The rate constant for the first order decomposition of H_(2)O_(2) is given by the following equation : logk=14.34 -1.25 xx 10^(4)K//T Calculate E_(a) for this reaction and at what temperature will its half-period be 256 minutes?

The rate constant for the first order decomposition of H_(2)O_(2) is g

1.	The rate constant for the first order decomposition of H_(2)O_(2) is given by the following equation : logk=14.34 -1.25 xx 10^(4)K//T Calculate E_(a) for this reaction and at what temperature will its half-period be 256 minutes?
Answer» Solution :According to Arrhenius EQUATION `K=Ae^(-E_(a)//RT)` Taking LOGARITHM of both sides, In k`="In A"-(E_(a))/(RT) or logk=logA-(E_(a))/(2.303RT)` Equating similar terms in the two equations `(E_(a))/(2.303RT)=(1.25xx10^(4)K)/(T) or E_(a)=2.303R xx 1.25 xx 10^(4)K` or `E_(a)=2.303 xx (8.314JK^(-1)"mol"^(-1))xx1.25xx10^(4)K=239.34"kJ mol"^(-1)` When `t_(1//2)=256"min", k=(0.693)/(256xx60s)=4.51xx10^(-5)s^(-1)` Substituting this value in the given equation, we GET `log(4.51xx10^(-5))=14.34-(1.25xx10^(4)K)/(T)` or `(-5+0.6542)=14.34-(1.25xx10^(4)K)/(T)` or `(1.25xx10^(4)K)/(T)=18.6858 or T=669K`.