Question

A substance undergoes first order decomposition. The decomposition follows two parallel first order reactions as

$k_1=1\cdot 26\times {10}^{-4}{s}^{-1},k_2=3\cdot 8\times {10}^{-5}{s}^{-1}$
The percentage distribution of B and C are

• A. $75\%$ B and $25\%$ C
• B. $80\%$ B and $20\%$ C
• C. $60\%$ B and $40\%$ C
• D. $90\%$ B and $10\%$ C
• E. $76\cdot 83\%$ B and $23\cdot 17\%$ C

Answer 1

The correct option is E $76\cdot 83\%$ B and $23\cdot 17\%$ C

At any time t
Rate of formation of B = $k_1{C}_A$
Rate of formation of C = $k_1{C}_A$
$\therefore \frac{C_B}{C_C}=\frac{k_1}{k_2}$
$=\frac{1\cdot 26\times {10}^{-4}}{3\cdot 8\times {10}^{-5}}$
$\%C_B=\frac{C_B}{C_B+C_C}\times 100$
$=\frac{1\cdot 26\times {10}^{-4}}{1\cdot 26\times {10}^{-4}+3\cdot 8\times {10}^{-5}}\times 100$
$=\frac{1\cdot 26}{1\cdot 64}\times 100=76\cdot 83\%$