Question

The following reaction occurs during rusting of iron

$\text{2H}^{\text{+}} \, \text{+} \, \text{2e} \, \text{+} \, \frac{\text{1}}{\text{2}} \text{O}_{\text{2}} \rightarrow \text{H}_{\text{2}} \text{O;} \, \text{E}^{\text{o}} \text{ =} \, \text{+1} \text{.23} \, \text{V}$

$\mathrm{Fe}^{2+}+2 \mathrm{e} \rightarrow \mathrm{Fe}(\mathrm{s}) ; \mathrm{E}^0=0.44 \mathrm{~V}$

Calculate magnitude of $\left(\text{ΔG}\right)^{\text{o}} \text{(kJ)}$ for the net process

$\text{Fe} \, \text{(s)} \, \text{+} \, \left(\text{2H}\right)^{\text{+}} \, \text{+} \, \frac{\text{1}}{\text{2}} \, \left(\text{O}\right)_{\text{2}} \rightarrow \left(\text{Fe}\right)^{\text{2+}} \, \text{+} \, \left(\text{H}\right)_{\text{2}} \text{O}$

Answer 1

$Fe ( s ) \rightarrow Fe ^{2+}+2 e ^{-} ; \Delta G _{1}^{0}$

$2 H ^{+}+2 e ^{-}+\frac{1}{2} O _{2} \rightarrow H _{2} O (1) ; \Delta G _{2}^{0}$

$Fe ( s )+2 H ^{+}+\frac{1}{2} O _{2} \rightarrow Fe ^{2+}+ H _{2} O ; \Delta G _{3}^{0}$

Applying, $\Delta G _{1}^{ o }+\Delta G _{2}^{0}=\Delta G _{3}^{0}$

$\Delta G _{3}^{ o }=(-2 F \times 0.44)+(-2 F \times 1.23)$

$\Delta G _{3}^{0}=(-2 \times 96500 \times 0.44)+(-2 \times 96500 \times 1.23)$

$\Delta G _{3}^{ o }=-322310 J$

$\therefore \Delta G _{3}^{ o }=-322 kJ$