During the electrolysis of concentrated $H_2SO_4$,perdisulphuric acid $(H_2S_2O_8)$ and $O_2$ are formed at the anode in equimolar amounts. The moles of $H_2$ that will form simultaneously at the other electrode will be (Given: $2H_2SO_4 \rightarrow H_2S_2O_8 + 2H^+ + 2e^-$)

All the energy released from the reaction $X \rightarrow Y, \Delta_{r}G^0 = -193 \ kJ \ mol^{-1}$ is used for oxidizing $M^{+}$ as $M^{+} \rightarrow M^{3+} + 2e^-, E^0 = -0.25 \ V$. Under standard conditions,the number of moles of $M^{+}$ oxidized when one mole of $X$ is converted to $Y$ is $\left[F = 96500 \ C \ mol^{-1}\right]$.

Consider an electrochemical cell: $A_{(s)} | A^{n+}(aq, 2 \ M) || B^{2n+}(aq, 1 \ M) | B_{(s)}$. The value of $\Delta H^{\ominus}$ for the cell reaction is twice that of $\Delta G^{\ominus}$ at $300 \ K$. If the emf of the cell is zero,the $\Delta S^{\ominus}$ (in $J \ K^{-1} \ mol^{-1}$) of the cell reaction per mole of $B$ formed at $300 \ K$ is. . . . . . . (Given: $\ln(2) = 0.7, R = 8.3 \ J \ K^{-1} \ mol^{-1}$.)

The equilibrium constant of a $2$ electron redox reaction at $298 \, K$ is $3.8 \times 10^{-3}$. The cell potential $E^{\circ}$ (in $V$) and the free energy change $\Delta G^{\circ}$ (in $kJ \, mol^{-1}$) for this equilibrium,respectively are

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.

Which of the following statements is not correct $:-$