The electrochemical cell shown below is a concentration cell. M|M2+ (saturated solution of a sparingly soluble salt, MX2) || M2+ (0.001 mol dm–3) | M The emf of the cell depends on the difference in concentrations of M2+ ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.

Engineering

Chemistry

Concentration cell Metal Metal Sparingly Salt and Amalgam Electrode

Question

The electrochemical cell shown below is a concentration cell.

M|M²⁺ (saturated solution of a sparingly soluble salt, MX₂) || M²⁺ (0.001 mol dm^–3) | M

The emf of the cell depends on the difference in concentrations of M²⁺ ions at the two electrodes.

The emf of the cell at 298 K is 0.059 V.

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Linked Question 1

The solubility product (Ksp ; mol³ dm^–9) of MX₂ at 298 K based on the information available for the given concentration cell is (take 2.303 × R × 298/F = 0.059 V)

1 × 10^–12

1 × 10^–15

4 × 10^–15

4 × 10^–12

$E_{cell} = E_{cell}^{o} - \frac{2 .303 RT}{nF} \cdot logQ$

$or 0 .0509 = 0 - \frac{0 .059}{2} . \log \frac{S}{0 .001}$

$∴$ S = 10^–5 M

Now, MX₂ (s) ⇌ M²⁺ (aq) + 2 X¯ (aq)

S M 2 SM

$∴$ K_sp = [M²⁺] [X¯]² = S. (2s)² = 4s³

= 4 × 10^–15 M³

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Linked Question 2

The value of ΔG (kJ mol^–1) for the given cell is (take 1 F = 96500 C mol^–1)

– 5.7

– 11.4

5.7

11.4

The cell reaction is

Left electrode: M (s) ⇌ M²⁺ (s M) + 2 e¯

Right electrodes : M²⁺ (0.001 M) + 2e ¯ ⇌ M (s)

__________________________________________________

Net cell reaction : M(s) + M²⁺ (0.001 M) ⇌ M²⁺(s M) + M (s)

ΔG = – nFE_cell = – 2 × 96500 × 0.059

= – 11387 J mol^–1 $\approx$ – 11.4 kJ mol^–1

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