At $300 \ K$,the conductivity of $0.01 \ mol \ dm^{-3}$ aqueous solution of acetic acid is $19.5 \times 10^{-5} \ S \ cm^{-1}$ and the limiting molar conductivity of acetic acid at the same temperature is $390 \ S \ cm^2 \ mol^{-1}$. The degree of dissociation of acetic acid is:

If molar conductance at infinite dilution for $CH_3COO^-$ and $H^+$ ions are $50 \text{ S cm}^2 \text{mol}^{-1}$ and $350 \text{ S cm}^2 \text{mol}^{-1}$ respectively, and the molar conductivity of $5 \times 10^{-2} \text{ M}$ $CH_3COOH$ is $20 \text{ S cm}^2 \text{mol}^{-1}$, what is the hydrogen ion concentration in $\text{mol/dm}^3$ of $CH_3COOH$?

Column $I$	Column $II$
$(A)$. Kohlrausch law can calculate	$(P)$. $\frac{\Lambda_m^c}{\Lambda_m^o}$
$(B)$. Molar conductance $\Lambda_m$	$(Q)$. $\frac{1}{R} \times \frac{l}{A}$
$(C)$. Specific conductance $\kappa$	$(R)$. $\Lambda_m^o$ of $Ca_3(PO_4)_2$
$(D)$. Degree of ionization of weak electrolyte	$(S)$. $\frac{\kappa \times 1000}{M}$

Which of the following options shows the correct matches?

Given below are two statements:
Statement $I$: For $KI$,molar conductivity increases steeply with dilution.
Statement $II$: For carbonic acid,molar conductivity increases slowly with dilution.
In the light of the above statements,choose the correct answer from the options given below:

The standard reduction potentials of $2H^{+}/H_2$,$Cu^{2+}/Cu$,$Zn^{2+}/Zn$,and $NO_3^{-}, H^{+}/NO$ are $0.0 \ V$,$0.34 \ V$,$-0.76 \ V$,and $0.97 \ V$ respectively. Observe the following reactions:
$I$. $Zn + HCl \rightarrow$
$II$. $Cu + HCl \rightarrow$
$III$. $Cu + HNO_3 \rightarrow$
Which reactions do not liberate $H_{2(g)}$?

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