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Question:

For the electrochemical cell, Mg(s)|Mg²⁺(aq, 1M)||Cu²⁺(aq, 1M)|Cu(s), the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg²⁺ is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is _________. (Given F/R = 11500 K V⁻¹, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)

Solution:

Cell reaction, Mg(s) + Cu²⁺(aq) → Mg²⁺(aq) + Cu(s)
E⁰cell = 2.70 V; Ecell = 2.67 V; Mg²⁺ = x M; Cu²⁺ = 1 M
Ecell = E⁰cell – (RT/nF)lnQ
2.67 = 2.70 – (RT/2F)lnx
0.03 = (RT/2F)lnx
lnx = 0.03 × 2 × 11500 / 300
lnx = 2.30 = ln(10)
∴ x = 10