Question

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-

• A. 1
• B. 2
• C. 0.693
• D. 1.44

Answer 1

Answer: (C)

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 $=\frac{\frac{1}{0.693}}{{\left(\frac{1}{0.693}\right)}^2}$

$=\frac{1}{0.693}\times 0.693\times 0.693=0.693$