(a) Derive an integrated rate equation for the rate constant of a first order reaction.(b) The specific reaction rate of a reaction quadruples when temperature changes from 30^(0) to 50^(0).Calculate the energy of activation of the reaction.[Given:R = 8.314 JK^(-1)mol^(-1)].

(a) Derive an integrated rate equation for the rate constant of a firs

1.	(a) Derive an integrated rate equation for the rate constant of a first order reaction.(b) The specific reaction rate of a reaction quadruples when temperature changes from 30^(0) to 50^(0).Calculate the energy of activation of the reaction.[Given:R = 8.314 JK^(-1)mol^(-1)].
Answer» SOLUTION :(a)Consider a zero order reaction `R to P` `-d[R]/dt= -k.dt` where k is the velocity constant of the FIRST order reaction `-d[R]/[R]= -k.dt` Integrating the equation `intd[R]/[R] = -INT k.dt` In[R]=-kt+I…..(1) I is constant of integration when t=0 [R]=`[R]_(0)` where `[R]_(0)` is initial concentration of the reactant . `In[R]_(0)= -Kxx0 +1` I = `In[R]_(0)` Substituting I in equation..(1) `ln[R] = -kt + ln[R](0)` `k=2.303/t log[R](0)/[R]` (b)`logk_(2)/k_(1)=E_(a)/2.303 xx R[T_(2)-T_(1)/T_(1)xxT_(2)]` `log4=E_(a)/2.303 xx 8.314[323-303/(303)(323)]` `0.6021 = E_(a)/(2.303 xx 8.314) xx 20/303xx323` `E_(a) = (0.6021 xx 2.303 xx 8.314 xx 303 xx 323)/20`