 00:01:25.190
that addition is associative.

00:01:25.190 --> 00:01:28.950
It doesn't matter if you
add the 10 plus 4 first

00:01:28.950 --> 00:01:32.060
and then you add the 3, or
you add the 4 plus 3 first

00:01:32.060 --> 00:01:34.190
and then you add the 10.

00:01:34.190 --> 00:01:36.620
So this could easily be the 10.

00:01:36.620 --> 00:01:37.710
Let's check our answer.

00:01:37.710 --> 00:01:38.900
Let's do another one.

00:01:38.900 --> 00:01:41.250
What could replace this
little-- almost looks

00:01:41.250 --> 00:01:43.167
like what you'd see in
a Do Not Smoking sign

00:01:43.167 --> 00:01:45.250
if there was a cigarette
behind it, so this little

00:01:45.250 --> 00:01:47.970
slash between the inside
of a circle below.

00:01:47.970 --> 00:01:49.020
So 9 times 6.

00:01:49.020 --> 00:01:51.280
Well, multiplication
is also commutative.

00:01:51.280 --> 00:01:55.030
9 times 6 is the exact
same thing as 6 times 9,

00:01:55.030 --> 00:01:57.525
so this thing could be a 9.

00:01:57.525 --> 00:02:00.370
It could be replaced with a 9.

00:02:00.370 --> 00:02:03.040
I guess I'm all
out of questions.


Distributive property exercise examples

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:02.530
We're asked to rewrite
the expression 7

00:00:02.530 --> 00:00:08.370
times open parentheses 5
plus 11 close parentheses

00:00:08.370 --> 00:00:11.217
as the sum of 35 and
another whole number.

00:00:11.217 --> 00:00:12.800
So really what they're
asking us to do

00:00:12.800 --> 00:00:14.530
is just apply the
distributive property.

00:00:14.530 --> 00:00:18.150
We have 7 times the
quantity 5 plus 11.

00:00:18.150 --> 00:00:19.400
Now this is easy to calculate.

00:00:19.400 --> 00:00:23.750
You could just say 5 plus 11 is
16 and then 16 times 7 is what?

00:00:23.750 --> 00:00:26.427
That's 70 plus 42
which would be 112.

00:00:26.427 --> 00:00:28.260
But that's not what
they're asking us to do.

00:00:28.260 --> 00:00:30.030
They're not saying
just calculate this.

00:00:30.030 --> 00:00:31.530
They're saying
express this as a sum

00:00:31.530 --> 00:00:32.960
of 35 and another whole number.

00:00:32.960 --> 00:00:34.950
So let's apply the
distributive property

00:00:34.950 --> 00:00:37.390
and let's see if we
can get a sum of 35

00:00:37.390 --> 00:00:38.770
and another whole number.

00:00:38.770 --> 00:00:45.860
So 7 times 5 plus 11, that's
the same thing as 7 times 5

00:00:45.860 --> 00:00:51.359
plus 7 times 11.

00:00:51.359 --> 00:00:53.150
And you can see with
this expression editor

00:00:53.150 --> 00:00:54.990
right over here,
it tells you-- it

00:00:54.990 --> 00:00:56.790
puts it kind of the
nice math formatting

00:00:56.790 --> 00:00:59.200
for what it looks
like for the computer.

00:00:59.200 --> 00:01:01.740
So if we're distributing
the 7 over the 5 and the 11,

00:01:01.740 --> 00:01:04.599
it's 7 times 5 plus 7 times 11.

00:01:04.599 --> 00:01:07.760
Well, 7 times 5 is 35.

00:01:07.760 --> 00:01:11.430
And 7 times 11 is 77.

00:01:11.430 --> 00:01:13.380
Now, have we done what
they're asking us?

00:01:13.380 --> 00:01:14.970
They said rewrite
this expression

00:01:14.970 --> 00:01:17.464
as the sum of 35 and
another whole number.

00:01:17.464 --> 00:01:18.380
Well, we've done that.

00:01:18.380 --> 00:01:21.530
We've written it as a sum of
35 and another whole number

00:01:21.530 --> 00:01:24.660
and we were able to do it using
the distributive property.

00:01:24.660 --> 00:01:27.780
So let's check to make sure
that we got the right answer.

00:01:27.780 --> 00:01:28.330
Yes, we did.

00:01:28.330 --> 00:01:30.240
Let's do one more of these.

00:01:30.240 --> 00:01:35.330
Rewrite the expression 12 plus
75 in the following form--

00:01:35.330 --> 00:01:42.870
a times 4 plus c where a and
c represent whole numbers.

00:01:42.870 --> 00:01:45.410
Now this might look
complex, but they're really

00:01:45.410 --> 00:01:49.250
asking us to factor
out an a-- factoring

00:01:49.250 --> 00:01:51.940
out an a out of this
expression right over here.

00:01:51.940 --> 00:01:53.870
Seeing how much
we can factor out

00:01:53.870 --> 00:01:57.570
so that one of these
two numbers becomes a 4.

00:01:57.570 --> 00:01:59.200
So let's think about
how to do that.

00:01:59.200 --> 00:02:03.120
If we look at these two numbers,
the greatest common divisor

00:02:03.120 --> 00:02:09.060
of 12 and 75 looks like it is 3.

00:02:09.060 --> 00:02:11.180
Both of them are divisible by 3.

00:02:11.180 --> 00:02:12.540
So you can write 12.

00:02:12.540 --> 00:02:15.930
12 is the same
thing as 3 times 4.

00:02:15.930 --> 00:02:22.760
And 75 is the same
thing as 3 times 25.

00:02:22.760 --> 00:02:27.890
Now what we could do is we could
essentially factor out the 3.

00:02:27.890 --> 00:02:31.150
So this is where you could say
we're undistributing the 3.

00:02:31.150 --> 00:02:32.460
So that's the same thing.

00:02:32.460 --> 00:02:34.910
3 times 4 plus 3
times 25, that's

00:02:34.910 --> 00:02:40.850
the same thing as
3 times 4 plus 25.

00:02:46.730 --> 00:02:49.590
And it looks like we've
actually put it in the form

00:02:49.590 --> 00:02:53.425
that they want us to put
it in, where 3 is a and 4

00:02:53.425 --> 00:02:54.050
is right there.

00:02:54.050 --> 00:02:54.550
It's 4.

00:02:54.550 --> 00:02:56.120
And then c is 25.

00:02:56.120 --> 00:02:58.490
So we've put it
in the right form.

00:02:58.490 --> 00:03:00.010
Let's check our answer.

00:03:00.010 --> 00:03:02.080
We got it right.