Given that for a reaction of order n. the intergrated form of the rate equation is `k= (1)/(t(n-1))[(1)/(C^(n-1))-(1)/(C_(0)^(n-1))]` where `C_(0)` and C are the values after time t. What is the relationship between `t_(3//4)` and `t_(1//2)` where `t_(3//4)` is the time required for C to become `1//4C_(0)-`

Options

A. `t_(3//4) = t_(1//2)[2^(n-1) +1]`
B. `t_(3//4) =t_(1//2)[2^(n-1)-1]`
C. `t_(3//4) =t_(1//2) [2^(n+1) -1]`
D. `t_(3//4) =t_(1//2) [2^(n+1)+1]`

Answer

A

Explanation

`t_(3//4)(1)/(K(n-1))[(1)/(((C_(0))/(4))^(n-1))-(1)/(C_(0)^(n-1)]]`
`= (1)/(k(n-1)) (4^(n-1)-1)C_(0)^(n-1)`
`:. t_(1//2)=(1)/(K(n-1))(2^(n-1)-1)`
`So (t_(3//4))/(t_(1//2)) =2^(n-1)+1`