An acidic solution of dichromate is electrolyzed for $8 \ min$ using $2 \ A$ current. As per the following equation: $Cr_{2}O_{7}^{2-} + 14H^{+} + 6e^{-} \rightarrow 2Cr^{3+} + 7H_{2}O$. The amount of $Cr^{3+}$ obtained was $0.104 \ g$. The efficiency of the process (in $\%$) is (Take: $F = 96000 \ C$,At. mass of chromium $= 52$)

What will be the weight of $Al$ deposited at the cathode when $0.5 \ F$ of electricity is passed through an aqueous solution of $AlCl_3$ (in $g$)? (Atomic mass of $Al = 27$)

State Faraday's laws of electrolysis and mention their uses.

The electric charge required for the electrolytic decomposition of one gram equivalent of a substance is

Electricity is passed through an acidic solution of $Cu^{2+}$ until all the $Cu^{2+}$ is exhausted, leading to the deposition of $300 \ mg$ of $Cu$ metal. Subsequently, a current of $600 \ mA$ is passed through the same solution for another $28 \ minutes$ while keeping the total volume of the solution fixed at $200 \ mL$. The total volume of oxygen evolved at $STP$ during the entire process is . . . . . . $mL$. (Nearest integer) [Given: $Cu^{2+}_{(aq)} + 2e^{-} \rightarrow Cu_{(s)}$, $E_{red}^0 = +0.34 \ V$; $O_{2(g)} + 4H^{+} + 4e^{-} \rightarrow 2H_2O$, $E_{red}^0 = +1.23 \ V$; Molar mass of $Cu = 63.54 \ g \ mol^{-1}$; Faraday Constant $= 96500 \ C \ mol^{-1}$; Molar volume at $STP = 22.4 \ L$]

Calculate the amount of electricity required in coulombs to convert $0.08 \ mol$ of $MnO_4^{-}$ to $Mn^{2+}$. (in $C$)