The reactant concentrations of a first order reaction at various times, 0 , t , 2t and 3t are `c_(0).a^(x)c_(0).a^(y)c_(0) and a^(z)c_(0)` , respectively, where 'a' is a constant and `0lealt1` . Establish a relation between x , y and z.

Explanation

The rate constant of a first order reaction is given by,
`k=(2.303)/(t)log.([A]_(0))/([A])([A]_(0) and [A]` are the concentrations of the reactant at times t = 0 and t. )
Therefore, (1) `k=(2.303)/(t)log.(c_(0))/(a^(x)c_(0))=-xxx(2.303)/(t)loga`
(2) `k=(2.303)/(2t)log.(c_(0))/(a^(y)c_(0))=-yxx(2.303)/(2t)loga`
(3) `k=(2.303)/(3t)log.(c_(0))/(a^(z)c_(0))=-zxx(2.303)/(3t)loga`
From equations [1] and [2], we get, `x=(y)/(2)` and from equations [1] and[3] , we get , `x=(z)/(3)thereforex=(y)/(2)=(z)/(3).`