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

If `[R]_(1)` and `[R]_(2)` are the concentrations of the reactants at time `t_(1)` and `t_(2)` respectively, then for a first order reaction
`k= (2.303)/(t_(2)-t_(1)) log (([R]_(1))/([R]_(2)))`
`= (2.303)/((60 min - 0 min)) log ((1.24xx10^(-2)mol L^(-1))/(0.20xx10^(-2)mol L^(-1)))`
`= (2.303)/(60 min) log 6.2`
`= 0.0304 min^(-1)`