For a first order homogenous gaseous reaction `A rarr2B +C` if the total pressure after time `t` was `p_(t)` and after long time `(t rarr infty)` was `p_(infty)` then k in terms of `p_(t), p_(infty)` and `t` is

Options

A. `k=(2.303)/(t)log(p_(infty)/(p_infty-p_(t)))`
B. `k=(2.303)/(t)log({2p_(infty)}/(p_infty+p_(t)))`
C. `k=(2.303)/(t)log( {2p_(infty)}/(3(p_infty-p_(t))))`
D. `k=(2.303)/(t)log(p_(infty)/(p_infty+p_(t)))`

Answer

C

Explanation

`A rarr 2B + C`
`t rarr infty 0 2p_(i) p_(i)`
As we know k =`(2.303)/(t )log (p_(i))/(p_(i)-x)` so `k=(2.303)/(t)log (2p_(infty))/(3(p_(infty)-p_(t))`