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KCET · Chemistry · Chemical Kinetics

\( 1 \mathrm{~L} \) of \( 2 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH} \) is mixed with \( 1 \mathrm{~L} \) of \( 3 \mathrm{M} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \) to form an ester. The rate of the
reaction with respect to the initial rate when each solution is diluted with an equal volume of
water will be

  1. A \( 0.5 \) times
  2. B \( 4 \) times
  3. C \( 0.25 \) times
  4. D \( 2 \) times
Verified Solution

Answer & Solution

Correct Answer

(C) \( 0.25 \) times

Step-by-step Solution

Detailed explanation

(C)
Esterification is a second order reaction
\(\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H} 5+\mathrm{H}_{2} \mathrm{O}\)
\(\mathrm{r}=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]\)
Order \(=2\)
When equal volume of two solutions are mixed, concentration of the solutions reduces to half the initial value. Hence,
rate of reaction gets reduced to \(\frac{1}{4}\) initial rate.