Q.The molar conductivity of a $0.5\ mol\ dm^{-3}$ solution of $AgNO_3$ with specific conductance $5.76 \times 10^{-3}\,S\,cm^{-1}$ at 298 K is :

Because different concentrations of the same electrolyte contain different numbers of ions per unit volume, raw specific conductance κ cannot fairly compare how well different electrolytes conduct. Molar conductivity, $\Lambda_m$, fixes this by standardising to a fixed AMOUNT of electrolyte — one mole — giving $\Lambda_m\ (\text{S m}^2\text{mol}^{-1}) = \dfrac{\kappa\times10^{-3}}{M}$; equivalent conductance does the same using gram-equivalents and normality instead of moles and molarity.

Kohlrausch found experimentally that molar conductance always rises on dilution, following the empirical relationship $\Lambda_m = \Lambda_m^{o} - k\sqrt{C}$ for strong electrolytes — a straight line in $\Lambda_m$ vs $\sqrt{C}$ whose intercept, $\Lambda_m^{o}$, is the limiting molar conductivity at infinite dilution, where ion-ion interactions vanish (the Debye–Hückel–Onsager equation supplies the theoretical basis for exactly why this line is straight). A weak electrolyte's plot is not linear — it stays flat then rises sharply only very close to zero concentration, because dilution there increases the actual DEGREE OF DISSOCIATION rather than merely spreading already-free ions apart — so its $\Lambda_m^{o}$ cannot be read off by extrapolation. …