= Solution
The solid <electrolyte> conducts oxide <ions>. Equilibrating <oxygen> at the two interfaces couples one $\mathrm{O_2}$ molecule to four <electrons>. Taking the positive measured <electromotive force> as the air-reference potential relative to the Ni/NiO side, the <Nernst equation> is
$$
E=\frac{RT}{4F}\ln\frac{p_{\rm air}}{p_{\rm eq}},\qquad \frac{p_{\rm eq}}{p^\circ}=\frac{p_{\rm air}}{p^\circ}\exp\left(-\frac{4FE}{RT}\right).
$$
Assume air at one bar with $p_{\rm air}/p^\circ=0.21$, pure solid phases of unit <thermodynamic activity>, and $p^\circ=1\,\mathrm{bar}$. For the reaction normalized to one mole of <oxygen>,
$$
2\mathrm{Ni}(s)+\mathrm{O_2}(g)\longrightarrow2\mathrm{NiO}(s),\qquad \Delta_rG^\circ=RT\ln\frac{p_{\rm eq}}{p^\circ}=RT\ln0.21-4FE.
$$
The negative sign is physically consistent with a strongly reducing Ni/NiO equilibrium relative to air. Using the supplied $R$ and $F$ gives
$$
\begin{array}{c|c|r}
T\ (\mathrm K)&p_{\rm eq}\ (\mathrm{bar})&\Delta_rG^\circ\ (\mathrm{kJ\,mol_{O_2}^{-1}})\\\hline
900&6.92\times10^{-19}&-312.88\\
1000&3.95\times10^{-16}&-294.87\\
1100&7.75\times10^{-14}&-276.09
\end{array}
$$
\b[The tabulated <free energies> are per mole of $\mathrm{O_2}$, not per mole of NiO.] Values normalized to one mole of NiO would be half as large. A reliable <oxygen concentration cell> measurement requires reversible interfaces, calibrated uniform <temperature>, a known reference <oxygen> <pressure> and predominantly ionic rather than electronic conduction through <yttria-stabilized zirconia>. Air is not pure <oxygen>: dropping the $RT\ln0.21$ term changes the inferred <entropy>.
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