The decomposition of `N_(2)O_(5)` in a carbon tetrachloride solutioin has been investigated.
`N_(2)O_(5)("solution") to 2NO_(3)` (solution) +`1//2O_(2)(g)` ltrbgt The reaction has been found to be of the first order in `N_(2)O_(5)` with a first order rate-constant = `6.2 xx 10^(-4)s^(-1)`. Calculate the rate of the reaction when (a) `[N_(2)O_(5)]` = 1.25 mol `L^(-1)` and b) `[N_(2)O_(5)]` = 0.25 mol `L^(-1)`. c) What concentration of `N_(2)O_(5)` would give a rate of `2.4 xx 10^(-3) mol L^(-1)s^(-1)` ?

Explanation

(a) Rate `=k[N_(2)O_(5)]=(6.2xx10^(-4)s^(-1))(1.25" mol L"^(-1))=7.75xx10^(-4)" mol L"^(-1)s^(-1)`
(b) Rate `=(6.2xx10^(-4)s^(-1))(0.25" mol L"^(-1))=1.55xx10^(-4)" mol L"^(-1)s^(-1)`
(c) `2.4xx10^(-3)" mol L"^(-1)s^(-1)=(6.2xx10^(-4)s^(-1))[N_(2)O_(5)]" or "[N_(2)O_(5)]=3.87" mol L"^(-1).`