$A$ 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 $/3$)?

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).

During electrolysis of aqueous $NaOH$,$4 \ g$ of $O_2$ gas is liberated at $NTP$ at the anode. The volume of $H_2$ gas liberated at the cathode in $litres$ is $..............$

At $298 \, K$, the standard Gibbs free energy of formation for $H_2O_{(l)}$, $CO_{2(g)}$, and $C_5H_{12(g)}$ are $-237.2$, $-394.4$, and $-8.2 \, kJ \, mol^{-1}$ respectively. What is the potential of a pentane-oxygen fuel cell in $V$?

Consider the change in oxidation state of Bromine corresponding to different $emf$ values as shown in the diagram below:
$BrO_4^{-}$ $\xrightarrow{1.82 \ V} BrO_3^{-}$ $\xrightarrow{1.5 \ V} HBrO$ $\xrightarrow{1.0652 \ V} Br_2$ $\xrightarrow{1.595 \ V} Br^{-}$
Then the species undergoing disproportionation is:

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: $2H_2SO_4 \rightarrow H_2S_2O_8 + 2H^+ + 2e^-$)