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Question #44087

Difficulty: 8/10 | 🟢 Free

The Question

The thermodynamic solubility product ( $K_{sp}^{\circ}$ ) of \ce{Mg(OH)2 (s)} at $298\text{ K}$ is $1.25 \times 10^{-11}$ . An electrochemical cell is constructed to measure the solubility of \ce{Mg(OH)2} in a $0.10\text{ M}$ \ce{NaOH (aq)} solution. During the measurement, a liquid junction potential ( $E_{lj}$ ) of $+1.5\text{ mV}$ is observed at the salt bridge interface. If the mean ionic activity coefficient ( $\gamma_{\pm}$ ) of \ce{Mg(OH)2} in this highly ionic medium is $0.50$ , what is the true molar solubility of \ce{Mg(OH)2} in the solution? (Assume the contribution of dissolved \ce{Mg(OH)2} to the ionic strength and \ce{OH-} concentration is negligible).

Options

A.
$1.0 \times 10^{-8}\text{ M}$
B.
$1.25 \times 10^{-9}\text{ M}$
C.
$5.0 \times 10^{-9}\text{ M}$
D.
$2.5 \times 10^{-9}\text{ M}$

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

Common Ion Effect on Solubility|Solubility Product (Ksp) vs. Ionic Product (Qsp)|Liquid Junction Potential

Why This Question Is Tricky

Common Mistakes

This problem tests the student's understanding of non-ideal solution thermodynamics and the Debye-Huckel effect.

The primary trap is calculating solubility using standard concentration-based $K_{sp}$ equations ( $K_{sp} = [A][B]^2$ ), which ignores the activity coefficient ( $\gamma_{\pm}$ ) and leads to Option B.

The secondary trap is incorrectly applying the mean ionic activity coefficient by failing to raise it to the power of $\nu = \nu_+ + \nu_- = 3$ for an $AB_2$ electrolyte, leading to Options C or D.

Finally, the inclusion of the Liquid Junction Potential serves as a conceptual distractor to test if the student can separate electrochemical measurement artifacts from pure thermodynamic equilibrium states.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Common Ion Effect on Solubility
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free