Rate constants – temperature and reactant dependence for second-order reactions For a second-order reaction, which statements about the specific rate constant are correct?

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:

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).