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Question #44068

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The Question

The standard Gibbs free energy change for the dissolution and dissociation of a gaseous weak acid $\ce{HA(g)}$ in water at $320\text{ K}$ is $\Delta G^\circ = 12.25\text{ kJ mol}^{-1}$ . $\ce{HA(g) <=> H+(aq) + A-(aq)}$ The standard states are defined as $P^\circ = 1\text{ bar}$ for the gas and $m^\circ = 1\text{ mol kg}^{-1}$ for the aqueous species. At $320\text{ K}$ , the density of pure water is $0.95\text{ kg L}^{-1}$ .

If the equilibrium pressure of $\ce{HA(g)}$ is maintained at $1\text{ atm}$ ( $1\text{ atm} = 1.013\text{ bar}$ ), what is the equilibrium concentration of $\ce{H+(aq)}$ in molarity ( $\text{mol L}^{-1}$ )?

Assume ideal behavior for the gas and the solution, and that the solution is sufficiently dilute such that its density equals that of pure water. (Given: $R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}$ , $e^{-4.604} = 0.01$ )

Options

A.
$0.0956\text{ mol L}^{-1}$
B.
$0.1006\text{ mol L}^{-1}$
C.
$0.0950\text{ mol L}^{-1}$
D.
$0.1000\text{ mol L}^{-1}$

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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

Relationship between Kp and Kc|Concentration Units Dependency|Spontaneity Criteria

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous thermodynamic definition of the equilibrium constant $K^\circ$ using activities.

Students often fall into two traps: (1) Ignoring the standard state pressure ( $1\text{ bar}$ ) and directly using $1\text{ atm}$ , which leads to an incorrect activity for the gas. (2) Assuming that $K^\circ$ directly yields molarity ( $\text{mol L}^{-1}$ ).

In rigorous thermodynamics, the standard state for solutes is molality ( $1\text{ mol kg}^{-1}$ ).

To find molarity, one must account for the solvent's density at the given temperature.

Failing the pressure conversion yields $0.0950\text{ M}$ , failing the density conversion yields $0.1006\text{ M}$ , and failing both yields $0.1000\text{ M}$ .

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Relationship between Kp and Kc
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free