Pick out the incorrect statement $:-$

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.

Consider a $70 \%$ efficient hydrogen-oxygen fuel cell working under standard conditions at $1 \ bar$ and $298 \ K$. Its cell reaction is
$H_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow H_2O(\ell)$
The work derived from the cell on the consumption of $1.0 \times 10^{-3} \ mol$ of $H_{2(g)}$ is used to compress $1.00 \ mol$ of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in $K$) of the ideal gas?
The standard reduction potentials for the two half-cells are given below.
$O_{2(g)} + 4H^{+}(aq.) + 4e^- \rightarrow 2H_2O(\ell), E^{\circ} = 1.23 \ V$
$2H^{+}(aq.) + 2e^- \rightarrow H_{2(g)}, E^{\circ} = 0.00 \ V$
Use $F = 96500 \ C \ mol^{-1}, R = 8.314 \ J \ mol^{-1} \ K^{-1}$

$A$ negative $e.m.f.$ for a cell represents:

Chemical reactions involve the interaction of atoms and molecules. $A$ large number of atoms/molecules (approximately $6.023 \times 10^{23}$) are present in a few grams of any chemical compound,varying with their atomic/molecular masses. To handle such large numbers conveniently,the mole concept was introduced. This concept has implications in diverse areas such as analytical chemistry,biochemistry,electrochemistry,and radiochemistry. The following example illustrates a typical case involving a chemical/electrochemical reaction,which requires a clear understanding of the mole concept. $A$ $4.0 \ M$ aqueous solution of $NaCl$ is prepared and $500 \ mL$ of this solution is electrolysed. This leads to the evolution of chlorine gas at one of the electrodes (atomic mass: $Na=23, Hg=200; 1 \ F = 96500 \ C$).
$1.$ The total number of moles of chlorine gas evolved is:
$(A)$ $0.5$ $(B)$ $1.0$ $(C)$ $2.0$ $(D)$ $3.0$
$2.$ If the cathode is a $Hg$ electrode,the maximum weight $(g)$ of amalgam formed from this solution is:
$(A)$ $200$ $(B)$ $225$ $(C)$ $400$ $(D)$ $446$
$3.$ The total charge (coulombs) required for complete electrolysis is:
$(A)$ $24125$ $(B)$ $48250$ $(C)$ $96500$ $(D)$ $193000$

Identify the correct statements from the following:
$(A)$ At $298 \ K$,the potential of a hydrogen electrode placed in a solution of $pH = 10$ is $-0.59 \ V$.
$(B)$ The limiting molar conductivity of $Ca^{2+}$ and $Cl^{-}$ are $119$ and $76 \ S \ cm^2 \ mol^{-1}$ respectively. The limiting molar conductivity of $CaCl_2$ is $195 \ S \ cm^2 \ mol^{-1}$.
$(C)$ The correct relationship between $K_{c}$ and $E_{cell}^{0}$ is $E_{cell}^{0} = \frac{2.303 RT}{nF} \log K_{c}$.