# Molar Conductivity

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Define Molar Conductivity

Electrochemistry is quite an important topic in JEE and other competitive engineering exams. Molar conductivity is a very significant topic under electrochemistry which you need to learn about in order to score well. Molar conductivity is defined as the conductivity of the solution of an electrolyte divided by the molar concentration of the electrolyte, and so gauges the efficiency with which an allotted electrolyte conducts electricity in solution. This is to say that molar conductivity is the conducting power of all the ions that are developed by dissolving a mole of electrolyte in a solution.

Molar Conductivity Formula

The below-given expression is used to mathematically denote molar conductivity.

Λm = K / C

Where

K = specific conductivity

C = concentration in mole per liter.

The si unit of molar conductivity is S⋅m²⋅mol⁻¹.

Molar Conductance

The Molar conductance is described as the conductance of all ions produced by one mole of an electrolyte present in a fixed volume of the solution.

It is given as:

Molar conductance μ = k ×V

Where,

V = volume in (mL) having 1 g mole of the electrolyte. If c is the solution in g mole/litre, then μ = k × 1000/c

Units of molar conductance:  Omega- cm-² mol²

Equivalent conductance = (Molar conductance)/n

Where

n = (Molecular mass) / (Equivalent mass)

Variation of Molar Conductivity with Concentration

It is important to note that molar conductivity of both strong and weak electrolytes increases with the depletion in dilution. You must be aware already that the molar conductivity is the conductivity provided by one mole of ions. Even after dilution, we are taking into account the same unit mole of ions. However, the increased dilution causes dissociation of more electrolytes into ions and optimally increasing the number of active ions in the concentration. These active ions set forth more conductivity.

The visual representation explains that for strong electrolytes, the molar conductivity is increasing steadily with the dilution. If EO m is the restricting molar conductivity (the molar conductivity at [0] concentration), then the standard equation for the strong electrolyte can be delineated using the Kohlrausch’s law as below;

Λm = Eom – A√c

Where,

A = slope of the graph. It typically depends on the kind of the electrolyte at a given temperature for an assigned solvent.

For strong electrolytes, the increase in concentration yields a striking increment in conductivity. Nevertheless, weak electrolytes carry significantly low values of specific conductivity at lower concentration and the value moderately shows an increase as the concentration is increased. This is because of an increase in the number of active ions present in the solution due to concentration.

However, for weak electrolytes, the molar conductivity strikes at lower concentrations. On the contrary, such electrolytes are contained in lower molar conductivity at higher concentrations because of the reduced degree of dissociation.

In an instance of specific conductivity, it is observed that the concentration of the electrolyte increases with the increase in conductivity. The specific conductivity relies upon the number of ions that exists in the unit volume of the solution. On dilution, the dissociation increases, leading to current-containing ions to increase in the solution. Due to the dilution, the number of ions available in a unit volume of the solution decreases. This gives rise to a reduction in conductivity.

Solved Examples on Molar Conductivity

Problem1: Find out the molar conductivity of the KCl solution?

Solution:

Given:

Molarity (M) = 0.60M

Conductivity at 298 K (k) = 0.047 S cm–

Now, Using the Molar conductivity formula = (1000 × k) / M

= (1000 × 0.047) / 0.60

= 78.33 cm² mol⁻¹

Therefore, molar conductivity of the KCl solution is 78.33 cm² mol⁻¹

Problem 2: The Molar conductance measures at infinite dilution of Na+ and Cl- ions are 32.54 × 10⁻² Sm²mol⁻¹ and 67.12 × 10⁻² Sm²mol⁻¹ respectively. Find out the total molar conductance of NaCl?

Solution:

Calculating the Molar conductance at infinite dilution, given is

λ+Na = 32.54 × 10⁻² Sm²mol⁻¹

λ+Cl = 67.12 × 10⁻² Sm²mol⁻¹

Molar conductance of NaCl = [λ+Na] + [λ+Cl]

= 32.54 × 10⁻² + 67.12 × 10⁻²

= 99.66 ×10⁻² Sm²mol⁻¹

Therefore, Molar conductance of NaCl is 99.66 ×10⁻² Sm²mol⁻¹