1
00:00:00 --> 00:00:01
 
 

2
00:00:01 --> 00:00:02
The following content is
provided under a Creative

3
00:00:02 --> 00:00:03
Commons license.
 

4
00:00:03 --> 00:00:06
Your support will help MIT
OpenCourseWare continue to

5
00:00:06 --> 00:00:10
offer high-quality educational
resources for free.

6
00:00:10 --> 00:00:13
To make a donation or view
additional materials from

7
00:00:13 --> 00:00:15
hundreds of MIT courses,
visit MIT OpenCourseWare

8
00:00:15 --> 00:00:17
at ocw.mit.edu.
 

9
00:00:17 --> 00:00:21
PROFESSOR: All right.
 

10
00:00:21 --> 00:00:27
So today we're starting the
last unit of this class,

11
00:00:27 --> 00:00:28
which is kinetics.
 

12
00:00:28 --> 00:00:33
So, we're moving toward the end
of the semester, and today will

13
00:00:33 --> 00:00:36
just be an introductory
lecture on kinetics.

14
00:00:36 --> 00:00:40
So, again, kinetics are the
rates of chemical reactions,

15
00:00:40 --> 00:00:42
and so we're going to talk
about, we're going to introduce

16
00:00:42 --> 00:00:46
you to rate expressions
and rate laws.

17
00:00:46 --> 00:00:49
So, when you're considering a
chemical reaction, we've been

18
00:00:49 --> 00:00:52
asking so far in this class
whether the reaction

19
00:00:52 --> 00:00:54
will go spontaneously.
 

20
00:00:54 --> 00:00:57
So we've been talking a lot
about thermodynamics, we've

21
00:00:57 --> 00:00:59
been talking a lot
about delta g.

22
00:00:59 --> 00:01:02
But we also need to consider
how fast a reaction goes,

23
00:01:02 --> 00:01:04
and that's kinetics.
 

24
00:01:04 --> 00:01:07
So, a kinetic experiment is one
in which you measure the rate

25
00:01:07 --> 00:01:09
at which something's happening.
 

26
00:01:09 --> 00:01:12
The rate at which a
concentration is disappearing

27
00:01:12 --> 00:01:15
or whether the rate at which a
concentration is forming.

28
00:01:15 --> 00:01:19
You're measuring some kind of
change of a reaction, change

29
00:01:19 --> 00:01:24
in composition versus time.
 

30
00:01:24 --> 00:01:27
So, I'm going to give, for
an example, of why kinetics

31
00:01:27 --> 00:01:31
are important talking about
the oxidation of glucose.

32
00:01:31 --> 00:01:34
And I'm going to ask --
we're going to do a little

33
00:01:34 --> 00:01:37
experiment, and I'm going to
ask the TA's to help me.

34
00:01:37 --> 00:01:42
Everyone needs to have
something to do an experiment

35
00:01:42 --> 00:01:45
with, something that might
have some glucose in it

36
00:01:45 --> 00:01:47
to do this experiment.
 

37
00:01:47 --> 00:01:51
So, if the TA's could help
me hand out the ingredients

38
00:01:51 --> 00:01:56
for this experiment.
 

39
00:01:56 --> 00:02:06
So, don't open your
experimental apparatus

40
00:02:06 --> 00:02:09
until I give the OK.
 

41
00:02:09 --> 00:02:13
So, just collect it and let me
set up the experiment for you

42
00:02:13 --> 00:02:24
while we're handing things out.
 

43
00:02:24 --> 00:02:28
So you're all familiar with
this reaction, so we have

44
00:02:28 --> 00:02:36
glucose and oxygen go
to c o 2 and water.

45
00:02:36 --> 00:02:42
And so we've talked a lot about
delta g for this reaction, and

46
00:02:42 --> 00:02:51
delta g again, is equal to
delta h minus t delta s.

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

48
00:02:55 --> 00:02:59
delta h nought, so what does
negative delta h mean

49
00:02:59 --> 00:03:03
about this reaction?
 

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

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

52
00:03:12 --> 00:03:15
delta s nought is positive?
 

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

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

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

56
00:03:29 --> 00:03:33
So, in terms of thermodynamics,
what does this mean?

57
00:03:33 --> 00:03:36
Is this reaction spontaneous?
 

58
00:03:36 --> 00:03:39
Yes, it's very spontaneous,
it's very thermodynamically

59
00:03:39 --> 00:03:41
favorable.
 

60
00:03:41 --> 00:03:45
Now, when glucose in products
are wrapped, they're often

61
00:03:45 --> 00:03:49
wrapped under a nitrogen
environment, so, oxygen is not

62
00:03:49 --> 00:03:54
sealed up in this container, in
the wrapper, and they do that

63
00:03:54 --> 00:03:57
to prevent bacterial
contamination and

64
00:03:57 --> 00:03:58
things like that.
 

65
00:03:58 --> 00:04:03
So, the glucose that would
be in a wrapped candy is

66
00:04:03 --> 00:04:05
not exposed to oxygen.
 

67
00:04:05 --> 00:04:08
And so if you look at this
thermodynamic information up

68
00:04:08 --> 00:04:14
here, one might imagine that if
you ripped this open, and

69
00:04:14 --> 00:04:18
oxygen came in, that there
might be some kind of level of

70
00:04:18 --> 00:04:23
explosion with c o 2 coming
out and water coming out.

71
00:04:23 --> 00:04:26
Now, you know, you might say
well, if you have one sort of

72
00:04:26 --> 00:04:30
little thing it might not, but
now if everyone has one, and we

73
00:04:30 --> 00:04:37
all open it at the same time,
what do you expect to happen?

74
00:04:37 --> 00:04:41
Let's try it.
 

75
00:04:41 --> 00:04:45
Oh, we need some
more down here.

76
00:04:45 --> 00:04:54
Anybody else need any?
 

77
00:04:54 --> 00:04:59
All right, so I'm trying mine,
and I'm not really noticing

78
00:04:59 --> 00:05:04
anything happening.
 

79
00:05:04 --> 00:05:08
So the situation is the
following, It is a spontaneous

80
00:05:08 --> 00:05:12
reaction, but it's slow.
 

81
00:05:12 --> 00:05:19
So here, kinetics
are very important.

82
00:05:19 --> 00:05:23
So, how many of you are having
Thanksgiving with a small child

83
00:05:23 --> 00:05:26
around, younger siblings
or something like that?

84
00:05:26 --> 00:05:30
When you see them eat a lot of
sugar, which can happen over

85
00:05:30 --> 00:05:35
Thanksgiving, it sometimes
seems like an explosion has

86
00:05:35 --> 00:05:38
occurred, that there's all of a
sudden hyper energy

87
00:05:38 --> 00:05:39
running around.
 

88
00:05:39 --> 00:05:44
But that could be due to this
reaction biochemically, getting

89
00:05:44 --> 00:05:48
a lot of energy into the
system, but probably you will

90
00:05:48 --> 00:05:53
not see c o 2 and water coming
off of the small child

91
00:05:53 --> 00:05:57
as they run around.
 

92
00:05:57 --> 00:06:00
So, let me introduce you to
a couple of terms, if you

93
00:06:00 --> 00:06:02
haven't heard these already.
 

94
00:06:02 --> 00:06:05
So people are often talking
about compounds being

95
00:06:05 --> 00:06:07
stable or unstable.
 

96
00:06:07 --> 00:06:09
When they're doing this,
they're talking about the

97
00:06:09 --> 00:06:12
thermodynamics of a system,
the tendency to decompose,

98
00:06:12 --> 00:06:16
whether the reaction
is spontaneous or not.

99
00:06:16 --> 00:06:18
Then you can also hear people
talking about whether the

100
00:06:18 --> 00:06:23
compound is labile or
non-labile or inert, and this

101
00:06:23 --> 00:06:27
refers to the rate at which
that tendency is realized.

102
00:06:27 --> 00:06:30
So you might have a very
unstable compound,

103
00:06:30 --> 00:06:34
thermodynamically it wants to
decompose, but it also might be

104
00:06:34 --> 00:06:38
very non-labile, it might be
fairly inert, that kinetically

105
00:06:38 --> 00:06:42
that decomposition is going to
take such a long amount of

106
00:06:42 --> 00:06:47
time, that you're not going to
notice the tendency

107
00:06:47 --> 00:06:48
to decompose.
 

108
00:06:48 --> 00:06:50
So, these two can
play off each other.

109
00:06:50 --> 00:06:53
So, you can have materials that
are very unstable

110
00:06:53 --> 00:06:56
thermodynamically, but you
won't really see them decompose

111
00:06:56 --> 00:07:00
because the rate is just
way, way too slow.

112
00:07:00 --> 00:07:03
So, you know for this
particular reaction, this is

113
00:07:03 --> 00:07:07
how we get energy -- we make
ATP's of energy for the body.

114
00:07:07 --> 00:07:12
So it's slow, but in the body
we have to do something about

115
00:07:12 --> 00:07:16
that because we need energy to
keep going, and so to be a

116
00:07:16 --> 00:07:20
useful energy source, the
oxidation must be fast enough.

117
00:07:20 --> 00:07:23
So, does anyone know in the
body what happens to make

118
00:07:23 --> 00:07:26
that reaction faster?
 

119
00:07:26 --> 00:07:28
Enzymes, right.
 

120
00:07:28 --> 00:07:31
So, enzymes are catalysts
and they will speed

121
00:07:31 --> 00:07:35
up the reaction.
 

122
00:07:35 --> 00:07:39
So, let me just give
one more example.

123
00:07:39 --> 00:07:42
Some of you may have heard the
commercial from deBeers, "a

124
00:07:42 --> 00:07:46
diamond is forever." If you
haven't, you will probably hear

125
00:07:46 --> 00:07:50
that quite often between now
and the Christmas season.

126
00:07:50 --> 00:07:53
This is a very popular time,
I guess, for people to

127
00:07:53 --> 00:07:55
buy each other diamonds.
 

128
00:07:55 --> 00:07:59
But if you look at that the
thermodynamics of this,

129
00:07:59 --> 00:08:03
graphite is actually much
more stable than diamonds

130
00:08:03 --> 00:08:06
by 2,900 joules.
 

131
00:08:06 --> 00:08:11
So, one could argue that
graphite is forever, not

132
00:08:11 --> 00:08:14
that diamonds are forever.
 

133
00:08:14 --> 00:08:19
Of course, here kinetics are
on the side of the diamond,

134
00:08:19 --> 00:08:22
they're relatively kinetically
inert, it's a huge activation

135
00:08:22 --> 00:08:25
energy barrier, which we're
going to be talking about in

136
00:08:25 --> 00:08:27
this unit for the conversion.
 

137
00:08:27 --> 00:08:31
So, diamonds do, in fact,
stay around for a long time.

138
00:08:31 --> 00:08:34
One could still argue that,
perhaps, a better gift would be

139
00:08:34 --> 00:08:40
a graphite ring than a diamond
ring, but I have a feeling that

140
00:08:40 --> 00:08:44
probably even if the person
receiving said ring was a

141
00:08:44 --> 00:08:51
chemist, they might still not a
100% appreciate that gesture.

142
00:08:51 --> 00:08:57
So, it's important, the
thermodynamics are important,

143
00:08:57 --> 00:09:00
but kinetics are also really
important to understand what

144
00:09:00 --> 00:09:06
kind of chemical reactions
are going to occur.

145
00:09:06 --> 00:09:09
So, let's think about what
are some factors that would

146
00:09:09 --> 00:09:17
affect rates of reactions.
 

147
00:09:17 --> 00:09:20
So let's write down, and you
can think about what are some

148
00:09:20 --> 00:09:31
factors affecting rates.
 

149
00:09:31 --> 00:09:33
What's one thing people can
think of that might affect

150
00:09:33 --> 00:09:35
the rate of a reaction?
 

151
00:09:35 --> 00:09:37
STUDENT: Temperature.
 

152
00:09:37 --> 00:09:44
PROFESSOR: Temperature,
definitely.

153
00:09:44 --> 00:09:52
And this is used quite often in
cooking to get things to occur.

154
00:09:52 --> 00:09:58
What else affects the
rate of a reaction?

155
00:09:58 --> 00:10:10
OK, yeah, so pressure could --
if you're changing things,

156
00:10:10 --> 00:10:14
applying pressure to sort
of switch things around.

157
00:10:14 --> 00:10:19
That will depend, say, for
pressure on the nature of the

158
00:10:19 --> 00:10:22
material and things like that
of what you're talking about.

159
00:10:22 --> 00:10:25
So let's make that a bigger
category and put nature

160
00:10:25 --> 00:10:31
of the material.
 

161
00:10:31 --> 00:10:35
What type of material it is.
 

162
00:10:35 --> 00:10:39
And also, along with that, if
you're thinking about a

163
00:10:39 --> 00:10:42
particular reaction and how
it's going to go and how you

164
00:10:42 --> 00:10:46
might get it to sort of push
one way or the other, you're

165
00:10:46 --> 00:10:51
also thinking about the
mechanism of that reaction.

166
00:10:51 --> 00:10:57
So what's reacting with what
will make a difference.

167
00:10:57 --> 00:11:05
I think I also heard someone
talk about concentration,

168
00:11:05 --> 00:11:09
how much of it you have.
 

169
00:11:09 --> 00:11:12
And you told me the last one
that we're going to talk about

170
00:11:12 --> 00:11:17
in this unit, when we were
talking about how the body gets

171
00:11:17 --> 00:11:22
the oxidation of glucose to
go, what was necessary there?

172
00:11:22 --> 00:11:27
A catalyst, right.
 

173
00:11:27 --> 00:11:30
So, those are all the things
we're going to talk about in

174
00:11:30 --> 00:11:34
factors affecting rates of
reaction in this next unit.

175
00:11:34 --> 00:11:46
So now, chemistry is an
experimental science, and

176
00:11:46 --> 00:11:49
so a lot of kinetics are
involved with measuring

177
00:11:49 --> 00:11:52
the rates of reactions.
 

178
00:11:52 --> 00:11:54
So let's talk about how
one might measure the

179
00:11:54 --> 00:11:56
rate of a reaction.
 

180
00:11:56 --> 00:11:59
So here's a particular
reaction, we have n o 2 plus

181
00:11:59 --> 00:12:05
carbon monoxide, going to n o
plus carbon dioxide, and one

182
00:12:05 --> 00:12:11
could measure the rate of
decrease of the reactants or

183
00:12:11 --> 00:12:14
the amount of increase
of the products.

184
00:12:14 --> 00:12:16
So let's just look at
one of the products.

185
00:12:16 --> 00:12:21
So one might be plotting a
change in the concentration

186
00:12:21 --> 00:12:25
of one of the
products versus time.

187
00:12:25 --> 00:12:28
And you may find that it goes
up, and then maybe starts to

188
00:12:28 --> 00:12:32
level off a little
bit over time.

189
00:12:32 --> 00:12:35
And now, how are you going to
measure a rate out of this,

190
00:12:35 --> 00:12:38
the rate at which this
reaction is going?

191
00:12:38 --> 00:12:42
Well, one could measure an
average rate, which would be

192
00:12:42 --> 00:12:46
some change in concentration
over some change in

193
00:12:46 --> 00:12:50
the amount of time.
 

194
00:12:50 --> 00:12:54
And you could express that as
the change in concentration

195
00:12:54 --> 00:12:56
over the change in time.
 

196
00:12:56 --> 00:13:00
So, you could pick a particular
interval, say, we want to

197
00:13:00 --> 00:13:04
measure the average rate from
time is 50 seconds to time

198
00:13:04 --> 00:13:09
equals 150 seconds, and
we'll look at how much the

199
00:13:09 --> 00:13:13
concentration has changed
over that time interval.

200
00:13:13 --> 00:13:16
So, we can do a little
calculation of the average

201
00:13:16 --> 00:13:19
rate and get a number, 1 .
 

202
00:13:19 --> 00:13:24
2 8 times 10 to the minus
4 molar per second, and

203
00:13:24 --> 00:13:26
that's an average rate.
 

204
00:13:26 --> 00:13:28
But if we had picked at
different interval, we would

205
00:13:28 --> 00:13:30
have gotten a different number.
 

206
00:13:30 --> 00:13:33
So the average rate depends
on the time interval, so

207
00:13:33 --> 00:13:35
that's not always ideal.
 

208
00:13:35 --> 00:13:38
You don't always want to know
an average rate, which might be

209
00:13:38 --> 00:13:42
different depending on which
particular unit you pick.

210
00:13:42 --> 00:13:45
So often, when you're talking
about rates, you talk

211
00:13:45 --> 00:13:48
about instantaneous rates.
 

212
00:13:48 --> 00:13:51
So the rate at a particular
instance of time.

213
00:13:51 --> 00:13:55
And so let's look at
instantaneous rate.

214
00:13:55 --> 00:13:59
So, we have the same reaction,
same plot, but now we're going

215
00:13:59 --> 00:14:05
to be considering instead of
the average rate, the rate at a

216
00:14:05 --> 00:14:09
limit when your time interval
is going to zero -- at a very,

217
00:14:09 --> 00:14:13
very small time interval,
so the rate at the

218
00:14:13 --> 00:14:15
particular instance.
 

219
00:14:15 --> 00:14:20
And so this can be expressed as
d times the concentration of

220
00:14:20 --> 00:14:24
a product, n o, over d t.
 

221
00:14:24 --> 00:14:30
So, as delta t approaches zero,
the rate becomes the slope of

222
00:14:30 --> 00:14:35
the line tangent to the point,
that particular time point

223
00:14:35 --> 00:14:39
that you're interested in.
 

224
00:14:39 --> 00:14:43
So, let's find an instantaneous
rate at 150 seconds.

225
00:14:43 --> 00:14:48
What is the rate of this
reaction at 150 seconds?

226
00:14:48 --> 00:14:53
So we can look for 150 seconds,
we can have a point on

227
00:14:53 --> 00:14:56
the curve at 150 seconds.
 

228
00:14:56 --> 00:14:59
And so as our time interval
approaches zero, the

229
00:14:59 --> 00:15:03
rate will approach the
slope of this line.

230
00:15:03 --> 00:15:07
So we can draw a slope that's
tangent to the curve at the

231
00:15:07 --> 00:15:11
time t, it's time 150 seconds,
and then we can calculate

232
00:15:11 --> 00:15:14
the slope of that line.
 

233
00:15:14 --> 00:15:20
And so we can do that math,
calculating the slope, and

234
00:15:20 --> 00:15:24
here we find that at an
instantaneous rate that time

235
00:15:24 --> 00:15:28
equals 150 seconds, change
in -- this is the slope of

236
00:15:28 --> 00:15:30
the line -- the change in
concentration over change in

237
00:15:30 --> 00:15:32
time, and that gives you 7 .
 

238
00:15:32 --> 00:15:36
7 times 10 to the minus
5 molar per second.

239
00:15:36 --> 00:15:41
So, that's instantaneous
rate at a particular time.

240
00:15:41 --> 00:15:43
What do you think the
instantaneous rate is called

241
00:15:43 --> 00:15:46
at time equals zero?
 

242
00:15:46 --> 00:15:48
Any guess?
 

243
00:15:48 --> 00:15:49
Initial rate, yeah.
 

244
00:15:49 --> 00:15:52
So, initial rate, instantaneous
rate at time equals

245
00:15:52 --> 00:15:53
zero seconds.
 

246
00:15:53 --> 00:15:58
So that's instantaneous rate.
 

247
00:15:58 --> 00:16:02
So now, let's talk about rate
expressions, and then we're

248
00:16:02 --> 00:16:04
going to talk about rate laws.
 

249
00:16:04 --> 00:16:05
So, same equation.
 

250
00:16:05 --> 00:16:08
Again, you can monitor how
much your reactants are

251
00:16:08 --> 00:16:12
disappearing, you can monitor
the amounts of your products

252
00:16:12 --> 00:16:15
being formed, and you can
express this in the

253
00:16:15 --> 00:16:17
following way.
 

254
00:16:17 --> 00:16:21
So we could say that the rate
is going to be equal to the

255
00:16:21 --> 00:16:24
decrease in one of the
reactants, so minus d

256
00:16:24 --> 00:16:29
times the concentration
of n o 2 over d t.

257
00:16:29 --> 00:16:33
We could also express it in
terms of the second reactant,

258
00:16:33 --> 00:16:38
so minus d times change in
the concentration of the

259
00:16:38 --> 00:16:41
other reactant over time.
 

260
00:16:41 --> 00:16:46
Or we can express this in terms
of the products being formed,

261
00:16:46 --> 00:16:50
so here there's no negative
sign, so we have d

262
00:16:50 --> 00:16:58
concentration of n o over d t,
or our last product, d times

263
00:16:58 --> 00:17:02
the concentration of c o 2 d t.
 

264
00:17:02 --> 00:17:06
So this would be a rate
expression, and these would all

265
00:17:06 --> 00:17:09
be equal to each other, if we
make the following assumption.

266
00:17:09 --> 00:17:12
We're going to make the
assumption here that there's no

267
00:17:12 --> 00:17:17
intermediate species that's
being formed, or that if there

268
00:17:17 --> 00:17:22
are intermediate species, that
their change in concentration

269
00:17:22 --> 00:17:24
is independent of time.
 

270
00:17:24 --> 00:17:27
So if there were some other
really complicated thing going

271
00:17:27 --> 00:17:30
on here, then those rates may
not be equal and we might have

272
00:17:30 --> 00:17:34
something else in the mechanism
that would cause one thing to

273
00:17:34 --> 00:17:36
disappear a lot faster than
something else that's

274
00:17:36 --> 00:17:37
being formed.
 

275
00:17:37 --> 00:17:41
But these should all be equal
if you assume no intermediate

276
00:17:41 --> 00:17:44
species, or make
assumptions about those

277
00:17:44 --> 00:17:48
intermediate species.
 

278
00:17:48 --> 00:17:53
So, then the general expression
for a rate expression, if we

279
00:17:53 --> 00:17:58
have an equation, a plus b
going to c plus d, where we

280
00:17:58 --> 00:18:01
have coefficients of the
reaction, small a, coefficient

281
00:18:01 --> 00:18:05
small b, coefficient small c,
and coefficient small d.

282
00:18:05 --> 00:18:11
So we could express the overall
rate then, minus 1 over a times

283
00:18:11 --> 00:18:18
d a t t minus 1 over b, d b d
t, 1 over c, d c e t,

284
00:18:18 --> 00:18:23
1 over d d d d d t.
 

285
00:18:23 --> 00:18:24
That was not easy.
 

286
00:18:24 --> 00:18:29
All right, so that's the
general form for the

287
00:18:29 --> 00:18:30
rate expression.
 

288
00:18:30 --> 00:18:33
So just to make sure that
everyone's on the same page,

289
00:18:33 --> 00:19:10
why don't you do a rate
expression for me for this one.

290
00:19:10 --> 00:19:25
OK, just 10 more seconds.
 

291
00:19:25 --> 00:19:29
Excellent.
 

292
00:19:29 --> 00:19:31
So you just have to pay
attention to your minus

293
00:19:31 --> 00:19:37
signs, your stoichiometry.
 

294
00:19:37 --> 00:19:40
So, it's minus for the
disappearance, stoichiometry 1

295
00:19:40 --> 00:19:45
over 2, and then no negatives
for your products of things

296
00:19:45 --> 00:19:48
that are appearing.
 

297
00:19:48 --> 00:19:48
Very good.
 

298
00:19:48 --> 00:19:52
Rate expressions, not
that complicated.

299
00:19:52 --> 00:19:54
All right, so now we're going
to talk about rate laws, which

300
00:19:54 --> 00:19:58
are slightly more complicated
than rate expressions.

301
00:19:58 --> 00:20:03
So, a rate law is -- you
come up with a rate law

302
00:20:03 --> 00:20:06
experimentally, and it's the
relationship between the

303
00:20:06 --> 00:20:09
rate and the concentration.
 

304
00:20:09 --> 00:20:12
So we have -- we're going to
introduce a term called the

305
00:20:12 --> 00:20:15
rate constant, which is
the small letter k.

306
00:20:15 --> 00:20:18
And so the rate constant is
going to tell you about the

307
00:20:18 --> 00:20:23
relationship between the rate
and the concentration of your

308
00:20:23 --> 00:20:27
reactants in a reaction.
 

309
00:20:27 --> 00:20:32
So, if we had that same
reaction here, we could also

310
00:20:32 --> 00:20:36
write that the rate is equal to
a rate constant times the

311
00:20:36 --> 00:20:42
concentration of your reactant,
a, raised to a power m, and

312
00:20:42 --> 00:20:45
b raised to a power n.
 

313
00:20:45 --> 00:20:50
So here, m and n are the order
of the reaction with respect to

314
00:20:50 --> 00:20:56
a and b respectively, so m is
the order of the reaction in a,

315
00:20:56 --> 00:20:59
and n is the order of the
reaction in b, and our

316
00:20:59 --> 00:21:04
small letter k here
is the rate constant.

317
00:21:04 --> 00:21:07
So that would be an
expression for rate law.

318
00:21:07 --> 00:21:09
And so, now I'm going to tell
you a lot of things that

319
00:21:09 --> 00:21:14
are true about rate laws.
 

320
00:21:14 --> 00:21:19
So, a rate law, again, comes
from experiment, so you can't

321
00:21:19 --> 00:21:22
just look at the stoichiometry
of the reaction and

322
00:21:22 --> 00:21:24
predict the rate law.
 

323
00:21:24 --> 00:21:28
So m is not the stoichiometry
of the reaction in terms of the

324
00:21:28 --> 00:21:33
a, that is, unless the reaction
is what we call an elementary

325
00:21:33 --> 00:21:36
reaction, or a step in a
reaction, and we're going to

326
00:21:36 --> 00:21:39
talk more about that next week
-- then you can, if it's an

327
00:21:39 --> 00:21:42
elementary reaction, then you
can use stoichiometry

328
00:21:42 --> 00:21:43
to predict.
 

329
00:21:43 --> 00:21:46
But for other reactions you
can't, and that'll become

330
00:21:46 --> 00:21:51
more clear next week when we
talk about this in detail.

331
00:21:51 --> 00:21:55
So, rate laws are not limited
to reactants, sometimes

332
00:21:55 --> 00:21:56
a product will show up.
 

333
00:21:56 --> 00:21:59
It's not that common, but it's
possible, and again, it's

334
00:21:59 --> 00:22:01
experimentally determined.
 

335
00:22:01 --> 00:22:05
So the experiment would have
to tell you whether that term

336
00:22:05 --> 00:22:06
is going to be there or not.
 

337
00:22:06 --> 00:22:13
So, occasionally you'll see a
product term in a rate law.

338
00:22:13 --> 00:22:19
So, in terms of m and n, the
orders of the reaction, m and n

339
00:22:19 --> 00:22:25
can be integers, they can be
whole numbers, or fractions,

340
00:22:25 --> 00:22:32
negative or positive, lots
of options for m and n.

341
00:22:32 --> 00:22:35
And let me tell you about all
the options for -- we're

342
00:22:35 --> 00:22:37
going to use m here.
 

343
00:22:37 --> 00:22:40
So, you have this table in your
notes, most of it is blank,

344
00:22:40 --> 00:22:43
some of it is filled in, and
we're going to fill in

345
00:22:43 --> 00:22:46
the parts that are not
filled in right now.

346
00:22:46 --> 00:22:50
So we're going to start in the
middle where the order of the

347
00:22:50 --> 00:22:55
reaction is one here, m equals
1, and that's called a

348
00:22:55 --> 00:22:58
first order reaction.
 

349
00:22:58 --> 00:23:02
So these names are pretty
much intuitive when

350
00:23:02 --> 00:23:03
you look at them.
 

351
00:23:03 --> 00:23:07
So here, the rate law for a
first order reaction would be

352
00:23:07 --> 00:23:14
our rate constant, k, times
the concentration of a.

353
00:23:14 --> 00:23:18
So let's think about what
that rate law would mean.

354
00:23:18 --> 00:23:21
Say you double the
concentration of a, what

355
00:23:21 --> 00:23:27
would happen to the
rate of the reaction?

356
00:23:27 --> 00:23:31
How many people say
double, raise your hand.

357
00:23:31 --> 00:23:33
Good, that's what happens.
 

358
00:23:33 --> 00:23:38
All right, so it doubled
the rate of the reaction.

359
00:23:38 --> 00:23:41
So now let's think
about m equals 2.

360
00:23:41 --> 00:23:45
See on your handout that that's
called second order -- again

361
00:23:45 --> 00:23:47
these names make sense.
 

362
00:23:47 --> 00:23:54
The rate law for this would be
k times the concentration of a

363
00:23:54 --> 00:24:01
squared, so m equals 2, and
that's shown over here.

364
00:24:01 --> 00:24:11
If you double the concentration
of a, what would happen?

365
00:24:11 --> 00:24:18
So you should
quadruple the rate.

366
00:24:18 --> 00:24:21
So what about if you
tripled the concentration?

367
00:24:21 --> 00:24:24
Why don't you go ahead and tell
me if you triple it for m

368
00:24:24 --> 00:25:03
equals 2, what would
happen to the rate?

369
00:25:03 --> 00:25:16
OK, let's just take
10 more seconds.

370
00:25:16 --> 00:25:19
Excellent.
 

371
00:25:19 --> 00:25:23
That's right, 9 times.
 

372
00:25:23 --> 00:25:26
So, you're definitely
getting the hang of this.

373
00:25:26 --> 00:25:28
All right, so let's move
down and talk about

374
00:25:28 --> 00:25:31
m equals minus 1.
 

375
00:25:31 --> 00:25:33
If you think of a good name for
this let me know, because no

376
00:25:33 --> 00:25:38
one ever calls that anything,
so we can leave that blank.

377
00:25:38 --> 00:25:42
And go ahead and talk about
what the rate would be

378
00:25:42 --> 00:25:45
there and how we would
write the rate law.

379
00:25:45 --> 00:25:49
And so, the rate law, then,
would be k, our rate constant,

380
00:25:49 --> 00:25:52
times the concentration of
a raised to the minus 1.

381
00:25:52 --> 00:26:01
All right, if we double
the concentration here,

382
00:26:01 --> 00:26:06
just yell out what you
think would happen.

383
00:26:06 --> 00:26:10
You would 1/2 the rate of the
reaction, or you can think

384
00:26:10 --> 00:26:14
about as 2 to the minus 1, 1/2
the rate of the reaction.

385
00:26:14 --> 00:26:17
And you will have problems on
problem-set 10, which will be

386
00:26:17 --> 00:26:20
due a week from Friday where
you're going to be given

387
00:26:20 --> 00:26:23
experimental data, and you have
to look at it and see, OK, what

388
00:26:23 --> 00:26:26
happened to the rate, and then
what does that mean about

389
00:26:26 --> 00:26:28
the order of the reaction.
 

390
00:26:28 --> 00:26:35
So this is a lot of what the
problems are like in this unit.

391
00:26:35 --> 00:26:39
All right, also there is no
name that I'm aware of for when

392
00:26:39 --> 00:26:44
n equals minus 1/2, but we
can write the rate law.

393
00:26:44 --> 00:26:47
So that's just going to be k
times the concentration of a

394
00:26:47 --> 00:26:52
raised to the minus 1/2 --
again, for the order of

395
00:26:52 --> 00:26:55
reaction, they can be integers,
they can be fractions, they can

396
00:26:55 --> 00:26:59
be negative, and they
can be positive.

397
00:26:59 --> 00:27:04
So, tell me for doubling the
concentration here of this

398
00:27:04 --> 00:27:44
one, what's going to
happen to the rate?

399
00:27:44 --> 00:27:59
OK, let's just take
10 more seconds.

400
00:27:59 --> 00:28:06
Yup, so most people
got that right.

401
00:28:06 --> 00:28:08
So, if we go back here, 0 .
 

402
00:28:08 --> 00:28:11
7 times the rate, you could
think about this as 2

403
00:28:11 --> 00:28:13
raised to the minus 1/2.
 

404
00:28:13 --> 00:28:15
These get a little more
complicated and are some of the

405
00:28:15 --> 00:28:19
harder ones on the problem-set
to recognize the relationship.

406
00:28:19 --> 00:28:22
So if you remember all the
possibilities, it's going to

407
00:28:22 --> 00:28:25
help you think about what's
going on when you see

408
00:28:25 --> 00:28:26
the experimental data.
 

409
00:28:26 --> 00:28:32
All right, so let's go up to m
equals 1/2 here, and this one

410
00:28:32 --> 00:28:34
sometimes does have a name --
anyone want to guess what

411
00:28:34 --> 00:28:38
that one might be called?
 

412
00:28:38 --> 00:28:41
Half order, very good.
 

413
00:28:41 --> 00:28:46
So, half order, and so here our
rate, then, is going to be

414
00:28:46 --> 00:28:52
equal to k times a to the 1/2.
 

415
00:28:52 --> 00:28:55
So, if we double the
concentration here, what

416
00:28:55 --> 00:29:05
happens to the rate?
 

417
00:29:05 --> 00:29:15
Someone want to yell it out?
 

418
00:29:15 --> 00:29:16
So, 1 .
 

419
00:29:16 --> 00:29:20
4 times the rate.
 

420
00:29:20 --> 00:29:26
And m equals 0 -- any guess
of what that's called?

421
00:29:26 --> 00:29:31
Zero order.
 

422
00:29:31 --> 00:29:37
And the rate law here, the rate
is going to be equal to what?

423
00:29:37 --> 00:29:41
K, and that's it.
 

424
00:29:41 --> 00:29:43
So the rate equals k.
 

425
00:29:43 --> 00:29:46
So what does that mean -- if
you double the concentration,

426
00:29:46 --> 00:29:49
what happens to the rate?
 

427
00:29:49 --> 00:29:51
Yup, no effect on rate.
 

428
00:29:51 --> 00:29:54
So that's zero order -- the
concentration term, it doesn't

429
00:29:54 --> 00:30:00
matter what the concentration
is, and there will be some that

430
00:30:00 --> 00:30:02
you'll see on a problem-set
like that, so if there's no

431
00:30:02 --> 00:30:06
effect on rate, you
have a zero order.

432
00:30:06 --> 00:30:10
So those are the possibilities
that you will see for the order

433
00:30:10 --> 00:30:14
of reactions, and again, you'll
be given experimental data

434
00:30:14 --> 00:30:16
and have to figure out the
order of the reactions.

435
00:30:16 --> 00:30:19
And often, it's not just as
simple as one thing, there'll

436
00:30:19 --> 00:30:22
probably be two things in
there, so you'll have to figure

437
00:30:22 --> 00:30:25
out the order with respect to
both of those two things.

438
00:30:25 --> 00:30:29
So that makes it a little
more complicated.

439
00:30:29 --> 00:30:34
All right, a couple more things
that are true about rate laws.

440
00:30:34 --> 00:30:39
So the overall reaction
order is this sum of the

441
00:30:39 --> 00:30:41
exponents in the rate law.
 

442
00:30:41 --> 00:30:47
So then, if you had this rate
law, rate equals k times a to

443
00:30:47 --> 00:30:53
the 2, second order, and b
1, the overall order

444
00:30:53 --> 00:30:55
for this would be?
 

445
00:30:55 --> 00:30:57
3.
 

446
00:30:57 --> 00:30:59
So, we have third order.
 

447
00:30:59 --> 00:31:02
Sum of 2 plus 1.
 

448
00:31:02 --> 00:31:05
So for this particular one,
your second order with respect

449
00:31:05 --> 00:31:12
to a, first order with respect
to b, third order overall.

450
00:31:12 --> 00:31:14
Units.
 

451
00:31:14 --> 00:31:17
Units for k are a lot of fun.
 

452
00:31:17 --> 00:31:21
So it depends on what the
reaction is, and often, for a

453
00:31:21 --> 00:31:24
problem, you'll have to figure
out what the units for k are,

454
00:31:24 --> 00:31:28
depending on are we talking
about molar per second

455
00:31:28 --> 00:31:30
or what's going on.
 

456
00:31:30 --> 00:31:34
So just pay attention to the
units for k, they can vary.

457
00:31:34 --> 00:31:37
And sometimes one of the
problems will be what are the

458
00:31:37 --> 00:31:40
units for this particular k,
so you'll have to figure

459
00:31:40 --> 00:31:47
that out per problem.
 

460
00:31:47 --> 00:31:51
So now, again, kinetics is
experimental -- we determine

461
00:31:51 --> 00:31:55
rate laws experimentally, and
sometimes this is not easy,

462
00:31:55 --> 00:32:00
because sometimes there'll be
very small changes that you're

463
00:32:00 --> 00:32:03
looking at, or those changes
will happen really quickly, so

464
00:32:03 --> 00:32:06
the interval of time
is very short.

465
00:32:06 --> 00:32:08
And sometimes when you're
trying to measure these

466
00:32:08 --> 00:32:12
changes, the reaction's
happening faster than your

467
00:32:12 --> 00:32:15
equipment can record
those changes.

468
00:32:15 --> 00:32:20
So this can be technically very
difficult, and so one thing

469
00:32:20 --> 00:32:24
that scientists do is they
use integrated rate laws.

470
00:32:24 --> 00:32:28
So in this way, you can express
concentrations directly as a

471
00:32:28 --> 00:32:31
function of time and you don't
have to worry so much now about

472
00:32:31 --> 00:32:35
measuring those small amounts
of changes that occur

473
00:32:35 --> 00:32:36
are very, very quickly.
 

474
00:32:36 --> 00:32:40
So let's talk about
integrated rate laws.

475
00:32:40 --> 00:32:44
And here, we're going to
start a derivation of

476
00:32:44 --> 00:32:48
an integrated rate law.
 

477
00:32:48 --> 00:32:51
So here's -- we're told this is
a first order reaction, and so

478
00:32:51 --> 00:32:54
we're going to do the first
order integrated rate law.

479
00:32:54 --> 00:32:58
And in this reaction, a is
going to b -- we can write a

480
00:32:58 --> 00:33:03
rate expression for this. so
we can talk about the

481
00:33:03 --> 00:33:08
disappearance minus
d a over d t.

482
00:33:08 --> 00:33:12
We can also now write the rate
law for a first order reaction,

483
00:33:12 --> 00:33:16
and we know that that is our
rate constant, small k, times

484
00:33:16 --> 00:33:18
the concentration of a.
 

485
00:33:18 --> 00:33:21
So we know we can write the
rate expression, and we can

486
00:33:21 --> 00:33:25
write a rate law for this
first order reaction.

487
00:33:25 --> 00:33:30
So now, we can do a derivation.
 

488
00:33:30 --> 00:33:32
So, in this derivation,
we're going to separate

489
00:33:32 --> 00:33:35
our concentration terms
and our time terms.

490
00:33:35 --> 00:33:37
So we're going to move
everything with concentration

491
00:33:37 --> 00:33:41
to one side, and things with
time to the other side.

492
00:33:41 --> 00:33:45
So, on one side, then, we can
have 1 over the concentration

493
00:33:45 --> 00:33:47
of a, we're going to
bring that down here.

494
00:33:47 --> 00:33:52
We have d a over here, and then
we have our negative sign, and

495
00:33:52 --> 00:33:58
our k over here, and move d t
also over to the other side.

496
00:33:58 --> 00:34:02
So now we have concentration
terms on one side and time

497
00:34:02 --> 00:34:05
terms on the other side.
 

498
00:34:05 --> 00:34:08
And now, as you might have
guessed from the name

499
00:34:08 --> 00:34:13
integrated rate laws, we can
integrate, and so we can look

500
00:34:13 --> 00:34:15
at the interval from the
initial concentration or

501
00:34:15 --> 00:34:19
original concentration of a,
to concentration of

502
00:34:19 --> 00:34:21
a at some time, t.
 

503
00:34:21 --> 00:34:25
And we can also look at
from some time, 0, to the

504
00:34:25 --> 00:34:30
time, t, in question.
 

505
00:34:30 --> 00:34:34
So there's that
expression again.

506
00:34:34 --> 00:34:37
Now you can write this
expression also in

507
00:34:37 --> 00:34:39
terms of natural log.
 

508
00:34:39 --> 00:34:43
So we can re-write this in
terms of the natural log of the

509
00:34:43 --> 00:34:47
concentration of a at time, t,
minus the natural log of the

510
00:34:47 --> 00:34:52
concentration of a at our
original time, or the

511
00:34:52 --> 00:34:58
original concentration,
equals minus k t.

512
00:34:58 --> 00:35:02
And you can also express it in
this term, so you can just

513
00:35:02 --> 00:35:06
bring this guy over to the
other side of the equation, and

514
00:35:06 --> 00:35:09
this is one expression for the
integrated rate law

515
00:35:09 --> 00:35:10
that you will see.
 

516
00:35:10 --> 00:35:14
There's also another expression
that you'll see, and let's

517
00:35:14 --> 00:35:15
show you what that is.
 

518
00:35:15 --> 00:35:21
So you can also take the
natural log and bring

519
00:35:21 --> 00:35:23
these two terms together.
 

520
00:35:23 --> 00:35:26
So natural log of your
concentration of a at time

521
00:35:26 --> 00:35:30
t, over your original
concentration of a

522
00:35:30 --> 00:35:33
equals minus k t.
 

523
00:35:33 --> 00:35:36
And now you can take the
inverse natural log of

524
00:35:36 --> 00:35:39
both sides, so just your
concentration at time t over

525
00:35:39 --> 00:35:44
your initial concentration
equals e to the minus k t.

526
00:35:44 --> 00:35:48
And that expression is often
written in your book or on

527
00:35:48 --> 00:35:52
equation sheets as a
concentration at a particular

528
00:35:52 --> 00:35:57
time equals the concentration
of the original material,

529
00:35:57 --> 00:35:59
e to the minus k t.
 

530
00:35:59 --> 00:36:02
And these are the two
expressions that you'll

531
00:36:02 --> 00:36:05
see the most often.
 

532
00:36:05 --> 00:36:08
This one is often referred to
as your integrated first order

533
00:36:08 --> 00:36:13
rate law, whereas this one is
the equation for

534
00:36:13 --> 00:36:15
a straight line.
 

535
00:36:15 --> 00:36:19
So these two are the ones that
you will see the most often for

536
00:36:19 --> 00:36:23
integrated first
order rate laws.

537
00:36:23 --> 00:36:27
So one was an equation for a
straight line, so let's come

538
00:36:27 --> 00:36:29
up with a straight line.
 

539
00:36:29 --> 00:36:33
So if you plot your data, if
you've measured your

540
00:36:33 --> 00:36:39
concentration of a at various
times, you can take the natural

541
00:36:39 --> 00:36:42
log of those concentrations
that you measured and

542
00:36:42 --> 00:36:45
plot them against time.
 

543
00:36:45 --> 00:36:48
And if you do this, and it
is, in fact, a first order

544
00:36:48 --> 00:36:51
reaction, you should
get a straight line.

545
00:36:51 --> 00:36:57
So here, we can look at this in
terms of a straight line, so on

546
00:36:57 --> 00:37:01
y-axis, we have the natural log
of the concentration of a at a

547
00:37:01 --> 00:37:06
particular time, and that's
plotted against time,

548
00:37:06 --> 00:37:08
over here in seconds.
 

549
00:37:08 --> 00:37:12
And so, what does that mean in
terms of what is this, what

550
00:37:12 --> 00:37:21
is the intercept here?
 

551
00:37:21 --> 00:37:22
Yup.
 

552
00:37:22 --> 00:37:25
So the natural log of
your initial original

553
00:37:25 --> 00:37:27
concentration of a.
 

554
00:37:27 --> 00:37:30
And what is the
slope of this line?

555
00:37:30 --> 00:37:35
The slope is negative k,
and so the slope is really

556
00:37:35 --> 00:37:37
what people are after.
 

557
00:37:37 --> 00:37:40
So often what you want to do is
measure rate constants for

558
00:37:40 --> 00:37:47
particular reactions, and if
you can then measure the

559
00:37:47 --> 00:37:50
concentration of a at
particular times and plot it

560
00:37:50 --> 00:37:54
this way, you can come out
with your rate constant.

561
00:37:54 --> 00:37:56
And that's what you want to
know, and those are some

562
00:37:56 --> 00:37:58
of the problems that
you're going to see.

563
00:37:58 --> 00:38:00
Are you going to see
experimental data for what

564
00:38:00 --> 00:38:04
happens to rate at particular
concentrations, and you can

565
00:38:04 --> 00:38:11
come up with values for
your rate constants.

566
00:38:11 --> 00:38:17
So, let's talk about one other
thing, which is half life.

567
00:38:17 --> 00:38:21
So people are often very
concerned with half life.

568
00:38:21 --> 00:38:25
When do you hear about
half life a lot?

569
00:38:25 --> 00:38:27
Does anyone know?
 

570
00:38:27 --> 00:38:30
Yeah, when we talk about
radioactivity, which we'll be

571
00:38:30 --> 00:38:33
talking about next class.
 

572
00:38:33 --> 00:38:36
They're very concerned about
the half life, which is the

573
00:38:36 --> 00:38:39
time it takes for the full
amount of your original

574
00:38:39 --> 00:38:46
material to be
reduced by a 1/2.

575
00:38:46 --> 00:38:50
So we can look at an equation
that we had up above for our

576
00:38:50 --> 00:38:54
integrated first order half
life, and we can think

577
00:38:54 --> 00:38:58
about this in terms of a
half life expression.

578
00:38:58 --> 00:39:02
So here, t has a particular
special meaning -- we have

579
00:39:02 --> 00:39:07
t, 1/2, which is the
abbreviation for half life.

580
00:39:07 --> 00:39:11
And so half life by definition
is the amount of time it takes

581
00:39:11 --> 00:39:14
for the original concentration
to be reduced by 1/2.

582
00:39:14 --> 00:39:18
So here we have our final
concentration, concentration

583
00:39:18 --> 00:39:20
of a at a time t.
 

584
00:39:20 --> 00:39:24
So when we're talking about
half life, we're going to

585
00:39:24 --> 00:39:28
have 1/2 as much as we
had when we started.

586
00:39:28 --> 00:39:33
So our a t is going to be our
original divided by 2, 1/2 the

587
00:39:33 --> 00:39:36
amount we had in the beginning.
 

588
00:39:36 --> 00:39:41
And so, now t has a special
name, it's t to the 1/2 here.

589
00:39:41 --> 00:39:46
So now we can simplify this
expression to come up with

590
00:39:46 --> 00:39:52
an expression for half life
for a first order reaction.

591
00:39:52 --> 00:39:57
So, the a to the 0, our
original concentrations cancel

592
00:39:57 --> 00:40:03
out, and so we have the natural
log of 1/2 equals minus k, our

593
00:40:03 --> 00:40:07
rate constant, times t 1/2.
 

594
00:40:07 --> 00:40:10
The natural log of
1/2 is minus 0 .

595
00:40:10 --> 00:40:13
6 9 3 1.
 

596
00:40:13 --> 00:40:19
We can get rid of our negative
signs and solve for t 1/2,

597
00:40:19 --> 00:40:23
because this is a half life
expression, so t 1/2 equals 0 .

598
00:40:23 --> 00:40:28
6 9 3 1 over k.
 

599
00:40:28 --> 00:40:34
So that's an expression just
for a first order half life.

600
00:40:34 --> 00:40:37
And notice that half
life does not depend

601
00:40:37 --> 00:40:39
on concentration here.
 

602
00:40:39 --> 00:40:42
That term dropped out.
 

603
00:40:42 --> 00:40:46
So half life depends on our
rate constant, k, and k depends

604
00:40:46 --> 00:40:48
on the material in question.
 

605
00:40:48 --> 00:40:55
So, for radioactive material,
some radioactive materials have

606
00:40:55 --> 00:40:58
short half lifes, so their k's
are very different from each

607
00:40:58 --> 00:41:01
other, and so that can be very
important, especially when

608
00:41:01 --> 00:41:05
you're thinking about
storing radioactive waste.

609
00:41:05 --> 00:41:11
So, using that value, tell me,
for the same material then,

610
00:41:11 --> 00:41:15
does it take longer to go
from 1 ton to a 1/2 ton, or

611
00:41:15 --> 00:41:43
from 1 gram to 1/2 gram?
 

612
00:41:43 --> 00:41:57
Let's just take
10 more seconds.

613
00:41:57 --> 00:42:01
Yup, it takes the
same amount of time.

614
00:42:01 --> 00:42:06
And then just to finish up
here, we have one more thing

615
00:42:06 --> 00:42:07
to do and then we're done.
 

616
00:42:07 --> 00:42:11
So here, in a plot for a first
order half life, the

617
00:42:11 --> 00:42:17
concentration of the material
at the first half life

618
00:42:17 --> 00:42:22
has dropped by how much?
 

619
00:42:22 --> 00:42:22
1/2.
 

620
00:42:22 --> 00:42:25
At the second half
life is what?

621
00:42:25 --> 00:42:30
STUDENT: 1/4.
 

622
00:42:30 --> 00:42:34
PROFESSOR: And the
third half life?

623
00:42:34 --> 00:42:34
STUDENT: 1/8
 

624
00:42:34 --> 00:42:38
PROFESSOR: Yup, so that's
first order half life.

625
00:42:38 --> 00:42:40
All right, everybody, have
a happy Thanksgiving.

626
00:42:40 --> 00:42:41