Page 123 - Mechanism and Theory in Organic Chemistry

k-, are both fast compared with the rate of step k,. What is the kinetic order?

5. Define the terms microscopic rate constant and observed rate constant.
6. Derive the rate equation for formation of F in terms of concentrations of A, B,
and D in the following mechanisms, assuming that A, B, and C are in equilibrium and
E is a highly reactive intermediate.

7. Estimate the heat of hydrogenation of benzene and of a hypothetical benzene
with three fixed double bonds, each reacting with three moles of Hz to yield cyclohexane.
8. Verify analytically that the effect of adding a linear perturbation of the form
y = mx to a parabola is to maintain its curvature but to shift it in the sense concluded
in the text, p. 104. The general formula for a parabola is

where 4p = - E/A, h = - D/2A, k = D2/4AE - FIE. The parabola opens upward ifp
is positive and downward if p is negative; the vertex is at x = h, y = k.
9. Verify the expression for the equilibrium isotope effect, K,,, (Equation A2.15
in Appendix 2).
10. Verify by reference to the equilibrium isotope effect equation, A2.15 in
Appendix 2, the statement that the heavy isotope will concentrate, relative to the light,
at that site where it is more strongly bound.
11. Rationalize the observation that D30 + is a stronger acid than H30 +.
12. Verify that a decrease in H-C (D-C) vibrational frequency on dissociation
will cause the observed secondary equilibrium isotope effect K,/K, > 1 for dissociation
of HCOOH (DCOOH).
13. Estimate (a) AH," for triethylamine; (b) So for 1,l-dimethylhydrazine.

REFERENCES FOR PROBLEMS
8. G. B. Thomas, Jr., Calculus and Analytic Geometry, Addison-Wesley, Reading, Mass.,
1953, p. 237.
9. K. B. Wiberg, Physical Organic Chemistry, Wiley, New York, 1964, p. 273.
13. S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal,
A. S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969).