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 138 K.

Explanation

For first order reaction
`k = (2.303)/((t_(2) - t_(1)))log.([R]_(1))/([R]_(2))`
where `[R]_(1)` is the initial concentration of reactant (i.e., `N_(2)O_(5)`) and `[R]_(2)` is the final concentration of reactant after time (i.e., `t_(2) - t_(1)`)
`:. k = (2.303)/((60-0)min)log.(1.24 xx 10^(-2)M)/(0.20 xx 10^(-2)M)`
`= ((2.303)/(60) log 6.2)min^(-1) = 0.0304 min^(-1)`