The conductivity of $0.01 \ M$ aqueous acetic acid measured with a conductivity cell of cell constant $0.5 \ cm^{-1}$ at $298 \ K$ is $3.12 \times 10^{-4} \ S$. If the limiting molar conductivities of $H^{+}$ and $CH_3COO^{-}$ at the same temperature are $349$ and $41 \ S \ cm^2 \ mol^{-1}$ respectively,the dissociation constant of acetic acid is

The molar conductance of $NaCl$,$HCl$,and $CH_{3}COONa$ at infinite dilution are $126.45$,$426.16$,and $91.0 \ S \ cm^{2} \ mol^{-1}$ respectively. The molar conductance of $CH_{3}COOH$ at infinite dilution is. Choose the right option for your answer. (In $S \ cm^{2} \ mol^{-1}$)

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

$A$ hydrogen electrode is immersed in a solution with $pH = 0$ $(HCl)$. By how much will the potential (reduction) change if an equivalent amount of $NaOH$ is added to the solution? (Take $pH_2 = 1 \ atm$,$T = 298 \ K$).

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 $F = 96500 \ C \ mol^{-1}, R = 8.314 \ J \ mol^{-1} \ K^{-1}$

Consider the following statements pertaining to fuel cells :-
$(a)$ Hydrogen-oxygen fuel cells make use of concentrated $KOH$ solution as an electrolyte and porous graphite impregnated with platinum as electrodes.
$(b)$ The efficiency of a fuel cell is less than unity due to polarization at electrodes and the resistance offered by the electrode and the electrolyte.
$(c)$ The electrical work,assuming the cell to be working reversibly,may be represented as $-\Delta G = W_{\text{electrical}} = -\Delta H + T\Delta S$.
Which of the above statements are correct?