Question

$1$ $mL$ of methyl acetate was added to a flask containing $20$ $mL$ of $N/20$ $HCl$ maintained at ${25}^{o}C$. $2$ $mL$ of the reaction mixture were withdrawn at different intervals and titrated with a standard alkali solution. The following results were obtained:

Time (min)	$0$	$75$	$119$	$183$	$\infty$
Alkali used ($mL$)	$19.24$	$24.20$	$26.60$	$29.32$	$42.03$

Show that the reaction follows first order kinetics.

Answer 1

In case the hydrolysis follows first order kinetics, then
$k=\frac{2.303}{t}{\log }_{10}\frac{{\left[A\right]}_0}{\left[A\right]}=\frac{2.303}{t}{\log }_{10}\frac{V_{\infty }-V_0}{V_{\infty }-V_t}$
When, $t=75$ min, $V_{\infty }=42.03$, $V_0=19.24$, $V_t=24.20$
$k=\frac{2.303}{75}{\log }_{10}\frac{(42.03-19.24)}{(42.03-24.20)}=\frac{2.303}{75}{\log }_{10}\frac{22.79}{17.83}$
$=0.00327{min}^{-1}$
$t=119$ min, $V_{\infty }=42.03$, $V_0=19.24$, $V_t=26.60$
$k=\frac{2.303}{119}{\log }_{10}\frac{(42.03-19.24)}{(42.03-26.60)}$
$=\frac{2.303}{119}{\log }_{10}\frac{22.79}{15.43}$
$=0.00327$
Since, the values of $k$ are constant, hence, it follows first order kinetics.