Before You Begin

Question #44217

Difficulty: 8/10 | 🟢 Free

The Question

Initially, $1.0 \text{ mol}$ of $\ce{N2O4(g)}$ is placed in a cylinder fitted with a frictionless piston maintained at a constant pressure of $1.0 \text{ atm}$ and a constant temperature $T$ . At equilibrium, the degree of dissociation of $\ce{N2O4(g)}$ into $\ce{NO2(g)}$ is $0.5$ .

Subsequently, $7.8 \text{ mol}$ of an ideal inert gas (He) is reversibly and isothermally added to the cylinder, maintaining the constant pressure of $1.0 \text{ atm}$ .

What is the magnitude of the expansion work done by the system during the addition of the inert gas? (Assume ideal gas behavior for all gases)

Options

A.
$8.1 RT$
B.
$7.8 RT$
C.
$8.6 RT$
D.
$9.6 RT$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Reversible Expansion Work|Spontaneity Criteria|Le Chatelier’s Principle: Inert Gas Addition

Why This Question Is Tricky

Common Mistakes

This problem tests the integration of Chemical Thermodynamics with Chemical Equilibrium.

The 'hidden variable' is the shift in the degree of dissociation ( $\alpha$ ) upon the addition of an inert gas at constant pressure.

Students often memorize $W = P\Delta V = \Delta n RT$ but incorrectly assume that the only change in moles is due to the added inert gas ( $\Delta n = 7.8$ ), leading to the trap answer $7.8 RT$ .

By applying Le Chatelier's Principle, one must recognize that the increased volume lowers the partial pressures of the reacting gases, driving the equilibrium forward ( $\alpha$ increases from $0.5$ to $0.8$ ).

The true $\Delta n$ must account for both the added inert gas and the additional moles of gas produced by the equilibrium shift.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Thermodynamics - Class 11 Part 1
Concept	Reversible Expansion Work
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free