A certain amount of methyl acetate was hydrolysed in the presence of excess of `"0.05 M HCl at "25^(@)C`. 20 mL of reaction mixture were removed and titrated with `NaOH` solution, the volume V of alkali required for neutralisation after time ‘t’ were as follows :
`{:("t(min)",0,20,40,60,oo),("v(mL)",20.2,25.6,29.5,32.8,50.5):}`
Show that the reaction is the first order reaction.

Explanation

`k=(2.303)/(t)log""((V_(oo)-V_(o))/((V_(oo)-V_(t))))`
`V_(oo)-V_(o)=50.4-20.2=30.2`
When `t="20 mts. "k=(2.303)/(20)log""(50.4-20.2)/(50.4-25.6)`
`=0.1151 log""(30.2)/(24.8)`
`=0.1151 log 1.2479`
`=01151 xx 0.0959 =11.03xx10^(-3)" min"^(-1)`
when t=40 mts
`k=(2.303)/(40)log""(50.4-20.2)/(50.2-29.5)`
`=0.0576xxlog""(30.2)/(20.9)=0.0576xx0.1596`
`=9.19xx10^(-3)" min"^(-1)`
`" when "t="60 mts"`
`k=(2.303)/(60)log""(50.4-20.2)/(50.2-32.8)=0.03838xxlog""(30.2)/(17.6)`
`=0.03838xx0.2343=8.99xx10^(-3)" min"^(-1)`
The constant values of k show that the reaction is of first order.