Question

1L of 2 M $C{H}_{3}COOH$ is mixed with 1L of $3M{C}_2{H}_{5}OH$ 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

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

Answer 1

The correct option is A 0.25 times

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

Initial rate: $r_1=k\times \left(a\right)\times \left(b\right)$

The "final", $r_2=k\times \left(\frac{a}{2}\right)\times \left(\frac{b}{2}\right)$

$\left(\frac{r_2}{r_1}\right)=\frac{\left[k\right(\frac{a}{2}\left)\right(\frac{b}{2}\left)\right]}{\left[k\right(a\times b\left)\right]}$
$=\frac{\left[\frac{a\times b}{4}\right]}{[a\times b]}$
$=\frac{1}{4}\to \frac{r_2}{r_1}$
$=0.25\to r_2=\left(0.25\right)\times r_1$

The final rate, is 0.25 times the inital rate.