Question

The limiting molar conductivities of ${\text{NaCl, KBr}}$ and ${\text{KCl}}$ are respectively $126,152,15{\text{0 Sc}}{{\text{m}}^{\text{2}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$. The limiting molar conductivity for $NaBr$ is:
A.$302{\text{ Sc}}{{\text{m}}^2}mo{l^{ - 1}}$
B.$17{\text{6 Sc}}{{\text{m}}^{\text{2}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$
C.${\text{278 Sc}}{{\text{m}}^{\text{2}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$
D.${\text{128 Sc}}{{\text{m}}^{\text{2}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$

Answer 1

Hint: Conductance is defined as the reciprocal of the resistance i.e. it is defined as the ability to conduct heat and electricity.
Conductivity: It is defined as the measure of the ability to conduct heat and electricity.
Molar conductivity: It is defined as the conductivity divided by its molar concentration.

Complete step by step solution:
First of all let us talk about conductivity, conductance and molar conductivity.
Conductance is defined as the reciprocal of the resistance i.e. it is defined as the ability to conduct heat and electricity.
Conductivity: It is defined as the measure of the ability to conduct heat and electricity.
Molar conductivity: It is defined as the conductivity divided by its molar concentration. It is represented by ${\Delta _m}$. As the name indicates, molar conductivity changes with concentration of the solution. There are two types of electrolytes: weak and strong electrolytes. Weak electrolytes are those electrolytes which do not undergo full ionization. And the strong electrolytes are those electrolytes which undergo ionization completely. As strong electrolytes i.e. salt, strong acids and strong bases are completely ionisable so they do not depend on the concentration i.e. the value of molar conductivity does not change with the concentration. But weak electrolytes are not completely ionizable so they depend on the concentration i.e. on changing the value of the concentration the value of the molar conductivity also changes. And the change will be according to the formula: ${\Delta _m} = {\Delta _m}^ \circ - K\sqrt c $, where ${\Delta _m}^ \circ $ is molar conductivity at infinite solution, $K$ is Kohlrausch coefficient and $c$ is the concentration.
Limiting molar conductivity: It is defined as the molar conductivity at infinite dilution i.e. zero concentration. It is represented as ${\lambda ^\infty }$.
 If we know the limiting molar conductivities of all the atoms present in the compound then we can find the limiting molar conductivity of the required compound.
For example: If we know the limiting molar conductivities of ${\text{NaCl, KBr}}$ and ${\text{KCl}}$ are $126,152,15{\text{0 Sc}}{{\text{m}}^{\text{2}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$ respectively, then we can find the limiting molar conductivity for $NaBr$as:
$
  {\lambda ^\infty }_{NaBr} = {\lambda ^\infty }_{NaCl} + {\lambda ^\infty }_{KBr} - {\lambda ^\infty }_{KCl} \\
\Rightarrow {\lambda ^\infty }_{NaBr} = 126 + 152 - 150 \\
 $
$\Rightarrow$ \[{\lambda ^\infty }_{NaBr} = 12{\text{8 Sc}}{{\text{m}}^2}{\text{mo}}{{\text{l}}^{ - 1}}\].

So option D is correct.

Note: For weak electrolytes, if dilution is increasing then the molar conductivity will be increasing as electrolyte will dissociate into more ions on increasing the dilution. But for strong electrolytes the electrolyte is already completely ionised so there is no so much effect of the dilution on strong electrolytes.