Question

One litre of $2M$ acetic acid is mixed with one litre of $2M$ ethyl alcohol to form ester as follows:

$C{H}_{3}COOH+C_2{H}_{5}OH\to C{H}_{3}COO{C}_2{H}_5+H_{2}O$.

Decrease in initial reaction rate if each solution is diluted by an equal volume of water would be:

• A. $1/2$ times
• B. $1/4$ times
• C. $2$ times
• D. $4$ times

Answer 1

The correct option is B $1/4$ times

The reaction is of first order with respect to both reactants.
The rate law expression is

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

When the solution is diluted with an equal volume of water, the concentration of two reactants is reduced to half.

$r_1=k\left[\frac{C{H}_{3}COOH}{2}\right]\left[\frac{C_2{H}_{5}OH}{2}\right]=\frac{1}{4}k\left[C{H}_{3}COOH\right]\left[C_2{H}_{5}OH\right].$

Hence, the correct option is $\text{B}$