Q37 / 180 · KCET 2015 · Chemistry
\( 100 \mathrm{~cm}^{3} \) of \( 1 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH} \) was mixed with \( 100 \mathrm{~cm}^{3} \) of \( 2 \mathrm{MCH}_{3} \mathrm{OH} \) to form an ester. The
change in the initial rate if each solution is diluted with equal volume of water would be
change in the initial rate if each solution is diluted with equal volume of water would be
- A\( 2 \) times
- B\( 4 \) times
- C\( 0.5 \) times
- Correct answerD\( 0.25 \) times
Solution
For the esterification reaction
\[ \begin{array}{l} \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{CH}_{3} \mathrm{COOCH}_{3}+\mathrm{H}_{2} \mathrm{O} \\ \quad_{1 \mathrm{M}} \\ r_{1}=k\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\left[\mathrm{CH}_{3} \mathrm{OH}\right] \\ =k[1][2] \\ r_{1}=2 k \rightarrow(1) \end{array} \]
when solution is diluted with equal volume of water, concentration is reduced to half
\[ \begin{array}{l} r_{2}=k\left[\frac{1}{2}\right]\left[\frac{2}{2}\right] \\ r_{2}=\frac{k}{2} \rightarrow(2) \end{array} \]
Divide Eq. (1) by Eq. (2), we get
\[ \begin{array}{l} \frac{r_{1}}{r_{2}}=\frac{2 k}{\frac{k}{2}}=4 \\ r_{2}=\frac{r_{1}}{4}=0.25 r_{1} \end{array} \]
Therefore, the rate of the reaction will reduce to \( 0.25 \) times of the initial rate.
\[ \begin{array}{l} \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{CH}_{3} \mathrm{COOCH}_{3}+\mathrm{H}_{2} \mathrm{O} \\ \quad_{1 \mathrm{M}} \\ r_{1}=k\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\left[\mathrm{CH}_{3} \mathrm{OH}\right] \\ =k[1][2] \\ r_{1}=2 k \rightarrow(1) \end{array} \]
when solution is diluted with equal volume of water, concentration is reduced to half
\[ \begin{array}{l} r_{2}=k\left[\frac{1}{2}\right]\left[\frac{2}{2}\right] \\ r_{2}=\frac{k}{2} \rightarrow(2) \end{array} \]
Divide Eq. (1) by Eq. (2), we get
\[ \begin{array}{l} \frac{r_{1}}{r_{2}}=\frac{2 k}{\frac{k}{2}}=4 \\ r_{2}=\frac{r_{1}}{4}=0.25 r_{1} \end{array} \]
Therefore, the rate of the reaction will reduce to \( 0.25 \) times of the initial rate.
Hence, the correct answer is option: 'D'.