A reactive substance A simultaneously undergoes two parallel first-order decomposition reactions to — Chemical Kinetics Chemistry Question
Question
A reactive substance A simultaneously undergoes two parallel first-order decomposition reactions to independently form products B and C. The respective specific rate constants are $k_1 = 1.26 \times 10^{-4} \text{ s}^{-1}$ and $k_2 = 3.80 \times 10^{-5} \text{ s}^{-1}$. Assuming no side reactions, what is the exact percentage yield distribution of product B in the final mixture at infinite time?
💡 Solution & Explanation
For parallel first-order reactions $A \rightarrow B$ and $A \rightarrow C$, the fractional percentage yield of B is given by $\frac{k_1}{k_1 + k_2} \times 100$. Calculating the sum: $k_{total} = (1.26 \times 10^{-4}) + (0.38 \times 10^{-4}) = 1.64 \times 10^{-4} \text{ s}^{-1}$. The yield of B is $(1.26 \times 10^{-4} / 1.64 \times 10^{-4}) \times 100 = (1.26 / 1.64) \times 100 \approx 76.83\%$.