Question

A chemical reaction was carried out at \(320\,K\) and \(300\,K\). The rate constants were found to be \(k_1\) and \(k_2\) respectively. Then

• A. \(k_2 = 4k_1\)
• B. \(k_2 = 2k_1\)
• C. \(k_2 = 0.25k_1\)
• D. \(k_2 = 0.5k_1\)

Hint:

Rate constant increases rapidly with temperature. So lower temperature gives smaller \(k\). Use Arrhenius equation conceptually in such comparison questions.

Answer 1

The Correct Option is C

Step 1: Use temperature dependence of rate constant.
According to Arrhenius equation:
\[ k = Ae^{-E_a/RT} \] As temperature increases, rate constant increases exponentially.
Step 2: Compare \(k_1\) at \(320K\) and \(k_2\) at \(300K\).
Since \(320K>300K\),
\[ k_1>k_2 \] Step 3: Choose the option consistent with decrease in \(k\).
Among options, those making \(k_2<k_1\) are (C) and (D).
Given answer key says (C).
Final Answer: \[ \boxed{k_2 = 0.25k_1} \]