The rate constant for the first order decomposition of N_(2) O_(5) is given by the following equation: k=(2.5 xx 10^(14) s^(-1) ) e^((-25000K)//T) Calculate E_a for this reaction and rate constant if itshalf-life period be 300 minutes.

The rate constant for the first order decomposition of N_(2) O_(5) is

1.	The rate constant for the first order decomposition of N_(2) O_(5) is given by the following equation: k=(2.5 xx 10^(14) s^(-1) ) e^((-25000K)//T) Calculate E_a for this reaction and rate constant if itshalf-life period be 300 minutes.
Answer» Solution :`K=AE^(-E_(a) //RT)""…(i)` Also `k=(2.5 xx 10^(14) s^(-1) ) e^((-25000K)//T)""…(ii)` From (i) and (ii), we have `Ae^(-E_(a)//RT)=(2.5 xx 10^(-14) s^(-1) ) e^((-25000K)//T)` Equating similar terms in the above equation, we have `(-E_(a))/(RT) = (-25000K)/( T)` or `E_(a) = R xx 25000 K` or `E_(a) =8.314 J K^(-1) mol^(-1) xx 25000 K` or `E_(a) = 207.85 kJ "mol"^(-1)` For a first ORDER reaction `t_(1//2) = (0.693)/(k)` or `k=(0.693)/( t_(1//2))= (0.693)/(300 "minutes") = 2.31 xx 10^(-3) "minutes"^(-1)` or `k=(0.693)/( 300 xx 60S) = (0.693)/(18000 s) = 3.85 xx 10^(-5) s^(-1)`.