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PROFESSOR: All right.

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00:00:21,890 --> 00:00:27,790
So today we're starting the last
unit of this class, which

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is kinetics.

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00:00:28,990 --> 00:00:33,180
So, we're moving toward the end
of the semester, and today

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00:00:33,180 --> 00:00:36,680
will just be an introductory
lecture on kinetics.

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00:00:36,680 --> 00:00:40,370
So, again, kinetics are the
rates of chemical reactions,

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00:00:40,370 --> 00:00:41,630
and so we're going to talk
about, we're going to

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00:00:41,630 --> 00:00:46,240
introduce you to rate
expressions and rate laws.

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00:00:46,240 --> 00:00:49,670
So, when you're considering a
chemical reaction, we've been

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00:00:49,670 --> 00:00:53,100
asking so far in this class
whether the reaction will go

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00:00:53,100 --> 00:00:54,500
spontaneously.

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00:00:54,500 --> 00:00:57,150
So we've been talking a lot
about thermodynamics, we've

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00:00:57,150 --> 00:00:59,180
been talking a lot
about delta g.

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00:00:59,180 --> 00:01:02,930
But we also need to consider how
fast a reaction goes, and

22
00:01:02,930 --> 00:01:04,560
that's kinetics.

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00:01:04,560 --> 00:01:07,310
So, a kinetic experiment is one
in which you measure the

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00:01:07,310 --> 00:01:09,280
rate at which something's
happening.

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00:01:09,280 --> 00:01:12,310
The rate at which a
concentration is disappearing

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00:01:12,310 --> 00:01:15,980
or whether the rate at which
a concentration is forming.

27
00:01:15,980 --> 00:01:19,820
You're measuring some kind of
change of a reaction, change

28
00:01:19,820 --> 00:01:24,410
in composition versus time.

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00:01:24,410 --> 00:01:27,990
So, I'm going to give, for an
example, of why kinetics are

30
00:01:27,990 --> 00:01:31,310
important talking about the
oxidation of glucose.

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00:01:31,310 --> 00:01:34,080
And I'm going to ask -- we're
going to do a little

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00:01:34,080 --> 00:01:37,730
experiment, and I'm going to
ask the TA's to help me.

33
00:01:37,730 --> 00:01:42,110
Everyone needs to have something
to do an experiment

34
00:01:42,110 --> 00:01:46,010
with, something that might have
some glucose in it to do

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00:01:46,010 --> 00:01:47,370
this experiment.

36
00:01:47,370 --> 00:01:51,220
So, if the TA's could help me
hand out the ingredients for

37
00:01:51,220 --> 00:01:56,270
this experiment.

38
00:01:56,270 --> 00:02:07,440
So, don't open your experimental
apparatus until I

39
00:02:07,440 --> 00:02:09,420
give the OK.

40
00:02:09,420 --> 00:02:13,720
So, just collect it and let me
set up the experiment for you

41
00:02:13,720 --> 00:02:24,180
while we're handing
things out.

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00:02:24,180 --> 00:02:28,110
So you're all familiar with
this reaction, so we have

43
00:02:28,110 --> 00:02:36,920
glucose and oxygen go
to c o 2 and water.

44
00:02:36,920 --> 00:02:40,300
And so we've talked a lot
about delta g for this

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00:02:40,300 --> 00:02:44,890
reaction, and delta g again,
is equal to delta h

46
00:02:44,890 --> 00:02:51,580
minus t delta s.

47
00:02:51,580 --> 00:02:55,670
So for this particular reaction,
we have a negative

48
00:02:55,670 --> 00:03:00,220
delta h nought, so what does
negative delta h mean about

49
00:03:00,220 --> 00:03:03,840
this reaction?

50
00:03:03,840 --> 00:03:06,870
It's exothermic.

51
00:03:06,870 --> 00:03:12,780
Delta s nought is positive, what
does that mean, if delta

52
00:03:12,780 --> 00:03:15,970
s nought is positive?

53
00:03:15,970 --> 00:03:17,960
What's increasing?

54
00:03:17,960 --> 00:03:24,070
Entropy or disorder of the
system, which is favorable.

55
00:03:24,070 --> 00:03:29,120
So, our delta g nought is
a big negative number.

56
00:03:29,120 --> 00:03:32,130
So, in terms of thermodynamics,

57
00:03:32,130 --> 00:03:33,170
what does this mean?

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00:03:33,170 --> 00:03:36,200
Is this reaction spontaneous?

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00:03:36,200 --> 00:03:38,450
Yes, it's very spontaneous,
it's very

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00:03:38,450 --> 00:03:41,090
thermodynamically favorable.

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00:03:41,090 --> 00:03:45,880
Now, when glucose in products
are wrapped, they're often

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00:03:45,880 --> 00:03:49,920
wrapped under a nitrogen
environment, so, oxygen is not

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00:03:49,920 --> 00:03:54,560
sealed up in this container,
in the wrapper, and they do

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00:03:54,560 --> 00:03:57,540
that to prevent bacterial
contamination

65
00:03:57,540 --> 00:03:58,620
and things like that.

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00:03:58,620 --> 00:04:03,470
So, the glucose that would be
in a wrapped candy is not

67
00:04:03,470 --> 00:04:05,350
exposed to oxygen.

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00:04:05,350 --> 00:04:08,700
And so if you look at this
thermodynamic information up

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00:04:08,700 --> 00:04:14,320
here, one might imagine that if
you ripped this open, and

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00:04:14,320 --> 00:04:18,620
oxygen came in, that there might
be some kind of level of

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00:04:18,620 --> 00:04:23,740
explosion with c o 2 coming
out and water coming out.

72
00:04:23,740 --> 00:04:26,780
Now, you know, you might say
well, if you have one sort of

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00:04:26,780 --> 00:04:30,400
little thing it might not, but
now if everyone has one, and

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00:04:30,400 --> 00:04:33,590
we all open it at the
same time, what do

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00:04:33,590 --> 00:04:37,560
you expect to happen?

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00:04:37,560 --> 00:04:41,410
Let's try it.

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00:04:41,410 --> 00:04:45,600
Oh, we need some
more down here.

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00:04:45,600 --> 00:04:54,940
Anybody else need any?

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00:04:54,940 --> 00:04:59,540
All right, so I'm trying mine,
and I'm not really noticing

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00:04:59,540 --> 00:05:04,080
anything happening.

81
00:05:04,080 --> 00:05:08,390
So the situation is the
following, It is a spontaneous

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00:05:08,390 --> 00:05:12,360
reaction, but it's slow.

83
00:05:12,360 --> 00:05:19,430
So here, kinetics are
very important.

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00:05:19,430 --> 00:05:23,100
So, how many of you are having
Thanksgiving with a small

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00:05:23,100 --> 00:05:26,950
child around, younger siblings
or something like that?

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00:05:26,950 --> 00:05:30,880
When you see them eat a lot of
sugar, which can happen over

87
00:05:30,880 --> 00:05:35,200
Thanksgiving, it sometimes seems
like an explosion has

88
00:05:35,200 --> 00:05:37,800
occurred, that there's
all of a sudden hyper

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00:05:37,800 --> 00:05:39,460
energy running around.

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00:05:39,460 --> 00:05:44,030
But that could be due to this
reaction biochemically,

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00:05:44,030 --> 00:05:48,700
getting a lot of energy into the
system, but probably you

92
00:05:48,700 --> 00:05:53,510
will not see c o 2 and water
coming off of the small child

93
00:05:53,510 --> 00:05:57,070
as they run around.

94
00:05:57,070 --> 00:06:00,690
So, let me introduce you to
a couple of terms, if you

95
00:06:00,690 --> 00:06:02,550
haven't heard these already.

96
00:06:02,550 --> 00:06:06,050
So people are often talking
about compounds being stable

97
00:06:06,050 --> 00:06:07,350
or unstable.

98
00:06:07,350 --> 00:06:09,080
When they're doing this, they're
talking about the

99
00:06:09,080 --> 00:06:12,950
thermodynamics of a system,
the tendency to decompose,

100
00:06:12,950 --> 00:06:16,200
whether the reaction is
spontaneous or not.

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00:06:16,200 --> 00:06:18,730
Then you can also hear people
talking about whether the

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00:06:18,730 --> 00:06:23,130
compound is labile or non-labile
or inert, and this

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00:06:23,130 --> 00:06:27,530
refers to the rate at which
that tendency is realized.

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00:06:27,530 --> 00:06:30,550
So you might have a very
unstable compound,

105
00:06:30,550 --> 00:06:34,370
thermodynamically it wants to
decompose, but it also might

106
00:06:34,370 --> 00:06:37,560
be very non-labile, it might
be fairly inert, that

107
00:06:37,560 --> 00:06:41,710
kinetically that decomposition
is going to take such a long

108
00:06:41,710 --> 00:06:46,730
amount of time, that you're
not going to notice the

109
00:06:46,730 --> 00:06:48,640
tendency to decompose.

110
00:06:48,640 --> 00:06:50,820
So, these two can play
off each other.

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00:06:50,820 --> 00:06:53,690
So, you can have materials
that are very unstable

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00:06:53,690 --> 00:06:56,030
thermodynamically, but you
won't really see them

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00:06:56,030 --> 00:07:00,980
decompose because the rate is
just way, way too slow.

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00:07:00,980 --> 00:07:03,320
So, you know for this particular
reaction, this is

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00:07:03,320 --> 00:07:07,960
how we get energy -- we make
ATP's of energy for the body.

116
00:07:07,960 --> 00:07:12,480
So it's slow, but in the body we
have to do something about

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00:07:12,480 --> 00:07:16,040
that because we need energy to
keep going, and so to be a

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00:07:16,040 --> 00:07:20,360
useful energy source, the
oxidation must be fast enough.

119
00:07:20,360 --> 00:07:23,520
So, does anyone know in the body
what happens to make that

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00:07:23,520 --> 00:07:26,420
reaction faster?

121
00:07:26,420 --> 00:07:28,010
Enzymes, right.

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00:07:28,010 --> 00:07:30,820
So, enzymes are catalysts
and they will

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00:07:30,820 --> 00:07:35,890
speed up the reaction.

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00:07:35,890 --> 00:07:39,190
So, let me just give
one more example.

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00:07:39,190 --> 00:07:42,520
Some of you may have heard the
commercial from deBeers, "a

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00:07:42,520 --> 00:07:45,740
diamond is forever." If you
haven't, you will probably

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00:07:45,740 --> 00:07:50,490
hear that quite often between
now and the Christmas season.

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00:07:50,490 --> 00:07:54,160
This is a very popular time, I
guess, for people to buy each

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00:07:54,160 --> 00:07:55,760
other diamonds.

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00:07:55,760 --> 00:07:59,250
But if you look at that the
thermodynamics of this,

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00:07:59,250 --> 00:08:02,220
graphite is actually much
more stable than

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00:08:02,220 --> 00:08:06,890
diamonds by 2,900 joules.

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00:08:06,890 --> 00:08:12,050
So, one could argue that
graphite is forever, not that

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00:08:12,050 --> 00:08:14,200
diamonds are forever.

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00:08:14,200 --> 00:08:19,000
Of course, here kinetics are
on the side of the diamond,

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00:08:19,000 --> 00:08:22,640
they're relatively kinetically
inert, it's a huge activation

137
00:08:22,640 --> 00:08:25,480
energy barrier, which we're
going to be talking about in

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00:08:25,480 --> 00:08:27,140
this unit for the conversion.

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00:08:27,140 --> 00:08:31,050
So, diamonds do, in fact, stay
around for a long time.

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00:08:31,050 --> 00:08:33,860
One could still argue that,
perhaps, a better gift would

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00:08:33,860 --> 00:08:38,100
be a graphite ring than a
diamond ring, but I have a

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00:08:38,100 --> 00:08:43,650
feeling that probably even if
the person receiving said ring

143
00:08:43,650 --> 00:08:49,490
was a chemist, they might still
not a 100% appreciate

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00:08:49,490 --> 00:08:51,280
that gesture.

145
00:08:51,280 --> 00:08:57,250
So, it's important, the
thermodynamics are important,

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00:08:57,250 --> 00:09:00,510
but kinetics are also really
important to understand what

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00:09:00,510 --> 00:09:06,750
kind of chemical reactions
are going to occur.

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00:09:06,750 --> 00:09:10,320
So, let's think about what are
some factors that would affect

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00:09:10,320 --> 00:09:17,310
rates of reactions.

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00:09:17,310 --> 00:09:20,500
So let's write down, and you can
think about what are some

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00:09:20,500 --> 00:09:31,300
factors affecting rates.

152
00:09:31,300 --> 00:09:33,850
What's one thing people can
think of that might affect the

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00:09:33,850 --> 00:09:35,010
rate of a reaction?

154
00:09:35,010 --> 00:09:37,020
STUDENT: Temperature.

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00:09:37,020 --> 00:09:44,760
PROFESSOR: Temperature,
definitely.

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00:09:44,760 --> 00:09:48,240
And this is used quite
often in cooking to

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00:09:48,240 --> 00:09:52,420
get things to occur.

158
00:09:52,420 --> 00:09:58,110
What else affects the
rate of a reaction?

159
00:09:58,110 --> 00:10:10,600
OK, yeah, so pressure could --
if you're changing things,

160
00:10:10,600 --> 00:10:14,060
applying pressure to sort
of switch things around.

161
00:10:14,060 --> 00:10:19,350
That will depend, say, for
pressure on the nature of the

162
00:10:19,350 --> 00:10:22,490
material and things like that of
what you're talking about.

163
00:10:22,490 --> 00:10:25,640
So let's make that a bigger
category and put

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00:10:25,640 --> 00:10:31,480
nature of the material.

165
00:10:31,480 --> 00:10:35,490
What type of material it is.

166
00:10:35,490 --> 00:10:39,460
And also, along with that, if
you're thinking about a

167
00:10:39,460 --> 00:10:42,590
particular reaction and how it's
going to go and how you

168
00:10:42,590 --> 00:10:46,060
might get it to sort of push one
way or the other, you're

169
00:10:46,060 --> 00:10:51,260
also thinking about the
mechanism of that reaction.

170
00:10:51,260 --> 00:10:57,700
So what's reacting with what
will make a difference.

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00:10:57,700 --> 00:11:05,630
I think I also heard someone
talk about concentration, how

172
00:11:05,630 --> 00:11:11,830
much of it you have. And you
told me the last one that

173
00:11:11,830 --> 00:11:13,620
we're going to talk about in
this unit, when we were

174
00:11:13,620 --> 00:11:18,840
talking about how the body gets
the oxidation of glucose

175
00:11:18,840 --> 00:11:22,240
to go, what was necessary
there?

176
00:11:22,240 --> 00:11:27,900
A catalyst, right.

177
00:11:27,900 --> 00:11:30,470
So, those are all the things
we're going to talk about in

178
00:11:30,470 --> 00:11:34,690
factors affecting rates of
reaction in this next unit.

179
00:11:34,690 --> 00:11:47,350
So now, chemistry is an
experimental science, and so a

180
00:11:47,350 --> 00:11:49,890
lot of kinetics are involved
with measuring

181
00:11:49,890 --> 00:11:52,320
the rates of reactions.

182
00:11:52,320 --> 00:11:54,790
So let's talk about how
one might measure

183
00:11:54,790 --> 00:11:56,100
the rate of a reaction.

184
00:11:56,100 --> 00:11:59,660
So here's a particular reaction,
we have n o 2 plus

185
00:11:59,660 --> 00:12:05,420
carbon monoxide, going to n o
plus carbon dioxide, and one

186
00:12:05,420 --> 00:12:11,690
could measure the rate of
decrease of the reactants or

187
00:12:11,690 --> 00:12:14,700
the amount of increase
of the products.

188
00:12:14,700 --> 00:12:16,990
So let's just look at
one of the products.

189
00:12:16,990 --> 00:12:21,780
So one might be plotting a
change in the concentration of

190
00:12:21,780 --> 00:12:25,370
one of the products
versus time.

191
00:12:25,370 --> 00:12:28,870
And you may find that it goes
up, and then maybe starts to

192
00:12:28,870 --> 00:12:32,300
level off a little
bit over time.

193
00:12:32,300 --> 00:12:35,380
And now, how are you going to
measure a rate out of this,

194
00:12:35,380 --> 00:12:38,820
the rate at which this
reaction is going?

195
00:12:38,820 --> 00:12:42,590
Well, one could measure an
average rate, which would be

196
00:12:42,590 --> 00:12:46,780
some change in concentration
over some change in

197
00:12:46,780 --> 00:12:50,470
the amount of time.

198
00:12:50,470 --> 00:12:54,140
And you could express that as
the change in concentration

199
00:12:54,140 --> 00:12:56,400
over the change in time.

200
00:12:56,400 --> 00:12:59,830
So, you could pick a particular
interval, say, we

201
00:12:59,830 --> 00:13:04,150
want to measure the average rate
from time is 50 seconds

202
00:13:04,150 --> 00:13:09,110
to time equals 150 seconds, and
we'll look at how much the

203
00:13:09,110 --> 00:13:13,690
concentration has changed
over that time interval.

204
00:13:13,690 --> 00:13:16,980
So, we can do a little
calculation of the average

205
00:13:16,980 --> 00:13:19,720
rate and get a number, 1 .

206
00:13:19,720 --> 00:13:24,530
2 8 times 10 to the minus 4
molar per second, and that's

207
00:13:24,530 --> 00:13:26,320
an average rate.

208
00:13:26,320 --> 00:13:28,720
But if we had picked at
different interval, we would

209
00:13:28,720 --> 00:13:30,200
have gotten a different
number.

210
00:13:30,200 --> 00:13:33,910
So the average rate depends on
the time interval, so that's

211
00:13:33,910 --> 00:13:35,740
not always ideal.

212
00:13:35,740 --> 00:13:38,290
You don't always want to know
an average rate, which might

213
00:13:38,290 --> 00:13:39,860
be different depending on which

214
00:13:39,860 --> 00:13:42,120
particular unit you pick.

215
00:13:42,120 --> 00:13:46,240
So often, when you're talking
about rates, you talk about

216
00:13:46,240 --> 00:13:48,190
instantaneous rates.

217
00:13:48,190 --> 00:13:51,670
So the rate at a particular
instance of time.

218
00:13:51,670 --> 00:13:55,050
And so let's look at
instantaneous rate.

219
00:13:55,050 --> 00:13:59,250
So, we have the same reaction,
same plot, but now we're going

220
00:13:59,250 --> 00:14:04,990
to be considering instead of the
average rate, the rate at

221
00:14:04,990 --> 00:14:08,500
a limit when your time interval
is going to zero --

222
00:14:08,500 --> 00:14:13,140
at a very, very small time
interval, so the rate at the

223
00:14:13,140 --> 00:14:15,370
particular instance.

224
00:14:15,370 --> 00:14:20,040
And so this can be expressed as
d times the concentration

225
00:14:20,040 --> 00:14:24,900
of a product, n o, over d t.

226
00:14:24,900 --> 00:14:30,090
So, as delta t approaches zero,
the rate becomes the

227
00:14:30,090 --> 00:14:34,820
slope of the line tangent to
the point, that particular

228
00:14:34,820 --> 00:14:39,240
time point that you're
interested in.

229
00:14:39,240 --> 00:14:40,670
So, let's find an

230
00:14:40,670 --> 00:14:43,570
instantaneous rate at 150 seconds.

231
00:14:43,570 --> 00:14:48,680
What is the rate of this
reaction at 150 seconds?

232
00:14:48,680 --> 00:14:53,160
So we can look for 150 seconds,
we can have a point

233
00:14:53,160 --> 00:14:56,150
on the curve at 150 seconds.

234
00:14:56,150 --> 00:15:00,220
And so as our time interval
approaches zero, the rate will

235
00:15:00,220 --> 00:15:03,250
approach the slope
of this line.

236
00:15:03,250 --> 00:15:07,720
So we can draw a slope that's
tangent to the curve at the

237
00:15:07,720 --> 00:15:11,930
time t, it's time 150 seconds,
and then we can calculate the

238
00:15:11,930 --> 00:15:14,760
slope of that line.

239
00:15:14,760 --> 00:15:20,230
And so we can do that math,
calculating the slope, and

240
00:15:20,230 --> 00:15:24,150
here we find that at an
instantaneous rate that time

241
00:15:24,150 --> 00:15:28,060
equals 150 seconds, change in
-- this is the slope of the

242
00:15:28,060 --> 00:15:30,840
line -- the change in
concentration over change in

243
00:15:30,840 --> 00:15:32,670
time, and that gives you 7 .

244
00:15:32,670 --> 00:15:36,410
7 times 10 to the minus
5 molar per second.

245
00:15:36,410 --> 00:15:41,020
So, that's instantaneous rate
at a particular time.

246
00:15:41,020 --> 00:15:43,390
What do you think the
instantaneous rate is called

247
00:15:43,390 --> 00:15:46,030
at time equals zero?

248
00:15:46,030 --> 00:15:48,130
Any guess?

249
00:15:48,130 --> 00:15:49,710
Initial rate, yeah.

250
00:15:49,710 --> 00:15:52,155
So, initial rate, instantaneous
rate at time

251
00:15:52,155 --> 00:15:53,980
equals zero seconds.

252
00:15:53,980 --> 00:15:58,660
So that's instantaneous rate.

253
00:15:58,660 --> 00:16:02,090
So now, let's talk about rate
expressions, and then we're

254
00:16:02,090 --> 00:16:04,300
going to talk about rate laws.

255
00:16:04,300 --> 00:16:05,830
So, same equation.

256
00:16:05,830 --> 00:16:08,950
Again, you can monitor how
much your reactants are

257
00:16:08,950 --> 00:16:12,440
disappearing, you can monitor
the amounts of your products

258
00:16:12,440 --> 00:16:15,420
being formed, and you
can express this in

259
00:16:15,420 --> 00:16:17,310
the following way.

260
00:16:17,310 --> 00:16:21,140
So we could say that the rate
is going to be equal to the

261
00:16:21,140 --> 00:16:24,435
decrease in one of the
reactants, so minus d times

262
00:16:24,435 --> 00:16:29,080
the concentration of
n o 2 over d t.

263
00:16:29,080 --> 00:16:33,640
We could also express it in
terms of the second reactant,

264
00:16:33,640 --> 00:16:38,380
so minus d times change in the
concentration of the other

265
00:16:38,380 --> 00:16:41,200
reactant over time.

266
00:16:41,200 --> 00:16:45,930
Or we can express this in terms
of the products being

267
00:16:45,930 --> 00:16:50,710
formed, so here there's no
negative sign, so we have d

268
00:16:50,710 --> 00:16:58,810
concentration of n o over d t,
or our last product, d times

269
00:16:58,810 --> 00:17:02,930
the concentration
of c o 2 d t.

270
00:17:02,930 --> 00:17:05,820
So this would be a rate
expression, and these would

271
00:17:05,820 --> 00:17:09,040
all be equal to each other,
if we make the following

272
00:17:09,040 --> 00:17:09,890
assumption.

273
00:17:09,890 --> 00:17:12,450
We're going to make the
assumption here that there's

274
00:17:12,450 --> 00:17:17,950
no intermediate species that's
being formed, or that if there

275
00:17:17,950 --> 00:17:22,760
are intermediate species, that
their change in concentration

276
00:17:22,760 --> 00:17:24,320
is independent of time.

277
00:17:24,320 --> 00:17:27,730
So if there were some other
really complicated thing going

278
00:17:27,730 --> 00:17:30,720
on here, then those rates may
not be equal and we might have

279
00:17:30,720 --> 00:17:34,320
something else in the mechanism
that would cause one

280
00:17:34,320 --> 00:17:36,740
thing to disappear a lot faster
than something else

281
00:17:36,740 --> 00:17:37,790
that's being formed.

282
00:17:37,790 --> 00:17:41,550
But these should all be equal if
you assume no intermediate

283
00:17:41,550 --> 00:17:44,030
species, or make assumptions
about those

284
00:17:44,030 --> 00:17:48,840
intermediate species.

285
00:17:48,840 --> 00:17:52,490
So, then the general expression
for a rate

286
00:17:52,490 --> 00:17:56,620
expression, if we have an
equation, a plus b going to c

287
00:17:56,620 --> 00:17:59,950
plus d, where we have
coefficients of the reaction,

288
00:17:59,950 --> 00:18:03,970
small a, coefficient small b,
coefficient small c, and

289
00:18:03,970 --> 00:18:05,870
coefficient small d.

290
00:18:05,870 --> 00:18:09,840
So we could express the overall
rate then, minus 1

291
00:18:09,840 --> 00:18:17,360
over a times d a t t minus 1
over b, d b d t, 1 over c, d c

292
00:18:17,360 --> 00:18:23,280
e t, 1 over d d d d d t.

293
00:18:23,280 --> 00:18:24,520
That was not easy.

294
00:18:24,520 --> 00:18:29,350
All right, so that's the general
form for the rate

295
00:18:29,350 --> 00:18:30,430
expression.

296
00:18:30,430 --> 00:18:33,480
So just to make sure that
everyone's on the same page,

297
00:18:33,480 --> 00:18:35,010
why don't you do a
rate expression

298
00:18:35,010 --> 00:19:10,890
for me for this one.

299
00:19:10,890 --> 00:19:25,360
OK, just 10 more seconds.

300
00:19:25,360 --> 00:19:29,760
Excellent.

301
00:19:29,760 --> 00:19:32,620
So you just have to pay
attention to your minus signs,

302
00:19:32,620 --> 00:19:37,540
your stoichiometry.

303
00:19:37,540 --> 00:19:40,680
So, it's minus for the
disappearance, stoichiometry 1

304
00:19:40,680 --> 00:19:45,620
over 2, and then no negatives
for your products of things

305
00:19:45,620 --> 00:19:48,410
that are appearing.

306
00:19:48,410 --> 00:19:48,920
Very good.

307
00:19:48,920 --> 00:19:52,490
Rate expressions, not
that complicated.

308
00:19:52,490 --> 00:19:54,930
All right, so now we're going to
talk about rate laws, which

309
00:19:54,930 --> 00:19:58,260
are slightly more complicated
than rate expressions.

310
00:19:58,260 --> 00:20:03,040
So, a rate law is -- you
come up with a rate law

311
00:20:03,040 --> 00:20:06,950
experimentally, and it's the
relationship between the rate

312
00:20:06,950 --> 00:20:09,600
and the concentration.

313
00:20:09,600 --> 00:20:12,250
So we have -- we're going to
introduce a term called the

314
00:20:12,250 --> 00:20:15,680
rate constant, which is
the small letter k.

315
00:20:15,680 --> 00:20:18,890
And so the rate constant is
going to tell you about the

316
00:20:18,890 --> 00:20:23,070
relationship between the rate
and the concentration of your

317
00:20:23,070 --> 00:20:27,710
reactants in a reaction.

318
00:20:27,710 --> 00:20:32,780
So, if we had that same reaction
here, we could also

319
00:20:32,780 --> 00:20:36,660
write that the rate is equal to
a rate constant times the

320
00:20:36,660 --> 00:20:41,900
concentration of your reactant,
a, raised to a power

321
00:20:41,900 --> 00:20:45,760
m, and b raised to a power n.

322
00:20:45,760 --> 00:20:50,370
So here, m and n are the order
of the reaction with respect

323
00:20:50,370 --> 00:20:55,530
to a and b respectively, so m
is the order of the reaction

324
00:20:55,530 --> 00:20:59,840
in a, and n is the order of
the reaction in b, and our

325
00:20:59,840 --> 00:21:04,850
small letter k here is
the rate constant.

326
00:21:04,850 --> 00:21:07,430
So that would be an expression
for rate law.

327
00:21:07,430 --> 00:21:09,670
And so, now I'm going to tell
you a lot of things that are

328
00:21:09,670 --> 00:21:14,030
true about rate laws.

329
00:21:14,030 --> 00:21:19,040
So, a rate law, again, comes
from experiment, so you can't

330
00:21:19,040 --> 00:21:23,220
just look at the stoichiometry
of the reaction and predict

331
00:21:23,220 --> 00:21:24,050
the rate law.

332
00:21:24,050 --> 00:21:28,370
So m is not the stoichiometry
of the reaction in terms of

333
00:21:28,370 --> 00:21:32,370
the a, that is, unless the
reaction is what we call an

334
00:21:32,370 --> 00:21:36,620
elementary reaction, or a step
in a reaction, and we're going

335
00:21:36,620 --> 00:21:39,620
to talk more about that next
week -- then you can, if it's

336
00:21:39,620 --> 00:21:41,750
an elementary reaction,
then you can use

337
00:21:41,750 --> 00:21:43,870
stoichiometry to predict.

338
00:21:43,870 --> 00:21:47,160
But for other reactions you
can't, and that'll become more

339
00:21:47,160 --> 00:21:51,700
clear next week when we talk
about this in detail.

340
00:21:51,700 --> 00:21:55,360
So, rate laws are not limited
to reactants, sometimes a

341
00:21:55,360 --> 00:21:56,610
product will show up.

342
00:21:56,610 --> 00:21:59,540
It's not that common, but it's
possible, and again, it's

343
00:21:59,540 --> 00:22:01,350
experimentally determined.

344
00:22:01,350 --> 00:22:05,210
So the experiment would have to
tell you whether that term

345
00:22:05,210 --> 00:22:06,850
is going to be there or not.

346
00:22:06,850 --> 00:22:13,450
So, occasionally you'll see a
product term in a rate law.

347
00:22:13,450 --> 00:22:19,440
So, in terms of m and n, the
orders of the reaction, m and

348
00:22:19,440 --> 00:22:25,030
n can be integers, they can be
whole numbers, or fractions,

349
00:22:25,030 --> 00:22:32,120
negative or positive, lots
of options for m and n.

350
00:22:32,120 --> 00:22:35,610
And let me tell you about all
the options for -- we're going

351
00:22:35,610 --> 00:22:37,440
to use m here.

352
00:22:37,440 --> 00:22:40,080
So, you have this table in
your notes, most of it is

353
00:22:40,080 --> 00:22:43,180
blank, some of it is filled in,
and we're going to fill in

354
00:22:43,180 --> 00:22:46,720
the parts that are not
filled in right now.

355
00:22:46,720 --> 00:22:50,530
So we're going to start in the
middle where the order of the

356
00:22:50,530 --> 00:22:56,470
reaction is one here, m equals
1, and that's called a first

357
00:22:56,470 --> 00:22:58,400
order reaction.

358
00:22:58,400 --> 00:23:01,570
So these names are pretty
much intuitive

359
00:23:01,570 --> 00:23:03,800
when you look at them.

360
00:23:03,800 --> 00:23:07,680
So here, the rate law for a
first order reaction would be

361
00:23:07,680 --> 00:23:14,490
our rate constant, k, times
the concentration of a.

362
00:23:14,490 --> 00:23:18,090
So let's think about what that
rate law would mean.

363
00:23:18,090 --> 00:23:21,640
Say you double the concentration
of a, what would

364
00:23:21,640 --> 00:23:27,210
happen to the rate
of the reaction?

365
00:23:27,210 --> 00:23:31,830
How many people say double,
raise your hand.

366
00:23:31,830 --> 00:23:33,260
Good, that's what happens.

367
00:23:33,260 --> 00:23:38,370
All right, so it doubled the
rate of the reaction.

368
00:23:38,370 --> 00:23:41,760
So now let's think
about m equals 2.

369
00:23:41,760 --> 00:23:44,730
See on your handout that that's
called second order --

370
00:23:44,730 --> 00:23:47,960
again these names make sense.

371
00:23:47,960 --> 00:23:54,080
The rate law for this would be k
times the concentration of a

372
00:23:54,080 --> 00:24:01,430
squared, so m equals 2, and
that's shown over here.

373
00:24:01,430 --> 00:24:04,740
If you double the
concentration of

374
00:24:04,740 --> 00:24:11,760
a, what would happen?

375
00:24:11,760 --> 00:24:18,840
So you should quadruple
the rate.

376
00:24:18,840 --> 00:24:21,880
So what about if you tripled
the concentration?

377
00:24:21,880 --> 00:24:24,930
Why don't you go ahead and tell
me if you triple it for m

378
00:24:24,930 --> 00:25:03,410
equals 2, what would
happen to the rate?

379
00:25:03,410 --> 00:25:16,870
OK, let's just take
10 more seconds.

380
00:25:16,870 --> 00:25:19,430
Excellent.

381
00:25:19,430 --> 00:25:23,430
That's right, 9 times.

382
00:25:23,430 --> 00:25:26,400
So, you're definitely getting
the hang of this.

383
00:25:26,400 --> 00:25:28,800
All right, so let's move
down and talk about m

384
00:25:28,800 --> 00:25:31,220
equals minus 1.

385
00:25:31,220 --> 00:25:33,600
If you think of a good name for
this let me know, because

386
00:25:33,600 --> 00:25:36,470
no one ever calls that
anything, so we

387
00:25:36,470 --> 00:25:38,980
can leave that blank.

388
00:25:38,980 --> 00:25:42,460
And go ahead and talk about what
the rate would be there

389
00:25:42,460 --> 00:25:45,580
and how we would write
the rate law.

390
00:25:45,580 --> 00:25:49,260
And so, the rate law, then,
would be k, our rate constant,

391
00:25:49,260 --> 00:25:52,570
times the concentration of
a raised to the minus 1.

392
00:25:52,570 --> 00:26:02,700
All right, if we double the
concentration here, just yell

393
00:26:02,700 --> 00:26:06,690
out what you think
would happen.

394
00:26:06,690 --> 00:26:10,110
You would 1/2 the rate of the
reaction, or you can think

395
00:26:10,110 --> 00:26:14,550
about as 2 to the minus 1, 1/2
the rate of the reaction.

396
00:26:14,550 --> 00:26:17,810
And you will have problems on
problem-set 10, which will be

397
00:26:17,810 --> 00:26:20,240
due a week from Friday where
you're going to be given

398
00:26:20,240 --> 00:26:23,420
experimental data, and you have
to look at it and see,

399
00:26:23,420 --> 00:26:26,350
OK, what happened to the rate,
and then what does that mean

400
00:26:26,350 --> 00:26:28,240
about the order of
the reaction.

401
00:26:28,240 --> 00:26:30,980
So this is a lot of what
the problems are

402
00:26:30,980 --> 00:26:35,280
like in this unit.

403
00:26:35,280 --> 00:26:39,430
All right, also there is no
name that I'm aware of for

404
00:26:39,430 --> 00:26:44,360
when n equals minus 1/2, but
we can write the rate law.

405
00:26:44,360 --> 00:26:47,750
So that's just going to be k
times the concentration of a

406
00:26:47,750 --> 00:26:52,150
raised to the minus 1/2 --
again, for the order of

407
00:26:52,150 --> 00:26:54,850
reaction, they can be integers,
they can be

408
00:26:54,850 --> 00:26:56,520
fractions, they can
be negative,

409
00:26:56,520 --> 00:26:59,050
and they can be positive.

410
00:26:59,050 --> 00:27:04,270
So, tell me for doubling the
concentration here of this

411
00:27:04,270 --> 00:27:44,830
one, what's going to
happen to the rate?

412
00:27:44,830 --> 00:27:59,560
OK, let's just take
10 more seconds.

413
00:27:59,560 --> 00:28:06,870
Yup, so most people
got that right.

414
00:28:06,870 --> 00:28:08,540
So, if we go back here, 0 .

415
00:28:08,540 --> 00:28:11,860
7 times the rate, you could
think about this as 2 raised

416
00:28:11,860 --> 00:28:13,140
to the minus 1/2.

417
00:28:13,140 --> 00:28:15,790
These get a little more
complicated and are some of

418
00:28:15,790 --> 00:28:18,590
the harder ones on the
problem-set to recognize the

419
00:28:18,590 --> 00:28:19,600
relationship.

420
00:28:19,600 --> 00:28:22,110
So if you remember all the
possibilities, it's going to

421
00:28:22,110 --> 00:28:25,380
help you think about what's
going on when you see the

422
00:28:25,380 --> 00:28:26,590
experimental data.

423
00:28:26,590 --> 00:28:32,040
All right, so let's go up to m
equals 1/2 here, and this one

424
00:28:32,040 --> 00:28:34,840
sometimes does have a name --
anyone want to guess what that

425
00:28:34,840 --> 00:28:38,040
one might be called?

426
00:28:38,040 --> 00:28:41,960
Half order, very good.

427
00:28:41,960 --> 00:28:46,490
So, half order, and so here our
rate, then, is going to be

428
00:28:46,490 --> 00:28:52,530
equal to k times a to the 1/2.

429
00:28:52,530 --> 00:28:55,540
So, if we double the
concentration here, what

430
00:28:55,540 --> 00:29:05,120
happens to the rate?

431
00:29:05,120 --> 00:29:15,400
Someone want to yell it out?

432
00:29:15,400 --> 00:29:16,160
So, 1 .

433
00:29:16,160 --> 00:29:20,080
4 times the rate.

434
00:29:20,080 --> 00:29:26,960
And m equals 0 -- any guess
of what that's called?

435
00:29:26,960 --> 00:29:31,440
Zero order.

436
00:29:31,440 --> 00:29:34,730
And the rate law here,
the rate is going

437
00:29:34,730 --> 00:29:37,480
to be equal to what?

438
00:29:37,480 --> 00:29:41,200
K, and that's it.

439
00:29:41,200 --> 00:29:43,660
So the rate equals k.

440
00:29:43,660 --> 00:29:46,990
So what does that mean -- if you
double the concentration,

441
00:29:46,990 --> 00:29:49,750
what happens to the rate?

442
00:29:49,750 --> 00:29:51,780
Yup, no effect on rate.

443
00:29:51,780 --> 00:29:54,800
So that's zero order -- the
concentration term, it doesn't

444
00:29:54,800 --> 00:29:59,920
matter what the concentration
is, and there will be some

445
00:29:59,920 --> 00:30:02,570
that you'll see on a problem-set
like that, so if

446
00:30:02,570 --> 00:30:06,810
there's no effect on rate,
you have a zero order.

447
00:30:06,810 --> 00:30:09,960
So those are the possibilities
that you will see for the

448
00:30:09,960 --> 00:30:13,470
order of reactions, and again,
you'll be given experimental

449
00:30:13,470 --> 00:30:16,840
data and have to figure out the
order of the reactions.

450
00:30:16,840 --> 00:30:19,630
And often, it's not just as
simple as one thing, there'll

451
00:30:19,630 --> 00:30:21,930
probably be two things in
there, so you'll have to

452
00:30:21,930 --> 00:30:24,150
figure out the order with
respect to both

453
00:30:24,150 --> 00:30:25,550
of those two things.

454
00:30:25,550 --> 00:30:29,740
So that makes it a little
more complicated.

455
00:30:29,740 --> 00:30:31,340
All right, a couple more
things that are

456
00:30:31,340 --> 00:30:34,370
true about rate laws.

457
00:30:34,370 --> 00:30:40,050
So the overall reaction order
is this sum of the exponents

458
00:30:40,050 --> 00:30:41,680
in the rate law.

459
00:30:41,680 --> 00:30:47,800
So then, if you had this rate
law, rate equals k times a to

460
00:30:47,800 --> 00:30:53,220
the 2, second order, and
b 1, the overall order

461
00:30:53,220 --> 00:30:55,960
for this would be?

462
00:30:55,960 --> 00:30:57,750
3.

463
00:30:57,750 --> 00:30:59,430
So, we have third order.

464
00:30:59,430 --> 00:31:02,540
Sum of 2 plus 1.

465
00:31:02,540 --> 00:31:05,470
So for this particular one, your
second order with respect

466
00:31:05,470 --> 00:31:12,830
to a, first order with respect
to b, third order overall.

467
00:31:12,830 --> 00:31:14,630
Units.

468
00:31:14,630 --> 00:31:17,470
Units for k are a lot of fun.

469
00:31:17,470 --> 00:31:21,120
So it depends on what the
reaction is, and often, for a

470
00:31:21,120 --> 00:31:24,590
problem, you'll have to figure
out what the units for k are,

471
00:31:24,590 --> 00:31:28,520
depending on are we talking
about molar per second or

472
00:31:28,520 --> 00:31:30,150
what's going on.

473
00:31:30,150 --> 00:31:34,560
So just pay attention to the
units for k, they can vary.

474
00:31:34,560 --> 00:31:37,110
And sometimes one of the
problems will be what are the

475
00:31:37,110 --> 00:31:40,930
units for this particular k, so
you'll have to figure that

476
00:31:40,930 --> 00:31:47,450
out per problem.

477
00:31:47,450 --> 00:31:51,410
So now, again, kinetics is
experimental -- we determine

478
00:31:51,410 --> 00:31:55,670
rate laws experimentally, and
sometimes this is not easy,

479
00:31:55,670 --> 00:32:00,120
because sometimes there'll be
very small changes that you're

480
00:32:00,120 --> 00:32:03,760
looking at, or those changes
will happen really quickly, so

481
00:32:03,760 --> 00:32:06,290
the interval of time
is very short.

482
00:32:06,290 --> 00:32:08,990
And sometimes when you're
trying to measure these

483
00:32:08,990 --> 00:32:12,180
changes, the reaction's
happening faster than your

484
00:32:12,180 --> 00:32:15,050
equipment can record
those changes.

485
00:32:15,050 --> 00:32:19,800
So this can be technically very
difficult, and so one

486
00:32:19,800 --> 00:32:24,240
thing that scientists do is they
use integrated rate laws.

487
00:32:24,240 --> 00:32:27,760
So in this way, you can
express concentrations

488
00:32:27,760 --> 00:32:30,840
directly as a function of time
and you don't have to worry so

489
00:32:30,840 --> 00:32:34,680
much now about measuring those
small amounts of changes that

490
00:32:34,680 --> 00:32:36,890
occur are very, very quickly.

491
00:32:36,890 --> 00:32:40,700
So let's talk about integrated
rate laws.

492
00:32:40,700 --> 00:32:44,800
And here, we're going to start
a derivation of an

493
00:32:44,800 --> 00:32:48,230
integrated rate law.

494
00:32:48,230 --> 00:32:51,410
So here's -- we're told this is
a first order reaction, and

495
00:32:51,410 --> 00:32:54,290
so we're going to do the first
order integrated rate law.

496
00:32:54,290 --> 00:32:58,310
And in this reaction, a is going
to b -- we can write a

497
00:32:58,310 --> 00:33:03,150
rate expression for this.
so we can talk about the

498
00:33:03,150 --> 00:33:08,030
disappearance minus
d a over d t.

499
00:33:08,030 --> 00:33:11,500
We can also now write the rate
law for a first order

500
00:33:11,500 --> 00:33:14,930
reaction, and we know that that
is our rate constant,

501
00:33:14,930 --> 00:33:18,710
small k, times the concentration
of a.

502
00:33:18,710 --> 00:33:21,510
So we know we can write the rate
expression, and we can

503
00:33:21,510 --> 00:33:25,840
write a rate law for this
first order reaction.

504
00:33:25,840 --> 00:33:30,010
So now, we can do
a derivation.

505
00:33:30,010 --> 00:33:32,430
So, in this derivation, we're
going to separate our

506
00:33:32,430 --> 00:33:35,780
concentration terms and our time
terms. So we're going to

507
00:33:35,780 --> 00:33:38,620
move everything with
concentration to one side, and

508
00:33:38,620 --> 00:33:41,910
things with time to
the other side.

509
00:33:41,910 --> 00:33:45,120
So, on one side, then, we can
have 1 over the concentration

510
00:33:45,120 --> 00:33:47,780
of a, we're going to bring
that down here.

511
00:33:47,780 --> 00:33:51,910
We have d a over here, and
then we have our negative

512
00:33:51,910 --> 00:33:57,130
sign, and our k over here, and
move d t also over to the

513
00:33:57,130 --> 00:33:58,650
other side.

514
00:33:58,650 --> 00:34:02,130
So now we have concentration
terms on one side and time

515
00:34:02,130 --> 00:34:05,600
terms on the other side.

516
00:34:05,600 --> 00:34:08,200
And now, as you might have
guessed from the name

517
00:34:08,200 --> 00:34:13,230
integrated rate laws, we can
integrate, and so we can look

518
00:34:13,230 --> 00:34:15,910
at the interval from the initial
concentration or

519
00:34:15,910 --> 00:34:19,410
original concentration of
a, to concentration of a

520
00:34:19,410 --> 00:34:21,190
at some time, t.

521
00:34:21,190 --> 00:34:27,330
And we can also look at from
some time, 0, to the time, t,

522
00:34:27,330 --> 00:34:30,380
in question.

523
00:34:30,380 --> 00:34:34,780
So there's that expression
again.

524
00:34:34,780 --> 00:34:37,860
Now you can write this
expression also in terms of

525
00:34:37,860 --> 00:34:39,660
natural log.

526
00:34:39,660 --> 00:34:42,940
So we can re-write this in terms
of the natural log of

527
00:34:42,940 --> 00:34:47,340
the concentration of a at time,
t, minus the natural log

528
00:34:47,340 --> 00:34:52,340
of the concentration of a at
our original time, or the

529
00:34:52,340 --> 00:34:58,990
original concentration,
equals minus k t.

530
00:34:58,990 --> 00:35:02,430
And you can also express it in
this term, so you can just

531
00:35:02,430 --> 00:35:06,310
bring this guy over to the other
side of the equation,

532
00:35:06,310 --> 00:35:09,680
and this is one expression for
the integrated rate law that

533
00:35:09,680 --> 00:35:10,830
you will see.

534
00:35:10,830 --> 00:35:13,640
There's also another expression
that you'll see,

535
00:35:13,640 --> 00:35:15,870
and let's show you
what that is.

536
00:35:15,870 --> 00:35:22,180
So you can also take the natural
log and bring these

537
00:35:22,180 --> 00:35:23,480
two terms together.

538
00:35:23,480 --> 00:35:26,970
So natural log of your
concentration of a at time t,

539
00:35:26,970 --> 00:35:30,540
over your original concentration
of a

540
00:35:30,540 --> 00:35:33,630
equals minus k t.

541
00:35:33,630 --> 00:35:36,580
And now you can take the inverse
natural log of both

542
00:35:36,580 --> 00:35:39,280
sides, so just your
concentration at time t over

543
00:35:39,280 --> 00:35:44,040
your initial concentration
equals e to the minus k t.

544
00:35:44,040 --> 00:35:48,690
And that expression is often
written in your book or on

545
00:35:48,690 --> 00:35:52,380
equation sheets as a
concentration at a particular

546
00:35:52,380 --> 00:35:57,910
time equals the concentration of
the original material, e to

547
00:35:57,910 --> 00:35:59,890
the minus k t.

548
00:35:59,890 --> 00:36:03,160
And these are the two
expressions that you'll see

549
00:36:03,160 --> 00:36:05,040
the most often.

550
00:36:05,040 --> 00:36:08,560
This one is often referred to as
your integrated first order

551
00:36:08,560 --> 00:36:13,180
rate law, whereas this
one is the equation

552
00:36:13,180 --> 00:36:15,020
for a straight line.

553
00:36:15,020 --> 00:36:19,250
So these two are the ones that
you will see the most often

554
00:36:19,250 --> 00:36:23,960
for integrated first
order rate laws.

555
00:36:23,960 --> 00:36:27,830
So one was an equation for a
straight line, so let's come

556
00:36:27,830 --> 00:36:29,840
up with a straight line.

557
00:36:29,840 --> 00:36:33,690
So if you plot your data,
if you've measured your

558
00:36:33,690 --> 00:36:38,470
concentration of a at various
times, you can take the

559
00:36:38,470 --> 00:36:41,210
natural log of those
concentrations that you

560
00:36:41,210 --> 00:36:45,040
measured and plot them
against time.

561
00:36:45,040 --> 00:36:48,650
And if you do this, and it is,
in fact, a first order

562
00:36:48,650 --> 00:36:51,730
reaction, you should get
a straight line.

563
00:36:51,730 --> 00:36:55,750
So here, we can look at this in
terms of a straight line,

564
00:36:55,750 --> 00:36:59,800
so on y-axis, we have the
natural log of the

565
00:36:59,800 --> 00:37:03,700
concentration of a at a
particular time, and that's

566
00:37:03,700 --> 00:37:08,610
plotted against time, over
here in seconds.

567
00:37:08,610 --> 00:37:12,570
And so, what does that mean in
terms of what is this, what is

568
00:37:12,570 --> 00:37:21,020
the intercept here?

569
00:37:21,020 --> 00:37:22,190
Yup.

570
00:37:22,190 --> 00:37:25,240
So the natural log of your
initial original

571
00:37:25,240 --> 00:37:27,190
concentration of a.

572
00:37:27,190 --> 00:37:30,880
And what is the slope
of this line?

573
00:37:30,880 --> 00:37:35,730
The slope is negative k, and
so the slope is really what

574
00:37:35,730 --> 00:37:37,100
people are after.

575
00:37:37,100 --> 00:37:40,770
So often what you want to do is
measure rate constants for

576
00:37:40,770 --> 00:37:47,890
particular reactions, and if
you can then measure the

577
00:37:47,890 --> 00:37:50,860
concentration of a at particular
times and plot it

578
00:37:50,860 --> 00:37:54,270
this way, you can come out
with your rate constant.

579
00:37:54,270 --> 00:37:56,650
And that's what you want to
know, and those are some of

580
00:37:56,650 --> 00:37:58,280
the problems that you're
going to see.

581
00:37:58,280 --> 00:38:00,390
Are you going to see
experimental data for what

582
00:38:00,390 --> 00:38:04,200
happens to rate at particular
concentrations, and you can

583
00:38:04,200 --> 00:38:11,390
come up with values for
your rate constants.

584
00:38:11,390 --> 00:38:17,660
So, let's talk about one other
thing, which is half life.

585
00:38:17,660 --> 00:38:21,400
So people are often very
concerned with half life.

586
00:38:21,400 --> 00:38:25,440
When do you hear about
half life a lot?

587
00:38:25,440 --> 00:38:27,930
Does anyone know?

588
00:38:27,930 --> 00:38:30,480
Yeah, when we talk about
radioactivity, which we'll be

589
00:38:30,480 --> 00:38:33,460
talking about next class.

590
00:38:33,460 --> 00:38:36,620
They're very concerned about
the half life, which is the

591
00:38:36,620 --> 00:38:39,830
time it takes for the full
amount of your original

592
00:38:39,830 --> 00:38:46,460
material to be reduced
by a 1/2.

593
00:38:46,460 --> 00:38:50,330
So we can look at an equation
that we had up above for our

594
00:38:50,330 --> 00:38:54,520
integrated first order half
life, and we can think about

595
00:38:54,520 --> 00:38:58,260
this in terms of a half
life expression.

596
00:38:58,260 --> 00:39:03,610
So here, t has a particular
special meaning -- we have t,

597
00:39:03,610 --> 00:39:07,770
1/2, which is the abbreviation
for half life.

598
00:39:07,770 --> 00:39:11,500
And so half life by definition
is the amount of time it takes

599
00:39:11,500 --> 00:39:14,870
for the original concentration
to be reduced by 1/2.

600
00:39:14,870 --> 00:39:18,740
So here we have our final
concentration, concentration

601
00:39:18,740 --> 00:39:20,390
of a at a time t.

602
00:39:20,390 --> 00:39:25,080
So when we're talking about half
life, we're going to have

603
00:39:25,080 --> 00:39:28,180
1/2 as much as we had
when we started.

604
00:39:28,180 --> 00:39:33,490
So our a t is going to be our
original divided by 2, 1/2 the

605
00:39:33,490 --> 00:39:36,700
amount we had in
the beginning.

606
00:39:36,700 --> 00:39:41,930
And so, now t has a special
name, it's t to the 1/2 here.

607
00:39:41,930 --> 00:39:46,930
So now we can simplify this
expression to come up with an

608
00:39:46,930 --> 00:39:52,620
expression for half life for
a first order reaction.

609
00:39:52,620 --> 00:39:57,790
So, the a to the 0, our original
concentrations cancel

610
00:39:57,790 --> 00:40:01,280
out, and so we have the natural
log of 1/2 equals

611
00:40:01,280 --> 00:40:07,480
minus k, our rate constant,
times t 1/2.

612
00:40:07,480 --> 00:40:10,700
The natural log of
1/2 is minus 0 .

613
00:40:10,700 --> 00:40:13,810
6 9 3 1.

614
00:40:13,810 --> 00:40:19,540
We can get rid of our negative
signs and solve for t 1/2,

615
00:40:19,540 --> 00:40:21,950
because this is a half
life expression, so t

616
00:40:21,950 --> 00:40:23,640
1/2 equals 0 .

617
00:40:23,640 --> 00:40:28,670
6 9 3 1 over k.

618
00:40:28,670 --> 00:40:34,410
So that's an expression just for
a first order half life.

619
00:40:34,410 --> 00:40:37,730
And notice that half life
does not depend on

620
00:40:37,730 --> 00:40:39,000
concentration here.

621
00:40:39,000 --> 00:40:42,030
That term dropped out.

622
00:40:42,030 --> 00:40:46,220
So half life depends on our
rate constant, k, and k

623
00:40:46,220 --> 00:40:48,550
depends on the material
in question.

624
00:40:48,550 --> 00:40:53,480
So, for radioactive material,
some radioactive materials

625
00:40:53,480 --> 00:40:57,980
have short half lifes, so their
k's are very different

626
00:40:57,980 --> 00:41:00,730
from each other, and so that
can be very important,

627
00:41:00,730 --> 00:41:02,450
especially when you're thinking
about storing

628
00:41:02,450 --> 00:41:05,330
radioactive waste.

629
00:41:05,330 --> 00:41:11,110
So, using that value, tell me,
for the same material then,

630
00:41:11,110 --> 00:41:15,530
does it take longer to go from
1 ton to a 1/2 ton, or from 1

631
00:41:15,530 --> 00:41:43,180
gram to 1/2 gram?

632
00:41:43,180 --> 00:41:57,670
Let's just take 10
more seconds.

633
00:41:57,670 --> 00:42:01,220
Yup, it takes the same
amount of time.

634
00:42:01,220 --> 00:42:06,110
And then just to finish up here,
we have one more thing

635
00:42:06,110 --> 00:42:07,900
to do and then we're done.

636
00:42:07,900 --> 00:42:11,790
So here, in a plot for a first
order half life, the

637
00:42:11,790 --> 00:42:17,950
concentration of the material
at the first half life has

638
00:42:17,950 --> 00:42:22,040
dropped by how much?

639
00:42:22,040 --> 00:42:22,860
1/2.

640
00:42:22,860 --> 00:42:25,020
At the second half
life is what?

641
00:42:25,020 --> 00:42:30,380
STUDENT: 1/4.

642
00:42:30,380 --> 00:42:34,120
PROFESSOR: And the
third half life?

643
00:42:34,120 --> 00:42:34,450
STUDENT: 1/8

644
00:42:34,450 --> 00:42:38,900
PROFESSOR: Yup, so that's
first order half life.

645
00:42:38,900 --> 00:42:40,790
All right, everybody, have
a happy Thanksgiving.