For the given first-order reaction, the rate equation is
=
k[N2O5] The concentration of the reactant at any time t is given by
t =
()log where a = 100 and a – x = 100 – 99.6 = 0.4. Hence, concentration of
N2O5 decreases exponentially with time.
Half-life period for first-order reaction
t =
=
It is independent of the concentration of the reactant. We know that k increases with increase in temperature (according to Arrhenius equation) and since
t is inversely proportional to k, so
t decreases, when k increases with increase in temperature. When the reaction is 99.6% complete, then
t99.6 =
()log t99.6 =
()2.4 =
8× =
8t