The Gibbs energy for the decomposition of Al₂O₃ at 500^oC is as follows :

$${2 \over 3}A{l_2}{O_3}$$ $$\to$$ $${4 \over 3}Al + {O_2}$$, $${\Delta _r}G$$ = + 966 kJ mol^–1

The potential difference needed for electrolytic reduction of Al₂O₃ at 500^oC is at least :

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is
CH₃OH(l) + 3/2O₂ $$\to$$ CO₂ (g) + 2H₂O (l)
At 298K standard Gibb’s energies of formation for CH₃OH(l), H₂O(l) and CO₂ (g) are -166.2, -237.2 and -394.4 kJ mol⁻¹ respectively. If standard enthalpy of combustion of methanol is -726 kJ mol⁻¹, efficiency of the fuel cell will be

Given : $$E_{F{e^{3 + }}/Fe}^o$$ = -0.036V; $$E_{F{e^{2 + }}/Fe}^o$$ = -0.439 V
The value of standard electrode potential for the change,
Fe³⁺ (aq) + e^- $$\to$$ Fe²⁺ (aq) will be

Given $$E_{C{r^{3 + }}/Cr}^o$$ = -0.72 V; $$E_{Fe^{2+}/Fe}^o$$ = -0.42V, The potential for the cell Cr | Cr³⁺ (0.1M) || Fe²⁺ (0.01 M) | Fe is