The rusting of iron takes place as follows. Calculate $\Delta G^o$ for the net process in $kJ \ mol^{-1}$.
$2H^{+} + 2e^- + \frac{1}{2}O_2 \longrightarrow H_2O_{(l)} ; E^o = +1.23 \ V$
$Fe^{2+} + 2e^- \longrightarrow Fe_{(s)} ; E^o = -0.44 \ V$

Consider the following statements pertaining to fuel cells :-
$(a)$ Hydrogen-oxygen fuel cells make use of concentrated $KOH$ solution as an electrolyte and porous graphite impregnated with platinum as electrodes.
$(b)$ The efficiency of a fuel cell is less than unity due to polarization at electrodes and the resistance offered by the electrode and the electrolyte.
$(c)$ The electrical work,assuming the cell to be working reversibly,may be represented as $-\Delta G = W_{\text{electrical}} = -\Delta H + T\Delta S$.
Which of the above statements are correct?

Using the standard electrode potentials,predict if the reaction between the following is feasible:
$(a) Fe_{(aq)}^{3+} \text{ and } I_{(aq)}^{-}$
$(b) Ag_{(aq)}^{+} \text{ and } Cu_{(s)}$
$(c) Fe_{(aq)}^{3+} \text{ and } Cu_{(s)}$
$(d) Ag_{(s)} \text{ and } Fe_{(aq)}^{3+}$
$(e) Br_{2(aq)} \text{ and } Fe_{(aq)}^{2+}$

The molar conductivity of a solution of a weak acid $HX$ $(0.01 \ M)$ is $10$ times smaller than the molar conductivity of a solution of a weak acid $HY$ $(0.10 \ M)$. If $\lambda_{X^{-}}^0 \approx \lambda_{Y^{-}}^0$,the difference in their $pK_a$ values,$pK_a(HX) - pK_a(HY)$,is (consider degree of ionization of both acids to be $\ll 1$)

An aqueous solution containing $6.5 \ g$ of $NaCl$ of $90 \%$ purity was subjected to electrolysis. After the complete electrolysis,the solution was evaporated to get solid $NaOH$. The volume of $1 \ M$ acetic acid required to neutralize $NaOH$ obtained above is (in $cm^{3}$)

Calculate the standard cell potentials of galvanic cells in which the following reactions take place:
$(i)$ $2Cr_{(s)} + 3Cd^{2+}_{(aq)} \rightarrow 2Cr^{3+}_{(aq)} + 3Cd_{(s)}$
$(ii)$ $Fe^{2+}_{(aq)} + Ag^{+}_{(aq)} \rightarrow Fe^{3+}_{(aq)} + Ag_{(s)}$
Calculate the $\Delta_r G^\Theta$ and equilibrium constant of the reactions.