$2H_2(g) + O_2(g) \to 2H_2O(l)$ ; $\Delta _fH^o_{298}(H_2O(l)) = -285.5\, kJ/mol$
What is $\Delta S^o_{298}$ for the given fuel cell reaction ?
Given $: O_2(g) + 4H^+(aq) + 4e^- \to 2H_2O(l)$ $E^o = 1.23\, V$
$\Delta H \text { forthisreaction }=285.5 \times 2 \frac{k j}{m o l}$
$\Delta G=\Delta H-T \Delta S$
$\Delta G^o=-2.303 R T \ln K(i)$
$E^o=\frac{.06}{n} \ln K \text { (ii) }$
using these $2$ equations we will get the $\Delta G^o$ value.
so $\Delta G^o=2.303 R T \times 82$
$\Delta G=\Delta H-T \Delta S$
$2.303 R T \times 82=2.85 \times 2-298 \Delta S$
$\Delta S=-0.322\, \frac{k j}{m o l}$
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($R = 0.082\, L\, atm\, mol^{-1}\, K^{-1}$, Molar mass of $S = 32\, g\, mol^{-1}$, molar mass of $N = 14\, g\, mol^{-1}$)
