Page 192 - Essentials of physical chemistry

154 Essentials of Physical Chemistry

7.6 It is sometimes said that many organic reactions double their rate for an increase of only 108C.
Assuming that is true, use the Arrhenius dependence of reaction rates on temperature to
determine the approximate value of E* that would lead to a doubling of an organic reaction
rate when heated from 258Cto358C.
1 0 1
1
0
7.7 Consider the decay of free neutrons n ! 1 e þ H with t 1=2 ¼ 10.3 min. How long will it take
for 1% of 1 mol of free neutrons to decay?
7.8 To make sure you understand the mathematical steps, repeat the derivation of the formula for
N B in the A ! B ! C reaction sequence and calculate the time of the maximum number of
204 Bi atoms if 204 Po ¼ 1000 atoms at t ¼ 0 given the half-life of 204 Po is 3.53 h and the half-life
83 84 84
of 204 Bi is 11.2 h. Calculate the maximum number of 204 Bi atoms and the number of 204 Po and
83 83 84
204 Pb atoms, when 204 Bi is at a maximum. Check your results against Figure 7.6.
82 83
7.9 Predict the products of the following nuclear reactions based only on integer mass units, ignore
2
1
1
energy balance, DE ¼ (Dm)c and emission of gamma rays. Some possibilities are n, p,
0 1
4 a ¼ He , and 0 0 b.
4
þ
2 2 1 e ¼ 1
1
4
(a) 24 Mg þ n ! 24 Na þ ? (b) 14 N þ He ! 17 O þ ?
11
7
0
12
8
2
9 4 12 27 4 30
2
4
2
(c) Be þ He ! 6 C þ ? (d) 13 Al þ He ! 15 P þ ?
(e) 14 1 11 B þ ? (f) 31 1 28 Al þ ?
0
7 N þ n ! 5 15 P þ n ! 13
0
(g) 24 24 Mg þ ?
11 Na ! 12
REFERENCES
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FL, p. 11–155.
2. Anonymous physicist, http:==universe-review.ca=F14-nucleus.htm#shell
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(1972).
5. Svirbely, S. J. and J. F. Roth, Carbonyl reactions. I. The kinetics of cyanohydrin formation in aqueous
solution, J. Am. Chem. Soc., 75, 3106 (1953).
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heated catalytic and non-catalytic surfaces, Comb. and Flame, 93, 185 (1993).
2
9. Bodanis, D., E ¼ mc , Berkley Books, New York, 2000, Chap. 9.
10. Sasin, G. and R. Sasin, Theory and Problems in General Chemistry, Drexel Institute of Technology,
1952. Private Communication from R. Sasin, Emeritus Dean, Franklin and Marshall College.
11. Shillady, D., R. Sasin, and M. Hobbs, Chemistry in the news (coursepack for CHEM 112 at Virginia
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