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Question #44835

Difficulty: 8/10 | 🟢 Free

The Question

A sealed vessel contains a radioactive gaseous molecule $A(g)$ . It undergoes two parallel first-order processes:

Process I: Radioactive decay to a solid $B(s)$ with decay constant $\lambda_1$ . Process II: Chemical decomposition to a stable gas $C(g)$ with rate constant $k_2$ .

At $300\text{ K}$ , the effective half-life of $A(g)$ is $34.65\text{ min}$ , and the molar yield of $C(g)$ is exactly $50\%$ . The temperature coefficient for the chemical decomposition is $\mu = 2$ . If the same initial amount of $A(g)$ is allowed to completely react at $340\text{ K}$ , what is the ratio of the number of moles of $C(g)$ to $B(s)$ formed?

Options

A.
16
B.
1
C.
8
D.
0.0625

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Temperature Coefficient (Q10)|Radioactive Decay as Kinetics

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Kinetic Independence of External Factors' for nuclear processes.

Students are heavily conditioned to apply temperature coefficients ( $\mu$ or $Q_{10}$ ) to all rate constants when the temperature changes.

The trap is applying the temperature coefficient to the radioactive decay constant ( $\lambda_1$ ), which would incorrectly yield a ratio of 1 (Option B).

The logical blueprint requires distinguishing between electronic rearrangements (chemical reactions, which are T-dependent) and nuclear destabilization (radioactive decay, which is T-independent).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Temperature Coefficient (Q10)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free