Question

$100{cm}^3$ of $1M$ ${CH}_{3}COOH$ was mixed with $100{cm}^3$ of $2M$ ${CH}_{3}OH$ to form as ester. The change in the initial rate if each solution is diluted with equal volume of water would be:

• A. $0.5$ times
• B. $2$ times
• C. $0.25$ times
• D. $4$ times

Answer 1

The correct option is C $0.25$ times

$R=k\left[C{H}_{3}COOH\right]\left[C_2{H}_{5}OH\right]$

Initial rate: $R_1=k\left(a\right)\left(b\right)$
The final : $R_2=k\left(\frac{a}{2}\right)\left(\frac{b}{2}\right)$

$\left(\frac{R_2}{R_1}\right)=\frac{\left[k\right(a/2\left)\right(b/2\left)\right]}{\left[k\right(a\left)\right(b\left)\right]}=\frac{\left[ab/4\right]}{[ab}]=\frac{1}{4}$
$\frac{R_2}{R_1}=0.25$