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Question #44206

Difficulty: 8/10 | 🟢 Free

The Question

Consider the elementary reversible gas-phase reaction $\ce{A(g) <=> B(g)}$ at $300\text{ K}$ . The standard Gibbs free energy change is $\Delta G^\circ = -300 R\text{ J mol}^{-1}$ and the standard entropy change is $\Delta S^\circ = -30 R\text{ J K}^{-1}\text{ mol}^{-1}$ . The temperature coefficient ( $Q_{10}$ ) for the forward reaction between $300\text{ K}$ and $310\text{ K}$ is given by $\ln(Q_{10, f}) = 1.5$ . Assuming $\Delta H^\circ$ and $\Delta S^\circ$ are independent of temperature, what is the value of $\ln(Q_{10, b})$ for the backward reaction in the same temperature range? ( $R$ is the universal gas constant)

Options

A.
$2.5$
B.
$0.5$
C.
$1.5$
D.
$3.5$

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

State vs Path Functions|Gibbs Energy and Spontaneity|Temperature Coefficient (Q10)

Why This Question Is Tricky

Common Mistakes

This question tests the critical distinction between thermodynamic state functions ( $\Delta G^\circ$ , $\Delta H^\circ$ ) and path-dependent kinetic parameters ( $Q_{10}$ , $E_a$ ).

The primary trap is the assumption that Gibbs Free Energy ( $\Delta G^\circ$ ) dictates the temperature dependence of the reaction rate or equilibrium.

Students often erroneously substitute $\Delta G^\circ$ into the Arrhenius or van 't Hoff equations instead of $\Delta H^\circ$ .

A secondary trap involves a sign error in calculating $\Delta H^\circ$ or setting up the ratio $\ln(Q_{10, f}) - \ln(Q_{10, b})$ , which leads directly to the distractor 0.5.

By forcing the calculation of $\Delta H^\circ$ from $\Delta G^\circ$ and $\Delta S^\circ$ , the problem ensures the student understands that while $\Delta G^\circ$ determines spontaneity at a specific temperature, $\Delta H^\circ$ governs how the equilibrium shifts with temperature.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Thermodynamics - Class 11 Part 1
Concept	State vs Path Functions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free