The initial concentration of `N_2 O_5` in the following first order reaction, `N_2 O_5 (g) to 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 minutes was `0.20 xx 10^(-2) mol L^(-1)` . Calculate the rate constant of the reaction at 318 K.

Answer

`0.0304 min""^(-1)`

Explanation

For a first order reaction `, log ([A]_1)/( [A]_2)= ( k(t_2 -t_1))/( 2.303)`
` or k=( 2.303 )/((t_2 -t_1)) log"" ([A]_1)/([A]_2)`
`=( 2.303 )/( ( 60 min -0)) log"" ( 1.24 x 10^(-2) mol L^(-1))/( 0.20 xx 10^(-2) mol L^(-1))`
` = ( 2.303 )/(60 ) log "" 6.02 min""^(-1) = 0.0304 min""^(-1)`