For a generic single-reactant reaction , the experimentally measured half-life is strictly when the — Chemical Kinetics Chemistry Question
Question
For a generic single-reactant reaction $A \rightarrow B$, the experimentally measured half-life is strictly $10 \text{ minutes}$ when the initial molar concentration is $0.1 \text{ M}$. When the experiment is reset and run with an initial concentration of $0.2 \text{ M}$, the half-life drastically collapses to exactly $5 \text{ minutes}$. What is the integral order of this reaction?
Answer: 2
💡 Solution & Explanation
The generalized half-life proportionality states $t_{1/2} \propto a^{1-n}$. By setting up a ratio: $10 \propto (0.1)^{1-n}$ and $5 \propto (0.2)^{1-n}$. Dividing the equations yields $10/5 = (0.1/0.2)^{1-n} \Rightarrow 2 = (1/2)^{1-n} \Rightarrow 2^1 = 2^{n-1}$. Equating the exponents gives $n - 1 = 1 \Rightarrow n = 2$. It is a second-order reaction.
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