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Question #44073

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The Question

A $1.0\text{ L}$ aqueous solution is prepared by dissolving $12.5\text{ mmol}$ of a diprotic acid $\ce{H2A}$ ( $K_{a1} = 1.0 \times 10^{-2}$ , $K_{a2} = 1.0 \times 10^{-3}$ ) and $30.0\text{ mmol}$ of its monosodium salt $\ce{NaHA}$ at $298\text{ K}$ . Assuming ideal behavior (activity coefficients = 1), calculate the exact equilibrium concentration of $\ce{H+}$ ions in the solution.

Options

A.
$4.17 \times 10^{-3}\text{ M}$
B.
$5.00 \times 10^{-3}\text{ M}$
C.
$2.91 \times 10^{-3}\text{ M}$
D.
$3.16 \times 10^{-3}\text{ M}$

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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

Degree of Dissociation (α) approximation|Polyprotic Acid Dissociation|Common Ion Effect on Solubility

Why This Question Is Tricky

Common Mistakes

The problem tests the limitations of the Henderson-Hasselbalch approximation and the assumption that secondary dissociations can be ignored in polyprotic buffers.

Students typically rely on rote heuristics ( $[\ce{H+}] \approx K_{a1} \frac{C_a}{C_s}$ ), which yields a 16% error here.

The 'Hidden Variable' is the disproportionation-like shift where the secondary dissociation of $\ce{HA-}$ produces enough $\ce{H+}$ to completely suppress the primary dissociation of $\ce{H2A}$ , making the exact proton condition mandatory.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Degree of Dissociation (α) approximation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free