Question

Consider the two different first order reactions given below

A + B → C (Reaction 1) 

P → Q (Reaction 2)

The ratio of the half life of Reaction 1 : Reaction 2 is 5 : 2. If \(t_1\) and \(t_2\) represent the time taken to complete \(\frac {2}{3}rd\) and \(\frac {4}{5} th\) of Reaction 1 and Reaction 2, respectively, then the value of the ratio \(t_1 : t_2 \) is _____ \(\times 10 ^{-1}\) (nearest integer).

[Given: \(log _ {10} (3)= 0.477\) and \(log _ {10} \)(5) = 0.699]

Answer 1

Correct answer is : 17

\(\frac {(t_{1/2})_I}{(t_{1/2})_{II}}=\frac {K_2}{K_1}=\frac {5}{2}\)

\(\therefore K_1t_1=ln \frac {1}{1-\frac{2}{3}}=ln3\)

\(K_2t_2 = ln \frac {1}{1-\frac {4}{5}}= l n5\)

\(\Rightarrow \frac {K_1}{K_2} \times \frac {t_1}{t_2} = \frac {0.477}{0.699}\)

\(\Rightarrow \frac {t_1}{t_2} = \frac {0.477}{0.699} \times \frac {5}{2} = 1.7 = 17 \times 10 ^{-1}\)