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 rusting of iron takes place as follows. Calculate $\Delta G^o$ for the net process in $kJ \ mol^{-1}$.
$2H^{+} + 2e^- + \frac{1}{2}O_2 \longrightarrow H_2O_{(l)} ; E^o = +1.23 \ V$
$Fe^{2+} + 2e^- \longrightarrow Fe_{(s)} ; E^o = -0.44 \ V$

Which of the following statements is incorrect?

Solutions $A$,$B$,and $C$ of the same strong electrolyte offered resistances of $50 \ \Omega$,$100 \ \Omega$,and $150 \ \Omega$ in a given conductivity cell. The resistance observed if they are mixed in a volume proportion which is the reciprocal of their resistances and tested in the same conductivity cell would be ............. $\Omega$.

In a fuel cell,methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is
$CH_3OH_{(l)} + \frac{3}{2} O_{2(g)} \rightarrow CO_{2(g)} + 2H_2O_{(l)}$
At $298 \ K$,standard Gibbs energies of formation for $CH_3OH_{(l)}$,$H_2O_{(l)}$,and $CO_{2(g)}$ are $-166.2$,$-237.2$,and $-394.4 \ kJ \ mol^{-1}$ respectively. If the standard enthalpy of combustion of methanol is $-726 \ kJ \ mol^{-1}$,the efficiency of the fuel cell will be .......... $\%$.

Which one of the following graphs between molar conductivity $\left(\Lambda_m\right)$ versus $\sqrt{C}$ is correct?