GATE 2024 MT – Question 57
At 298 K, the Cu$^{2+}$ concentration needed to make the potential of pure copper 0.17 V is ______ $\times10^{-6}$ gram-mol L$^{-1}$ (two decimal places). Given: $R=8.314$ J mol$^{-1}$ K$^{-1}$, $F=96500$ C mol$^{-1}$ of electrons, and standard Cu reduction potential $E^\circ=0.34$ V.
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Correct answer: 1.6 to 1.9
Explanation
For $\mathrm{Cu}^{2+}+2e^-\rightleftharpoons\mathrm{Cu}$, Nernst’s equation gives $E=E^\circ+(RT/2F)\ln a_{Cu^{2+}}$.
Thus $\ln a=2(96500)(0.17-0.34)/(8.314\times298)=-13.2428\ldots$.
Taking activity as concentration relative to 1 mol/L gives $1.77\times10^{-6}$ mol/L.
The coefficient is **1.77**, using the dilute ideal-electrolyte approximation.