The Baylis-Hillman reaction is a DABCO (1,4-diazabicyclo[2.2.2]octane) catalyzed reaction of an α,β-unsaturated carbonyl compound with an aldehyde to form an allylic alcohol. Propose a mechanism for the reaction. (Hint: DABCO serves as both a nucleophile and as a base in the reaction.)

The pK_a values of the carboxylic acid groups of oxaloacetic acid are 2.22 and 3.98.

b. The amount of hydrate present in an aqueous solution of oxaloacetic acid depends on the pH of the solution: 95% at pH 0, 81% at pH 1.3, 35% at pH 3.1, 13% at pH 4.7, 6% at pH 6.7, and 6% at pH 12.7. Explain this pH dependence.

Show how each of the following compounds can be prepared from the given starting material. In each case, you will need to use a protecting group.

a.

b.

When a cyclic ketone reacts with diazomethane, the next larger cyclic ketone is formed. This is called a ring-expansion reaction. Draw a mechanism for the following ring-expansion reaction.

To solve this problem, you need to read the description of the Hammett $\sigma$, $\rho$ treatment given in [Chapter 15, Problem 92]. When the rate constants for the hydrolysis of several morpholine enamines of para-substituted propiophenones are determined at pH 4.7, the $\rho$ value is positive; however, when the rates of hydrolysis are determined at pH 10.4, the $\rho$ value is negative.

b. What is the rate-determining step of the hydrolysis reaction when it is carried out in an acidic solution?

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Propose a mechanism for each of the following reactions:

b.