GATE 2022 CY – Question 61
At 25 °C and 1 bar, cell $Cu\mid CuSO_4(aq,1.0\ mol/kg)\mid Hg_2SO_4(s)\mid Hg(l)\mid Pt$ has EMF 0.36 V. The mean activity coefficient of $CuSO_4$ is ______ (three decimal places). Standard reduction potentials for $Cu^{2+}+2e^-\to Cu$ and $Hg_2SO_4+2e^-\to2Hg+SO_4^{2-}$ are 0.34 V and 0.62 V, respectively. Use $RT/F=0.0256$ V.
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Correct answer: 0.042 to 0.046
Explanation
The cell reaction is Cu+Hg2SO4→Cu2++SO4²−+2Hg. Nernst gives E=E°−(RT/2F)ln(aCu aSO4). At unit molality, aCu aSO4=γ±², so E=0.28−0.0256lnγ±.
Therefore γ±=exp[(0.28−0.36)/0.0256]=0.0439369, rounded **0.044**.