?In the vapor phase, acetic acid molecules associate to a certain extent to form

Chapter 15, Problem 125P

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In the vapor phase, acetic acid molecules associate to a certain extent to form dimers:

\(2 \mathrm{CH}_{3} \mathrm{COOH}(g) \rightleftharpoons\left(\mathrm{CH}_{3} \mathrm{COOH}\right)_{2}(g)\)

At \(51^{\circ} \mathrm{C}\) the pressure of a certain acetic acid vapor system is 0.0342 atm in a 360-mL flask. The vapor is condensed and neutralized with 13.8 mL of 0.0568 M NaOH.

(a) Calculate the degree of dissociation \((\alpha)\) of the dimer under these conditions:

\(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)_{2} \rightleftharpoons 2 \mathrm{CH}_{3} \mathrm{COOH}\)

(Hint: See Problem 14.117 for general procedure.)

(b) Calculate the equilibrium constant \(K_{P}\) for the reaction in (a).

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