Rate constants – temperature and reactant dependence for second-order reactions For a second-order reaction, which statements about the specific rate constant are correct?
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AIt is independent of temperature.
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BIt varies with temperature.
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CIt depends on the nature (identity) of the reactants.
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DBoth (b) and (c).
Answer
Correct Answer: Both (b) and (c).
Explanation
Introduction / Context:The specific rate constant k characterizes intrinsic kinetics for a given reaction mechanism and order. Correct understanding of its dependencies is essential for reactor design and temperature control strategies.
Given Data / Assumptions:
- Second-order overall reaction (e.g., A + B → products or 2A → products).
- Arrhenius behavior applies over the temperature range of interest.
Concept / Approach:According to the Arrhenius equation, k = A * exp(−E_a/(R T)), the rate constant depends strongly on absolute temperature and activation energy E_a. The pre-exponential factor A and E_a are properties of the specific reaction system, which are determined by the nature of the reacting species and mechanism. Therefore, k varies with T and depends on the reactants involved.
Step-by-Step Solution:
Recognize temperature dependence: increasing T typically increases k exponentially.Recognize chemical identity dependence: different reactant pairs have different A and E_a → different k values at the same T.Hence statements (b) and (c) are both correct.Verification / Alternative check:Experimental Arrhenius plots (ln k vs. 1/T) for different reagent pairs yield distinct slopes (−E_a/R) and intercepts (ln A), confirming dependence on both T and reactant identity.
Why Other Options Are Wrong:
- Independent of temperature: Contradicts Arrhenius behavior observed for most reactions.
Common Pitfalls:Confusing reaction order (which affects units of k) with temperature dependence; order does not eliminate k’s Arrhenius dependence.
Final Answer:Both (b) and (c).