If in a reaction `A rarr` Products, the concentrations of reactant `A` are `c_(0), ac_(0), a^(2)c_(0) a^(3)c_(0)`, …after time interval `0,t,2t,3t`…. Where `a` is constant, given, `0 lt alt 1`, show that the reaction is of first order. Also calculate the relation in `k, a`, and `t`.

Explanation

`k = (2.303)/(t) log.(a)/(a-x)`
If `t = t, a = c_(0)` and `(a-x) = ac_(0)`
`k = (2.303)/(t)log.(c_(0))/(ac_(0)) = (2.303)/(t)log.(1)/(a)`
If `t = 2t, a = c_(0), (a-x) = a^(2)c_(0)`
`k = (2.303)/(2t) log.(c_(0))/(a^(2)c_(0)) = (2.303)/(t) log.(1)/(a)`
If `t = 3t, k = (2.303)/(3t)log.(c_(0))/(a^(3)c_(0)) = (2.303)/(t)log.(1)/(a)`
`k` comes constant and thus it is a first order reaction.
Also, `k = (2.303)/(t)log.(1)/(a)`