The initial concentration of `N_(2)O_(5)` in the following first order reaction:
`N_(2)O_(5)(g) rarr 2NO_(2)(g)+(1)/(2)O_(2)(g)`
was `1.24 xx 10^(-2) mol L^(-1)` at `318 K`. The concentration of `N_(2)O_(5)` after `60 min` was `0.20 xx 10^(-2) mol L^(-1)`. Calculate the rate constant of the reaction at `318 K`.

Explanation

For the first order reaction,
`k=2.303/t log (a/(a-x))`
`a=1.24 xx 10^(-2) mol L^(-1)`,
`(a-x) = 0.20 xx 10^(-2) mol L^(-1)`,
`t=60` min
`k=2.303/(60min) xx log((1.24 xx 10^(-2) mol L^(-1))/(0.20 xx 10^(-2) mol L^(-1)))= 2.303/(60 min)log6.2`
`=2.303/(60 min) xx 0.7924 = 0.0304 "min"^(-1)`