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Question #44716

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The Question

An $\alpha$ -amino acid has $pK_{a1} = 2.0$ and $pK_{a2} = 9.0$ . The intrinsic solubility of its zwitterionic form ( $HA^\pm$ ) in pure water at $300\text{ K}$ is $S_0 = 0.05\text{ M}$ . An excess of the solid amino acid is added to water, and the solution is titrated with concentrated $\ce{HNO3}$ until the equilibrium pH of the solution reaches $2.0$ . Assuming the volume change upon adding $\ce{HNO3}$ is negligible, what is the osmotic pressure of the resulting saturated solution at $300\text{ K}$ ? (Given: $R = 0.082\text{ L atm K}^{-1}\text{ mol}^{-1}$ )

Options

A.
2.46 atm
B.
2.95 atm
C.
4.18 atm
D.
4.92 atm

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Solubility of Solids in Liquids|Amino Acid Zwitterion pH Sensitivity|Van’t Hoff Factor (i) Application

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of ionic equilibrium and colligative properties.

The 'Hidden Variable' trap is the dynamic nature of the Van't Hoff factor ( $i$ ) and the counterions.

Students frequently calculate the total dissolved amino acid ( $0.10\text{ M}$ ) and use it directly to find osmotic pressure (Option A).

They fail to account for the fact that adjusting the pH requires adding a strong acid (like $\ce{HNO3}$ ), which introduces spectator ions ( $NO_3^-$ ) into the solution.

Furthermore, the concentration of $NO_3^-$ is not merely equal to the free $[H^+]$ (Option B), but must also include the stoichiometric equivalents of $H^+$ consumed to protonate the zwitterion into its cationic form.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Solutions - Class 12
Concept	Solubility of Solids in Liquids
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free