Molar Conductivity - Practice Questions & MCQ

Molar Conductance
The molar conductance is defined as the conductance of all the ions produced by the ionisation of 1 mole of an electrolyte when present in V ml of solution. It is denoted by Λm.
Molar conductance $\left(\wedge_{\mathrm{m}}\right)=\kappa \times \mathrm{V}$
where V is the volume in ml containing 1 gm mole of the electrolyte.
If c is the concentration of the solution in mole per litre, then:

$\wedge_{\mathrm{m}}=\kappa \times \frac{1000}{\mathrm{c}}$
where c is the concentration of the solution in M. The units of  $\Lambda_m$ are ohm^-1 cm² mol^-1 or S cm² mol^-1  When the units of $\kappa$ is S cm^-1.

It is to be noted that changing the units of the quantities involved will lead to a  change in the formula. For the sake of homogeneity, $\Lambda_m=\frac{\kappa}{C}$ when all the quantities are expressed in their SI unit.

Also, if A_xB_y is an electrolyte dissociating as:
$A_x B_y \rightleftharpoons x A^{y+}+y B^{x-}$Thus, $\wedge_{\mathrm{m}} \mathrm{A}_x \mathrm{~B}_{\mathrm{y}}=x \cdot \wedge_{\mathrm{m}}\left(\mathrm{A}^{\mathrm{y}+}\right)+\mathrm{y} \cdot \wedge_{\mathrm{m}}\left(\mathrm{B}^{x-}\right)$

Equivalent Conductance
One of the factors on which the conductance of an electrolytic solution depends is the concentration of the solution. In order to obtain comparable results for different electrolytes, it is necessary to take equivalent conductance.
It is defined as the conductance of all the ions produced by one gram equivalent of an electrolyte in a given solution. It is denoted by Λ_eq.
$\wedge_{\mathrm{eq}}=\frac{1000 \times \kappa}{\mathrm{N}}$
If ‘V’ is the volume in ml containing 1 gm equivalent of the electrolyte, the above equation can be written as:
$\wedge_{\mathrm{eq}}=\kappa \times \mathrm{V}$
Its units are ohm^-1 cm² equiv^-1 or S cm² equiv^-1. A similar constraint of units exists in the formula as that in molar conductance.
Equivalent conductance is also given as follows:$\begin{aligned} & \text { Equivalent conductance }=\frac{\text { Molar conductance }}{x}, \\ & \text { where } x=\frac{\text { Molecular mass }}{\text { Equivalent mass }}=\mathrm{n}-\text { factor }\end{aligned}$

Effect on conductance

• Conductance of a solution increases with increase in the number of solute molecules/ions and decreases with decrease in the number of solute molecules/ions.
• Conductance of a solution increases with dilution as the interactions between the molecules/ions decreases due to increase in the average distance between the molecules/ions.

Effect on degree of dissociation

• Strong electrolytes: There is almost no change in the degree of dissociation (as it is already close to unity).
• Weak electrolytes: With dilution, degree of dissociation increases rapidly and thus, the number of molecules increases.

Effect on Molar and Equivalent conductance
Both Λ_m and Λ_eq increases with dilution as conductance increases with dilution.
For strong electrolytes, the increase in Λ_m and Λ_eq is relatively small as increase in the number of molecules/ions is very small.
For weak electrolytes, the increase in Λ_m and Λ_eq is large and rapid as  increases with dilution.

Effect on Conductivity
On dilution, the number of molecules/ions per ml of the solution decreases. Since conductivity is defined as the conductance of one ml of the solution, conductivity decreases with dilution (due to a decrease in the conductance).

When addition of water doesn’t bring about any further change in the conductance of a solution, this situation is referred to as Infinte Dilution.

• Strong Electrolytes: When infinite dilution is approached, the conductance of a solution of strong electrolyte approaches a limiting value and can be obtained by extrapolating the curve between Λ_m and c^1/2 as shown in the figure given below:
  
  
  
  The molar conductivity of strong electrolytes is found to vary with concentration as:
  $\wedge_{\mathrm{m}}=\lambda_{\mathrm{m}}^0-\mathrm{B} \sqrt{\mathrm{c}}$
  where B is a constant depending upon the type of electrolyte, the nature of the solvent, and the temperature. This equation is known as the Debye Huckel-Onsage equation and is found to hold good at low concentrations.

  All electrolytes having same formula type have the same value of B e.g. (KCl, NaCl) and (CaCl₂, MgCl₂)

• Weak Electrolytes: When infinite dilution is approached, the conductance of a solution of the weak electrolyte increases very rapidly and thus, cannot be obtained through extrapolation. Also, the variation between Λ_m and c^1/2 is not linear at low concentrations.