The rate constant for the first order decomposition of H_(2)O_(2) is given by the following equation : logk=14.2 - (1.0xx10^(4))/(T) Calculate E_(a) for this reaction and rate constant k if its half-life period be 200 minutes. [Given : R=8.314 JK^(-1)"mol"^(-1)]

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=14.2 - (1.0xx10^(4))/(T) Calculate E_(a) for this reaction and rate constant k if its half-life period be 200 minutes. [Given : R=8.314 JK^(-1)"mol"^(-1)]
Answer» Solution :A general equation relating log k and `E_(a)` is GIVEN by `log k =log A-(E_(a))/(2.303RT) ""…(i)` The given equation is `log k=14.2 -(1.0xx10^(4))/(T)""…(ii)` On comparing equations (i) and (ii), we have `(E_(a))/(2.303RT)=(1.0xx10^(4))/(T)` or `E_(a)=1.0xx10^(4)xx2.303 xx R "" ...(III)` Substituting the value of R in equation (iii), we have `E_(a)=1.0xx10^(4)xx2.303xx8.314=191471.4"J mol"^(-1)` Half-life PERIOD for a first order reaction `t_(1//2)=(0.693)/(k)` or `ko=(0.693)/(t_(1//2))=(0.693)/(200"min")=0.0034" min"^(-1)`