For any generalized pure first-order chemical reaction, what is the exact mathematical ratio linking — Chemical Kinetics Chemistry Question
Question
For any generalized pure first-order chemical reaction, what is the exact mathematical ratio linking the time required to reach 99.9% completion ($t_{99.9\%}$) compared directly against the time to reach 90% completion ($t_{90\%}$)?
Answer: C
💡 Solution & Explanation
For first order kinetics, $t \propto \log(\frac{a}{a-x})$. Thus, $t_{90\%} \propto \log(100/10) = \log 10 = 1$. Similarly, $t_{99.9\%} \propto \log(100/0.1) = \log 1000 = 3$. The precise calculated ratio evaluating $t_{99.9\%} / t_{90\%}$ resolves to exactly $3 / 1 = 3$.
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