For the sequential first-order reaction , consider the highly specific limiting case where the rate — Chemical Kinetics Chemistry Question
Question
For the sequential first-order reaction $A \xrightarrow{k_1} B \xrightarrow{k_2} C$, consider the highly specific limiting case where the rate constants are exactly equal ($k_1 = k_2 = k$). Applying L'Hôpital's limit theory, what does the formula for $t_{max}$ collapse into?
Answer: B
💡 Solution & Explanation
When $k_1$ precisely equals $k_2$, the standard logarithmic $t_{max}$ formula produces an undefined $0/0$ division. Applying mathematical limit operations as $k_1 \rightarrow k_2$ robustly proves that the timestamp simplifies perfectly to $t_{max} = 1 / k$.
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