For the reaction `PrarrR` , the rate of the reaction = r. On doubling the concentration of P, the reaction-rate reduces to `(1)/(4)` th of it initial value. Find the unit of the rate constant for the reaction.

Explanation

Let, the order of the reaction = x, reaction -rate, `r=k[P]^(x)`
On doubling the concentration of P , the reaction -rate reduces `(1)/(4)` th of its initial value .
`therefore(1)/(4)r=k[2P]^(x)=2^(x)xxk[P]^(x)=2^(x)xxr`
or, `2^(x)=(1)/(4)=2^(-2) " or, "x=-2`
Hence , the unit of `k=("mol.L"^(-1))^([1-(-2)]).s^(-1)="mol"^(3).L^(-3).s^(-1)`