Half life of reaction `: H_(2)O_(2)(aq) rarr H_(2)O(l)+(1)/(2)O_(2)(g)`is independent of initial concentration of `H_(2)O_(2)` volume of `O_(2)` gas after 20 minute is `5L` at `1 atm` and `27^(@)C` and after completion of reaction is `50L`. The rate constant is `:`

Options

A. `(1)/(20)log 10 mi n^(-1)`
B. `(2.303)/(20)log 10 mi n^(-1)`
C. `(2.303)/(20)log. (50)/(45)mi n^(-1)`
D. `(2.303)/(20)log. (45)/(50)mi n^(-1)`

Answer

3

Explanation

`t_(1//2)` is independent of initial concentration a, for first order reaction
`x alphaV_91)(=5L` at `t=20` minutes )
`a prop V_(1)(=50L` at completion)
`k=(2.303)/(t)log.(a)/(a-x)log.(50)/(45)`