The rate constant for the first order decomposition of H_(2)O_(2) is given by the following equation : logk=14.34-1.25xx10^(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=14.34-1.25xx10^(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="A e"^(-E_(a)//"RT")` or `lnk=lnA-(E_(a))/(RT)" or "logk=logA-(E_(a))/(2.303"RT")` Comparing with the given equation, `(E_(a))/(2.303" RT")=(1.25xx10^(4)"K")/(T)` or `E_(a)=2.303" R "xx1.25xx10^(4)" K"=2.303xx(8.314" JK"^(-1)" mol"^(-1))xx1.25xx10^(4)" K"=239.347" kJ mol"^(-1)` When `t_(1//2)=256" min",k=(0.693)/(256xx60"s")=4.51xx10^(-5)s^(-1)` Substituting this value in the given equation, `log(4.51xx10^(-5))=14.34-(1.25xx10^(4)" K")/(T),i.e.,(-5+0.6542)=14.34-(1.25xx10^(4)"K")/(T)` or `(1.25xx10^(4)K)/(T)=18.6858" or "T=669" K".`