Thank you for reporting, we will resolve it shortly
Q.
Half life of first orders reaction and half life of $2^{\text {nd }}$ order reaction are equal. Hence the ratio of their rates at the start of the reaction is/are-
Chemical Kinetics
Solution:
Half life of first order rxn , $t _{1 / 2}=\frac{0.693}{ k }$
Half life of $2^{ nd }$ order reaction, $t _{1 / 2}=\frac{1}{( A )_{0} k }$
Since, half lives are equal, $\therefore =[ A ]_{0}=\frac{1}{0.693}$
Rate of first order reaction $= k \frac{1}{(0.693)^{1}} ...(i)$
Rate of 2 nd order reaction $= k \frac{1}{(0.693)^{2}}....(2)$
-Ratio of rates $=\frac{\frac{1}{0.693}}{\left(\frac{1}{0.693}\right)^{2}}$