Question

A substance undergoes first order decomposition. The decomposition follows two parallel first order reactions as :
$If k_{1}=1.26\times10^{-4} s^{-1}, k_{2}=3.8 \times10^{-5} s^{-1},$ then the percentage distributions of B and C are respectively

• A. $80\%, 20\%$
• B. $76.83\%, 23.17\%$
• C. $90\%, 10\%$
• D. $63.94\%, 36.06 \%$

Answer 1

Answer: (B)

For parallel path reaction,
$k_{average} =k_{1}+k_{2}=1.26\times10^{-4}+3.8\times10^{-5}=1.64\times10^{-4} s^{-1}$
Fractional yield of B$=\frac{k_{1}}{k_{average}}=\frac{1.26\times10^{-4}}{1.64\times10^{-4}}=0.7683$
Percentage distribution of B = 76.83%
Fractional yield of $C=\frac{k_{2}}{k_{average}}=\frac{3.8\times10^{-5}}{1.64\times10^{-4}}=0.2317$
Percentage distribution of C = 23.17%