Methyl acetate was subjected to hydrolyiss in `N-HCl` at `298 K`. `5mL` of the mixture is withdraw at different intervals and titrated with constant with about `N//8NaOH`. The following results were obtained:
`|{:("Time (min)",0,25,40,61,oo),("Vol of alkali used (mL)",19.24,24.20,26.60,29.50,42.1):}|`
Show that the reaction is of first order.

Explanation

`CH_(3)COOCH_(3)+H_(2)O overset(H^(o+))rarrCH_(3)COOH+CH_(3)OH`
`k = (2.303)/(t)log.(V_(oo) - V_(0))/(V_(oo)-V_(t))`
(a) `k = (2.303)/(25)log.(42.1-19.24)/(42.1-24.2)`
`= (2.303)/(25)log.(22.86)/(17.9)`
`= (2.303)/(25) xx 0.16 = 0.0097 min^(-1)`
(b) `k = (2.303)/(40)log.(42.1-19.24)/(42.1-26.6)`
`= (2.303)/(40) xx 0.1687 = 0.0097 min^(-1)`
( c) `k = (2.303)/(61)log.(42.1-19.24)/(42.1-29.5) = 0.0097 min^(-1)`
The value of `k` is constant. Hence, first order reaction.