Frequently a species can react in different ways to give a variety of products For example toluene can be nitrated at the ortho meta or para positions we shall consider the simplest case, that of two competing irreversible first- order reactions: `A overset(k_(1)) rarr C` and `A overset (k_(2)) rarr D` where the stoichimetric coefficients are taken as unity for simplicity. THe rate law is `((d[A])/(dt))=-k_(1)[A] -k_(2)[A] =-(k_(1)+k_(2))[A]` `Rightarrow [A] = [A]_(0)e^-(k_(1)+k_(2))t` For C, we have `((d[C])/(dt))=k_(1)[A] =k_(1)[A]_(0)e^-(k_(1)+k_(2))t` Multiplication by dt and integration from time 0(where `[C]_(0)=0` to an arbitary time t gives `[C] =(k_(1)[A]_(0))/(k_(1)+k_(2))(1-e^-(k_(1)+k_(2))t)` Similarly integration of `((d[D])/(dt))` gives `[D] = (k_(2)[A]_(0))/(k_(1)+k_(2))(1-e^-(k_(1)+k_(2))t)` The sum of the rate constants `k_(1)+k_(2)` appears in the exponentials for both [C] and [D] At any time, we also have, `[C]/[D] = k_(1)/k_(2)` At high temperature, acetic acid decomposition into `CO_(2)` and `CH_(4)` and simultaneously into `CH_(2)CO` (ketene) and `H_(2)O` (i) `CH_(3)COOH overset (k_(1)=3s^(-1)rarr CH_(4)+CO_(2)` (ii) `CH_(3)COOH overset(k_(2)=4s^(-1)rarr CH_(2)CO+H_(2)O` What is the fraction of acetic acid is reacting as per reaction(i)?A. `3/4`B. `3/7`C. `4/7`D. None of these