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Question #44697

Difficulty: 8/10 | 🟢 Free

The Question

A student attempts to predict the successive acid dissociation constants of a hypothetical diprotic acid, $\ce{H2A}$ (aq), at $298\text{ K}$ using a modified Bohr model. The student assumes that the standard free energy of dissociation ( $\Delta G^\circ$ ) scales exactly like the ionization energy of hydrogenic species in a vacuum, where removing the second proton from $\ce{HA^-}$ experiences an effective nuclear charge twice that of removing the first proton from $\ce{H2A}$ ( $Z_{\text{eff}, 2} = 2 Z_{\text{eff}, 1}$ ), ignoring solvent effects.

Given $pK_{a1} = 3.0$ for $\ce{H2A}$ (aq). The student calculates the pH of a $0.1\text{ M}$ aqueous solution of $\ce{NaHA}$ based on this theoretical model.

However, the actual dissociation is driven by solvent-ion stabilization. The hydration of $\ce{A^{2-}}$ (aq) provides an additional stabilization energy of $17.1\text{ kJ/mol}$ relative to the student's vacuum electrostatic model.

Calculate the absolute difference between the student's predicted pH and the actual pH of the $0.1\text{ M}$ $\ce{NaHA}$ solution. (Given: $2.303 RT = 5.7\text{ kJ/mol}$ at $298\text{ K}$ )

Options

A.
1.5
B.
3.0
C.
4.5
D.
0.0

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Bohr’s Model Limitations|Successive Equilibrium Constants|Amphiprotic Ion pH

Why This Question Is Tricky

Common Mistakes

This problem tests the fundamental limitation of applying gas-phase physical quantization (Bohr's model) to aqueous chemical thermodynamics.

Students often conflate successive ionization energies (which scale with $Z_{\text{eff}}^2$ in a vacuum) with successive acid dissociation constants ( $K_{a1}, K_{a2}$ ).

The 'Hidden Variable' is the solvent-ion stabilization energy (hydration energy).

While Bohr's model relies purely on electrostatic potential, aqueous dissociation is thermodynamically driven by the solvent's ability to stabilize highly charged species like A^{2-}.

The trap forces students to quantitatively evaluate the failure of the Bohr model in a solvent system and apply it to the pH calculation of an amphiprotic salt.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Bohr’s Model Limitations
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free