COMEDK · Chemistry · 19. Chemical Kinetics

Two chemical reactions of the same order have equal Frequency factor value.
Their Activation energies differ by \(26.8 \mathrm{~kJ} / \mathrm{mol}\). At 300 K if \(k_2=x k_1\) find the value of \(x\).

A \(1.143 \times 10^3\)
B \(4.665\)
C \(4.639 \times 10^4\)
D \(2.286 \times 10^3\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(4.639 \times 10^4\)

Step-by-step Solution

Detailed explanation

The Arrhenius equation is given by \(k = A e^{-E_a / (RT)}\). Given that the frequency factors are equal, \(A_1 = A_2 = A\). The rate constants for the two reactions are \(k_1 = A e^{-E_{a1} / (RT)}\) and \(k_2 = A e^{-E_{a2} / (RT)}\). Taking the ratio…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Two chemical reactions of the same order have equal Frequency factor value.Their Activation energies differ by \(26.8 \mathrm{~kJ} / \mathrm{mol}\). At 300 K if \(k_2=x k_1\) find the value of \(x\).

Step-by-step Solution

Two chemical reactions of the same order have equal Frequency factor value.
Their Activation energies differ by \(26.8 \mathrm{~kJ} / \mathrm{mol}\). At 300 K if \(k_2=x k_1\) find the value of \(x\).