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Question #44064

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The Question

Excess \ce{AgNO2(s)} is added to a large volume of a buffer solution at pH = 3.0. The system is maintained in a closed vessel with a constant partial pressure of \ce{NO(g)} at 1 bar. Given the following standard reduction potentials and constants at 298 K:

$E^\circ(\ce{NO3^- / HNO2}) = 0.94\text{ V}$ $E^\circ(\ce{HNO2 / NO}) = 1.12\text{ V}$ $K_{sp}(\ce{AgNO2}) = 3.0 \times 10^{-3}$ $K_a(\ce{HNO2}) = 1.0 \times 10^{-3}$ $\frac{2.303 RT}{F} = 0.06\text{ V}$

Calculate the equilibrium concentration of \ce{Ag^+} ions in the solution. (Assume activity coefficients are unity and no other complexation occurs).

Options

A.
3.0 M
B.
0.077 M
C.
0.53 M
D.
2.28 M

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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

Homogeneous vs. Heterogeneous Equilibrium|KMnO₄ Redox pH Dependency|Auto-Redox in Oxyacids

Why This Question Is Tricky

Common Mistakes

The problem tests the coupling of a heterogeneous solubility equilibrium with a homogeneous redox disproportionation.

The 'Hidden Variable' is the massive thermodynamic sink created by the auto-redox of \ce{HNO2}.

Students commonly fall into the trap of treating the solubility of \ce{AgNO2} purely as an acid-base problem (yielding 0.077 M), ignoring Le Chatelier's Principle where the continuous consumption of \ce{HNO2} 'pulls' the equilibrium, amplifying the solubility by nearly 40-fold.

Additionally, it tests the ability to correctly apply mass balance stoichiometry ( $[\ce{Ag^+}] \approx 3[\ce{NO3^-}]$ ) derived from the disproportionation reaction, accounting for the nitrogen lost to the gas phase.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Homogeneous vs. Heterogeneous Equilibrium
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free