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PROFESSOR: OK, OK.

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00:00:22,680 --> 00:00:25,520
Let's get started.

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00:00:25,520 --> 00:00:27,160
Going to go right
into the lesson.

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00:00:27,160 --> 00:00:31,020
Last day we started looking
at kinetics, which was the

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00:00:31,020 --> 00:00:32,300
description of rate and

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00:00:32,300 --> 00:00:35,550
mechanism of chemical reactions.

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00:00:35,550 --> 00:00:38,640
We looked at the general rate
law, which shows us that the

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00:00:38,640 --> 00:00:42,570
instant change in concentration
of species i

16
00:00:42,570 --> 00:00:45,740
goes as the instant
concentration.

17
00:00:45,740 --> 00:00:48,550
So rate is proportional
to concentration.

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00:00:48,550 --> 00:00:54,360
And the order of reaction
is shown here as n and

19
00:00:54,360 --> 00:00:57,710
proportionality constant
is the rate constant k.

20
00:00:57,710 --> 00:01:02,150
So we saw that we can make the
rate of reaction increase by

21
00:01:02,150 --> 00:01:04,720
increasing the concentration
in the reactor.

22
00:01:04,720 --> 00:01:06,940
We saw there was a second way
to increase the rate of

23
00:01:06,940 --> 00:01:09,390
reaction, and that was to
raise the temperature.

24
00:01:09,390 --> 00:01:12,800
And this is the Arrhenius
relationship that shows that

25
00:01:12,800 --> 00:01:16,350
the rate constant changes with
temperature according to this

26
00:01:16,350 --> 00:01:19,020
exponential relationship.

27
00:01:19,020 --> 00:01:21,500
In the denominator, we have the
product of the Boltzmann

28
00:01:21,500 --> 00:01:24,370
constant and the absolute
temperature, which is a

29
00:01:24,370 --> 00:01:27,840
measure of the ambient thermal
energy that's available to

30
00:01:27,840 --> 00:01:29,250
promote reaction.

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00:01:29,250 --> 00:01:32,940
And in the numerator we have a
barrier energy, which we call

32
00:01:32,940 --> 00:01:34,810
the activation energy.

33
00:01:34,810 --> 00:01:37,130
We'll say a little bit more
about that today.

34
00:01:37,130 --> 00:01:40,080
And the constant of
proportionality out here is A,

35
00:01:40,080 --> 00:01:42,800
which is in honor of Arrhenius,
who first

36
00:01:42,800 --> 00:01:44,970
annunciated the law.

37
00:01:44,970 --> 00:01:48,210
So what I want to do today is to
look at some common orders

38
00:01:48,210 --> 00:01:48,685
of reactions.

39
00:01:48,685 --> 00:01:52,110
So we're going to look at
the values of n that are

40
00:01:52,110 --> 00:01:54,990
encountered in not

41
00:01:54,990 --> 00:01:59,000
insignificant number of reactions.

42
00:01:59,000 --> 00:02:00,680
So let's start with
the simplest one.

43
00:02:00,680 --> 00:02:03,850
The simplest one
is first order.

44
00:02:03,850 --> 00:02:05,100
First order reactions.

45
00:02:07,850 --> 00:02:12,570
That means n equals 1 in this
rate law expression.

46
00:02:12,570 --> 00:02:17,840
And here's an example of
something that we could use.

47
00:02:17,840 --> 00:02:24,230
The decomposition of
N2O5 into NO2.

48
00:02:24,230 --> 00:02:30,970
And gives us half a
mole of oxygen.

49
00:02:30,970 --> 00:02:35,400
And we can write this rate law
in terms of the rate of

50
00:02:35,400 --> 00:02:37,650
disappearance of N2O5.

51
00:02:37,650 --> 00:02:41,040
So I can write minus
d by dt of--

52
00:02:41,040 --> 00:02:43,680
I'm going to use square brackets
to indicate the

53
00:02:43,680 --> 00:02:44,592
concentration--

54
00:02:44,592 --> 00:02:47,030
of N2O5.

55
00:02:47,030 --> 00:02:48,830
And this has been measured.

56
00:02:48,830 --> 00:02:50,450
You can't predict this from the

57
00:02:50,450 --> 00:02:52,520
stoichiometry of the equation.

58
00:02:52,520 --> 00:02:55,410
You have to measure this, and
on the basis of measurements

59
00:02:55,410 --> 00:03:02,780
it's found that the rate of
change of N2O5 goes as the

60
00:03:02,780 --> 00:03:05,840
concentration of N2O5.

61
00:03:05,840 --> 00:03:07,860
And there's a constant
out here.

62
00:03:07,860 --> 00:03:08,900
The rate constant.

63
00:03:08,900 --> 00:03:11,390
So just to make the point, I'm
going to put a 1 here.

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00:03:11,390 --> 00:03:14,150
Meaning that n equals 1 and
that's why this is a

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00:03:14,150 --> 00:03:15,710
first-order reaction.

66
00:03:15,710 --> 00:03:16,680
But this is messy.

67
00:03:16,680 --> 00:03:17,950
There's too many characters
here.

68
00:03:17,950 --> 00:03:21,270
So I'm going to compress this
and give myself a nicer font,

69
00:03:21,270 --> 00:03:29,110
so I'm going to let the
concentration of N2O5, just in

70
00:03:29,110 --> 00:03:30,850
this expression, just be c.

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00:03:30,850 --> 00:03:31,700
Lowercase c.

72
00:03:31,700 --> 00:03:33,680
That way I can speed
this thing up.

73
00:03:33,680 --> 00:03:38,490
So I can rewrite this expression
here as minus dc by

74
00:03:38,490 --> 00:03:42,850
dt equals k times c.

75
00:03:42,850 --> 00:03:43,540
All right.

76
00:03:43,540 --> 00:03:45,790
And so we know what this
is going to look like.

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00:03:45,790 --> 00:03:47,980
They all look like this.

78
00:03:47,980 --> 00:03:51,630
If we plot concentration versus
temperature we expect

79
00:03:51,630 --> 00:03:54,540
to have the maximum value
of this at time zero.

80
00:03:54,540 --> 00:03:57,420
So at time zero I
start off with--

81
00:03:57,420 --> 00:04:00,120
if you want c-star or c max--

82
00:04:00,120 --> 00:04:02,900
and you know, this
thing attenuates.

83
00:04:02,900 --> 00:04:06,350
But I can't look at that and
decide whether it's first

84
00:04:06,350 --> 00:04:07,050
order or not.

85
00:04:07,050 --> 00:04:10,730
The only thing the eye
can really tell

86
00:04:10,730 --> 00:04:12,350
is a straight line.

87
00:04:12,350 --> 00:04:15,910
So what I want to do is I want
to modify this thing.

88
00:04:15,910 --> 00:04:19,500
I want to map c into
some f of c.

89
00:04:19,500 --> 00:04:22,590
And I want to map t
into some g of t.

90
00:04:22,590 --> 00:04:28,490
So that if I plot f versus
g, I get a straight line.

91
00:04:28,490 --> 00:04:31,790
And then I can take one look at
that and go, bingo, this is

92
00:04:31,790 --> 00:04:32,690
first order.

93
00:04:32,690 --> 00:04:33,440
Or not.

94
00:04:33,440 --> 00:04:36,880
Or maybe it's first order and
the data are very noisy.

95
00:04:36,880 --> 00:04:38,730
So what we'll do is
we're going to

96
00:04:38,730 --> 00:04:40,190
integrate that equation.

97
00:04:40,190 --> 00:04:42,760
So I'm going to play with
this a little bit.

98
00:04:42,760 --> 00:04:44,340
So I'm going to transpose.

99
00:04:44,340 --> 00:04:50,630
I'll get minus dc over
c equals kdt.

100
00:04:50,630 --> 00:04:57,830
And then I can integrate this
because I know at time 0, t

101
00:04:57,830 --> 00:05:00,550
equals 0, c equals
some value--

102
00:05:00,550 --> 00:05:03,450
I can call it c-star
or c naught--

103
00:05:03,450 --> 00:05:08,360
and at any arbitrary time later,
I can go down that

104
00:05:08,360 --> 00:05:12,180
curve and put some value of time
and then I'll end up with

105
00:05:12,180 --> 00:05:16,300
some arbitrary value
of concentration c.

106
00:05:16,300 --> 00:05:18,340
And I know there's some math
people in the audience who are

107
00:05:18,340 --> 00:05:22,500
probably horrified that the
limits and the integrand are

108
00:05:22,500 --> 00:05:23,540
both the same.

109
00:05:23,540 --> 00:05:25,370
So I'll put a little tilde
here that way I

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00:05:25,370 --> 00:05:26,790
don't go to math jail.

111
00:05:26,790 --> 00:05:28,820
So now I'm not integrating c.

112
00:05:28,820 --> 00:05:32,460
If I wanted to be a pedant and
really make the math instead

113
00:05:32,460 --> 00:05:37,080
of me enslaving the math, the
math enslaving me, watch this.

114
00:05:37,080 --> 00:05:38,590
What I could do is I
could make this a

115
00:05:38,590 --> 00:05:40,480
carrier variable, s.

116
00:05:40,480 --> 00:05:42,180
You know what I'm talking
about now, right?

117
00:05:42,180 --> 00:05:43,700
But let's get really crazy.

118
00:05:43,700 --> 00:05:45,520
This is how bad the
math can get.

119
00:05:45,520 --> 00:05:47,070
You can do this in
a chemistry book.

120
00:05:47,070 --> 00:05:48,120
Let's use some Greek.

121
00:05:48,120 --> 00:05:51,080
So I'll make this
d xi over xi.

122
00:05:51,080 --> 00:05:53,430
Now I've totally left the
class behind, but it's

123
00:05:53,430 --> 00:05:55,636
mathematically correct.

124
00:05:55,636 --> 00:05:58,170
What we will do is we'll
put the t back and put

125
00:05:58,170 --> 00:05:59,550
a tilde over it.

126
00:05:59,550 --> 00:06:02,950
And now everybody is happy, and
heaven forbid, the student

127
00:06:02,950 --> 00:06:07,140
might even understand
the lesson.

128
00:06:07,140 --> 00:06:07,470
All right.

129
00:06:07,470 --> 00:06:09,120
So we do that and
what do we get?

130
00:06:09,120 --> 00:06:13,910
The integral of dc over c
is a natural log of c.

131
00:06:13,910 --> 00:06:17,810
This'll be natural log of c
equals natural log of c

132
00:06:17,810 --> 00:06:21,310
naught minus kt.

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00:06:21,310 --> 00:06:24,870
OK, so integrating this thing
gives us this expression.

134
00:06:24,870 --> 00:06:31,870
And that means if I plot the
natural log of c versus time I

135
00:06:31,870 --> 00:06:33,910
should get a straight line.

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00:06:33,910 --> 00:06:38,750
And furthermore, the slope
is equal to minus k.

137
00:06:38,750 --> 00:06:42,770
So here's an example that's
taken from your book.

138
00:06:42,770 --> 00:06:45,740
It happens to be another
first-order reaction and it

139
00:06:45,740 --> 00:06:48,850
shows the decomposition
of cisplatin.

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00:06:48,850 --> 00:06:51,600
This is a compound that's used
in certain cancer treatments.

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00:06:51,600 --> 00:06:54,040
And you can cisplatin hydrolyzes
to form this

142
00:06:54,040 --> 00:06:56,540
monster cation plus
a chloride.

143
00:06:56,540 --> 00:07:00,160
And it turns out that the rate
of decomposition of cisplatin

144
00:07:00,160 --> 00:07:01,030
is first order.

145
00:07:01,030 --> 00:07:02,530
Will you look at that curve?

146
00:07:02,530 --> 00:07:03,590
That purple line?

147
00:07:03,590 --> 00:07:04,635
I don't know what that means.

148
00:07:04,635 --> 00:07:05,790
But watch.

149
00:07:05,790 --> 00:07:10,040
If I instead plot the natural
logarithm of the concentration

150
00:07:10,040 --> 00:07:12,970
of cisplatin as a function of
time, you get a nice straight

151
00:07:12,970 --> 00:07:16,120
line, and furthermore,
the value of k is

152
00:07:16,120 --> 00:07:18,210
obvious from the slope.

153
00:07:18,210 --> 00:07:22,490
So this is an indication of the
power of taking the proper

154
00:07:22,490 --> 00:07:27,000
order of reaction and
then using it in--

155
00:07:27,000 --> 00:07:30,290
if you'll pardon the pun--
straightening things out.

156
00:07:30,290 --> 00:07:32,920
And a couple other things
worth noting.

157
00:07:32,920 --> 00:07:35,830
I mentioned at the end of last
day, radioactive decay.

158
00:07:35,830 --> 00:07:40,440
Even though radioactive decay
is not a chemical reaction--

159
00:07:40,440 --> 00:07:43,750
it has to do with nuclear
phenomena-- and we know

160
00:07:43,750 --> 00:07:46,910
chemistry is restricted to
the life and times of the

161
00:07:46,910 --> 00:07:49,080
electron, we don't go
into the nucleus.

162
00:07:49,080 --> 00:07:51,310
We simply know there's something
in there, there's

163
00:07:51,310 --> 00:07:54,150
neutrons, protons, and a whole
bunch of other particles.

164
00:07:54,150 --> 00:07:56,300
But chemistry is about
the life and

165
00:07:56,300 --> 00:07:58,200
times of the electron.

166
00:07:58,200 --> 00:08:02,590
Radioactive decay turns
out to be first order.

167
00:08:02,590 --> 00:08:05,370
It's good to know that
because then you can

168
00:08:05,370 --> 00:08:06,620
appreciate what goes on.

169
00:08:06,620 --> 00:08:09,040
So for example, you could
take something like the

170
00:08:09,040 --> 00:08:14,220
decomposition of uranium-238.

171
00:08:14,220 --> 00:08:17,260
One of its decompositions
gives you

172
00:08:17,260 --> 00:08:22,740
thorium-234 plus helium.

173
00:08:22,740 --> 00:08:26,140
And it turns out that this is
first order, which means that

174
00:08:26,140 --> 00:08:29,380
if you were to take a plot
of the natural log of the

175
00:08:29,380 --> 00:08:33,280
concentration of uranium
versus time, you get a

176
00:08:33,280 --> 00:08:34,220
straight line.

177
00:08:34,220 --> 00:08:37,030
And this slope would be the
k, the rate constant.

178
00:08:37,030 --> 00:08:40,980
But it turns out that the
nuclear chemists, nuclear

179
00:08:40,980 --> 00:08:46,040
engineers, prefer not to talk
about the rate of reaction in

180
00:08:46,040 --> 00:08:46,850
terms of k.

181
00:08:46,850 --> 00:08:49,710
But instead, they like to
use the inverse of k,

182
00:08:49,710 --> 00:08:51,640
which is the half-life.

183
00:08:51,640 --> 00:09:01,160
So instead, express k
through half-life.

184
00:09:01,160 --> 00:09:04,410
And the half-life, as the name
implies, is the time it takes

185
00:09:04,410 --> 00:09:08,170
to decrease the concentration
of the species by half.

186
00:09:08,170 --> 00:09:14,080
So if I start off here at c1 and
down here I have c2 equals

187
00:09:14,080 --> 00:09:19,780
1/2 c1, then this is the time
it takes to cut the

188
00:09:19,780 --> 00:09:22,160
concentration in half.

189
00:09:22,160 --> 00:09:24,410
So through half-life--

190
00:09:24,410 --> 00:09:29,040
and we can go through this
equation here, just put c

191
00:09:29,040 --> 00:09:33,650
naught over 2 and do a little
bit of manipulation, you'll

192
00:09:33,650 --> 00:09:37,670
end up with the natural log
of 2 divided by the rate

193
00:09:37,670 --> 00:09:43,140
constant, which is 0.693
divided by k.

194
00:09:43,140 --> 00:09:45,910
So you can see that there's
a direct relationship.

195
00:09:45,910 --> 00:09:49,650
It turns out that the half-life
for this reaction is

196
00:09:49,650 --> 00:09:52,960
4 1/2 billion years.

197
00:09:52,960 --> 00:09:55,130
4 1/2 billion years.

198
00:09:55,130 --> 00:09:58,090
So that means after 4 1/2
billion years the

199
00:09:58,090 --> 00:10:01,400
concentration has gone down to
a half, but even then it's

200
00:10:01,400 --> 00:10:03,420
probably not safe for the
kids to go out and play.

201
00:10:03,420 --> 00:10:05,690
So you really need to think
about it in this way.

202
00:10:05,690 --> 00:10:08,750
So here it is shown
in your textbook.

203
00:10:08,750 --> 00:10:12,220
Concentration as a
function of time.

204
00:10:12,220 --> 00:10:15,120
They could have plotted it log
linear, then you would have

205
00:10:15,120 --> 00:10:16,250
ended up with this.

206
00:10:16,250 --> 00:10:18,560
But anyways, they're chemists,
so what can you expect.

207
00:10:18,560 --> 00:10:19,190
So here it is.

208
00:10:19,190 --> 00:10:21,860
Here it goes down to a half, and
then this is a half of a

209
00:10:21,860 --> 00:10:22,750
half as a quarter.

210
00:10:22,750 --> 00:10:24,460
It's the same time interval.

211
00:10:24,460 --> 00:10:26,710
And then half of a quarter is
an eighth, and it's the same

212
00:10:26,710 --> 00:10:27,810
time interval.

213
00:10:27,810 --> 00:10:28,650
So you get the sense.

214
00:10:28,650 --> 00:10:31,630
And the most important thing
is the half-life is

215
00:10:31,630 --> 00:10:33,830
independent of concentration.

216
00:10:33,830 --> 00:10:36,070
It doesn't matter what the
starting concentration is-- if

217
00:10:36,070 --> 00:10:39,150
you know what the half-life is,
you know how much time it

218
00:10:39,150 --> 00:10:40,400
takes to get to a half.

219
00:10:40,400 --> 00:10:41,450
And you know enough math.

220
00:10:41,450 --> 00:10:43,560
What if I said, well, what if I
didn't want to go to a half?

221
00:10:43,560 --> 00:10:45,680
What if I wanted to go to 10%?

222
00:10:45,680 --> 00:10:49,380
Well, you can figure out how
to modulate half-life into

223
00:10:49,380 --> 00:10:50,310
tenth-life.

224
00:10:50,310 --> 00:10:52,150
That's trivial.

225
00:10:52,150 --> 00:10:55,280
But the book, being a chemistry
book, will show you

226
00:10:55,280 --> 00:11:00,180
a table in which they give
half-life values for orders of

227
00:11:00,180 --> 00:11:01,930
reactions other than 1.

228
00:11:01,930 --> 00:11:05,790
And it's stupid because except
in the case of first order

229
00:11:05,790 --> 00:11:08,960
reactions, the value the
half-life is a function of the

230
00:11:08,960 --> 00:11:10,350
concentration.

231
00:11:10,350 --> 00:11:12,480
So what good is a constant
that's variable?

232
00:11:12,480 --> 00:11:15,010
I don't know, but I didn't
write the book.

233
00:11:15,010 --> 00:11:18,080
The only time I care about
half-life is in the case of a

234
00:11:18,080 --> 00:11:21,620
first order reaction, which
is when you have

235
00:11:21,620 --> 00:11:23,970
nuclear decay for sure.

236
00:11:23,970 --> 00:11:24,360
All right.

237
00:11:24,360 --> 00:11:26,710
So that's enough about
first order.

238
00:11:26,710 --> 00:11:28,790
Let's go look at second-order
reactions.

239
00:11:28,790 --> 00:11:31,440
So here's an example also
taken from the book.

240
00:11:31,440 --> 00:11:40,990
So second-order reaction, which
means that n equals 2 in

241
00:11:40,990 --> 00:11:42,670
the rate law expression.

242
00:11:42,670 --> 00:11:45,240
n equals 2 in the rate
law expression.

243
00:11:45,240 --> 00:11:49,460
And the example that
they gave was NO2.

244
00:11:49,460 --> 00:11:49,870
See, look.

245
00:11:49,870 --> 00:11:52,150
We went from N2O5 to NO2.

246
00:11:52,150 --> 00:11:54,600
And then we can keep the
decomposition going.

247
00:11:54,600 --> 00:12:03,100
NO2 goes to NO plus O2.

248
00:12:03,100 --> 00:12:06,070
And again, I'm going to let, in
this case, c will equal the

249
00:12:06,070 --> 00:12:09,450
concentration of NO2.

250
00:12:09,450 --> 00:12:13,120
And what you end up with in
this case is, if you go

251
00:12:13,120 --> 00:12:16,610
through the similar analysis,
you get minus dc by dt.

252
00:12:16,610 --> 00:12:20,730
It's been measured that the rate
of loss of NO2 goes as

253
00:12:20,730 --> 00:12:23,040
the square of its
concentration.

254
00:12:23,040 --> 00:12:26,350
So this is based on experimental
evidence.

255
00:12:26,350 --> 00:12:28,590
It's not because this is a 2.

256
00:12:28,590 --> 00:12:30,250
This is not.

257
00:12:30,250 --> 00:12:31,930
Please pay attention here.

258
00:12:31,930 --> 00:12:35,110
This 2 is not the consequences
of the stoichiometry.

259
00:12:35,110 --> 00:12:40,010
This 2 was determined
experimentally.

260
00:12:40,010 --> 00:12:41,950
I could have just written
this reaction NO2 goes

261
00:12:41,950 --> 00:12:43,305
to NO plus 1/2 O2.

262
00:12:43,305 --> 00:12:46,380
That doesn't make this
first order, does it?

263
00:12:46,380 --> 00:12:51,300
Experimentally in
the laboratory.

264
00:12:51,300 --> 00:12:51,580
All right.

265
00:12:51,580 --> 00:12:53,860
So now what we can do is we
can integrate this thing.

266
00:12:53,860 --> 00:12:57,156
And so we'll get minus the--

267
00:12:57,156 --> 00:12:59,460
let's do it this way.

268
00:12:59,460 --> 00:13:02,600
Boards are cheap, so let's jump
down to the next one.

269
00:13:02,600 --> 00:13:09,080
So now I can then put minus
the integral of dc tilde--

270
00:13:09,080 --> 00:13:10,080
cross multiply--

271
00:13:10,080 --> 00:13:17,050
so dc tilde over c tilde
squared equals k,

272
00:13:17,050 --> 00:13:19,230
the integral dt tilde.

273
00:13:19,230 --> 00:13:22,340
And we can integrate this from
zero to some time, and this

274
00:13:22,340 --> 00:13:25,750
will go from c naught to
some concentration.

275
00:13:25,750 --> 00:13:29,960
And that will give us 1
over c equals 1 over

276
00:13:29,960 --> 00:13:32,150
c naught plus kt.

277
00:13:32,150 --> 00:13:36,370
So this is now the new, improved
way of mapping c

278
00:13:36,370 --> 00:13:39,730
versus t into f of
c versus g of t.

279
00:13:39,730 --> 00:13:45,050
So f of c as 1 over c, which
means now if I plot 1 over c

280
00:13:45,050 --> 00:13:47,110
versus time, I'll get
a straight line.

281
00:13:47,110 --> 00:13:49,325
In this case, it's got
positive slope.

282
00:13:49,325 --> 00:13:51,360
It's got positive slope,
so that's what it's

283
00:13:51,360 --> 00:13:52,320
going to look like.

284
00:13:52,320 --> 00:13:54,180
And this is k.

285
00:13:54,180 --> 00:13:58,010
So if I take our data set and
I plot it like this, then I

286
00:13:58,010 --> 00:13:59,280
can make sense of it.

287
00:13:59,280 --> 00:14:02,670
And I think we've got
some data here.

288
00:14:02,670 --> 00:14:07,060
So here's the data from
this decomposition.

289
00:14:07,060 --> 00:14:08,360
And again, what do you see?

290
00:14:08,360 --> 00:14:09,650
A line that attenuates.

291
00:14:09,650 --> 00:14:10,990
Can you look at that line?

292
00:14:10,990 --> 00:14:13,900
Can you tell that line is second
order, whereas the

293
00:14:13,900 --> 00:14:15,960
other one that looks like
this was first order?

294
00:14:15,960 --> 00:14:16,850
Of course not.

295
00:14:16,850 --> 00:14:19,710
The only way you can tell
his to fit it into some

296
00:14:19,710 --> 00:14:21,280
linearizing function.

297
00:14:21,280 --> 00:14:22,610
So look at that.

298
00:14:22,610 --> 00:14:24,780
What they've done, that's
the least squares fit.

299
00:14:24,780 --> 00:14:27,770
They plugged it into a least
squares fitting equation.

300
00:14:27,770 --> 00:14:30,190
You can fit a straight line
through anything.

301
00:14:30,190 --> 00:14:31,150
It doesn't matter.

302
00:14:31,150 --> 00:14:33,130
But what's that mean?

303
00:14:33,130 --> 00:14:35,130
I don't know.

304
00:14:35,130 --> 00:14:36,910
So here's the log.

305
00:14:36,910 --> 00:14:38,080
This is really important--

306
00:14:38,080 --> 00:14:39,040
look carefully.

307
00:14:39,040 --> 00:14:42,590
So somebody took these data and
then plotted them as the

308
00:14:42,590 --> 00:14:45,880
natural log, which is what you
do if it's first order.

309
00:14:45,880 --> 00:14:46,950
And look at what happens--

310
00:14:46,950 --> 00:14:49,760
it gets a lot better but it's
still not a straight line.

311
00:14:49,760 --> 00:14:52,830
But if you were in a hurry,
you'd just say, force the fit.

312
00:14:52,830 --> 00:14:55,290
You'll get a straight line and
you'll assigned the value of k

313
00:14:55,290 --> 00:14:57,220
to it and party on.

314
00:14:57,220 --> 00:14:58,640
And it's wrong.

315
00:14:58,640 --> 00:14:59,980
So now let's try this.

316
00:15:02,690 --> 00:15:03,890
Beta.

317
00:15:03,890 --> 00:15:05,770
1 over c versus time.

318
00:15:05,770 --> 00:15:06,920
So what do we get from that?

319
00:15:06,920 --> 00:15:07,660
I get two things.

320
00:15:07,660 --> 00:15:10,360
First of all, the fact that
it's a straight line means

321
00:15:10,360 --> 00:15:14,520
that it confirms n equals 2 and
the slope of that line is

322
00:15:14,520 --> 00:15:16,640
the value of k.

323
00:15:16,640 --> 00:15:19,710
So in point of fact, what I've
been doing here is teaching

324
00:15:19,710 --> 00:15:22,110
you how to determine the
rate of reaction.

325
00:15:22,110 --> 00:15:23,130
So let's do it.

326
00:15:23,130 --> 00:15:24,730
Let's codify this.

327
00:15:24,730 --> 00:15:33,120
So determination of
order of reaction.

328
00:15:33,120 --> 00:15:36,120
So in other words, the way the
story goes is I give you a

329
00:15:36,120 --> 00:15:38,420
data set that looks
like this--

330
00:15:41,270 --> 00:15:41,770
pardon me.

331
00:15:41,770 --> 00:15:44,890
I give you a data set that looks
like this and I say,

332
00:15:44,890 --> 00:15:46,580
determine the order
of reaction.

333
00:15:46,580 --> 00:15:49,680
So there's two general
ways to do this.

334
00:15:49,680 --> 00:15:51,740
The first one is called
the integral method.

335
00:15:54,630 --> 00:15:57,100
And that's what we've been
doing up until now.

336
00:15:57,100 --> 00:16:00,590
The integral method, it's called
the integral method

337
00:16:00,590 --> 00:16:02,370
because it's using the
integrated form

338
00:16:02,370 --> 00:16:03,230
of the radio question.

339
00:16:03,230 --> 00:16:04,130
See?

340
00:16:04,130 --> 00:16:05,400
This is the integrative form.

341
00:16:05,400 --> 00:16:06,490
This is the integrative form.

342
00:16:06,490 --> 00:16:10,440
Hence, the integral method,
and it's trial and error.

343
00:16:10,440 --> 00:16:11,110
That's what we did.

344
00:16:11,110 --> 00:16:12,740
Trial and error.

345
00:16:12,740 --> 00:16:15,580
But we don't say trial and error
because we're at MIT.

346
00:16:15,580 --> 00:16:16,380
So what do we say?

347
00:16:16,380 --> 00:16:17,210
We have a lofty way.

348
00:16:17,210 --> 00:16:19,540
What's the lofty way of saying
trial and error?

349
00:16:19,540 --> 00:16:21,340
By inspection.

350
00:16:21,340 --> 00:16:23,510
By inspection.

351
00:16:23,510 --> 00:16:26,770
Never tell anybody you do things
by trial and error.

352
00:16:26,770 --> 00:16:27,670
We don't do trial and error.

353
00:16:27,670 --> 00:16:29,646
By inspection.

354
00:16:29,646 --> 00:16:31,560
It's $50,000 a year.

355
00:16:31,560 --> 00:16:32,880
It's what you get.

356
00:16:32,880 --> 00:16:35,410
OK, so here's what I do.

357
00:16:35,410 --> 00:16:38,300
I'm impatient, so I
try n equals 1.

358
00:16:38,300 --> 00:16:41,510
If I get a straight line
on the log plot, good.

359
00:16:41,510 --> 00:16:43,440
If not, I try n equals 2.

360
00:16:43,440 --> 00:16:45,870
If I got a straight line
on 1 over c, good.

361
00:16:45,870 --> 00:16:51,310
If not, go to the second
way of determining.

362
00:16:51,310 --> 00:16:51,970
I give up.

363
00:16:51,970 --> 00:16:54,170
Won't waste my time.

364
00:16:54,170 --> 00:16:56,930
It's a two strikes and
you're out thing.

365
00:16:56,930 --> 00:16:58,020
So what's the second method?

366
00:16:58,020 --> 00:17:04,570
The second method is called
the differential method.

367
00:17:04,570 --> 00:17:05,820
The differential method.

368
00:17:09,470 --> 00:17:13,700
And this is fun because it's
data fitting and it gets into

369
00:17:13,700 --> 00:17:15,380
some nice detail.

370
00:17:15,380 --> 00:17:19,410
So what I want to do is
to define the rate.

371
00:17:19,410 --> 00:17:20,040
What's the rate?

372
00:17:20,040 --> 00:17:21,100
The rate is over here.

373
00:17:21,100 --> 00:17:23,070
Minus dc by dt, right?

374
00:17:23,070 --> 00:17:27,870
You see up in the top left
corner the rate law.

375
00:17:27,870 --> 00:17:32,030
Minus dc by dt.

376
00:17:32,030 --> 00:17:34,740
I'm going to call
that positive r.

377
00:17:34,740 --> 00:17:36,510
I'm just compress-- this
is like French cooking.

378
00:17:36,510 --> 00:17:37,640
I started with this.

379
00:17:37,640 --> 00:17:38,580
Look at all those fonts.

380
00:17:38,580 --> 00:17:40,900
Then I compressed it down
to c, and now I

381
00:17:40,900 --> 00:17:42,550
compressed it even more.

382
00:17:42,550 --> 00:17:45,030
It's just so much information
compressed in

383
00:17:45,030 --> 00:17:47,070
that little r there.

384
00:17:47,070 --> 00:17:48,060
Poor little r.

385
00:17:48,060 --> 00:17:48,360
All right.

386
00:17:48,360 --> 00:17:51,110
So now, let's rewrite the
rate law expression.

387
00:17:51,110 --> 00:17:56,120
So that's r equals
kc to the n.

388
00:17:56,120 --> 00:17:57,310
There's the rate law expression

389
00:17:57,310 --> 00:17:59,390
written very compact.

390
00:17:59,390 --> 00:18:02,370
And now I'm going to take the
logarithm of both sides.

391
00:18:02,370 --> 00:18:05,660
So taking the log of both sides,
I can write natural log

392
00:18:05,660 --> 00:18:09,370
of r, the log of a product
is the sum of the log.

393
00:18:09,370 --> 00:18:13,130
So that's going to be natural
log of k plus the

394
00:18:13,130 --> 00:18:14,570
log of, da, da, da.

395
00:18:14,570 --> 00:18:17,160
n log c.

396
00:18:17,160 --> 00:18:17,870
n log c.

397
00:18:17,870 --> 00:18:20,180
And I don't care what kind
of logarithms you use.

398
00:18:20,180 --> 00:18:21,960
You can make this log base c.

399
00:18:21,960 --> 00:18:23,380
You can make it log base 10.

400
00:18:23,380 --> 00:18:25,720
If you're feeling like you
want solidarity with the

401
00:18:25,720 --> 00:18:27,860
Mayans, you can make
it log base 5.

402
00:18:27,860 --> 00:18:28,630
I don't care.

403
00:18:28,630 --> 00:18:30,450
But make them the same.

404
00:18:30,450 --> 00:18:31,290
Make them the same.

405
00:18:31,290 --> 00:18:33,840
And then what happens?

406
00:18:33,840 --> 00:18:35,980
Well, let me show you.

407
00:18:35,980 --> 00:18:39,960
So let's say we've got our data,
start off with this data

408
00:18:39,960 --> 00:18:41,100
set like so.

409
00:18:41,100 --> 00:18:44,210
So this is concentration
versus time and

410
00:18:44,210 --> 00:18:46,340
we end up with this.

411
00:18:46,340 --> 00:18:49,710
It comes down, down,
down, attenuates.

412
00:18:49,710 --> 00:18:51,360
Remember, what are we
trying to do here?

413
00:18:51,360 --> 00:18:54,310
We're trying to take this data
set and figure out, what is

414
00:18:54,310 --> 00:18:56,520
the value of n?

415
00:18:56,520 --> 00:18:58,470
We're trying to determine n.

416
00:18:58,470 --> 00:19:03,090
So what this thing says is.

417
00:19:03,090 --> 00:19:10,230
if I make a plot of r versus c
so that it's on a log scale,

418
00:19:10,230 --> 00:19:15,370
so if I plot log r versus log c,
the slope is going to be n.

419
00:19:15,370 --> 00:19:19,210
So how do I take c versus
t and construct log

420
00:19:19,210 --> 00:19:20,800
r verses log c?

421
00:19:20,800 --> 00:19:21,870
That's what we're going to do.

422
00:19:21,870 --> 00:19:26,920
So here we are and I can start
here that at time zero.

423
00:19:26,920 --> 00:19:28,870
This is time zero.

424
00:19:28,870 --> 00:19:30,320
That's the slope, right?

425
00:19:30,320 --> 00:19:33,070
The slope here is the rate.

426
00:19:33,070 --> 00:19:37,260
So slope, I'm going to
call it r naught.

427
00:19:37,260 --> 00:19:39,350
Because that's the time--

428
00:19:39,350 --> 00:19:46,430
it's dc by dt r naught
at t equals t naught.

429
00:19:46,430 --> 00:19:48,320
But there's no t on here.

430
00:19:48,320 --> 00:19:49,570
So what am I going to put?

431
00:19:49,570 --> 00:19:54,860
It's when t equals t naught
and c equals c naught.

432
00:19:54,860 --> 00:19:59,225
So now I'm going to take some
colored chalk and we're going

433
00:19:59,225 --> 00:20:00,430
to show you how to
construct this.

434
00:20:00,430 --> 00:20:05,170
So I've got the slope by taking
minus dc by dt here.

435
00:20:05,170 --> 00:20:08,240
So I'm going to take this value,
r naught, and this

436
00:20:08,240 --> 00:20:09,150
value, c naught--

437
00:20:09,150 --> 00:20:12,790
I want to gang them together,
I'll bring over here and put

438
00:20:12,790 --> 00:20:18,030
them right out here-- so
now I've got r naught.

439
00:20:18,030 --> 00:20:22,130
Well, actually I should put the
abscissa first. So this is

440
00:20:22,130 --> 00:20:26,410
going to be c naught r naught.

441
00:20:26,410 --> 00:20:27,380
And now let's do it again.

442
00:20:27,380 --> 00:20:29,780
So we'll come down here
to some later time.

443
00:20:29,780 --> 00:20:31,520
Let's call this t1.

444
00:20:31,520 --> 00:20:35,320
And at t1 the concentration has
fallen to c1, and I take

445
00:20:35,320 --> 00:20:36,170
the slope of this.

446
00:20:36,170 --> 00:20:37,200
Why am I taking the slope?

447
00:20:37,200 --> 00:20:38,850
Because it's dc by dt.

448
00:20:38,850 --> 00:20:40,220
That's what the rate is.

449
00:20:40,220 --> 00:20:48,580
So here now I've got slope
r1 at c equals c1.

450
00:20:48,580 --> 00:20:49,460
r versus c.

451
00:20:49,460 --> 00:20:50,500
Forget time.

452
00:20:50,500 --> 00:20:52,380
Time doesn't belong here.

453
00:20:52,380 --> 00:20:53,870
So take those.

454
00:20:53,870 --> 00:20:55,630
It's a lower concentration,
so it's kind of

455
00:20:55,630 --> 00:20:56,500
like a lower energy.

456
00:20:56,500 --> 00:20:59,950
So we'll take a lower
wavelength here.

457
00:20:59,950 --> 00:21:03,300
So r1 and c1 come over here.

458
00:21:07,070 --> 00:21:08,160
c1, r1.

459
00:21:08,160 --> 00:21:08,890
We'll do one more.

460
00:21:08,890 --> 00:21:10,020
Three's a charm.

461
00:21:10,020 --> 00:21:11,130
Come up to here.

462
00:21:11,130 --> 00:21:12,590
This is t2.

463
00:21:12,590 --> 00:21:16,210
Concentration has fallen to
c2, and I've got a slope.

464
00:21:16,210 --> 00:21:19,670
You see how the slope is getting
less and less steep?

465
00:21:19,670 --> 00:21:21,470
Because the rate loss says
the concentration

466
00:21:21,470 --> 00:21:22,830
falls, the rate falls.

467
00:21:22,830 --> 00:21:27,450
So this is slope r2
at c equals c2.

468
00:21:30,020 --> 00:21:31,626
That's lower energy.

469
00:21:31,626 --> 00:21:34,040
So I'll get the orange.

470
00:21:34,040 --> 00:21:36,650
Or maybe this is fuchsia.

471
00:21:36,650 --> 00:21:37,605
So we'll take this one.

472
00:21:37,605 --> 00:21:40,100
And this will put these
two together and bring

473
00:21:40,100 --> 00:21:41,620
them in like so.

474
00:21:41,620 --> 00:21:45,750
And this is now c2, r2. too
And what's this thing say?

475
00:21:45,750 --> 00:21:46,930
Take the slope.

476
00:21:46,930 --> 00:21:48,580
Look, it's a log, log plot.

477
00:21:48,580 --> 00:21:51,060
If you've got physical data and
you don't get a straight

478
00:21:51,060 --> 00:21:54,140
line on a log, log plot,
you're incompetent.

479
00:21:54,140 --> 00:21:56,290
You're a complete idiot.

480
00:21:56,290 --> 00:21:56,820
All right?

481
00:21:56,820 --> 00:21:59,690
There it is.

482
00:21:59,690 --> 00:22:02,510
And the slope here is n.

483
00:22:02,510 --> 00:22:05,540
And where it intersection,
obviously I can't get a

484
00:22:05,540 --> 00:22:09,680
negative number, so just allow
me to fix this just a wee bit.

485
00:22:09,680 --> 00:22:13,070
So there's the axis, and where
it hits the axis, this is now

486
00:22:13,070 --> 00:22:15,920
log k isn't it?

487
00:22:15,920 --> 00:22:17,430
So I determine the order
of reaction.

488
00:22:21,310 --> 00:22:21,790
Good.

489
00:22:21,790 --> 00:22:24,536
So now you know how to do it and
you'll get some practice

490
00:22:24,536 --> 00:22:27,095
if you work the homework.

491
00:22:27,095 --> 00:22:27,690
All right.

492
00:22:27,690 --> 00:22:30,600
A couple more things to say
and then we're done.

493
00:22:30,600 --> 00:22:33,230
So last thing, we talked about
increasing the rate of

494
00:22:33,230 --> 00:22:37,620
reaction by increasing the
temperature and increasing the

495
00:22:37,620 --> 00:22:38,510
concentration.

496
00:22:38,510 --> 00:22:40,250
There's one more thing
we can do.

497
00:22:40,250 --> 00:22:47,900
And what we can do is use a
catalyst. Increase rate by use

498
00:22:47,900 --> 00:22:48,500
of

499
00:22:48,500 --> 00:22:51,980
catalyst. OK.

500
00:22:51,980 --> 00:22:54,040
How does the catalyst work?

501
00:22:54,040 --> 00:22:55,250
How does the catalyst work?

502
00:22:55,250 --> 00:22:58,240
Well, let's go back to
this diagram here.

503
00:22:58,240 --> 00:23:02,010
Where we've got, this is called
the extent of reaction.

504
00:23:02,010 --> 00:23:04,500
Some kind of reaction
coordinate.

505
00:23:04,500 --> 00:23:07,826
And over here we had some kind
of energy coordinate.

506
00:23:07,826 --> 00:23:09,330
We had this energy coordinate.

507
00:23:09,330 --> 00:23:10,370
Remember, we had this thing?

508
00:23:10,370 --> 00:23:12,910
This silly thing here?

509
00:23:12,910 --> 00:23:14,245
So this is the reactions.

510
00:23:18,350 --> 00:23:20,990
And this is the product.

511
00:23:20,990 --> 00:23:25,520
And we reasoned that the
activation energy ea is

512
00:23:25,520 --> 00:23:28,830
sitting here.

513
00:23:28,830 --> 00:23:32,145
And we saw with the box, you had
to get a box up onto its

514
00:23:32,145 --> 00:23:35,410
ear, otherwise it wouldn't
fall over and so on.

515
00:23:35,410 --> 00:23:40,375
And there's a finite amount,
finite fraction of the

516
00:23:40,375 --> 00:23:42,000
Maxwell-Boltzmann
distribution.

517
00:23:42,000 --> 00:23:49,070
So if we plot energy and the
number of particles in the

518
00:23:49,070 --> 00:23:53,270
distribution have of given
energy, we get something that

519
00:23:53,270 --> 00:23:54,700
looks like this.

520
00:23:54,700 --> 00:23:55,890
Tails off.

521
00:23:55,890 --> 00:24:00,480
And we said that out
here we have the

522
00:24:00,480 --> 00:24:02,930
fracture under this line.

523
00:24:02,930 --> 00:24:08,060
This is the fraction that has
the energy to jump over the

524
00:24:08,060 --> 00:24:09,220
activation barrier.

525
00:24:09,220 --> 00:24:11,710
So fa is the--

526
00:24:11,710 --> 00:24:16,680
f is the activated, is the
fraction activated.

527
00:24:16,680 --> 00:24:17,850
And those are the only
ones that can

528
00:24:17,850 --> 00:24:19,030
participate in the reaction.

529
00:24:19,030 --> 00:24:20,630
These other ones can't surmount

530
00:24:20,630 --> 00:24:22,390
the activation barrier.

531
00:24:22,390 --> 00:24:26,950
Now, what the catalyst
does is it lowers

532
00:24:26,950 --> 00:24:29,230
the activation barrier.

533
00:24:29,230 --> 00:24:31,045
Catalyst lowers the activation
barrier.

534
00:24:31,045 --> 00:24:33,100
It doesn't change
the n points.

535
00:24:33,100 --> 00:24:36,200
The n points represent the
energy state of the reactants

536
00:24:36,200 --> 00:24:37,840
and the energy state
of the products.

537
00:24:37,840 --> 00:24:39,760
What the catalyst does
is it finds a

538
00:24:39,760 --> 00:24:42,700
low-energy barrier pathway.

539
00:24:42,700 --> 00:24:46,770
A low-energy barrier pathway,
which on this curve would mean

540
00:24:46,770 --> 00:24:52,070
that if this energy is lower,
then the fraction of any

541
00:24:52,070 --> 00:24:55,830
distribution that has the
requisite amount of energy is

542
00:24:55,830 --> 00:24:56,590
much higher.

543
00:24:56,590 --> 00:24:58,030
Can you see the area?

544
00:24:58,030 --> 00:25:03,400
The blue area is much, much
greater than the white area.

545
00:25:03,400 --> 00:25:07,415
So that means that this
fa catalyzed--

546
00:25:07,415 --> 00:25:09,530
I'm just going to
write cat here--

547
00:25:09,530 --> 00:25:16,060
fa catalyzed is much greater
than fa in the absence of a

548
00:25:16,060 --> 00:25:18,070
catalyst. And that promotes.

549
00:25:18,070 --> 00:25:19,090
What's an example of it?

550
00:25:19,090 --> 00:25:23,060
Well, in an automobile
catalyst one of their

551
00:25:23,060 --> 00:25:27,460
reactions we're trying to
promote is unburned

552
00:25:27,460 --> 00:25:28,380
hydrocarbons.

553
00:25:28,380 --> 00:25:32,300
There's some unburned gasoline
that comes out in the form of

554
00:25:32,300 --> 00:25:33,600
carbon monoxide.

555
00:25:33,600 --> 00:25:35,310
What we want to do is
convert the carbon

556
00:25:35,310 --> 00:25:38,380
monoxide to carbon dioxide.

557
00:25:38,380 --> 00:25:40,260
And this occurs on the catalyst
and I'll show you

558
00:25:40,260 --> 00:25:42,050
more of this at the end
of the lecture.

559
00:25:42,050 --> 00:25:44,670
But these are both gas molecules
and they're zooming

560
00:25:44,670 --> 00:25:45,790
through space.

561
00:25:45,790 --> 00:25:48,890
And if they're going to react
with one another, they really

562
00:25:48,890 --> 00:25:55,120
need to somehow move almost on
parallel lines so they get

563
00:25:55,120 --> 00:25:58,740
close enough to each other for
a long enough period of time

564
00:25:58,740 --> 00:26:02,480
that they can start thinking
about lower energy state.

565
00:26:02,480 --> 00:26:05,620
And say, well, gee, if we break
this bond and form a new

566
00:26:05,620 --> 00:26:07,330
bond, it's going to go to--

567
00:26:07,330 --> 00:26:09,480
you've got to get to know each
other, go have a few drinks,

568
00:26:09,480 --> 00:26:10,240
and da, da, da.

569
00:26:10,240 --> 00:26:11,990
So it's not happening.

570
00:26:11,990 --> 00:26:14,390
In the gas phase it
doesn't happen.

571
00:26:14,390 --> 00:26:18,380
So what we do instead is
we provide a service.

572
00:26:18,380 --> 00:26:22,300
This is the catalyst. The
catalyst is a solid surface

573
00:26:22,300 --> 00:26:26,250
and the CO sits down
next to another CO.

574
00:26:26,250 --> 00:26:30,610
They sit down and now they're
in place long enough in the

575
00:26:30,610 --> 00:26:36,180
right orientation to then form
CO2 and then desorb.

576
00:26:36,180 --> 00:26:38,070
So this is how the
catalyst assists.

577
00:26:38,070 --> 00:26:39,910
We call this-- especially,
imagine if

578
00:26:39,910 --> 00:26:41,630
it's the other way--

579
00:26:41,630 --> 00:26:45,350
what if this carbon monoxide
molecule is turn around so

580
00:26:45,350 --> 00:26:47,450
that the two carbons
are side by side.

581
00:26:47,450 --> 00:26:49,940
That's not going to promote the
reaction at all because

582
00:26:49,940 --> 00:26:53,540
this thing's got to whip
around and so on.

583
00:26:53,540 --> 00:26:53,960
This is a.

584
00:26:53,960 --> 00:26:55,440
Bad orientation

585
00:26:55,440 --> 00:26:58,320
And what's the Greek idea
for orientation?

586
00:26:58,320 --> 00:26:59,210
It's stereos.

587
00:26:59,210 --> 00:27:00,740
That's what stereophonic
sound is.

588
00:27:00,740 --> 00:27:02,440
If I close my eyes,
the two speakers

589
00:27:02,440 --> 00:27:04,340
give me spatial rendition.

590
00:27:04,340 --> 00:27:07,440
So this concept here, where
things are backwards and

591
00:27:07,440 --> 00:27:08,690
they're not the right place.

592
00:27:08,690 --> 00:27:11,180
It's called steric hindrance.

593
00:27:11,180 --> 00:27:13,580
This is steric hindrance.

594
00:27:13,580 --> 00:27:16,310
One of the functions of a
catalyst is to combat steric

595
00:27:16,310 --> 00:27:19,170
hindrance and put things
in their most favorable

596
00:27:19,170 --> 00:27:21,880
orientation to facilitate
reaction.

597
00:27:21,880 --> 00:27:25,750
So what are characteristics
of the catalyst?

598
00:27:25,750 --> 00:27:28,960
The catalyst needs to have the
following characteristics--

599
00:27:28,960 --> 00:27:33,500
first of all, it has to have an
affinity for the reactants.

600
00:27:33,500 --> 00:27:34,840
In this case, the CO.

601
00:27:34,840 --> 00:27:38,350
It has to have an affinity
for carbon monoxide.

602
00:27:38,350 --> 00:27:40,980
Affinity for reactants, so
they'll be attracted to the

603
00:27:40,980 --> 00:27:41,990
catalyst.

604
00:27:41,990 --> 00:27:43,860
But there's a second
piece here.

605
00:27:43,860 --> 00:27:47,560
If the catalyst doesn't get rid
of the CO2, can you see

606
00:27:47,560 --> 00:27:50,030
that after a very short period
of time, the surface of the

607
00:27:50,030 --> 00:27:52,860
catalyst will be covered with
carbon dioxide and then the

608
00:27:52,860 --> 00:27:54,460
reaction starves.

609
00:27:54,460 --> 00:27:55,570
It's choked.

610
00:27:55,570 --> 00:28:00,550
So it has to have a disaffinity
for the products.

611
00:28:00,550 --> 00:28:02,630
Disaffinity for the products.

612
00:28:06,000 --> 00:28:11,430
And in the real world, such as
in the gas exhaust stream of a

613
00:28:11,430 --> 00:28:14,190
car, it's not just
carbon monoxide.

614
00:28:14,190 --> 00:28:17,710
There's all kinds of other stuff
going on in there, and

615
00:28:17,710 --> 00:28:20,420
so the third thing that the
catalyst needs to have is

616
00:28:20,420 --> 00:28:21,950
selectivity.

617
00:28:21,950 --> 00:28:28,540
So it doesn't get distracted
by other reactions.

618
00:28:28,540 --> 00:28:31,890
And selectivity, most important
when you have a

619
00:28:31,890 --> 00:28:36,660
mixture of all sorts
of other species.

620
00:28:36,660 --> 00:28:39,230
So that's what the
catalyst does.

621
00:28:39,230 --> 00:28:40,510
Now there's one more thing.

622
00:28:40,510 --> 00:28:42,350
Just one second.

623
00:28:42,350 --> 00:28:42,990
Perfect.

624
00:28:42,990 --> 00:28:44,400
Gotcha just in time.

625
00:28:44,400 --> 00:28:45,480
So one more thing here.

626
00:28:45,480 --> 00:28:46,270
One more thing.

627
00:28:46,270 --> 00:28:50,240
We've shown what happens
when you catalyze.

628
00:28:50,240 --> 00:28:51,400
So I'm going to put this.

629
00:28:51,400 --> 00:28:56,410
This is ea under the influence
of catalysis.

630
00:28:56,410 --> 00:28:56,790
OK.

631
00:28:56,790 --> 00:28:58,250
This is the e of the catalyst.

632
00:28:58,250 --> 00:29:03,450
There are other substances that
can retard the reaction.

633
00:29:03,450 --> 00:29:04,960
These are called inhibitors.

634
00:29:04,960 --> 00:29:05,960
And what's an inhibitor do?

635
00:29:05,960 --> 00:29:08,500
It does the complimentary
action.

636
00:29:08,500 --> 00:29:11,690
So it raises the activation
barrier.

637
00:29:11,690 --> 00:29:15,380
So this is ea under the
influence of inhibitor.

638
00:29:18,260 --> 00:29:19,490
And what's the value of that?

639
00:29:19,490 --> 00:29:26,800
Well, if you buy some antifreeze
for use in the

640
00:29:26,800 --> 00:29:28,260
automobile cooling system.

641
00:29:28,260 --> 00:29:30,990
If you read carefully the label,
it's not just ethylene

642
00:29:30,990 --> 00:29:34,690
glycol, and water, 50/50
volume percent.

643
00:29:34,690 --> 00:29:36,160
There are other additives.

644
00:29:36,160 --> 00:29:37,250
What are those additives?

645
00:29:37,250 --> 00:29:40,080
Some of them are called
inhibitors.

646
00:29:40,080 --> 00:29:41,580
Oh, I didn't spell this right.

647
00:29:41,580 --> 00:29:43,120
No wonder you looked
so puzzled.

648
00:29:43,120 --> 00:29:44,920
I thought you didn't understand
the concept.

649
00:29:44,920 --> 00:29:46,170
Inhibitor.

650
00:29:49,510 --> 00:29:51,460
So it inhibits the reaction.

651
00:29:51,460 --> 00:29:52,300
What's going on?

652
00:29:52,300 --> 00:29:56,350
You've got the iron or aluminum
block of the engine,

653
00:29:56,350 --> 00:29:57,790
you got the water pump.

654
00:29:57,790 --> 00:30:00,150
It's taking heat away from the
engine, you're heating

655
00:30:00,150 --> 00:30:01,760
everything up, stirring
it around.

656
00:30:01,760 --> 00:30:05,170
It's a perfect environment
for enhancing corrosion.

657
00:30:05,170 --> 00:30:08,760
And we don't want the cooling
system to act as the corrosion

658
00:30:08,760 --> 00:30:10,640
system for the engine.

659
00:30:10,640 --> 00:30:16,240
And so we add components to the
antifreeze too reduce the

660
00:30:16,240 --> 00:30:18,400
rate of corrosion, to
lengthen the service

661
00:30:18,400 --> 00:30:19,840
lifetime of the vehicle.

662
00:30:19,840 --> 00:30:21,520
And so what does the
inhibitor do?

663
00:30:21,520 --> 00:30:25,120
It raises the activation barrier
for the corrosion

664
00:30:25,120 --> 00:30:29,040
reaction and thereby reduces
its rate of reaction

665
00:30:29,040 --> 00:30:29,870
substantially.

666
00:30:29,870 --> 00:30:31,435
So this is inhibited.

667
00:30:34,070 --> 00:30:36,610
OK, so this is catalyzed, this
is inhibited, and you can see

668
00:30:36,610 --> 00:30:44,200
that the fraction of active
species over the activation

669
00:30:44,200 --> 00:30:47,840
barrier, under the influence
of inhibition, is much less

670
00:30:47,840 --> 00:30:52,050
than the fraction otherwise.

671
00:30:52,050 --> 00:30:54,980
There's a time and a place for
all of these wonderful things.

672
00:30:54,980 --> 00:30:57,180
So that's the story
of kinetics.

673
00:30:57,180 --> 00:31:00,140
That's the story of kinetics,
but it's 11:35 and it's time

674
00:31:00,140 --> 00:31:01,820
to start a new topic.

675
00:31:01,820 --> 00:31:03,610
And now, we can erase.

676
00:31:03,610 --> 00:31:04,860
Thanks.

677
00:31:04,860 --> 00:31:05,090
OK.

678
00:31:05,090 --> 00:31:07,850
So let's talk about
something else.

679
00:31:07,850 --> 00:31:08,650
Let's talk about
something else.

680
00:31:08,650 --> 00:31:11,620
What I want to talk about today
is another topic that

681
00:31:11,620 --> 00:31:15,180
comes from the general area
of rate phenomena.

682
00:31:15,180 --> 00:31:18,220
I want to talk about something
else in rate phenomena.

683
00:31:18,220 --> 00:31:19,470
We're going to talk
about diffusion.

684
00:31:22,650 --> 00:31:26,770
And that's from the general
class of rate phenomena.

685
00:31:26,770 --> 00:31:30,770
That's why it appears with
chemical kinetics.

686
00:31:30,770 --> 00:31:33,260
And what do I mean by
rate phenomena?

687
00:31:33,260 --> 00:31:36,685
Rate phenomena means d
by dt is in the room.

688
00:31:36,685 --> 00:31:37,460
All right?

689
00:31:37,460 --> 00:31:40,560
We're looking at time,
domain processes.

690
00:31:40,560 --> 00:31:43,550
You know, chemistry, before you
came into this class, you

691
00:31:43,550 --> 00:31:45,580
probably thought, I know
what chemistry is.

692
00:31:45,580 --> 00:31:49,510
Chemistry is chemicals
reacting.

693
00:31:49,510 --> 00:31:50,480
That's what people think.

694
00:31:50,480 --> 00:31:52,520
Isn't that what the ancient
Egyptians said?

695
00:31:52,520 --> 00:31:54,510
khemia That's where the guys
knew how to embalm

696
00:31:54,510 --> 00:31:55,620
the dead and so on.

697
00:31:55,620 --> 00:31:56,920
It was about chemical
reactions.

698
00:31:56,920 --> 00:31:58,820
We've been talking about
structure, properties, all

699
00:31:58,820 --> 00:31:59,300
sorts of things.

700
00:31:59,300 --> 00:32:03,560
Well, now we're talking about
rates of reaction.

701
00:32:03,560 --> 00:32:08,040
If we want to run a reaction,
there's two things that we

702
00:32:08,040 --> 00:32:12,260
need to move around to
sustain a reaction.

703
00:32:12,260 --> 00:32:19,330
So transport of two important
quantities.

704
00:32:19,330 --> 00:32:21,780
One is matter and the
other is energy.

705
00:32:21,780 --> 00:32:22,945
We star something for energy.

706
00:32:22,945 --> 00:32:25,080
As we just saw, the
thing doesn't go.

707
00:32:25,080 --> 00:32:26,890
And if we starve it for
matter it doesn't go.

708
00:32:26,890 --> 00:32:31,690
So energy in motion is
under the general

709
00:32:31,690 --> 00:32:33,250
rubric of heat transfer.

710
00:32:33,250 --> 00:32:35,150
But we won't talk about heat
transfer because we've only

711
00:32:35,150 --> 00:32:36,370
got 14 weeks.

712
00:32:36,370 --> 00:32:38,380
I'd love to talk about it,
but we're out of time.

713
00:32:38,380 --> 00:32:43,410
So instead, we will talk
about mass transport.

714
00:32:43,410 --> 00:32:46,620
And mass transport in solids
occurs by diffusion.

715
00:32:53,530 --> 00:32:54,400
And we know what's critical.

716
00:32:54,400 --> 00:32:59,050
For example, we know in the case
of the Hindenburg, the

717
00:32:59,050 --> 00:33:00,750
Hindenburg didn't explode.

718
00:33:00,750 --> 00:33:02,590
Why didn't the Hindenburg
explode?

719
00:33:02,590 --> 00:33:05,410
Because there were 7 million
cubic feet of hydrogen, but we

720
00:33:05,410 --> 00:33:08,760
couldn't get 7 million cubic
feet of oxygen to the site.

721
00:33:08,760 --> 00:33:12,560
Because of the limitations of
mass transport, 2/3 of the

722
00:33:12,560 --> 00:33:14,240
people walked off
of that vessel.

723
00:33:14,240 --> 00:33:16,770
It was on fire, and many of
them died because they

724
00:33:16,770 --> 00:33:19,250
panicked and they jumped
to their deaths.

725
00:33:19,250 --> 00:33:21,730
Very few people were actually
affected by the fire.

726
00:33:21,730 --> 00:33:25,320
So it's a good example of mass
transport, negating the rate

727
00:33:25,320 --> 00:33:28,470
of what otherwise could have
been an explosive reaction.

728
00:33:28,470 --> 00:33:32,200
So I'm going to look at a
simple example today.

729
00:33:32,200 --> 00:33:35,560
And what I want to do is
look at the doping of

730
00:33:35,560 --> 00:33:36,930
semiconductors.

731
00:33:36,930 --> 00:33:38,790
You know, we've studied
semiconductors.

732
00:33:38,790 --> 00:33:41,820
Dave, could we cut to the
document camera, please?

733
00:33:41,820 --> 00:33:43,150
So what I've got here
is I'm going to show

734
00:33:43,150 --> 00:33:44,870
you a silicon wafer.

735
00:33:44,870 --> 00:33:47,570
And the silicon wafer has
got some features on it.

736
00:33:47,570 --> 00:33:48,670
So it's already been doped.

737
00:33:48,670 --> 00:33:50,360
Oh, that's pretty, isn't it?

738
00:33:50,360 --> 00:33:51,190
So cute.

739
00:33:51,190 --> 00:33:51,950
All right.

740
00:33:51,950 --> 00:33:55,640
So what we've got here, remember
this is the 8-inch

741
00:33:55,640 --> 00:33:57,870
diameter single crystal.

742
00:33:57,870 --> 00:34:01,110
So this was cut from a single
piece of silicon 8 inches in

743
00:34:01,110 --> 00:34:02,780
diameter, about 2 meters long.

744
00:34:02,780 --> 00:34:04,440
How did they make a
single crystal?

745
00:34:04,440 --> 00:34:08,000
They immersed the tiny single
crystal into the melt and

746
00:34:08,000 --> 00:34:10,870
gradually pulled the
single crystal out.

747
00:34:10,870 --> 00:34:13,280
Sort of the way you can grow
rock mountain candy.

748
00:34:13,280 --> 00:34:17,440
And if you're really careful,
the entire giant, 2 meter

749
00:34:17,440 --> 00:34:21,490
length, 8 inches in diameter,
is one single crystal.

750
00:34:21,490 --> 00:34:25,080
And then we take this and we cut
it with a diamond saw into

751
00:34:25,080 --> 00:34:28,540
wafers, Each of them about a
millimeter in thickness.

752
00:34:28,540 --> 00:34:31,380
And, of course, the width of
the saw turns into dust So

753
00:34:31,380 --> 00:34:32,450
your yield [SNAPS]

754
00:34:32,450 --> 00:34:34,190
right off the bat
is about 50%.

755
00:34:34,190 --> 00:34:35,100
Because [SAW SOUND]

756
00:34:35,100 --> 00:34:35,785
it's all gone.

757
00:34:35,785 --> 00:34:36,140
[SAW SOUND]

758
00:34:36,140 --> 00:34:38,120
it's all gone.

759
00:34:38,120 --> 00:34:40,520
And now what we're going to
do, is we want to dope it.

760
00:34:40,520 --> 00:34:42,550
So how do I get the
boron in here?

761
00:34:42,550 --> 00:34:44,690
We say, why don't we add the
boron to the melt, but what if

762
00:34:44,690 --> 00:34:46,110
I want to make pn-junctions?

763
00:34:46,110 --> 00:34:48,510
So I want to get some boron
and some phosphorous.

764
00:34:48,510 --> 00:34:50,210
If I add the boron and
the phosphorous,

765
00:34:50,210 --> 00:34:51,550
it then goes nuts.

766
00:34:51,550 --> 00:34:54,060
I need to have p-type
against n-type.

767
00:34:54,060 --> 00:34:55,940
So how do I get it in here?

768
00:34:55,940 --> 00:34:57,070
That's we're going
to talk about.

769
00:34:57,070 --> 00:35:01,950
We're going to talk about how
we make those features.

770
00:35:01,950 --> 00:35:02,810
See those features?

771
00:35:02,810 --> 00:35:05,480
Because if you're really good,
you start with those features

772
00:35:05,480 --> 00:35:08,070
and you cut them up and
then you end up with

773
00:35:08,070 --> 00:35:10,860
this, which is this.

774
00:35:10,860 --> 00:35:12,850
This is a Pentium chip.

775
00:35:12,850 --> 00:35:17,690
The amount of material science,
physical chemistry in

776
00:35:17,690 --> 00:35:20,320
that device is absolutely
phenomenal.

777
00:35:20,320 --> 00:35:23,730
What lies underneath this piece
of gold is absolutely

778
00:35:23,730 --> 00:35:24,190
phenomenal.

779
00:35:24,190 --> 00:35:27,830
It's what powers the
information age.

780
00:35:27,830 --> 00:35:29,990
And it all starts with
this stuff here.

781
00:35:29,990 --> 00:35:31,260
It's that simple.

782
00:35:31,260 --> 00:35:32,840
So how do we get the boron in?

783
00:35:32,840 --> 00:35:33,910
Dave, let's leave this up.

784
00:35:33,910 --> 00:35:34,920
It's a pretty image.

785
00:35:34,920 --> 00:35:39,900
It might soothe the natives,
so let's just leave it up.

786
00:35:39,900 --> 00:35:44,080
By the way, that spider network
is all the gold wires

787
00:35:44,080 --> 00:35:45,400
that are addressing.

788
00:35:45,400 --> 00:35:47,730
It doesn't do you any good to
have a gazillion features

789
00:35:47,730 --> 00:35:50,520
there but you can't get
information in and out.

790
00:35:50,520 --> 00:35:53,660
So if you've got a gazillion
features, you need a gazillion

791
00:35:53,660 --> 00:35:56,780
leads to take information
in and out.

792
00:35:56,780 --> 00:35:58,570
That's very, very thin gold.

793
00:35:58,570 --> 00:35:59,670
How do you do that?

794
00:35:59,670 --> 00:36:00,920
Not with a paint brush.

795
00:36:03,360 --> 00:36:05,090
It's all with this stuff.

796
00:36:05,090 --> 00:36:07,440
That's why I teach you
this instead some

797
00:36:07,440 --> 00:36:08,010
of the other stuff.

798
00:36:08,010 --> 00:36:08,330
OK.

799
00:36:08,330 --> 00:36:09,470
So now we're going to dope.

800
00:36:09,470 --> 00:36:11,310
We're going to dope the
silicon with boron.

801
00:36:11,310 --> 00:36:13,700
Number one point to remember--
we're going to dope the

802
00:36:13,700 --> 00:36:16,540
silicon in the solid state.

803
00:36:16,540 --> 00:36:19,570
We do not add boron
to molten silicon.

804
00:36:19,570 --> 00:36:23,050
We're going to add boron
to the silicon

805
00:36:23,050 --> 00:36:24,370
in the solid state.

806
00:36:24,370 --> 00:36:26,450
So I'm going to draw
this wafer.

807
00:36:26,450 --> 00:36:27,750
Only it's not to scale.

808
00:36:27,750 --> 00:36:32,640
It's going to look more like a
hockey puck than a thin wafer.

809
00:36:32,640 --> 00:36:34,370
Anyways, imagine it's this.

810
00:36:34,370 --> 00:36:35,190
OK?

811
00:36:35,190 --> 00:36:39,850
So this is the silicon wafer,
the silicon wafer on edge.

812
00:36:39,850 --> 00:36:41,420
And this is where all
the features were

813
00:36:41,420 --> 00:36:42,920
that I showed you.

814
00:36:42,920 --> 00:36:44,330
So we're going to do is
we're going to try

815
00:36:44,330 --> 00:36:46,045
to introduce boron.

816
00:36:46,045 --> 00:36:48,730
We want to get boron into the
silicon, we're going to bring

817
00:36:48,730 --> 00:36:50,720
it in from the surface.

818
00:36:50,720 --> 00:36:53,170
So this is a silicon
wafer, which means

819
00:36:53,170 --> 00:36:55,510
it's a single crystal.

820
00:36:55,510 --> 00:36:56,710
It's a single crystal.

821
00:36:56,710 --> 00:36:59,120
And we could use Laue methods
to figure out

822
00:36:59,120 --> 00:36:59,815
which is the face.

823
00:36:59,815 --> 00:37:01,410
Is that cut on the 0 1 1?

824
00:37:01,410 --> 00:37:02,440
Is it cut on a 1 1 1?

825
00:37:02,440 --> 00:37:05,570
And so on.

826
00:37:05,570 --> 00:37:12,000
So now we're going to
dope with boron.

827
00:37:12,000 --> 00:37:12,960
How do we do it?

828
00:37:12,960 --> 00:37:15,260
We decompose diborane.

829
00:37:15,260 --> 00:37:17,200
We introduce diborane,
it's a gas.

830
00:37:17,200 --> 00:37:19,130
B2H6.

831
00:37:19,130 --> 00:37:22,390
And we flow diborane over the
surface at some constant

832
00:37:22,390 --> 00:37:23,550
concentration.

833
00:37:23,550 --> 00:37:26,600
And what happens is that the
diborane decomposes.

834
00:37:26,600 --> 00:37:30,190
B2H6 on silicon.

835
00:37:30,190 --> 00:37:31,910
And I'm going to write
silicon with an x.

836
00:37:31,910 --> 00:37:33,060
What's the x mean?

837
00:37:33,060 --> 00:37:34,270
Crystalline.

838
00:37:34,270 --> 00:37:35,180
Single crystal.

839
00:37:35,180 --> 00:37:38,720
Make sure no one is thinking
this is being performed in the

840
00:37:38,720 --> 00:37:39,740
liquid phase.

841
00:37:39,740 --> 00:37:44,870
And this diborane decomposes
to elemental boron plus

842
00:37:44,870 --> 00:37:47,800
hydrogen gas.

843
00:37:47,800 --> 00:37:51,910
So hydrogen is a gas, and the
boron goes into the silicon.

844
00:37:51,910 --> 00:37:54,720
Boron goes into the silicon
where it goes on to the

845
00:37:54,720 --> 00:37:56,530
silicon sites.

846
00:37:56,530 --> 00:37:58,170
I could just write a rate
constant for this.

847
00:37:58,170 --> 00:38:00,240
We just studied kinetics.

848
00:38:00,240 --> 00:38:00,640
I don't know.

849
00:38:00,640 --> 00:38:01,000
What is it?

850
00:38:01,000 --> 00:38:02,280
Second order?

851
00:38:02,280 --> 00:38:04,350
You know, it doesn't have to be
integral order, by the way.

852
00:38:04,350 --> 00:38:06,730
It could be of order 1.5.

853
00:38:06,730 --> 00:38:10,160
Nothing is saying it has
to be integral order.

854
00:38:10,160 --> 00:38:11,110
OK.

855
00:38:11,110 --> 00:38:15,170
So now what I want to do is I
want to ask, what happens as

856
00:38:15,170 --> 00:38:16,530
the boron goes in?

857
00:38:16,530 --> 00:38:19,560
So that's the next question.

858
00:38:19,560 --> 00:38:20,960
As it diffuses in.

859
00:38:20,960 --> 00:38:24,110
So what I'm going to do is I'm
going to draw this little

860
00:38:24,110 --> 00:38:25,360
cartoon here.

861
00:38:27,850 --> 00:38:31,170
So I want to look at here's the
surface of the silicon.

862
00:38:31,170 --> 00:38:36,070
So I've got a gas phase here and
I've got boron going into

863
00:38:36,070 --> 00:38:38,580
the silicon crystal.

864
00:38:38,580 --> 00:38:40,610
So I'm going to now get a little
bit quantitative, if

865
00:38:40,610 --> 00:38:41,580
you'll permit.

866
00:38:41,580 --> 00:38:44,000
And so it's going to
look like this.

867
00:38:44,000 --> 00:38:46,630
And put it right underneath
here.

868
00:38:46,630 --> 00:38:50,530
So this is x. this
is depth from the

869
00:38:50,530 --> 00:38:52,660
surface of the silicon.

870
00:38:52,660 --> 00:38:54,650
So this is the free surface
of the silicon.

871
00:38:54,650 --> 00:38:57,390
And I start off with some
concentration surface

872
00:38:57,390 --> 00:38:58,670
value, c sub s.

873
00:38:58,670 --> 00:39:01,450
Meaning concentration
at the surface.

874
00:39:01,450 --> 00:39:03,460
And that's fixed.

875
00:39:03,460 --> 00:39:11,460
So cs fixed by B2H6

876
00:39:11,460 --> 00:39:13,910
concentration in the gas phase.

877
00:39:13,910 --> 00:39:14,660
So that's fixed.

878
00:39:14,660 --> 00:39:17,670
Now, question is, what
does it look like?

879
00:39:17,670 --> 00:39:19,060
The advance of the boron?

880
00:39:19,060 --> 00:39:20,190
So this is now the

881
00:39:20,190 --> 00:39:23,560
concentration of boron in silicon.

882
00:39:23,560 --> 00:39:25,860
This is the silicon
crystal here.

883
00:39:25,860 --> 00:39:26,840
So what does it look like?

884
00:39:26,840 --> 00:39:30,440
Well, one possibility is it goes
in like this as a front.

885
00:39:30,440 --> 00:39:34,290
See if I wait, goes in farther
and farther and farther.

886
00:39:34,290 --> 00:39:35,510
That doesn't happen.

887
00:39:35,510 --> 00:39:36,760
Sorry.

888
00:39:36,760 --> 00:39:38,330
Take that off.

889
00:39:38,330 --> 00:39:39,660
You know what happens?

890
00:39:39,660 --> 00:39:41,580
Same thing we've been
looking at all day.

891
00:39:44,870 --> 00:39:48,530
So now what's the question?

892
00:39:48,530 --> 00:39:50,870
Question is, what's the
functionality of this?

893
00:39:50,870 --> 00:39:52,470
Is this 1 over c?

894
00:39:52,470 --> 00:39:54,570
Is this log c?

895
00:39:54,570 --> 00:39:57,200
Is this some other
function of c?

896
00:39:57,200 --> 00:40:05,590
I want to map this into some f
of c versus g of x so I can

897
00:40:05,590 --> 00:40:06,840
get a straight line.

898
00:40:06,840 --> 00:40:07,900
Why do I want a straight line?

899
00:40:07,900 --> 00:40:09,330
Because I want to
be quantitative.

900
00:40:09,330 --> 00:40:12,900
Because you are in charge of
designing a fab line and they

901
00:40:12,900 --> 00:40:14,930
want to know what the resonance
time of a silicon

902
00:40:14,930 --> 00:40:18,990
wafer is supposed to be at
billion dollars multiples.

903
00:40:18,990 --> 00:40:22,230
You know, the units are in
billions of dollars.

904
00:40:22,230 --> 00:40:24,580
So you don't want to make the
fab line any bigger than it

905
00:40:24,580 --> 00:40:28,700
needs to be, the resident's
time any longer.

906
00:40:28,700 --> 00:40:30,680
This is only way you're going
to be able to design it.

907
00:40:30,680 --> 00:40:33,710
You have to understand this
because the design

908
00:40:33,710 --> 00:40:36,460
specification is going to
be dope to a certain

909
00:40:36,460 --> 00:40:38,490
concentration of a
certain depth.

910
00:40:38,490 --> 00:40:43,210
So how long does it take
to get boron in?

911
00:40:43,210 --> 00:40:44,360
You can tell me.

912
00:40:44,360 --> 00:40:48,040
Set the concentration here
and wait 5 minutes,

913
00:40:48,040 --> 00:40:50,020
10 minutes, 30 minutes.

914
00:40:50,020 --> 00:40:51,110
Two companies.

915
00:40:51,110 --> 00:40:54,480
One takes 30 minutes to process
the wafer, the other

916
00:40:54,480 --> 00:40:56,510
takes 10 minutes to
process the wafer.

917
00:40:56,510 --> 00:40:58,370
Guess which company is going
to be in business

918
00:40:58,370 --> 00:41:00,140
two years from now?

919
00:41:00,140 --> 00:41:02,730
It's not going to be the one
that takes a long time.

920
00:41:02,730 --> 00:41:04,320
Hint.

921
00:41:04,320 --> 00:41:07,560
So we need to know what
the rules are here.

922
00:41:07,560 --> 00:41:09,570
And the mathematical
formulation was

923
00:41:09,570 --> 00:41:12,930
set by Adolf Fick.

924
00:41:12,930 --> 00:41:18,440
Adolf Fick, 1855, answered
the question, what is the

925
00:41:18,440 --> 00:41:20,975
form of that line?

926
00:41:23,650 --> 00:41:25,010
He's an interesting guy.

927
00:41:25,010 --> 00:41:26,505
He was at the University
of Zurich.

928
00:41:29,510 --> 00:41:31,410
And it's sort of like
the Balmer story.

929
00:41:31,410 --> 00:41:32,120
Remember J.J.

930
00:41:32,120 --> 00:41:34,260
Balmer was the school teacher
in Switzerland.

931
00:41:34,260 --> 00:41:36,120
This guy was in Switzerland,
too.

932
00:41:36,120 --> 00:41:37,930
Something going on there in
Switzerland in the late

933
00:41:37,930 --> 00:41:39,060
eighteen hundreds.

934
00:41:39,060 --> 00:41:39,990
So remember J.J.

935
00:41:39,990 --> 00:41:40,900
Balmer?

936
00:41:40,900 --> 00:41:45,180
He fit not his own data, he
fit the data of Angstrom.

937
00:41:45,180 --> 00:41:46,610
Angstrom made the measurements,

938
00:41:46,610 --> 00:41:48,080
Balmer fit the data.

939
00:41:48,080 --> 00:41:50,700
Well, same thing here.

940
00:41:50,700 --> 00:41:52,310
Fick did not make the
measurements.

941
00:41:52,310 --> 00:41:56,120
He looked at some data that had
been taken back in 1833 by

942
00:41:56,120 --> 00:41:58,960
Thomas Graham.

943
00:41:58,960 --> 00:42:04,290
Thomas Graham had been making
measurements back in the 1830s

944
00:42:04,290 --> 00:42:08,110
of gases diffusing through
porous membranes.

945
00:42:15,670 --> 00:42:16,900
Or just say, through
membranes.

946
00:42:16,900 --> 00:42:18,270
Obviously, if they
weren't porous

947
00:42:18,270 --> 00:42:20,160
they wouldn't be diffusing.

948
00:42:20,160 --> 00:42:20,760
Redundancy.

949
00:42:20,760 --> 00:42:21,870
Department of Redundancy.

950
00:42:21,870 --> 00:42:23,690
This is diffusing through
membranes.

951
00:42:23,690 --> 00:42:26,290
So what happened was
that he modeled it.

952
00:42:26,290 --> 00:42:28,480
And here's what he
came up with.

953
00:42:28,480 --> 00:42:29,300
He came up with--

954
00:42:29,300 --> 00:42:31,270
oh, by the way.

955
00:42:31,270 --> 00:42:32,710
I didn't mention what he was.

956
00:42:32,710 --> 00:42:35,700
He was a physiologist. He
was a medical doctor.

957
00:42:35,700 --> 00:42:39,430
He just poured through the
scientific literature for

958
00:42:39,430 --> 00:42:41,350
amusement, evidently.

959
00:42:41,350 --> 00:42:41,690
OK.

960
00:42:41,690 --> 00:42:45,820
So this is what Fick gave us
as the model for the data.

961
00:42:45,820 --> 00:42:50,760
He gave us what we know as
Fick's First Law, Fick's First

962
00:42:50,760 --> 00:42:52,166
Law of Diffusion.

963
00:42:52,166 --> 00:42:56,200
And we'll just call it FFL,
Fick's First Law of Diffusion.

964
00:42:56,200 --> 00:42:58,780
And we'll write Ficks'
First Law J.

965
00:42:58,780 --> 00:43:02,190
J, which is the flux.

966
00:43:02,190 --> 00:43:06,710
This is the unit of measure of
mass transport, the flux,

967
00:43:06,710 --> 00:43:09,390
which obviously is the
mass flow rate.

968
00:43:09,390 --> 00:43:12,700
We said this is mass transport,
so this is the mass

969
00:43:12,700 --> 00:43:18,920
flow right of species i, OK?

970
00:43:18,920 --> 00:43:22,500
And we're going to say in the
x-direction because things

971
00:43:22,500 --> 00:43:23,850
diffuse in all directions,
right?

972
00:43:23,850 --> 00:43:27,530
If I open a perfume bottle here,
the diffusion will take

973
00:43:27,530 --> 00:43:28,670
place in all directions.

974
00:43:28,670 --> 00:43:30,510
So I'm going to make
this one dimension.

975
00:43:30,510 --> 00:43:34,210
So the flux is a mass flow rate
of i in the x-direction.

976
00:43:34,210 --> 00:43:36,840
J sub i in the x-direction.

977
00:43:36,840 --> 00:43:38,850
Remember we said the
Chemical Rate Law?

978
00:43:38,850 --> 00:43:43,310
We said the Chemical Rate Law
was that the rate of progress

979
00:43:43,310 --> 00:43:46,670
of a chemical reaction goes
as the concentration.

980
00:43:46,670 --> 00:43:50,900
Well, Fick studied Graham's
data and he said, the flux

981
00:43:50,900 --> 00:43:52,980
doesn't go as the
concentration.

982
00:43:52,980 --> 00:43:57,120
It goes as the gradient
in the concentration.

983
00:43:57,120 --> 00:43:58,770
That's how you linearize
those data.

984
00:43:58,770 --> 00:44:03,190
So you take the concentration
gradient, which is dc by dx.

985
00:44:03,190 --> 00:44:03,560
OK.

986
00:44:03,560 --> 00:44:06,870
So that's the concentration
gradient.

987
00:44:06,870 --> 00:44:12,820
Gradient in concentration
of i in the x-direction.

988
00:44:12,820 --> 00:44:15,520
You could write this as--

989
00:44:15,520 --> 00:44:16,430
make this vector--

990
00:44:16,430 --> 00:44:17,650
but we're not going
to do that.

991
00:44:17,650 --> 00:44:19,200
It would make it one-dimensional
here.

992
00:44:19,200 --> 00:44:22,390
And the constant of
proportionality is d sub i,

993
00:44:22,390 --> 00:44:25,470
which is called the diffusivity
or the diffusion

994
00:44:25,470 --> 00:44:26,720
coefficient.

995
00:44:30,320 --> 00:44:32,520
And puts the minus sign.

996
00:44:32,520 --> 00:44:34,010
Why?

997
00:44:34,010 --> 00:44:36,300
Well, you know things move from
high concentration to low

998
00:44:36,300 --> 00:44:37,950
concentration, right?

999
00:44:37,950 --> 00:44:41,130
So I open the perfume bottle,
the odor gets--

1000
00:44:41,130 --> 00:44:44,100
the odor, pardon me-- the
fragrance gets stronger as you

1001
00:44:44,100 --> 00:44:45,240
get closer to the bottle.

1002
00:44:45,240 --> 00:44:47,860
Things move from high
concentration the low

1003
00:44:47,860 --> 00:44:48,420
concentration.

1004
00:44:48,420 --> 00:44:51,020
So if I gave you this
concentration profile--

1005
00:44:51,020 --> 00:44:52,290
what's profile mean?

1006
00:44:52,290 --> 00:44:53,830
Profile means--

1007
00:44:53,830 --> 00:44:55,690
this is a concentration
profile--

1008
00:45:02,030 --> 00:45:04,830
if I draw someone like this,
this is head on, right?

1009
00:45:04,830 --> 00:45:07,760
And if I do the right view like

1010
00:45:07,760 --> 00:45:11,120
this, this is the profile.

1011
00:45:11,120 --> 00:45:11,730
Profile.

1012
00:45:11,730 --> 00:45:12,220
Side view.

1013
00:45:12,220 --> 00:45:13,840
This is profile.

1014
00:45:13,840 --> 00:45:17,540
Concentration profile,
obviously, the concentration

1015
00:45:17,540 --> 00:45:19,550
is higher to the left.

1016
00:45:19,550 --> 00:45:21,220
So things are moving
from left to right.

1017
00:45:21,220 --> 00:45:22,640
But look at the slope.

1018
00:45:22,640 --> 00:45:24,720
The slope is a negative
number.

1019
00:45:24,720 --> 00:45:26,790
So if the slope is a negative
number, but I want to get a

1020
00:45:26,790 --> 00:45:30,860
positive flux, I need to have
the minus sign in here.

1021
00:45:30,860 --> 00:45:32,050
Diffusivity is a physical
constant.

1022
00:45:32,050 --> 00:45:33,640
It has to be a positive
number.

1023
00:45:33,640 --> 00:45:34,900
So this is Fick's First Law.

1024
00:45:40,980 --> 00:45:43,470
I'll just give you the units
and then we'll stop.

1025
00:45:43,470 --> 00:45:44,220
So what are the units?

1026
00:45:44,220 --> 00:45:49,070
Well, the units in flux are in
SI units kilograms per second.

1027
00:45:49,070 --> 00:45:51,880
And we're going in one
direction, and so as we're

1028
00:45:51,880 --> 00:45:56,090
trying to diffuse into this
piece of silicon, we have to

1029
00:45:56,090 --> 00:45:58,100
normalize it per unit area.

1030
00:45:58,100 --> 00:46:00,980
So it's kilograms per meter
squared per second.

1031
00:46:00,980 --> 00:46:06,080
You know that concentration is
kilograms per cubic meter.

1032
00:46:06,080 --> 00:46:10,440
d by dx is 1 over meter, which
means then that the diffuse

1033
00:46:10,440 --> 00:46:14,600
coefficient or the diffusivity
has units of length squared

1034
00:46:14,600 --> 00:46:15,970
per unit time.

1035
00:46:15,970 --> 00:46:19,970
This is the units of the
diffusion coefficient.

1036
00:46:19,970 --> 00:46:21,490
And we'll get back to
business next day.

1037
00:46:21,490 --> 00:46:24,750
David, may we cut to the
slides again, please?

1038
00:46:31,920 --> 00:46:32,740
OK.

1039
00:46:32,740 --> 00:46:36,520
So I talked to you about--

1040
00:46:36,520 --> 00:46:36,720
oh, yeah.

1041
00:46:36,720 --> 00:46:37,330
There's all this.

1042
00:46:37,330 --> 00:46:39,500
You see they give
you a half-life?

1043
00:46:39,500 --> 00:46:40,410
Crazy.

1044
00:46:40,410 --> 00:46:41,420
Forget it.

1045
00:46:41,420 --> 00:46:42,010
OK.

1046
00:46:42,010 --> 00:46:44,880
There's the book talking about
activated catalog, da, da, da.

1047
00:46:44,880 --> 00:46:46,460
This is Fick's First Law.

1048
00:46:46,460 --> 00:46:48,820
This is the paper from 1855.

1049
00:46:48,820 --> 00:46:53,640
Go ahead. "On the Influence of
Diffusion" by Dr. Adolph Fick.

1050
00:46:53,640 --> 00:46:57,150
So the number one catalyst
in the world, number one

1051
00:46:57,150 --> 00:47:01,020
application is automotive
catalysts for exhaust. So

1052
00:47:01,020 --> 00:47:03,130
gasoline is octane.

1053
00:47:03,130 --> 00:47:05,520
C8H18, which we burn in air.

1054
00:47:05,520 --> 00:47:08,520
We burn it in air, we
make hydrocarbons.

1055
00:47:08,520 --> 00:47:10,880
Pardon me, we burn hydrocarbons,
which obviously

1056
00:47:10,880 --> 00:47:14,610
means the carbon goes to
CO2, ideally, and the

1057
00:47:14,610 --> 00:47:16,020
hydrogen goes to H2O.

1058
00:47:16,020 --> 00:47:17,870
But sometimes you get incomplete
combustion.

1059
00:47:17,870 --> 00:47:18,930
I already showed you that.

1060
00:47:18,930 --> 00:47:20,580
Maybe we stop it CO.

1061
00:47:20,580 --> 00:47:23,320
But remember, air
is 4/5 nitrogen.

1062
00:47:23,320 --> 00:47:26,020
So when you burn hydrocarbons
you also, at these high

1063
00:47:26,020 --> 00:47:31,980
temperatures, mix nitrogen
and oxygen and make NOx.

1064
00:47:31,980 --> 00:47:34,310
And is was actually the
precursor to smog.

1065
00:47:34,310 --> 00:47:39,620
So what we want to do is to
eliminate these imperfect

1066
00:47:39,620 --> 00:47:40,570
combustions.

1067
00:47:40,570 --> 00:47:43,590
So we want to convert the
unburned hydrocarbons.

1068
00:47:43,590 --> 00:47:49,490
There's actually some of the CH
compounds, volatile, then

1069
00:47:49,490 --> 00:47:50,190
don't get burned.

1070
00:47:50,190 --> 00:47:52,600
We want to burn those
to H2O in water--

1071
00:47:52,600 --> 00:47:54,570
pardon me, H2O in CO2.

1072
00:47:54,570 --> 00:47:57,670
The unburned CO has
to go to CO2.

1073
00:47:57,670 --> 00:48:00,120
You might say, but isn't
CO2 a greenhouse gas?

1074
00:48:00,120 --> 00:48:00,660
Yeah, it is.

1075
00:48:00,660 --> 00:48:04,260
But you know, given the choice
of carbon monoxide and carbon

1076
00:48:04,260 --> 00:48:07,750
dioxide, my advice is go
with carbon dioxide.

1077
00:48:07,750 --> 00:48:09,590
Carbon monoxide will
kill you at about

1078
00:48:09,590 --> 00:48:11,160
200 parts per million.

1079
00:48:11,160 --> 00:48:12,780
And then NOx, we
want to convert

1080
00:48:12,780 --> 00:48:14,960
that to carbon dioxide.

1081
00:48:14,960 --> 00:48:17,960
So GM alone tried over
1,500 catalysts.

1082
00:48:17,960 --> 00:48:18,950
Why GM?

1083
00:48:18,950 --> 00:48:20,240
Why not the auto industry?

1084
00:48:20,240 --> 00:48:22,900
Because the U.S. Government,
in its wisdom back in the

1085
00:48:22,900 --> 00:48:27,400
1970s, invoked the Sherman
Antitrust Act and forbid the

1086
00:48:27,400 --> 00:48:31,360
automobile industry to
collaborate in the search for

1087
00:48:31,360 --> 00:48:33,870
a catalyst. And since they
didn't understand the science

1088
00:48:33,870 --> 00:48:36,400
of catalysis it was
trial and error.

1089
00:48:36,400 --> 00:48:37,840
By inspection.

1090
00:48:37,840 --> 00:48:40,000
And it's a huge space,
trying things.

1091
00:48:40,000 --> 00:48:43,110
But they eventually found,
after 1,500 tests,

1092
00:48:43,110 --> 00:48:46,330
platinum-palladium works for
hydrocarbons and CO, and

1093
00:48:46,330 --> 00:48:47,680
rhodium works for NOx.

1094
00:48:47,680 --> 00:48:50,020
It's almost as though mother
nature said, I'll give you a

1095
00:48:50,020 --> 00:48:52,570
catalyst and it's going to be
the most expensive part of the

1096
00:48:52,570 --> 00:48:53,750
Periodic Table.

1097
00:48:53,750 --> 00:48:57,730
You buy this stuff at the
jewelry store, you see.

1098
00:48:57,730 --> 00:49:00,130
Furthermore, this is an
oxidation reaction.

1099
00:49:00,130 --> 00:49:02,030
This is an oxidation reaction.

1100
00:49:02,030 --> 00:49:03,660
This is a reduction reaction.

1101
00:49:03,660 --> 00:49:07,130
So if I told you I want you in
the same place at the same

1102
00:49:07,130 --> 00:49:10,560
time on a vehicle moving 80
miles an hour to conduct

1103
00:49:10,560 --> 00:49:14,020
simultaneous oxidation and
reduction reactions with no

1104
00:49:14,020 --> 00:49:16,600
intervention, you'd
say impossible.

1105
00:49:16,600 --> 00:49:17,680
They did it.

1106
00:49:17,680 --> 00:49:18,130
They did it.

1107
00:49:18,130 --> 00:49:22,320
This is the power of selectivity
of the catalyst.

1108
00:49:22,320 --> 00:49:24,980
So this is an old diagram
from GM literature.

1109
00:49:24,980 --> 00:49:28,360
Now we have fuel injectors,
here, but fuel goes into the

1110
00:49:28,360 --> 00:49:31,520
engine, out to the exhaust.
There's an oxygen sensor,

1111
00:49:31,520 --> 00:49:32,940
which I'll show you next day.

1112
00:49:32,940 --> 00:49:38,725
Oxygen sensor measures what
composition of the output gas

1113
00:49:38,725 --> 00:49:42,410
is, sends it to an electronic
control module, which then

1114
00:49:42,410 --> 00:49:43,890
goes back into the carburetor.

1115
00:49:43,890 --> 00:49:47,080
And the catalytic convert
is right here.

1116
00:49:47,080 --> 00:49:51,180
And Dave, if you show
the document camera.

1117
00:49:51,180 --> 00:49:52,230
This is the monolith.

1118
00:49:52,230 --> 00:49:56,000
This is a piece of ceramic
because platinum and rhodium

1119
00:49:56,000 --> 00:49:58,470
and all of these other elements
are so expensive.

1120
00:49:58,470 --> 00:50:00,245
See, this thing's having
a hard time.

1121
00:50:00,245 --> 00:50:01,480
So we'll cheat a little bit.

1122
00:50:01,480 --> 00:50:04,450
We'll put this here and
then it'll focus.

1123
00:50:04,450 --> 00:50:04,860
All right.

1124
00:50:04,860 --> 00:50:08,000
So what you're looking at,
these are long channels.

1125
00:50:08,000 --> 00:50:12,100
And just to give you a scale,
this is about a half of a

1126
00:50:12,100 --> 00:50:13,210
millimeter.

1127
00:50:13,210 --> 00:50:15,560
This is about a half a
millimeter square and they go

1128
00:50:15,560 --> 00:50:18,570
all the way down for a length
of about eight inches.

1129
00:50:18,570 --> 00:50:23,850
And then the walls, the interior
walls, are coated

1130
00:50:23,850 --> 00:50:26,400
with a very, very thin
layer of platinum,

1131
00:50:26,400 --> 00:50:27,750
palladium, and rhodium.

1132
00:50:27,750 --> 00:50:29,680
Because these are expensive
metals.

1133
00:50:29,680 --> 00:50:31,440
And it's a surface effect.

1134
00:50:31,440 --> 00:50:35,110
So you get no value if you have
an inch deep of platinum.

1135
00:50:35,110 --> 00:50:37,180
The only stuff that works
is the free surface.

1136
00:50:37,180 --> 00:50:39,390
What you'd really like
is a monolayer.

1137
00:50:39,390 --> 00:50:42,130
But a monolayer of platinum has
no mechanical strength.

1138
00:50:42,130 --> 00:50:45,710
So you put the platinum,
palladium, and rhodium down on

1139
00:50:45,710 --> 00:50:48,820
a catalyst support. and this
stuff is made of a ceramic,

1140
00:50:48,820 --> 00:50:52,180
it's magnesia, alumina silica
that's been extruded like

1141
00:50:52,180 --> 00:50:54,820
pasta, and then fired.

1142
00:50:54,820 --> 00:50:57,340
The technology is absolutely
phenomenal.

1143
00:50:57,340 --> 00:50:58,420
Goes into this.

1144
00:50:58,420 --> 00:51:00,540
And then to get the
platinum-palladium-rhodium

1145
00:51:00,540 --> 00:51:02,640
they have a very
thin acid wash.

1146
00:51:02,640 --> 00:51:06,480
chloroplatinic, chlororhodic
acid, wash, little bit of

1147
00:51:06,480 --> 00:51:10,660
surface tension, holds just a
little bit of water, fire, out

1148
00:51:10,660 --> 00:51:11,680
comes the metal.

1149
00:51:11,680 --> 00:51:13,770
Just thick enough.

1150
00:51:13,770 --> 00:51:16,830
If it's too thick, dilute the
concentration of the acid.

1151
00:51:16,830 --> 00:51:20,020
But use that precious
metal sparingly.

1152
00:51:20,020 --> 00:51:23,540
Platinum hit $2,000 an
ounce last year.

1153
00:51:23,540 --> 00:51:24,950
$2,000 an ounce.

1154
00:51:24,950 --> 00:51:26,846
You steal a car, throw
the car away, and get

1155
00:51:26,846 --> 00:51:28,096
the catalytic converter.

1156
00:51:31,230 --> 00:51:33,890
So anyway, that's underneath.

1157
00:51:33,890 --> 00:51:36,310
That's what's going on
underneath the car.

1158
00:51:36,310 --> 00:51:41,670
And actually, I'm holding for
you the elements of clean air,

1159
00:51:41,670 --> 00:51:42,850
the catalytic converter.

1160
00:51:42,850 --> 00:51:45,210
But the catalytic converter
can't work unless we control

1161
00:51:45,210 --> 00:51:47,540
the air to fuel ratio,
which we have to do

1162
00:51:47,540 --> 00:51:48,570
with an oxygen sensor.

1163
00:51:48,570 --> 00:51:49,660
I'll show you next day.

1164
00:51:49,660 --> 00:51:51,775
And you've got to feed
it into a CPU.

1165
00:51:51,775 --> 00:51:55,300
If you don't have a CPU, it
can't make rapid feedback to

1166
00:51:55,300 --> 00:51:57,610
keep adjusting the air-to-fuel
ratio.

1167
00:51:57,610 --> 00:51:59,770
All right, Dave. Let's
cut to slides and

1168
00:51:59,770 --> 00:52:01,870
we'll get out of here.

1169
00:52:01,870 --> 00:52:04,800
So I'll show you what
else is in here.

1170
00:52:04,800 --> 00:52:05,780
OK, there's that.

1171
00:52:05,780 --> 00:52:06,500
So there's the old thing.

1172
00:52:06,500 --> 00:52:07,640
There's the engine,
da, da, da.

1173
00:52:07,640 --> 00:52:09,500
Exhaust, the control module.

1174
00:52:09,500 --> 00:52:11,590
And look, in the old days
they actually had--

1175
00:52:11,590 --> 00:52:14,070
they look like little
ball bearings--

1176
00:52:14,070 --> 00:52:16,380
cost of these things
was phenomenal.

1177
00:52:16,380 --> 00:52:20,360
So last thing, we had to
go to unleaded gas.

1178
00:52:20,360 --> 00:52:23,070
Unleaded gas was brought in
because the lead would be

1179
00:52:23,070 --> 00:52:27,430
broken down into elemental lead
because lead is volatile

1180
00:52:27,430 --> 00:52:28,340
as an oxide.

1181
00:52:28,340 --> 00:52:30,230
The lead alloys with
the platinum.

1182
00:52:30,230 --> 00:52:31,970
Turns it into a lead
platinum alloy.

1183
00:52:31,970 --> 00:52:33,390
Lead has no catalytic value.

1184
00:52:33,390 --> 00:52:36,410
Because if it did, we would
use lead and not platinum.

1185
00:52:36,410 --> 00:52:36,750
OK.

1186
00:52:36,750 --> 00:52:39,890
We'll see you on Friday.