Before You Begin

Question #44062

Difficulty: 8/10 | 🟢 Free

The Question

Consider the reversible liquid-phase isomerization reaction: $\ce{A(l) \rightleftharpoons B(l)}$ .

At $350 \text{ K}$ , the liquid mixture of A and B exhibits non-ideal behavior. The system is simultaneously in vapor-liquid equilibrium and chemical equilibrium.

At this temperature, the mixture forms an azeotrope (where the vapor phase mole fractions equal the liquid phase mole fractions) at a liquid phase mole fraction of A, $x_A = 0.40$ .

Given that the vapor pressures of pure liquid A and pure liquid B at $350 \text{ K}$ are $250 \text{ torr}$ and $150 \text{ torr}$ , respectively, what is the standard Gibbs free energy change ( $\Delta G^\circ$ ) for the isomerization reaction at $350 \text{ K}$ ?

(Assume the vapor phase behaves ideally and the standard state for each component is the pure liquid at $350 \text{ K}$ ).

Options

A.
$-RT \ln(2.5)$
B.
$-RT \ln(1.5)$
C.
$-RT \ln(0.9)$
D.
$-RT \ln(0.6)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Homogeneous vs. Heterogeneous Equilibrium|Concentration Units Dependency|Azeotrope Boiling Point Logic

Why This Question Is Tricky

Common Mistakes

This problem tests the critical distinction between formal concentration (mole fraction) and thermodynamic activity in a non-ideal solution.

Students typically fall into the trap of assuming ideal behavior ( $a = x$ ) and calculate $K_{eq} = x_B/x_A = 1.5$ , leading to Option B.

By introducing an azeotrope, the problem provides a hidden pathway to determine the ratio of activity coefficients ( $\gamma_B/\gamma_A$ ) without needing the total pressure.

It weaponizes the deviation from Raoult's law, forcing the student to derive the true thermodynamic equilibrium constant using pure vapor pressures.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Homogeneous vs. Heterogeneous Equilibrium
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free