Question

The conductivities at infinite dilution of $N{{H}_{4}}Cl,NaOH,NaCl$ are 130, 218, and 120$oh{{m}^{-1}}c{{m}^{2}}e{{q}^{-1}}$ . If the equivalent conductance of $\frac{N}{100}$ solution of $N{{H}_{4}}OH$ is 10$oh{{m}^{-1}}c{{m}^{2}}e{{q}^{-1}}$, then degree of dissociation of $N{{H}_{4}}OH$ at this dilution is:
0.005
0.043
0.01
0.02

Answer 1

Hint: Kohlrausch observed some regularities when associating the values of the limiting molar conductivities of some strong electrolyte in a solution. It is independent of migration of ions.

Complete step by step solution:
Kohlrausch law of independent migration of ions explains about the limiting molar conductivity of an electrolyte can be denoted as the sum of the amounts of the individual contribution of its cations and anions. The conductivity of the solution decreases with dilution because only fewer ions are present for conduction.
Given in the question:
The conductivities at infinite dilution of $N{{H}_{4}}Cl$=130$oh{{m}^{-1}}c{{m}^{2}}e{{q}^{-1}}$
The conductivities at infinite dilution of $NaOH$=218$oh{{m}^{-1}}c{{m}^{2}}e{{q}^{-1}}$
The conductivities at infinite dilution of $NaCl$=120$oh{{m}^{-1}}c{{m}^{2}}e{{q}^{-1}}$
The equivalent conductance of $\frac{N}{100}$ solution of $N{{H}_{4}}OH$ is 10$oh{{m}^{-1}}c{{m}^{2}}e{{q}^{-1}}$
\[\begin{align}
  & \lambda _{m}^{0}(N{{H}_{4}}OH)=\lambda _{m}^{0}{{(N{{H}_{4}}^{+}+\lambda _{m}^{0})}^{-}} \\
 & \lambda _{m}^{0}(N{{H}_{4}}OH)=\lambda _{m}^{0}(N{{H}_{4}}Cl)+\lambda _{m}^{0}(NaOH)-\lambda _{m}^{0}(NaCl) \\
 & \lambda _{m}^{0}(N{{H}_{4}}OH)=130+218-120 \\
 & \lambda _{m}^{0}(N{{H}_{4}}OH)=228 \\
\end{align}\]
The value of degree of dissociation = $\frac{{{\lambda }_{m}}}{\lambda _{m}^{0}}=\frac{10}{228}=0.043$

Hence the correct answer is option (b) i.e. the degree of dissociation of $N{{H}_{4}}OH$ at this dilution is 0.043

Additional information:
It is very difficult to calculate the molar conductivity of weak electrolytes at infinite dilution, as the conductance of weak electrolytes is very low and the dissociation of these electrolytes is very less as compared to strong electrolytes. The value of degree of dissociation for strong electrolytes is approximately equal to one.

Note: Kohlrausch law is used to calculate the degree of dissociation of an electrolyte, it is also used to calculate the solubility of sparingly soluble salt in a solvent. It helps to calculate the dissociation constant for weak electrolytes in a solvent and the molar conductivity of weak electrolytes at infinite dilution.