The value of `t_(0.875)/(t_(0.50)` for `n^(th)` order reaction is

Options

A. `2^((2n-2))`
B. `2^((2n-2)-1)`
C. `(8^(n-1)-1)/(2^(n-1)-1)`
D. None of these

Answer

C

Explanation

`kt=(1)/(n-1)[(1)/(A_(t)^(n-1))-(1)/(A_(0)^(n-1))]`
`kt_(0.5)=kt=(1)/(n-1)[(1)/(((A_(0))/(2))^(n-1))-(1)/(A_(0)^(n-1))]=(1)/(n-1)[(2^(n-1)-1)/(A_(0)^(n-1))]`
`kt_(0.875)=(1)/(n-1)[(1)/(((A_(0))/(8))^(n-1))-(1)/(A_(0)^(n-1))]=(1)/(n-1)[(8^(n-1)-1)/(A_(0)^(n-1))]`
`(t_(0.875))/(t_(0.5))=(8^(n-1)-1)/(2^(n-1)-1)`