State any one condition under which a bimolecular reaction may be kinetically of first order?

Solution

During the hydrolysis of 0.01 mol of ethyl acetate with 10 mol of water, amounts of the various constituents at the beginning (t = 0) and completion (t) of the reaction are given as under.

${CH}_{3} - {COOC}_{2} H_{5} + HOH \to {CH}_{3} - COOH + C_{2} H_{5} - OH$
t = 0 0.01 mol 10 mol 0 mol 0 mol
t 0 mol 9.9 mol 0.01 mol 0.01 mol

The concentration of water does not get altered much during the course of the reaction. So, in the rate equation
$Rate = k [{CH}_{3} . {COOC}_{2} H_{5}]^{1} {[H_{2} O]}^{0} .$
the term [H2O] can be taken as constant. The equation, thus, becomes
Rate = k [CH₃COOC₂H₅]
where k = k′ [H2O]
and the reaction behaves as first order reaction