# Variations of Molar Conductivity

## Conductivity or Specific Conductivity

The conductance of a unit volume of solution held between two platinum electrodes with a unit area of cross-section and at a distance of unit length is known as specific conductivity or conductivity of an electrolytic solution at any given concentration. As the amount of ions per unit volume that bear the current in a solution decreases with dilution, the conductivity of the solution decreases. It is denoted by kappa(k). Unit of conductivity is given below-

k = siemen x m$^{-1}$

Factors Affecting Conductivity Includes-

1. Nature of an electrolyte

2. Size of the ion

3. The concentration of the solution

4. Temperature

5. Nature of the solvent

### Molar Conductivity

The conductance of volume V of a solution containing one mole of electrolyte held between two electrodes with a region of cross-section A and a distance of unit length is the molar conductivity of a solution at a given concentration.

Molar conductivity = ⋀$_{m}$ = $\frac{k}{c}$

Where,

⋀$_{m}$ = molar conductivity

k = Specific conductivity

C = concentration in moles per volume

Molar conductivity can be calculated using the equation

⋀$_{m}$(S cm2 mol-1) = $\frac{k(S/cm) \times 1000}{molarity(mol/L)}$

### Variation of Molar Conductivity

As the total volume, V, of a solution containing one mole of electrolyte increases, molar conductivity increases with decreasing concentration. The concentration drops as a result of dilution. The molar conductivity of a solution is known as limiting molar conductivity when the concentration reaches zero. Solid and weak electrolytes have different molar conductivity variations with concentration.

## Variations of Molar Conductivity With Concentration

### a. Strong Electrolyte

For strong electrolytes, the molar conductivity decreases with dilution. This decrease can be represented by the equation given below-

⋀$_{m}$ = ⋀$_{m}$⁰ - Ac1/2

If the graph is plotted between ⋀$_{m}$ and c1/2, a straight line is obtained with the intercept equal to limiting molar conductivity ⋀$_{m}$⁰ and the slope equals to -A. This value of A depends on the charges on both cation and anion obtained on the dissociation of an electrolyte in a solution.

So the value of the limiting molar conductivity can be calculated using either the graph or the Kohlrausch law.

Kohlrausch’s law of independent migration of ions states that limiting molar conductivity of an electrolyte is represented as the sum of the lof cation and anion of the electrolyte.

⋀$_{m}$⁰ = ⋀⁰$_{cation}$ + ⋀⁰$_{anion}$

### b. Weak Electrolyte

The molar conductivity of weak electrolytes, on the other hand, rises with concentration. Due to a decreased degree of dissociation, such electrolytes have lower molar conductivity at higher concentrations.

When it comes to basic conductivity, it's clear that the conductivity rises as the electrolyte concentration rises. The number of ions in a unit volume of the solution determines the specific conductivity. The dissociation increases with dilution, allowing the number of current-carrying ions in the solution to rising. Dilution, on the other hand, reduces the number of ions present in a unit volume of the solution. The conductivity is reduced as a result of this.

### Solved Examples

Example 1: If the Molarity is Given is 0.30M and the Conductivity is 0.023Sm-1. Calculate the Molar Conductivity of the Solution.

Solution:

⋀$_{m}$ = $\frac{k \times 1000}{c}$

⋀$_{m}$ = $\frac{0.023 \times 1000}{0.30}$

⋀$_{m}$ = 76.66 cm2 mol-1

Example 2: The Molar Conductivity of a 1.5M Solution of an Electrolyte is Found to be 138.9scm2mol-1. Calculate the Conductivity of this Solution.

Solution:

⋀$_{m}$ = $\frac{k \times 1000}{c}$

k =  $\frac{\Lambda m \times c}{1000}$

k = $\frac{138.9 \times 1.5}{1000}$

=0.208Scm-1

### Did You Know?

• The presence of free ions in electrolytes causes them to conduct electricity. It's analogous to how free electrons favor the conduction of electricity in metallic conductors. The Arrhenius equation or principle is used to describe electrolytic conduction.

• We're all familiar with electrolytic solutions, which are produced by dissolving some salts. The salts don't have to be ionic all of the time. The only requirement is that the compound is made up of ions of opposite charges.

• When a neutral electrolyte is dissolved in water, the electrolyte molecules are divided into two differently charged ions, according to the Arrhenius principle.

• The charged particles can freely travel around in the solution. Positive ions, or cations, may travel towards a negative electrode, or cathode, to reduce themselves. At the same time, negative ions or anions will travel towards the positive electrode or anode and oxidize themselves. Electric conduction is generated by the migration of charged particles.