UCSF School of Pharmacy
TL James
PC 111
Problem Set 4 (Chemical Kinetics)
1. A reaction is observed experimentally to have a negative entropy of activation.
Can it be concluded that the products of the reaction are in a more ordered state than that
of the reactants?
2. If a reversible isomerization reaction (Keq = 50) has a rate constant for the forward
reaction of 1.0 x 10-3 sec-l at 0 °C and 1.2 x 10-2 sec-1 at 25 °C, calculate the activation
enthalpy and activation entropy for the forward reaction and the activation enthalpy for
the reverse reaction. (State any assumptions you make).
3. The rate of bacterial hydrolysis of fish muscle is twice as great at 2.2 °C as at -1.1 °C.
Estimate ΔH‡, for this reaction. Is there any relation to the problem of storing fish for
food?
[Source: "Eco-Chem," J.A. Campbell, J. Chem. Educ. 52, 390 (1975)]
4. The electron-exchange reaction between naphthalene (C10H8) and its anion radical can
be expressed as
C10H¯8 + C10H8
 C10H8 + C10H¯8
The second order reaction is also bimolecular. The rate constants are
T (°K)
307 299 289 273
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k (M-1s-1) x 10-9
2.71
2.40
1.96
1.43
Calculate ΔH‡, ΔS‡, and ΔG‡ at 289 °K for the reaction. (Hint: plot log (k/T) vs. T-1)
5. The rate constant for the reaction between persulfate ions and iodide ions varies with the
ionic strength as follows:
k, l-mole-1-sec-1
1.05
1.12
1.16
1.18
1.26
1.39
µmole/l
0.00245
0.00365
0.00445
0.00645
0.00845
0.01245
Estimate the value of ZAZB. If the rate-limiting step is reaction between a persulfate ion
and an iodide ion (I-), what is the charge on the persulfate?
1
UCSF School of Pharmacy
TL James
6. The mutarotation of glucose follows first-order kinetics and is catalyzed by hydrogen
ions. The data below refer to aqueous HCl solutions at 20 °C.
(HCl), M
0.02
0.04
0.06
k, sec-1 x 10-4
3.7
5.1
6.5
Calculate the catalytic constant for hydrogen ions {in M-l sec-l) and the half-life for the
mutarotation reaction in pure water at 20 °C.
(Ans. kH = 7.0 x 10-3 M-1 sec-1 and t½= 3 .01 x I03 sec)
7. The hydrolysis of a substance is specifically catalyzed by hydrogen ions, the catalytic rate
constant being k = 4.7 x 10-2 (H+) sec-1. When the substance was dissolved in a 10-3 M
solution of HA, the rate constant was found to be 3.2 x 10-5 sec-l. Assume catalytic rate
>> uncatalyzed rate. Calculate the dissociation constant of the acid HA. (Ans. 1.45 x 10-3
M).
8. The initial rate of ATP dephosphorylation by the enzyme myosin can be estimated by the
amount of phosphate produced in 100 sec. Use the following data to evaluate the
Michaelis constant KM and Vmax, for the reaction at 25 °C. [Myosin] = 0.040 gm/l. All
concentrations are in µmoles/l.
___________________________________________
ATP
[Phosphate]100
ATP
[Phosphate]100
___________________________________________
7.1
2.4
70
6.2
11
3.5
77
6.7
23
5.3
100
7.1
(Ans. Vmax= 0.09 µmoles l-1 sec-1, KM = 19.2 µmole l-1)
9. Adenylosuccinate lyase catalyzes the cleavage of adenylosuccinate to fumaric acid and
adenylic acid in the final step of the synthetic pathway to adenylic acid. The reaction with
velocity V is inhibited by 8,5’-cyclo-AMP, as shown in the figure. The experimental
conditions were: 1 ml volume, 3.0 x 10-9 M enzyme binding site, pH 7.8, 20 mM Tris
buffer, 25 °C. Other studies indicated that the dissociation constant for adenylosuccinate
from the enzyme is 4.0 x 10-8 M. Assuming simple Michaelis kinetics, calculate the
Michaelis constant, Vmax, KI, k1, k-1 and k2 (in terms of M and min). (Note: A value of 2.0
on the abscissa corresponds to a substrate concentration of 5.0 x10-6 M.)
2
UCSF School of Pharmacy
TL James
Cleavage of adenylosuccinate by adenylosuccinate lyase: no inhibitor () : 5
µM 8,5'-cyclo-AMP ( ): 10 µM 8,5'-cyclo-AMP ( ). Velocity is in µmol/min.
10. For a particular enzyme-catalyzed reaction, the largest Vmax is achieved in the pH range
7.5 - 8.5 and, within the experimental error of -15%, does not change in that pH range.
However, decreasing the pH to 6.0 results in a Vmax only 20% as large as it is at pH 8.0.
Calculate the acid dissociation constant of the functional group on the enzyme that
appears to be critical for enzyme activity.
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