Page 216 - Essentials of physical chemistry

178 Essentials of Physical Chemistry

KINETICS CONCLUSIONS

While we are still self-constrained to limit our treatment to what we believe is essential to physical
chemistry, we have added further examples to the Chapter 7 treatment of reaction kinetics, which
include some aspects of multistep mechanisms and introduced the steady-state approximation. The
steady-state concept was then extended to the Eyring transition-state concept and used again for the
critical step in the Michaelis–Menten treatment of enzyme kinetics. This has been a fast tour of some
complicated algebra but in our experience students who ‘‘learn’’ the derivations have a deeper
appreciation for the concepts. Casual interviews of students from past classes have revealed that the
Michaelis–Menten derivations have been the most useful aspect of this chapter.

PROBLEMS

8.1 Use the data in Example 5 of Chapter 7 at 08C and 458C to compute the Arrhenius ‘‘A’’ and E*
values.
8.2 Use your answers from problem 8.1 above to calculate the temperature at which the reaction
rate would be twice the rate at 08C.
8.3 Use the data in Example 5 of Chapter 7 with the ‘‘two-point’’ method on page 159 to calculate
DH and DS at 358C using data from 358Cto458C. This is likely the method of choice in a test
y
y
situation, so you need to practice this ‘‘two-point method.’’ This method is less reliable when
the points are close together.
8.4 Use the data in Table 8.1 with the ‘‘graphical method’’ on pages 162–163 to calculate DH and
y
DS at 358C instead of 258C.
y
8.5 Rederive the Bodenstein–Lind rate law for the reaction of H 2 þ Br 2 and review what you were
taught in organic chemistry about the reactivity of free radicals. Look up the dissociation
energy of Br 2 ! 2Br in the chemical rubber handbook and compare it with the energy of
dissociation of H 2 ! 2H.
8.6 Given the table of data below for the reaction of o-diphenol oxidase with catechol, draw the
Lineweaver–Burk plot and find the slope of the graph and use the value of the y-intercept
(1=V max ) to obtain the K M value. Compare that value to the reciprocal of the x-intercept where
(1=V) ¼ 0. Submit your graph along with your calculations. We will need three significant
figures to compare with the data in the next problem to see the effect of an inhibitor.

[S] 4.8 mM 1.2 mM 0.6 mM 0.3 mM
1=[S] 0.21 0.83 1.67 3.33
DOD 540 (V i ) 0.081 0.048 0.035 0.020
1=V i 12.3 20.8 28.6 50.0

The values for (1=V i ) have been rounded to three significant figures for a smoother fit to the V i
values, which are only given to two significant figures. However, Prof. Kimball rounds (1=V 1 )
further to only two significant figures. In either event, biological data are often more scattered
than physical data but some of the (1=S) data are rounded to three significant figures; so we
carry three significant figures in (1=V 1 ). When using biological data, it is essential to use least-
squares fits.
8.7 Given the table of data below for the reaction of o-diphenol oxidase with catechol in the
presence of parahydroxy benzoic acid (a competitive inhibitor), draw the Lineweaver–Burk
plot and find the slope of the graph and use the value of the y-intercept (1=V max ) to obtain the
modified K M value. Calculate the value of K M from the slope and compare it with the reciprocal