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PROFESSOR: OK, so kinetics we're
continuing with today.

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00:00:26,160 --> 00:00:29,200
We talked on Wednesday about
first order kinetics and we'll

10
00:00:29,200 --> 00:00:31,080
do a brief review
of some of that.

11
00:00:31,080 --> 00:00:33,650
And we're going to talk about
second order kinetics.

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00:00:33,650 --> 00:00:38,210
Today we're going to come back
up and talk about chemical

13
00:00:38,210 --> 00:00:40,540
equilibrium, which is something
I love to do to

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00:00:40,540 --> 00:00:43,080
review things that we've
talked about before.

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00:00:43,080 --> 00:00:46,260
And we're going to start in on
reaction mechanisms. So, I

16
00:00:46,260 --> 00:00:48,780
thought I would mention, some of
you have may have seen the

17
00:00:48,780 --> 00:00:52,520
activity in the Infinite
Corridor, but today is world

18
00:00:52,520 --> 00:00:59,210
AIDS day, and today a lot of the
compounds that are being

19
00:00:59,210 --> 00:01:04,360
used to treat HIV were actually
designed based on

20
00:01:04,360 --> 00:01:06,850
making inhibitors to enzymes.

21
00:01:06,850 --> 00:01:11,410
And so, to design those
pharmaceuticals, people had to

22
00:01:11,410 --> 00:01:14,570
understand the reaction
mechanism of the enzyme, and

23
00:01:14,570 --> 00:01:17,240
enzymes, of course, are
catalysts in the body.

24
00:01:17,240 --> 00:01:22,510
So, knowledge of what medical
individuals needed to know to

25
00:01:22,510 --> 00:01:26,230
design these inhibitors to treat
HIV are actually a lot

26
00:01:26,230 --> 00:01:28,570
from this unit that we're going
to be talking about.

27
00:01:28,570 --> 00:01:30,740
So, we'll be talking about
reaction mechanisms, and we're

28
00:01:30,740 --> 00:01:33,600
also going to be talking about
enzyme catalysis, which were

29
00:01:33,600 --> 00:01:35,910
key points in being able to
come up with some of the

30
00:01:35,910 --> 00:01:40,390
current treatments
against HIV.

31
00:01:40,390 --> 00:01:46,330
All right, so just a little
review from last Wednesday.

32
00:01:46,330 --> 00:01:49,280
We talked about first
order half life.

33
00:01:49,280 --> 00:01:52,810
We talked about first order
kinetics, we came up with an

34
00:01:52,810 --> 00:01:56,510
integrated first order
rate law, and we also

35
00:01:56,510 --> 00:01:58,380
talked about half life.

36
00:01:58,380 --> 00:02:03,200
And you told me last time that
an example of first order half

37
00:02:03,200 --> 00:02:06,450
life is radioactivity, which
we're going to be talking

38
00:02:06,450 --> 00:02:07,520
about today.

39
00:02:07,520 --> 00:02:11,700
So, just a little review from
last time, you have your first

40
00:02:11,700 --> 00:02:17,160
order integrated rate law, and
the half life is defined as

41
00:02:17,160 --> 00:02:20,400
the time it takes for half of
the original material to go

42
00:02:20,400 --> 00:02:24,540
away, and half life is
abbreviated t 1/2, that's the

43
00:02:24,540 --> 00:02:28,030
symbol for half life, so the
time for half of the original

44
00:02:28,030 --> 00:02:30,360
material to go away.

45
00:02:30,360 --> 00:02:34,080
If you plug original material
divided by 2 in there, then

46
00:02:34,080 --> 00:02:40,500
the original material a to the
o for original, drops out and

47
00:02:40,500 --> 00:02:44,100
you come up with this equation
of the natural log of 1/2

48
00:02:44,100 --> 00:02:47,770
equals minus k t 1/2,
and k is, of

49
00:02:47,770 --> 00:02:49,370
course, our rate constant.

50
00:02:49,370 --> 00:02:52,610
And so, then we can take the
natural log of a 1/2 and we

51
00:02:52,610 --> 00:02:53,580
get a value.

52
00:02:53,580 --> 00:02:56,700
Rearranging that, you get
half life equals 0 .

53
00:02:56,700 --> 00:02:59,710
6 9 3 1 over k.

54
00:02:59,710 --> 00:03:04,010
And so you told me last time for
this plot for first order

55
00:03:04,010 --> 00:03:07,060
half life, each half life,
half of the original

56
00:03:07,060 --> 00:03:10,260
material goes away.

57
00:03:10,260 --> 00:03:14,520
So, one example of a first order
half life process is

58
00:03:14,520 --> 00:03:16,630
radioactive decay.

59
00:03:16,630 --> 00:03:20,100
And the reason why this is a
first order process is because

60
00:03:20,100 --> 00:03:25,530
the decay of the nucleus is
independent of the number of

61
00:03:25,530 --> 00:03:28,640
surrounding nuclei that
has been decayed.

62
00:03:28,640 --> 00:03:31,650
So it's independent of
the original starting

63
00:03:31,650 --> 00:03:34,850
concentration, and since it's
independent, notice that's a

64
00:03:34,850 --> 00:03:38,630
blank in your notes, since it's
independent, then that

65
00:03:38,630 --> 00:03:42,740
makes it a first
order process.

66
00:03:42,740 --> 00:03:47,380
So, we can apply first order
integrated rate laws to

67
00:03:47,380 --> 00:03:53,120
radioactive decay.

68
00:03:53,120 --> 00:03:56,500
So here were some of the
equations we had last time.

69
00:03:56,500 --> 00:04:00,090
We had, this is a different
expression of the first order

70
00:04:00,090 --> 00:04:04,930
rate law where the material,
concentration material of

71
00:04:04,930 --> 00:04:07,540
material a, at some particular
time equals the original

72
00:04:07,540 --> 00:04:11,890
concentration, e to the minus k
t, where you have your rate

73
00:04:11,890 --> 00:04:15,670
constant and the time that has
elapsed, and we also just

74
00:04:15,670 --> 00:04:21,690
talked about first order half
lifes with this equation here.

75
00:04:21,690 --> 00:04:25,200
So, we can use those same
equations, but often you don't

76
00:04:25,200 --> 00:04:29,280
see it in terms of concentration
of a, you

77
00:04:29,280 --> 00:04:32,660
usually see these expressions in
terms of either the number

78
00:04:32,660 --> 00:04:36,610
of nuclei or a different a,
which is a for activity.

79
00:04:36,610 --> 00:04:40,710
So instead of concentration,
we're talking about the number

80
00:04:40,710 --> 00:04:47,010
of nuclei that have decay
or capital N.

81
00:04:47,010 --> 00:04:50,460
So, we can write this same
expression, but now using N

82
00:04:50,460 --> 00:04:54,820
instead of concentration of a,
same thing, number of nuclei

83
00:04:54,820 --> 00:04:58,870
equal the original number of
nuclei, e, to the minus k t,

84
00:04:58,870 --> 00:05:02,220
where k is our rate constant,
or in this case decay

85
00:05:02,220 --> 00:05:09,430
constant, and t is time.

86
00:05:09,430 --> 00:05:12,620
So, with chemical kinetics,
we're usually talking about

87
00:05:12,620 --> 00:05:16,190
the change in concentration of
things over time, but with

88
00:05:16,190 --> 00:05:18,660
nuclear kinetics, we're talking
about the number of

89
00:05:18,660 --> 00:05:20,790
decay events, the number of
nuclei that have decayed.

90
00:05:20,790 --> 00:05:26,370
And so, here with nuclear
kinetics, we measure these

91
00:05:26,370 --> 00:05:29,410
events using a Geiger counter.

92
00:05:29,410 --> 00:05:34,390
So this can measure radiation,
and I'm going to come around

93
00:05:34,390 --> 00:05:37,360
and just check the room.

94
00:05:37,360 --> 00:05:40,510
And so, the gasket's ionized
and then you

95
00:05:40,510 --> 00:05:41,630
hear different clicks.

96
00:05:41,630 --> 00:05:47,030
See if you can hear the clicks
as I come around.

97
00:05:47,030 --> 00:05:59,580
So let's just see if we have
any problems over here.

98
00:05:59,580 --> 00:06:07,590
Oh, maybe a little bit.

99
00:06:07,590 --> 00:06:12,800
No, this is fine.

100
00:06:12,800 --> 00:06:18,190
There's always a little bit of
radioactivity, it's all fine.

101
00:06:18,190 --> 00:06:25,260
So, this is a Geiger counter,
which will measure nuclear

102
00:06:25,260 --> 00:06:29,460
kinetics, it will measure
radioactivity.

103
00:06:29,460 --> 00:06:33,230
And my lab has this particular
one, because we use x-rays in

104
00:06:33,230 --> 00:06:36,640
our experiments.

105
00:06:36,640 --> 00:06:42,330
OK, we'll leave this on low
just to check things

106
00:06:42,330 --> 00:06:43,620
out as we go along.

107
00:06:43,620 --> 00:06:49,390
All right, so we do have
a term, A, that we talk

108
00:06:49,390 --> 00:06:50,480
about in this unit.

109
00:06:50,480 --> 00:06:53,900
Instead of concentration
of A, it's activity.

110
00:06:53,900 --> 00:07:00,330
And so, activity here, sort of
the decay rate, is also called

111
00:07:00,330 --> 00:07:04,290
activity, capital A, and so this
is equal to the change in

112
00:07:04,290 --> 00:07:08,740
the number of nuclei or our
decay constant times the

113
00:07:08,740 --> 00:07:12,510
number of nuclei.

114
00:07:12,510 --> 00:07:14,520
And people will often talk
about the activity of

115
00:07:14,520 --> 00:07:18,290
particular radioactive
compounds.

116
00:07:18,290 --> 00:07:21,640
So, because activity is
proportional to the number of

117
00:07:21,640 --> 00:07:27,010
nuclei, you can also take this
expression and write it as

118
00:07:27,010 --> 00:07:28,160
this expression.

119
00:07:28,160 --> 00:07:30,580
So you can have either the
number of nuclei equal the

120
00:07:30,580 --> 00:07:34,500
original number of nuclei, e to
the k t, or you can do it

121
00:07:34,500 --> 00:07:39,150
in terms of activity -- that the
activity at some time is

122
00:07:39,150 --> 00:07:44,330
equal to the original activity,
e to the minus k t.

123
00:07:44,330 --> 00:07:51,580
So, all of these equations can
be re-written in this way.

124
00:07:51,580 --> 00:08:03,170
So, let's talk a minute
about units.

125
00:08:03,170 --> 00:08:08,480
All right, so the activity for
units, the new activity is Bq,

126
00:08:08,480 --> 00:08:11,750
Becquerel. and that,
actually is named

127
00:08:11,750 --> 00:08:14,010
after a French person.

128
00:08:14,010 --> 00:08:17,260
Henry was his first name,
and my French

129
00:08:17,260 --> 00:08:19,360
pronunciation is not very good.

130
00:08:19,360 --> 00:08:20,940
This is the current unit.

131
00:08:20,940 --> 00:08:24,930
It's equal to one radioactive
disintegration per second.

132
00:08:24,930 --> 00:08:28,080
The older unit, which you may
be familiar with, is called

133
00:08:28,080 --> 00:08:30,980
the Curie, and that is 3 .

134
00:08:30,980 --> 00:08:35,090
7 times 10 to the 10
disintegrations per second.

135
00:08:35,090 --> 00:08:38,940
Does anyone want to guess,
the Curie unit, who

136
00:08:38,940 --> 00:08:40,110
that was named after?

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00:08:40,110 --> 00:08:44,930
STUDENT: Marie Curie?

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00:08:44,930 --> 00:08:47,220
PROFESSOR: No, it was named
after her husband actually,

139
00:08:47,220 --> 00:08:49,200
Pierre Curie.

140
00:08:49,200 --> 00:08:54,530
And I actually always assume,
because Marie is actually more

141
00:08:54,530 --> 00:08:57,800
famous than her husband.

142
00:08:57,800 --> 00:09:01,860
But she, Marie Curie won two
Nobel prizes, so we shouldn't

143
00:09:01,860 --> 00:09:04,390
feel too sorry for her.

144
00:09:04,390 --> 00:09:08,540
Her husband shared the first
Nobel Prize with her in, I

145
00:09:08,540 --> 00:09:13,300
think it was 1903, but then in
1906 he was killed in a road

146
00:09:13,300 --> 00:09:16,020
accident, run over by something
that was crossing

147
00:09:16,020 --> 00:09:17,440
the street.

148
00:09:17,440 --> 00:09:21,570
So he did not share the second
Nobel Prize, because by the

149
00:09:21,570 --> 00:09:26,630
time that came around about
1911, he had passed away.

150
00:09:26,630 --> 00:09:30,240
So, at first, we had the Curie,
but then that turned

151
00:09:30,240 --> 00:09:32,400
out to be a really big number.

152
00:09:32,400 --> 00:09:36,610
And so, when you were talking
about sort of safe units for

153
00:09:36,610 --> 00:09:40,240
workers to be exposed to, if
they were being exposed to

154
00:09:40,240 --> 00:09:44,790
things 10 to the 10, that really
isn't very healthy.

155
00:09:44,790 --> 00:09:49,350
So they wanted to have sort
of a much smaller unit.

156
00:09:49,350 --> 00:09:53,840
And so I guess that Marie Curie
at that point talked

157
00:09:53,840 --> 00:09:58,790
about how her husband would feel
about having the Curie

158
00:09:58,790 --> 00:10:02,050
not being the standard unit,
but I guess she was OK with

159
00:10:02,050 --> 00:10:05,470
it, because if we had kept that
same unit, then people

160
00:10:05,470 --> 00:10:08,500
would have been using it and it
would of had to of been a

161
00:10:08,500 --> 00:10:13,320
really, really small number,
because it was sort of picked

162
00:10:13,320 --> 00:10:15,820
to be set up to something that
was too large, and she didn't

163
00:10:15,820 --> 00:10:18,410
want her husband's name
apparently associated with a

164
00:10:18,410 --> 00:10:22,360
sort of an infinitesimally small
quantity of something.

165
00:10:22,360 --> 00:10:25,550
So, the Curie was sort
of done away with.

166
00:10:25,550 --> 00:10:28,250
And Henry Becquerel, who was
one of the people who

167
00:10:28,250 --> 00:10:31,940
discovered radioactivity and
shared that first Nobel Prize,

168
00:10:31,940 --> 00:10:34,690
had the unit named after him.

169
00:10:34,690 --> 00:10:38,890
And I always ask the freshman
chemistry class that as they

170
00:10:38,890 --> 00:10:43,710
go through MIT, if they ever
discover a unit that is named

171
00:10:43,710 --> 00:10:46,120
after a female scientist,
to please come

172
00:10:46,120 --> 00:10:47,860
back and let me know.

173
00:10:47,860 --> 00:10:50,100
This was the one I thought
was named after a female

174
00:10:50,100 --> 00:10:52,560
scientist, but as it
turns out, it was

175
00:10:52,560 --> 00:10:54,670
actually Pierre Curie.

176
00:10:54,670 --> 00:10:57,200
So, if you hear of any,
please let me

177
00:10:57,200 --> 00:11:01,420
know for future reference.

178
00:11:01,420 --> 00:11:05,780
So, the current unit you'll
be using is Bq here for

179
00:11:05,780 --> 00:11:09,000
radioactivity.

180
00:11:09,000 --> 00:11:11,170
So, you're not responsible for
knowing all the different

181
00:11:11,170 --> 00:11:13,340
types of radioactivity.

182
00:11:13,340 --> 00:11:16,020
When you're working problems,
you can always get this

183
00:11:16,020 --> 00:11:17,110
information.

184
00:11:17,110 --> 00:11:19,840
I'll just mention that a number
of different kinds of

185
00:11:19,840 --> 00:11:23,890
radioactivity, some involve
a mass change, some do not

186
00:11:23,890 --> 00:11:25,400
involve a mass change.

187
00:11:25,400 --> 00:11:28,290
So, alpha decay, this isn't
actually in your notes,

188
00:11:28,290 --> 00:11:30,100
there's a reference to
where the table is.

189
00:11:30,100 --> 00:11:32,530
You're not responsible for
memorizing it, so I didn't put

190
00:11:32,530 --> 00:11:33,800
it in the notes.

191
00:11:33,800 --> 00:11:37,990
An alpha decay is equivalent to
a helium 4 nucleus, so you

192
00:11:37,990 --> 00:11:41,080
lose two protons,
two neutrons, so

193
00:11:41,080 --> 00:11:42,650
that's a big mass change.

194
00:11:42,650 --> 00:11:46,490
Whereas say a beta decay
involves a loss of electrons,

195
00:11:46,490 --> 00:11:49,440
so there's no mass change
associated with that.

196
00:11:49,440 --> 00:11:52,590
So just to be aware that there
are these differences in

197
00:11:52,590 --> 00:11:57,040
different types of radiation.

198
00:11:57,040 --> 00:11:59,760
There's also really big
differences in terms of half

199
00:11:59,760 --> 00:12:03,460
lives of radioactive isotopes,
and again, this information

200
00:12:03,460 --> 00:12:06,620
would be given to you on a test
or a problem-set, so you

201
00:12:06,620 --> 00:12:09,930
don't have to memorize it.

202
00:12:09,930 --> 00:12:13,620
So, this table is similar to
one in your book, and the

203
00:12:13,620 --> 00:12:17,180
point here is just how different
half lifes can be.

204
00:12:17,180 --> 00:12:23,670
So the abbreviation a here
is year, d is day.

205
00:12:23,670 --> 00:12:28,760
So you see some of these half
lifes are in multiple years,

206
00:12:28,760 --> 00:12:31,810
some of them are days, so there
are big differences in

207
00:12:31,810 --> 00:12:36,000
terms of the half life of some
of these radioactive isotopes.

208
00:12:36,000 --> 00:12:38,660
Some of them stay around
for a really, really,

209
00:12:38,660 --> 00:12:42,700
really, really long time.

210
00:12:42,700 --> 00:12:47,310
So, I thought I would share
with you a poem about half

211
00:12:47,310 --> 00:12:49,290
lifes today.

212
00:12:49,290 --> 00:12:52,400
And this was written by a former
graduate student at

213
00:12:52,400 --> 00:12:55,790
MIT, Mala Radhakrishnan, and
she is now a professor at

214
00:12:55,790 --> 00:13:01,690
Wellesley college right here in
Wellesley, Massachusetts.

215
00:13:01,690 --> 00:13:05,640
So, her poem entitled "Days of
our half lives," is from her

216
00:13:05,640 --> 00:13:08,900
collection of chemistry poetry,
"Chemistry for the

217
00:13:08,900 --> 00:13:16,360
Couch Potato." And this
particular poem involves the

218
00:13:16,360 --> 00:13:21,690
uranium 238 decay series.

219
00:13:21,690 --> 00:13:23,760
So, here we go.

220
00:13:23,760 --> 00:13:29,520
"Days of our half lives.

221
00:13:29,520 --> 00:13:33,050
My dearest love, I writing
you to tell you all

222
00:13:33,050 --> 00:13:34,450
that I've been through.

223
00:13:34,450 --> 00:13:38,720
I've changed my whole identity,
but loved, I can not

224
00:13:38,720 --> 00:13:40,380
pretend to be.

225
00:13:40,380 --> 00:13:45,950
When I was uranium 238, you
were on my case to start

226
00:13:45,950 --> 00:13:46,690
losing weight.

227
00:13:46,690 --> 00:13:52,580
For 5 billion years I'd hoped
and I prayed, and finally I

228
00:13:52,580 --> 00:13:55,890
had an alpha decay.

229
00:13:55,890 --> 00:14:00,200
Two protons, two neutrons went
right out the door, and now I

230
00:14:00,200 --> 00:14:03,230
was thorium 234.

231
00:14:03,230 --> 00:14:07,630
But my nucleus was still unfit
for your eyes, not positive

232
00:14:07,630 --> 00:14:10,970
enough for it's large size.

233
00:14:10,970 --> 00:14:14,360
But this time my half life was
really not very long, because

234
00:14:14,360 --> 00:14:17,290
my will to change was
quite strong.

235
00:14:17,290 --> 00:14:21,150
It took just a month, not even
a millennium, to beta decay

236
00:14:21,150 --> 00:14:24,550
into protactinium.

237
00:14:24,550 --> 00:14:27,490
But you still rejected
me right off the bat,

238
00:14:27,490 --> 00:14:30,050
protactinium, who's
heard of that?

239
00:14:30,050 --> 00:14:35,810
So, beta decay, I did much more
to become uranium 234.

240
00:14:35,810 --> 00:14:39,560
Myself again, but a new isotope,
you still weren't

241
00:14:39,560 --> 00:14:42,240
satisfied, but I
still had hope.

242
00:14:42,240 --> 00:14:45,850
Three alpha decays, it was hard,
but I stayed on through

243
00:14:45,850 --> 00:14:51,120
thorium, through radium,
and then radon.

244
00:14:51,120 --> 00:14:54,170
I thought I would finally please
you, my mass was a

245
00:14:54,170 --> 00:14:59,420
healthy 222, but you said,
although I like your mass, I

246
00:14:59,420 --> 00:15:04,500
do not want to be with
a noble gas.

247
00:15:04,500 --> 00:15:07,810
You had a point, I wasn't
reactive, so in order to

248
00:15:07,810 --> 00:15:10,140
please you, I stayed
proactive.

249
00:15:10,140 --> 00:15:13,420
A few days later I found you
and said, two more alpha

250
00:15:13,420 --> 00:15:18,870
decays and now I am lead.

251
00:15:18,870 --> 00:15:22,270
You shook your head, you
were not too keen on my

252
00:15:22,270 --> 00:15:24,310
mass number of 214.

253
00:15:24,310 --> 00:15:28,730
I had a bad experience with that
mass before, an unstable

254
00:15:28,730 --> 00:15:32,660
acitone walked right
out the door.

255
00:15:32,660 --> 00:15:36,350
So in order to change, I went
away, but all I could do was

256
00:15:36,350 --> 00:15:38,330
just beta decay.

257
00:15:38,330 --> 00:15:41,710
My hopes and my dreams started
to go under, because beta

258
00:15:41,710 --> 00:15:45,120
decays don't change
a mass number.

259
00:15:45,120 --> 00:15:50,310
To bismuth, then polonium, I
hoped and I beckoned, my half

260
00:15:50,310 --> 00:15:53,110
life was 164 micro seconds.

261
00:15:53,110 --> 00:15:57,510
And then finally I alpha decayed
and then I was lead

262
00:15:57,510 --> 00:16:02,130
with the prize worthy
mass of 210.

263
00:16:02,130 --> 00:16:05,030
I've got to admit I was getting
quite tired, my

264
00:16:05,030 --> 00:16:08,110
patience with you had
nearly expired.

265
00:16:08,110 --> 00:16:12,910
You were more demanding than
any I dated, and much of my

266
00:16:12,910 --> 00:16:17,800
energy had already
been liberated.

267
00:16:17,800 --> 00:16:20,920
But you still weren't happy,
but you had a fix, I really

268
00:16:20,920 --> 00:16:25,930
like the number of 206, So I
waited for years until the

269
00:16:25,930 --> 00:16:30,310
day, which began with another
beta decay, and then one more,

270
00:16:30,310 --> 00:16:34,010
and finally in the
end I alpha-ed to

271
00:16:34,010 --> 00:16:37,020
lead 206, my friend.

272
00:16:37,020 --> 00:16:40,260
To change any further I wouldn't
be able, no longer

273
00:16:40,260 --> 00:16:42,560
active, but happily stable.

274
00:16:42,560 --> 00:16:45,940
It took me billions of years
to do, and look how I've

275
00:16:45,940 --> 00:16:49,640
changed and all just for you.

276
00:16:49,640 --> 00:16:53,180
And wait, what did you say?

277
00:16:53,180 --> 00:16:57,460
You've gotten so old that
I'd rather be with a

278
00:16:57,460 --> 00:17:02,280
young lass of gold?

279
00:17:02,280 --> 00:17:04,740
Well, I give up, we're
through, my pumpkin.

280
00:17:04,740 --> 00:17:07,300
Shouldn't all my effort be
counting for something?

281
00:17:07,300 --> 00:17:10,440
Well, you won't be able to rule
me any more, because I'm

282
00:17:10,440 --> 00:17:16,360
leaving you, not for
one atom, but four.

283
00:17:16,360 --> 00:17:20,350
That's right, when you were
away defusing, I met some

284
00:17:20,350 --> 00:17:24,770
chlorines that I found
quite amusing.

285
00:17:24,770 --> 00:17:31,490
So we're going to form lead c l
4, and you won't be hearing

286
00:17:31,490 --> 00:17:33,360
from me any more.

287
00:17:33,360 --> 00:17:37,040
See, over the years I've grown
quite wise, I've learned that

288
00:17:37,040 --> 00:17:39,230
love is about compromise.

289
00:17:39,230 --> 00:17:43,650
You still have half of your half
lives to live, so now you

290
00:17:43,650 --> 00:17:48,500
go out there, it's your
turn to give."

291
00:17:48,500 --> 00:17:58,320
And that is "The days of our
half lives." So, Mala takes

292
00:17:58,320 --> 00:18:01,490
great effort to make sure that
all her poetry not only

293
00:18:01,490 --> 00:18:04,450
rhymes, but it is chemically
correct.

294
00:18:04,450 --> 00:18:08,430
So, it's a good way to review
material to read "Chemistry

295
00:18:08,430 --> 00:18:12,590
from the Couch Potato."

296
00:18:12,590 --> 00:18:16,750
All right, so let's do an
example now and think about

297
00:18:16,750 --> 00:18:19,950
how things will change
over time.

298
00:18:19,950 --> 00:18:23,520
So we have an example, we want
to know the original activity,

299
00:18:23,520 --> 00:18:26,210
and the activity after 17 years

300
00:18:26,210 --> 00:18:29,670
of a sample of plutonium.

301
00:18:29,670 --> 00:18:33,480
So let's take a look at how
we'll do this problem.

302
00:18:33,480 --> 00:18:36,700
So first, given the information
up there, the

303
00:18:36,700 --> 00:18:38,540
first thing we want
to do is find the

304
00:18:38,540 --> 00:18:44,840
original number of nuclei.

305
00:18:44,840 --> 00:18:53,070
So first, capital N o, the
original number of nuclei.

306
00:18:53,070 --> 00:18:57,750
So, we're given information
about grams, so we have 0 .

307
00:18:57,750 --> 00:19:03,670
5 grams. And now if we want to
know the number of nuclei,

308
00:19:03,670 --> 00:19:08,260
what's the first thing
I have to do?

309
00:19:08,260 --> 00:19:10,270
Convert from grams to what?

310
00:19:10,270 --> 00:19:11,980
STUDENT: Moles.

311
00:19:11,980 --> 00:19:13,190
PROFESSOR: Moles, right.

312
00:19:13,190 --> 00:19:19,250
And here we want to use the
molecular mass that's given to

313
00:19:19,250 --> 00:19:20,970
us in the form of
that isotope.

314
00:19:20,970 --> 00:19:29,190
So here, we are given
information about 239, and so

315
00:19:29,190 --> 00:19:34,710
that's the number we want to
use in our conversions.

316
00:19:34,710 --> 00:19:37,460
So we can convert that over,
but that's going to give us

317
00:19:37,460 --> 00:19:42,410
moles, so how do we go from
moles to molecules?

318
00:19:42,410 --> 00:19:50,780
Avagadro's number, 6.022
times 10 to the 23.

319
00:19:50,780 --> 00:19:53,260
This time we're going to talk
about it in terms of nuclei

320
00:19:53,260 --> 00:20:00,160
per mole, and so that's going
to give us 1.3 times

321
00:20:00,160 --> 00:20:03,070
10 to the 21 nuclei.

322
00:20:03,070 --> 00:20:13,210
OK, so now we know the original
number of nuclei.

323
00:20:13,210 --> 00:20:16,470
The next thing we're going
to want to do is find k.

324
00:20:16,470 --> 00:20:23,280
And k is our rate constant for
decay or our decay constant.

325
00:20:23,280 --> 00:20:29,970
So what do we know about k for
a first order process?

326
00:20:29,970 --> 00:20:34,310
We know the equation for what?

327
00:20:34,310 --> 00:20:36,490
For first order half
life, right.

328
00:20:36,490 --> 00:20:38,210
So that's o .

329
00:20:38,210 --> 00:20:44,610
6 9 3 1 over t 1/2.

330
00:20:44,610 --> 00:20:48,510
And in this problem we were
given, the half life, and

331
00:20:48,510 --> 00:20:50,890
often you will be given the half
life or you can look it

332
00:20:50,890 --> 00:20:55,350
up, and so we can put that
in, so we have 0 .

333
00:20:55,350 --> 00:20:59,710
6 9 3 1 over 7 .

334
00:20:59,710 --> 00:21:04,830
6 times 10 to the 11 seconds.

335
00:21:04,830 --> 00:21:09,270
And we can calculate our
constant, which is 9 .

336
00:21:09,270 --> 00:21:18,250
1 times 10 to the minus
13 per second.

337
00:21:18,250 --> 00:21:21,430
So now we were asked to find the
original activity and the

338
00:21:21,430 --> 00:21:27,930
activity after 17 years.

339
00:21:27,930 --> 00:21:34,770
So, first we'll find the
original activity, and the

340
00:21:34,770 --> 00:21:39,940
original activity is going to be
equal to our rate constant

341
00:21:39,940 --> 00:21:42,900
times our original
number of nuclei.

342
00:21:42,900 --> 00:21:46,000
So we've just solved for both of
these, so we can plug these

343
00:21:46,000 --> 00:21:48,160
in, so we had 9 .

344
00:21:48,160 --> 00:21:56,070
1 times 10 the minus 13 per
second times the number of

345
00:21:56,070 --> 00:21:57,690
nuclei, 1 .

346
00:21:57,690 --> 00:22:05,360
3 times 10 to the 21
nuclei, equals 1 .

347
00:22:05,360 --> 00:22:12,660
2 times 10 to the 9, and what
are the units here?

348
00:22:12,660 --> 00:22:22,910
It's just like a hum, it's
hard to understand.

349
00:22:22,910 --> 00:22:25,390
STUDENT: Nuclei per second.

350
00:22:25,390 --> 00:22:30,430
PROFESSOR: Nuclei per second,
which is the same as what?

351
00:22:30,430 --> 00:22:34,080
That's equal to something
else.

352
00:22:34,080 --> 00:22:39,410
Yup, so that's the same as the
Becquerel or the Bq, so it's

353
00:22:39,410 --> 00:22:43,280
defined as nuclei per second,
or number of disintegrations

354
00:22:43,280 --> 00:22:47,740
per second.

355
00:22:47,740 --> 00:22:59,220
All right, so let's
do the last one.

356
00:22:59,220 --> 00:23:10,130
OK, so now after 17 years, so
now we can say that the

357
00:23:10,130 --> 00:23:14,660
activity at some time is equal
to the original activity, e to

358
00:23:14,660 --> 00:23:20,590
the minus k t, and we can put
in the activity that we just

359
00:23:20,590 --> 00:23:21,820
found, which is 1 .

360
00:23:21,820 --> 00:23:31,250
2 times 10 to the 9 Bq, times e
to the minus k, which is 9 .

361
00:23:31,250 --> 00:23:38,100
1 times 10 to the minus 13 per
second times 17 years, which

362
00:23:38,100 --> 00:23:40,130
in seconds is 5 .

363
00:23:40,130 --> 00:23:44,190
4 times 10 to the 8 second.

364
00:23:44,190 --> 00:23:47,610
So here, we want to make sure
that our units are going to

365
00:23:47,610 --> 00:23:50,230
cancel, and this is where
people often run into

366
00:23:50,230 --> 00:23:54,130
problems. They'll plug in 17
years, and then a rate

367
00:23:54,130 --> 00:23:57,470
constant, which was calculated
in seconds, and things will

368
00:23:57,470 --> 00:23:59,210
not cancel appropriately.

369
00:23:59,210 --> 00:24:02,500
So make sure that you get your
units consistent so that your

370
00:24:02,500 --> 00:24:07,310
seconds are going to cancel.

371
00:24:07,310 --> 00:24:11,530
And so this term, if we do the
math out here with the number

372
00:24:11,530 --> 00:24:15,560
significant figures, we find
that that equals 1.2

373
00:24:15,560 --> 00:24:18,660
times 10 to 9 Bq.

374
00:24:18,660 --> 00:24:22,260
That term is insignificant
in our problem.

375
00:24:22,260 --> 00:24:27,110
So, the original radioactivity
and the activity after 17

376
00:24:27,110 --> 00:24:32,420
years are the same in terms of
the significant figures.

377
00:24:32,420 --> 00:24:37,480
And so, I choose this problem to
emphasize a problem that we

378
00:24:37,480 --> 00:24:40,810
have, and that is radioactive
waste.

379
00:24:40,810 --> 00:24:46,190
It takes a very long time for
some compounds to decay.

380
00:24:46,190 --> 00:24:50,690
And so you have to think about
storing radioactive waste, and

381
00:24:50,690 --> 00:24:54,050
think about a container
that will outlast

382
00:24:54,050 --> 00:24:55,760
that radioactive waste.

383
00:24:55,760 --> 00:24:58,900
And how do you know that the
container is going to outlast

384
00:24:58,900 --> 00:25:00,000
the radioactive waste.

385
00:25:00,000 --> 00:25:02,860
You can't really do an
experiment because the time

386
00:25:02,860 --> 00:25:05,770
involved in doing the
experiment, anyone who designs

387
00:25:05,770 --> 00:25:08,630
the container won't be alive by
the time you're concerned

388
00:25:08,630 --> 00:25:12,980
about whether the container is
going to be stable or not.

389
00:25:12,980 --> 00:25:16,380
So taking radioactivity
is an issue.

390
00:25:16,380 --> 00:25:19,300
You heard some in the
presidential campaign about

391
00:25:19,300 --> 00:25:23,190
whether both candidates believe
in nuclear energy or

392
00:25:23,190 --> 00:25:27,340
not, and I think that both of
them said, it needs to be

393
00:25:27,340 --> 00:25:31,320
considered, we need to have
everything on the table.

394
00:25:31,320 --> 00:25:34,340
If we're going to have a real
uniform energy policy, we need

395
00:25:34,340 --> 00:25:35,660
to think about everything.

396
00:25:35,660 --> 00:25:39,320
So, issues of radioactive
waste and how to handle

397
00:25:39,320 --> 00:25:43,290
radioactivity safely are going
to come back as being current,

398
00:25:43,290 --> 00:25:44,490
important topics.

399
00:25:44,490 --> 00:25:47,180
And so these may be topics
that you will, in your

400
00:25:47,180 --> 00:25:50,340
lifetime, have to deal with,
either as a scientist trying

401
00:25:50,340 --> 00:25:53,420
to come up with new
technologies, or as a citizen

402
00:25:53,420 --> 00:25:57,420
deciding whether having a
radioactive plant in your

403
00:25:57,420 --> 00:25:59,660
hometown is a good
idea or not.

404
00:25:59,660 --> 00:26:02,850
A lot of people are happy about
nuclear energy, as long

405
00:26:02,850 --> 00:26:06,260
as the power plants are nowhere
located near them.

406
00:26:06,260 --> 00:26:09,560
But, these are things that
you'll have to face, and you

407
00:26:09,560 --> 00:26:12,130
probably will be voting on this
in the future, if not

408
00:26:12,130 --> 00:26:13,900
dealing with it directly.

409
00:26:13,900 --> 00:26:19,770
So that's how you do
a problem in this.

410
00:26:19,770 --> 00:26:23,280
All right, so let's talk
about a medical use of

411
00:26:23,280 --> 00:26:24,690
radioactivity.

412
00:26:24,690 --> 00:26:28,010
Radioactivity can definitely
be our friend, as well as

413
00:26:28,010 --> 00:26:30,290
something to be concerned
about.

414
00:26:30,290 --> 00:26:33,920
And I think I mentioned this in
the first day of class, one

415
00:26:33,920 --> 00:26:37,990
of the ways that the Chemistry
Department has moved to being

416
00:26:37,990 --> 00:26:40,980
the number one ranked Chemistry
Department of U.S.

417
00:26:40,980 --> 00:26:45,230
News and World Report over the
years, is a little extra money

418
00:26:45,230 --> 00:26:48,770
that came in from the work of
-- a patent from Professor

419
00:26:48,770 --> 00:26:51,720
Alan Davidson that we were
able to do some pretty

420
00:26:51,720 --> 00:26:55,070
exciting things with that
money over the years.

421
00:26:55,070 --> 00:26:59,900
So I always like to mention
all the great money-making

422
00:26:59,900 --> 00:27:03,940
discoveries that occurred using
511-1 material, and this

423
00:27:03,940 --> 00:27:05,690
is another example.

424
00:27:05,690 --> 00:27:10,580
So, he used an isotope of
technetium, and it's being

425
00:27:10,580 --> 00:27:17,900
used organ scanning, bone scans,
it's one of the leading

426
00:27:17,900 --> 00:27:19,490
ones for heart imaging.

427
00:27:19,490 --> 00:27:22,920
It's also been used recently
in breast cancer.

428
00:27:22,920 --> 00:27:28,440
It's estimated 7 million uses
annually in the U.S. And so,

429
00:27:28,440 --> 00:27:33,070
this was patented as cardiolite,
and it's really

430
00:27:33,070 --> 00:27:35,180
just very simple chemistry.

431
00:27:35,180 --> 00:27:39,240
So you're using a d block metal,
an isotope of a d block

432
00:27:39,240 --> 00:27:42,110
metal, which has your
exciting d orbitals.

433
00:27:42,110 --> 00:27:47,180
And what did he do, he made a
coordination complex with that

434
00:27:47,180 --> 00:27:51,070
metal, an isotope of it, and
he found ligands, cyanide

435
00:27:51,070 --> 00:27:53,770
ligands, those are pretty
common ligands.

436
00:27:53,770 --> 00:27:56,410
You've seen a lot of
coordination complexes with

437
00:27:56,410 --> 00:27:59,530
cyanide ligands, and he tried
different ligands to get the

438
00:27:59,530 --> 00:28:04,090
desired properties of stability
and solubility, and

439
00:28:04,090 --> 00:28:05,410
that's all it was.

440
00:28:05,410 --> 00:28:08,980
So he used some knowledge of
radioactivity, knowledge of

441
00:28:08,980 --> 00:28:12,190
inorganic chemistry -- he was
an inorganic chemist, he's

442
00:28:12,190 --> 00:28:13,310
retired now.

443
00:28:13,310 --> 00:28:17,340
And simple coordination
chemistry, and made an

444
00:28:17,340 --> 00:28:21,110
enormous amount of money for
MIT, and particularly, the

445
00:28:21,110 --> 00:28:24,000
Chemistry Department,
and also, this has

446
00:28:24,000 --> 00:28:26,160
saved a lot of lives.

447
00:28:26,160 --> 00:28:28,710
So, imaging is something
that chemists

448
00:28:28,710 --> 00:28:30,460
do a lot of, actually.

449
00:28:30,460 --> 00:28:35,110
Not just imaging for cancer or
imaging of organs, but also

450
00:28:35,110 --> 00:28:38,470
imaging of live cells to try
to understand how the cell

451
00:28:38,470 --> 00:28:40,090
works when it's healthy.

452
00:28:40,090 --> 00:28:43,840
And so recently, Professor Alice
Ting, in the Chemistry

453
00:28:43,840 --> 00:28:49,630
Department, received an NIH
pioneer award, NIH is National

454
00:28:49,630 --> 00:28:52,400
Institutes of Health, and
started giving these pioneer

455
00:28:52,400 --> 00:28:56,740
awards for people coming up with
very innovative ideas,

456
00:28:56,740 --> 00:29:00,870
the kind of innovative ideas
that most people would not

457
00:29:00,870 --> 00:29:03,150
want to fund, because there's
a good chance it might not

458
00:29:03,150 --> 00:29:05,740
work, but if it did, it
would be spectacular.

459
00:29:05,740 --> 00:29:09,490
So she received one of these
awards for trying to develop

460
00:29:09,490 --> 00:29:13,360
technology to image
protein-protein interactions

461
00:29:13,360 --> 00:29:16,120
in living cells, which is
something that people would

462
00:29:16,120 --> 00:29:17,930
really, really love
to be able to do.

463
00:29:17,930 --> 00:29:20,520
And so she is involved in
developing technology.

464
00:29:20,520 --> 00:29:23,480
So developing of imaging tools
is something that a lot of

465
00:29:23,480 --> 00:29:26,590
chemists do, it's a very popular
area in chemistry.

466
00:29:26,590 --> 00:29:28,380
And if it's something that
you're interested in, there's

467
00:29:28,380 --> 00:29:31,020
definitely a lot of people
around that you could think

468
00:29:31,020 --> 00:29:33,290
about working with for
a UROP position.

469
00:29:33,290 --> 00:29:37,960
OK, so that is first order.

470
00:29:37,960 --> 00:29:41,400
And now let's go on and talk
about second order

471
00:29:41,400 --> 00:29:43,290
integrated rate laws.

472
00:29:43,290 --> 00:29:45,670
And we're going to have a little
derivation for you, I

473
00:29:45,670 --> 00:29:48,380
always like to warn people that
it's coming, because all

474
00:29:48,380 --> 00:29:51,830
of a sudden equations are coming
in and out, and you

475
00:29:51,830 --> 00:29:55,280
just want to know where these
equations are coming from.

476
00:29:55,280 --> 00:29:59,640
So, as we talked about last
time, this is an expression

477
00:29:59,640 --> 00:30:00,790
for rate law.

478
00:30:00,790 --> 00:30:03,480
You have your rate constant,
your concentration of

479
00:30:03,480 --> 00:30:07,380
something, a, and it's raised
to a coefficient, and here

480
00:30:07,380 --> 00:30:09,960
that coefficient is 2,
indicating it's a

481
00:30:09,960 --> 00:30:12,700
second order process.

482
00:30:12,700 --> 00:30:17,140
So if there's nothing
up there, that's 1.

483
00:30:17,140 --> 00:30:21,840
And then 2, and again, the order
of the reaction can be

484
00:30:21,840 --> 00:30:25,640
positive, negative, it can be
integers, it can be fractions.

485
00:30:25,640 --> 00:30:29,420
But this is second order,
so we have 2.

486
00:30:29,420 --> 00:30:32,710
Now, as we did with the first
order expression, we're going

487
00:30:32,710 --> 00:30:36,560
to separate our concentration
terms and our time terms. So

488
00:30:36,560 --> 00:30:39,240
we're going to bring our
concentration term over to one

489
00:30:39,240 --> 00:30:42,610
side, another concentration term
here, and we're going to

490
00:30:42,610 --> 00:30:47,400
have our rate constant and our
time term on the other side.

491
00:30:47,400 --> 00:30:49,640
And now we're going to
integrate, because it is an

492
00:30:49,640 --> 00:30:51,420
integrated rate law.

493
00:30:51,420 --> 00:30:55,030
So we can integrate from the
original concentration of a to

494
00:30:55,030 --> 00:30:59,760
the concentration of a at some
time, t, and then we'll also

495
00:30:59,760 --> 00:31:02,740
integrate from zero time
to that time, t,

496
00:31:02,740 --> 00:31:04,460
on the other side.

497
00:31:04,460 --> 00:31:06,880
Now, I'm going to take this
expression and just bring it

498
00:31:06,880 --> 00:31:09,490
up to the top of the page,
so that's the exact same

499
00:31:09,490 --> 00:31:11,590
expression, nothing
has happened.

500
00:31:11,590 --> 00:31:14,170
And now we're going to
solve that integral.

501
00:31:14,170 --> 00:31:17,550
So we can solve that integral,
and if you want to look at

502
00:31:17,550 --> 00:31:20,730
these -- the back of your
textbook has all of these

503
00:31:20,730 --> 00:31:23,950
conversions, if you want
to look at them.

504
00:31:23,950 --> 00:31:26,400
So, we're going to solve that
integral, now we have minus

505
00:31:26,400 --> 00:31:31,040
parentheses 1 over the
concentration of a at some

506
00:31:31,040 --> 00:31:34,150
time, t, minus 1 over the
original concentration

507
00:31:34,150 --> 00:31:36,940
equals minus k t.

508
00:31:36,940 --> 00:31:40,560
We can get rid of some
of these minus signs.

509
00:31:40,560 --> 00:31:46,110
So we're going to bring the
concentration of time, t, over

510
00:31:46,110 --> 00:31:49,050
on this side, we have our k t,
and now we have this other

511
00:31:49,050 --> 00:31:51,940
term, the original concentration
term is on the

512
00:31:51,940 --> 00:31:57,950
other side, and this is
expressed in a certain way

513
00:31:57,950 --> 00:32:01,720
that gives you the equation
for a straight line.

514
00:32:01,720 --> 00:32:05,530
And again, kinetics, you need
experimental data for

515
00:32:05,530 --> 00:32:08,630
kinetics, and so when you
measure your data, you plot

516
00:32:08,630 --> 00:32:11,800
your data, and so there's a lot
of equations for straight

517
00:32:11,800 --> 00:32:14,450
lines that you have, because
it's all about trying to plot

518
00:32:14,450 --> 00:32:19,910
data, and figure out what the
order is experimentally.

519
00:32:19,910 --> 00:32:24,090
So, here's an equation for a
straight line, and we can plot

520
00:32:24,090 --> 00:32:59,750
this, and you can tell me what
the intercept of this line is.

521
00:32:59,750 --> 00:33:13,020
OK, let's just take
10 more seconds.

522
00:33:13,020 --> 00:33:17,680
Yup, so all of you know how to
analyze the equation for a

523
00:33:17,680 --> 00:33:20,990
straight line.

524
00:33:20,990 --> 00:33:26,650
So, here we have 1 over the
original concentration, and

525
00:33:26,650 --> 00:33:32,980
then our slope is equal
to what here? k.

526
00:33:32,980 --> 00:33:36,500
So, you can plot your data as
your concentration of a

527
00:33:36,500 --> 00:33:37,610
changes with time.

528
00:33:37,610 --> 00:33:41,640
You can plot the data, and if
the data, if it's plotted as 1

529
00:33:41,640 --> 00:33:44,700
over the concentration of a
versus time and it gives you a

530
00:33:44,700 --> 00:33:47,250
straight line, that's consistent
with it being a

531
00:33:47,250 --> 00:33:50,940
second order process.

532
00:33:50,940 --> 00:33:54,700
So, in terms of second order
half life, we talked about

533
00:33:54,700 --> 00:33:59,590
first order half life, and for
any half life, it's just the

534
00:33:59,590 --> 00:34:04,530
time it takes for half of the
original material to go away.

535
00:34:04,530 --> 00:34:08,940
So we can rewrite this and
take a to the t, and

536
00:34:08,940 --> 00:34:13,100
substitute in the original
concentration divided by 2,

537
00:34:13,100 --> 00:34:18,080
and then we can have t have a
special name t 1/2, so that's

538
00:34:18,080 --> 00:34:19,500
the half life.

539
00:34:19,500 --> 00:34:23,410
And now we can just simplify
this expression.

540
00:34:23,410 --> 00:34:26,770
We can bring the 2 up here,
and now we can combine our

541
00:34:26,770 --> 00:34:28,970
concentration terms
on the side.

542
00:34:28,970 --> 00:34:32,890
So we take 2, we bring
this over, minus 1.

543
00:34:32,890 --> 00:34:37,440
And that simplifies 1 over the
concentration of the original

544
00:34:37,440 --> 00:34:40,720
material here.

545
00:34:40,720 --> 00:34:44,940
And now we can solve for it
in terms of the half life.

546
00:34:44,940 --> 00:34:49,760
So the half life for a second
order process equals 1 over k

547
00:34:49,760 --> 00:34:54,780
times the original concentration
of the material.

548
00:34:54,780 --> 00:35:01,140
So, a second order half life
depends on the starting

549
00:35:01,140 --> 00:35:02,640
concentration.

550
00:35:02,640 --> 00:35:05,460
So that's very different from
a first order half life

551
00:35:05,460 --> 00:35:10,260
process where concentration
term cancels out entirely.

552
00:35:10,260 --> 00:35:14,480
So for a first order process,
the concentration of the

553
00:35:14,480 --> 00:35:19,280
original material does not
affect the half life, or for

554
00:35:19,280 --> 00:35:23,010
radioactive decay, the original
number of nuclei --

555
00:35:23,010 --> 00:35:25,950
it's independent of how
many nuclei were

556
00:35:25,950 --> 00:35:27,300
around at the time.

557
00:35:27,300 --> 00:35:30,960
But for second order process,
the starting concentration

558
00:35:30,960 --> 00:35:36,160
does matter.

559
00:35:36,160 --> 00:35:38,920
So again, chemistry
is experimental.

560
00:35:38,920 --> 00:35:41,870
And so what you would be doing
in a lab, you would be trying

561
00:35:41,870 --> 00:35:45,720
to figure out what the order of
the reaction is, and so you

562
00:35:45,720 --> 00:35:47,080
could try out your data.

563
00:35:47,080 --> 00:35:50,130
You say I don't know if it's
first or second order, so for

564
00:35:50,130 --> 00:35:53,200
a first order plot, you're
going to be plotting the

565
00:35:53,200 --> 00:35:56,600
natural log of your
concentrations versus time,

566
00:35:56,600 --> 00:35:59,680
and if second order, you plot
1 over the concentration

567
00:35:59,680 --> 00:36:00,730
versus time.

568
00:36:00,730 --> 00:36:04,250
And so you could plot your data
and see that oh, look at

569
00:36:04,250 --> 00:36:08,040
this, it fits a straight line
really well if I plot it as 1

570
00:36:08,040 --> 00:36:09,680
over the concentration.

571
00:36:09,680 --> 00:36:13,170
If I plot it as the natural
log versus time, the data

572
00:36:13,170 --> 00:36:14,850
doesn't fit a straight
line at all.

573
00:36:14,850 --> 00:36:18,700
So this is not a first order
process, this is much more

574
00:36:18,700 --> 00:36:21,230
consistent with a second
order process.

575
00:36:21,230 --> 00:36:24,550
So again, figuring out where
something is first order or

576
00:36:24,550 --> 00:36:31,850
second order is done
experimentally.

577
00:36:31,850 --> 00:36:32,280
All right.

578
00:36:32,280 --> 00:36:35,110
Now we're going to talk
about kinetics

579
00:36:35,110 --> 00:36:37,330
and equilibrium constants.

580
00:36:37,330 --> 00:36:40,740
So, I always get very excited,
as you know, when we come back

581
00:36:40,740 --> 00:36:45,660
to equilibrium constants, so am
always very happy at this

582
00:36:45,660 --> 00:36:48,370
time in the course when we
can relate kinetics and

583
00:36:48,370 --> 00:36:50,690
equilibrium constants.

584
00:36:50,690 --> 00:36:53,580
So, at equilibrium, another
way to think about what's

585
00:36:53,580 --> 00:36:56,960
happening at equilibrium, is
that the rate of the forward

586
00:36:56,960 --> 00:37:01,210
reaction and the rate of the
reverse reaction are equal to

587
00:37:01,210 --> 00:37:04,310
each other.

588
00:37:04,310 --> 00:37:08,470
So, we can now talk about big
letter K, which is our

589
00:37:08,470 --> 00:37:11,780
equilibrium constant again,
and our little letter k's,

590
00:37:11,780 --> 00:37:13,730
which our rate constant.

591
00:37:13,730 --> 00:37:17,670
So the equilibrium constant for
a chemical reaction a plus

592
00:37:17,670 --> 00:37:21,600
b equals c plus d is going to
be equal to what, what do I

593
00:37:21,600 --> 00:37:25,560
put on the top?

594
00:37:25,560 --> 00:37:31,070
Concentration of? c, and
concentration of d, right.

595
00:37:31,070 --> 00:37:34,570
So our products, and at
the bottom we put our

596
00:37:34,570 --> 00:37:41,180
concentration of our reactants,
or a and b.

597
00:37:41,180 --> 00:37:47,210
Now, we can also think about
this reaction in terms of

598
00:37:47,210 --> 00:37:50,090
little rate constants.

599
00:37:50,090 --> 00:37:56,330
So we have small letter k 1 on
top, and small letter k to the

600
00:37:56,330 --> 00:37:59,070
minus 1 on the bottom.

601
00:37:59,070 --> 00:38:03,100
So, the forward reaction, the
rate of forward reaction is

602
00:38:03,100 --> 00:38:08,440
going to be equal to k 1 times
the concentration of a and the

603
00:38:08,440 --> 00:38:11,740
concentration of b.

604
00:38:11,740 --> 00:38:16,600
And on the bottom, our rate is
going to be equal to the

605
00:38:16,600 --> 00:38:20,120
little rate constant, so for the
reverse reaction it's the

606
00:38:20,120 --> 00:38:23,730
reverse rate constant, k minus
1, and in the reverse

607
00:38:23,730 --> 00:38:27,440
direction, our reactants are the
products for the forward

608
00:38:27,440 --> 00:38:32,780
direction, or c and d.

609
00:38:32,780 --> 00:38:37,610
So, here we have these rates,
and at equilibrium, those

610
00:38:37,610 --> 00:38:39,220
rates are going to be equal.

611
00:38:39,220 --> 00:38:43,300
So at equilibrium, little k 1, a
times b is going to be equal

612
00:38:43,300 --> 00:38:47,890
to little k minus 1
times c times d.

613
00:38:47,890 --> 00:38:59,460
And at equilibrium we had c d
over a b is equal to then k 1

614
00:38:59,460 --> 00:39:04,290
over k minus 1, so if we just
rearrange this expression and

615
00:39:04,290 --> 00:39:08,250
move the rate constants to one
side and concentration terms

616
00:39:08,250 --> 00:39:11,210
to the other side, this
expression is the same as this

617
00:39:11,210 --> 00:39:15,210
expression, and we also know
what this expression is equal

618
00:39:15,210 --> 00:39:20,800
to, which is our big K. So,
therefore, our equilibrium

619
00:39:20,800 --> 00:39:23,840
constant equals the rate
constant for the forward

620
00:39:23,840 --> 00:39:26,700
reaction over the rate constant

621
00:39:26,700 --> 00:39:29,660
for the reverse direction.

622
00:39:29,660 --> 00:39:32,780
And so here is an expression
that compares equilibrium

623
00:39:32,780 --> 00:39:37,920
constants with rate constants.

624
00:39:37,920 --> 00:39:41,760
So now, let's think about
what is true about this.

625
00:39:41,760 --> 00:39:44,800
So our equilibrium constant,
then, is the ratio or the

626
00:39:44,800 --> 00:39:48,000
forward rate over the
reverse rate for

627
00:39:48,000 --> 00:39:51,690
these elementary reactions.

628
00:39:51,690 --> 00:39:55,880
And if we think about rate
constants in kinetics terms,

629
00:39:55,880 --> 00:39:59,380
if k is greater than 1, if there
are more products than

630
00:39:59,380 --> 00:40:03,920
reactants at equilibrium,
what's true about k

631
00:40:03,920 --> 00:40:06,560
1 and k minus 1?

632
00:40:06,560 --> 00:40:12,670
Is k 1 greater than or
less than k minus 1?

633
00:40:12,670 --> 00:40:13,820
Right.

634
00:40:13,820 --> 00:40:17,100
So the forward rate constant
is greater than the reverse

635
00:40:17,100 --> 00:40:19,410
rate constant.

636
00:40:19,410 --> 00:40:23,810
And if K, big equilibrium
constant, K is less than 1, if

637
00:40:23,810 --> 00:40:28,690
at equilibrium there are more
reactants than products, what

638
00:40:28,690 --> 00:40:33,240
is true about this
relationship?

639
00:40:33,240 --> 00:40:35,590
It would be less than.

640
00:40:35,590 --> 00:40:39,070
So, you can think about
equilibrium constants now in

641
00:40:39,070 --> 00:40:42,070
terms of rate constants, which
we'll be doing a lot on

642
00:40:42,070 --> 00:40:43,870
Wednesday, too.

643
00:40:43,870 --> 00:40:44,980
All right.

644
00:40:44,980 --> 00:40:48,920
So let me introduce you to a
couple of more terms in the

645
00:40:48,920 --> 00:40:50,270
last few minutes.

646
00:40:50,270 --> 00:40:53,990
So reactions don't usually occur
in one step, but occur

647
00:40:53,990 --> 00:40:55,820
in a series of steps.

648
00:40:55,820 --> 00:41:02,070
Each step is called an
elementary reaction.

649
00:41:02,070 --> 00:41:07,340
So, the overall reaction, the
order and the rate law, can be

650
00:41:07,340 --> 00:41:13,180
derived from the stoichiometry
for an overall reaction, you

651
00:41:13,180 --> 00:41:16,370
can't use the stoichiometry,
but for an elementary

652
00:41:16,370 --> 00:41:18,000
reaction you can.

653
00:41:18,000 --> 00:41:21,120
So, for an elementary reaction,
say one step in the

654
00:41:21,120 --> 00:41:25,010
reaction mechanism, that step
occurs exactly as written so

655
00:41:25,010 --> 00:41:27,750
you can use stoichiometry.

656
00:41:27,750 --> 00:41:31,190
And that's going to be handy in
coming up with mechanisms.

657
00:41:31,190 --> 00:41:35,010
So, let's just look at one
example very briefly.

658
00:41:35,010 --> 00:41:38,780
So here we have the
decomposition of ozone, which

659
00:41:38,780 --> 00:41:42,790
is another environmental issue
that you will be faced with in

660
00:41:42,790 --> 00:41:45,760
your lifetime.

661
00:41:45,760 --> 00:41:49,940
So this is the overall reaction,
and you can't use

662
00:41:49,940 --> 00:41:53,160
the stoiciomery to figure out
the order of the reaction, but

663
00:41:53,160 --> 00:41:56,760
if you divide it up into
elementary reaction steps,

664
00:41:56,760 --> 00:42:01,000
then you can use the stoiciomery
to write the rate

665
00:42:01,000 --> 00:42:04,920
law for each step of
that reaction.

666
00:42:04,920 --> 00:42:08,740
So, the first step here is
a unimolecular step.

667
00:42:08,740 --> 00:42:15,130
You have one thing going to two
things, and molecularity

668
00:42:15,130 --> 00:42:18,760
is the number of reactant
molecules the come together to

669
00:42:18,760 --> 00:42:20,060
form product.

670
00:42:20,060 --> 00:42:24,410
So, unimolecular you just have
one thing that's forming some

671
00:42:24,410 --> 00:42:26,020
kind of product.

672
00:42:26,020 --> 00:42:28,350
What do you think it's called
if you have two

673
00:42:28,350 --> 00:42:32,260
things forming a product?

674
00:42:32,260 --> 00:42:34,030
Bimolecular.

675
00:42:34,030 --> 00:42:37,460
These are good little one or two
point questions on a test,

676
00:42:37,460 --> 00:42:40,660
they're not very hard,
they should be pretty

677
00:42:40,660 --> 00:42:42,410
easy to think about.

678
00:42:42,410 --> 00:42:46,110
So, we have unimolecular,
examples would be some kind of

679
00:42:46,110 --> 00:42:48,800
decomposition or radioactive
decay.

680
00:42:48,800 --> 00:42:50,930
Bimolecular, two reactants
coming

681
00:42:50,930 --> 00:42:52,740
together to form products.

682
00:42:52,740 --> 00:42:57,040
And termolecular is three
reactants coming together to

683
00:42:57,040 --> 00:43:00,770
form a product, and
that's rare.

684
00:43:00,770 --> 00:43:03,930
And you can remember that it's
rare if you think about how

685
00:43:03,930 --> 00:43:07,120
you would hold three tennis
balls in your hand and have

686
00:43:07,120 --> 00:43:10,620
them all come together at the
same time to form product,

687
00:43:10,620 --> 00:43:12,530
that is a difficult
thing to do.

688
00:43:12,530 --> 00:43:14,750
Two things coming together
is easy,

689
00:43:14,750 --> 00:43:16,800
bimolecular is very common.

690
00:43:16,800 --> 00:43:21,220
Termolecular not very common,
that they'd all come together

691
00:43:21,220 --> 00:43:25,090
at the same time to
form a product.

692
00:43:25,090 --> 00:43:32,310
All right, so we can write rate
laws for each step here.

693
00:43:32,310 --> 00:43:36,000
For the first step here, the
rate would be equal to a k --

694
00:43:36,000 --> 00:43:38,490
I don't have the k written up
here, but there's always going

695
00:43:38,490 --> 00:43:40,850
to be a little k
over the arrow.

696
00:43:40,850 --> 00:43:44,770
So, k times the reactant
would be here.

697
00:43:44,770 --> 00:43:48,740
For bimolecular, again,
assume a k over there.

698
00:43:48,740 --> 00:44:13,910
What's that rate going
to be equal to?

699
00:44:13,910 --> 00:44:16,890
OK, let's just take 10
more seconds since

700
00:44:16,890 --> 00:44:27,900
class is almost over.

701
00:44:27,900 --> 00:44:34,700
Yup, so it's this one
right down here.

702
00:44:34,700 --> 00:44:37,970
So we have the rate
is equal to k

703
00:44:37,970 --> 00:44:39,370
times these two reactants.

704
00:44:39,370 --> 00:44:43,760
You can sum up the steps and
get the overall reactants.

705
00:44:43,760 --> 00:44:47,300
Notice that o is an
intermediate, it's formed

706
00:44:47,300 --> 00:44:48,920
here, decayed here.

707
00:44:48,920 --> 00:44:53,070
It goes away, and so o doesn't
appear in the overall

708
00:44:53,070 --> 00:44:54,250
expression.

709
00:44:54,250 --> 00:44:56,190
So we're going to talk
a lot about reaction

710
00:44:56,190 --> 00:44:58,700
intermediates next time.

711
00:44:58,700 --> 00:45:01,730
And also, remember that you
can't prove reaction

712
00:45:01,730 --> 00:45:05,700
mechanisms to be correct,
they're just consistent with

713
00:45:05,700 --> 00:45:07,720
the data that you have.