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.

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)

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

If the value of K_sp for Hg₂Cl₂ (s) is X then calculate the value of $\frac{\mathrm{pX}}{3}$ where pX = – log X  .

Given : Hg₂Cl₂ (s) + 2e^– → 2Hg (l) + 2Cl¯   E° = 0.27 V                  

Hg₂²⁺  + 2e^– → 2Hg(l)   E° = 0.81 V

For the half-cell, Hg,Hg₂Cl₂|Cl^–(aq), values of electrode oxidation potential are plotted at different log[Cl^–]. Variation is represented by :

[ Eº_Hg²⁺/Hg =.79, K_sp(Hg₂Cl₂)=10^–18]