How to Calculate Cu²⁺ Concentration

Q.21 The value of standard half-cell potential of Cu2+/Cu couple (E0Cu2+,Cu) is 0.34 V. A wire of pure copper is immersed into a solution of copper nitrate. If the measured cell potential against standard hydrogen electrode at 298 K is 0.24 V, the molar concentration of copper nitrate is (Assume activity of Cu2+ = [Cu2+]). (A) 4.1 × 10−4 M (B) 2.0 × 10−2 M (C) 3.4 × 10−2 M (D) 1.8 × 10−1 M

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January 27, 2026
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Q.21 The value of standard half-cell potential of
Cu²⁺/Cu couple
(E⁰_Cu²⁺,Cu) is 0.34 V.
A wire of pure copper is immersed into a solution of copper nitrate.
If the measured cell potential against standard hydrogen electrode at
298 K is 0.24 V, the molar concentration of copper nitrate is
(Assume activity of Cu²⁺ = [Cu²⁺]).

(A) 4.1 × 10⁻⁴ M

(B) 2.0 × 10⁻² M

(D) 1.8 × 10⁻¹ M

Concept Used

This problem is based on the Nernst equation, which relates
electrode potential to ion concentration.

Step-by-Step Solution

Half-Cell Reaction

Cu²⁺ + 2e⁻ → Cu(s)

Nernst Equation

E = E⁰ − (0.0591 / n) log Q

For this reaction:

n = 2
Q = 1 / [Cu²⁺]

Therefore,

E = E⁰ + (0.0591 / 2) log [Cu²⁺]

Substitution of Values

0.24 = 0.34 + (0.0591 / 2) log [Cu²⁺]

−0.10 = 0.02955 log [Cu²⁺]

log [Cu²⁺] = −3.38

Final Calculation

[Cu²⁺] = 10^−3.38

[Cu²⁺] ≈ 4.1 × 10⁻⁴ M

Correct Answer

✅ Option (A): 4.1 × 10⁻⁴ M

Explanation of All Options

Option (A): 4.1 × 10⁻⁴ M

✔ Correct. This value is obtained by accurate application of the Nernst equation.

Option (B): 2.0 × 10⁻² M

✘ Incorrect. This concentration would give a higher electrode potential than 0.24 V.

Option (C): 3.4 × 10⁻² M

✘ Incorrect. This value is close to standard conditions and does not justify the
observed drop in potential.

Option (D): 1.8 × 10⁻¹ M

✘ Incorrect. Higher Cu²⁺ concentration increases electrode potential.

Concept Used