The initial concentratin of `N_(2)O_(5)` in the following first order reaction
`N_(2)O_(5)(g) to 2NO_(2)(g)+(1)/(2O_(2))(g) was 1.24 xx10^(-2) mol L^(-1)` at 318K. The concentration of `N_(2)O_(5)` after 60 minutes was `0.20xx10^(-2) mol L^(-1).` Calculate the rate constant of the reaction at 318 K.

Explanation

For the first order reaction.
`log [R_(1)]_(1)/[R_(2)]_(2) = (k(t_(2)-t_(1))/2.303) , k=2.303/(t_(2)-t_(1)) log [R]_(1)/[R]_(2)`
`=2.303/(60 min - 0 min) log (1.24 xx 10^(-2) mol L^(-1))/(0.20 xx 10^(-2) mol L^(-1))`
`=2.303/60 log 6.2 min^(-1)`
`k=0.0304 min^(-1)`