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One mole of ethanol is treated with one mole of ethanoic acid at \( 25 . \) One-forth of the acid changes into ester at equilibrium. The equilibrium constant for the reaction will be:

1. \( 1 / 9 \)
2. \( 4 / 9 \)
3. 9
4. \( 9 / 4 \)

Correct answer: \( 4 / 9 \)

Solution

If one-fourth of the acid reacts, then 0.25 mol each of ethanol and ethanoic acid are consumed, forming 0.25 mol ester and 0.25 mol water. Substituting these equilibrium amounts into the equilibrium expression gives K = (0.25×0.25)/(0.75×0.75) = 4/9.

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