Consider the following redox reaction :
$MnO_4^{-} + H^{+} + H_2C_2O_4 \rightleftharpoons Mn^{2+} + H_2O + CO_2$
The standard reduction potentials are given as below $(E_{red}^{\circ})$ :
$E_{MnO_4^{-} / Mn^{2+}}^{\circ} = +1.51 \ V$
$E_{CO_2 / H_2C_2O_4}^{\circ} = -0.49 \ V$
If the equilibrium constant of the above reaction is given as $K_{eq} = 10^x$,then the value of $x = $ . . . . . . (nearest integer).

On the basis of standard electrode potential values $(E^{\circ})$, suggest which of the following reactions would take place spontaneously? Given: $E^{\circ}_{Zn^{2+}/Zn} = -0.76 \ V$, $E^{\circ}_{Cu^{2+}/Cu} = +0.34 \ V$, $E^{\circ}_{Mg^{2+}/Mg} = -2.37 \ V$, $E^{\circ}_{Fe^{2+}/Fe} = -0.44 \ V$, $E^{\circ}_{Br_{2}/Br^{-}} = +1.09 \ V$, $E^{\circ}_{Cl_{2}/Cl^{-}} = +1.36 \ V$, $E^{\circ}_{Cd^{2+}/Cd} = -0.40 \ V$.

$A$ battery is constructed of $Cr$ and $Na_2Cr_2O_7$. The unbalanced chemical equation when such a battery discharges is: $Na_2Cr_2O_7 + Cr + H^{+} \to Cr^{3+} + H_2O + Na^{+}$. If one Faraday of electricity is passed through the battery during charging,the number of moles of $Cr^{3+}$ removed from the solution is:

For the reaction $4B_{(s)} + 3O_{2(g)} \rightarrow 2B_2O_{3(g)}$,the standard cell potential is $E^o_{cell} = 1.433 \ V$. Calculate the molar entropy $(S_m^o)$ of oxygen gas in $J/K \ mol$.
Given:
$(\Delta_fH^o)_{B_2O_3(g)} = -840 \ kJ/mol$
$(S_m^o)_{B_2O_3(g)} = 280 \ J/K \ mol$
$(S_m^o)_{B(s)} = 10 \ J/K \ mol$
Assume $\Delta_rG^o = -nFE^o_{cell}$ and $\Delta_rG^o = \Delta_rH^o - T\Delta_rS^o$ at $T = 298 \ K$.

$A$ battery is made from $Cr$ and $Na_2Cr_2O_7$. When this battery discharges according to the reaction $Na_2Cr_2O_7 + Cr + H^{+} \rightarrow Cr^{3+} + H_2O + Na^{+}$,the chemical equation is unbalanced. If $1 \ F$ (Faraday) of electricity is passed during the charging of the battery,what is the number of moles of $Cr^{3+}$ removed from the solution (in $/3$)?

Copper reduces $NO_{3}^{-}$ into $NO$ and $NO_{2}$ depending upon the concentration of $HNO_{3}$ in solution. Assuming fixed $[Cu^{2+}]$ and $P_{NO} = P_{NO_{2}} = 1 \ bar$,the $HNO_{3}$ concentration at which the thermodynamic tendency for reduction of $NO_{3}^{-}$ into $NO$ and $NO_{2}$ by copper is the same is $10^{x} \ M$. The value of $2x$ is ...... .
$[Given: E_{Cu^{2+} / Cu}^{\circ} = 0.34 \ V, E_{NO_{3}^{-} / NO}^{\circ} = 0.96 \ V, E_{NO_{3}^{-} / NO_{2}}^{\circ} = 0.79 \ V$ and at $298 \ K, \frac{RT}{F}(2.303) = 0.059]$