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Question #44655

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The Question

At $300 \text{ K}$ , the standard Gibbs free energy change for the gas-phase reaction: $\ce{N2(g) + 3H2(g) <=> 2NH3(g)}$ is $\Delta G^\circ = -11.49 \text{ kJ mol}^{-1}$ (Standard state: $P^\circ = 1 \text{ bar}$ ). Let $Y$ be the numerical value of the concentration-based equilibrium constant $K_c$ (Standard state: $c^\circ = 1 \text{ mol L}^{-1}$ ) for this reaction at $300 \text{ K}$ .

Additionally, at $300 \text{ K}$ , the ionic product of water is $K_w = 1.0 \times 10^{-14}$ . Let $\Delta G^\circ_w$ be the standard Gibbs free energy change for the autoionization reaction: $\ce{H2O(l) <=> H+(aq) + OH-(aq)}$

Which of the following correctly gives the values of $Y$ and $\Delta G^\circ_w$ ? (Given: $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$ , $\ln 10 = 2.303$ , $1 \text{ bar} = 10^5 \text{ Pa}$ , $1 \text{ atm} = 101325 \text{ Pa}$ , density of water $\approx 1 \text{ g mL}^{-1}$ )

Options

A.
$Y = 6.22 \times 10^4$ , $\Delta G^\circ_w = 80.42 \text{ kJ mol}^{-1}$
B.
$Y = 6.22 \times 10^8$ , $\Delta G^\circ_w = 90.44 \text{ kJ mol}^{-1}$
C.
$Y = 6.06 \times 10^4$ , $\Delta G^\circ_w = 80.42 \text{ kJ mol}^{-1}$
D.
$Y = 6.22 \times 10^8$ , $\Delta G^\circ_w = 34.92 \text{ kJ mol}^{-1}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

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Concepts Behind This Question

Dimensional Consistency of Constants|Relationship between Kp and Kc|Ionic Product of Water (Kw)

Why This Question Is Tricky

Common Mistakes

This problem tests the dimensional consistency of thermodynamic equilibrium constants and the definition of standard states.

Students often memorize $K_p = K_c(RT)^{\Delta n}$ without realizing that $R$ must carry units compatible with the standard states ( $P^\circ = 1 \text{ bar}$ , $c^\circ = 1 \text{ mol L}^{-1}$ ).

Using $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$ directly in this formula violates dimensional consistency.

Furthermore, the problem tests the standard state for pure liquids in heterogeneous equilibria; students frequently and incorrectly incorporate the concentration of water ( $55.5 \text{ M}$ ) into the thermodynamic equilibrium constant for autoionization, leading to an erroneous $\Delta G^\circ_w$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Dimensional Consistency of Constants
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free