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Question #44210

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The Question

Consider the following gas-phase equilibria at $298\text{ K}$ :

(1) $\ce{X(g) + 2Y(g) \rightleftharpoons 2Z(g)} \quad K_{p1} = 2 \times 10^8$ (2) $\ce{Z(g) \rightleftharpoons W(g) + Y(g)} \quad K_{p2} = 5 \times 10^{-4}$

A rigid reaction vessel at $298\text{ K}$ contains the gases with the following instantaneous partial pressures: $P_X = 0.5\text{ bar}$ , $P_Y = 2.0\text{ bar}$ , $P_Z = 1.0\text{ bar}$ , and $P_W = 5.0\text{ bar}$ .

For the overall transformation $\ce{X(g) \rightleftharpoons 2W(g)}$ , determine the standard Gibbs free energy change ( $\Delta G^\circ$ ) and the actual Gibbs free energy change ( $\Delta G$ ) at this instant.

Options

A.
$\Delta G^\circ = -RT \ln(50)$ , $\Delta G = 0$
B.
$\Delta G^\circ = -RT \ln(2 \times 10^5)$ , $\Delta G = -RT \ln(4 \times 10^3)$
C.
$\Delta G^\circ = -RT \ln(10^5)$ , $\Delta G = -RT \ln(2 \times 10^3)$
D.
$\Delta G^\circ = -RT \ln(50)$ , $\Delta G = RT \ln(50)$

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

State vs Path Functions|Stoichiometric Coefficient Division|Reaction Quotient vs. Equilibrium Constant

Why This Question Is Tricky

Common Mistakes

This problem tests the distinction between extensive state functions ( $\Delta G^\circ$ ) and equilibrium constants ( $K$ ).

A common trap is treating $K$ linearly when multiplying stoichiometric coefficients (e.g., calculating $K_{overall} = K_{p1} \times 2K_{p2}$ ), which leads to Option B.

Furthermore, it highlights a profound thermodynamic concept: an overall coupled reaction can have $\Delta G = 0$ (no driving force) even if its constituent elementary steps are far from equilibrium, emphasizing that $Q$ must be calculated strictly for the target stoichiometry.

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