Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 4 / d

Pure solid CeO${}_2$ and liquid water have unit thermodynamic activity in the stated approximation, soThe power 11 and the four-electron denominator follow from the balanced conventional reaction; using the deposition reaction without reversing the potential would give inconsistent signs.

The fixed nonproton thermodynamic activity ratio is $(0.1{)}^4(0.3)/(3\times 10^{-6})=10$. HenceUsing the supplied constants at $298\mathrm{K}$,At pH 7, $E\simeq 0.792\mathrm{V}$. This is the formal fixed-thermodynamic activity calculation requested; actual cerium speciation and thermodynamic activities would need to remain compatible with the chosen pH to realize it experimentally.