The acid catalysed reaction of acetic acid with ethanol: CH3COOH + C2H5OH → CH3COOC2H5 + H2O follows the rate law: r = K [H+] [CH3COOH] [C2H5OH] = K' [CH3COOH] [C2H5OH]. When [CH3COOH]0 = [C2H5OH]0 =

Question

The acid catalysed reaction of acetic acid with ethanol: CH3COOH + C2H5OH → CH3COOC2H5 + H2O follows the rate law: r = K [H+] [CH3COOH] [C2H5OH] = K' [CH3COOH] [C2H5OH]. When [CH3COOH]0 = [C2H5OH]0 = 0.2 M and pH = 3, the half-life for the reaction is 50 min. The value of true rate constant, K, of the reaction is

Prashant Kotian · Accepted Answer

Correct answer: C. The reaction is second order overall with equal initial concentrations. t_1/2 = 1 / (K' × C0) => 50 = 1 / (K' × 0.2) => K' = 0.1 M^-1 min^-1. K' = K[H+], and pH = 3 implies [H+] = 10^-3 M. Thus, K = 0.1 / 10^-3 = 100 M^-2 min^-1. Therefore, correct answer is C.

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