# Variation of Conductivity and Molar Conductivity with Concentration

Do you think the conductivity of a solution would vary when you alter its concentration? Never tried out an experiment like that? Well, it is an absolutely important concept and also digs deeper into the depths of this concept of variation of conductivity.

## What is Specific Conductivity?

The specific conductivity or conductivity of an electrolytic solution at any given concentration is the conductance of the unit volume of the solution. It is the conductance when kept between two platinum electrodes with a unit area of cross-section. The electrodes are at a distance of unit length.

Conductivity decreases with a decrease in concentration as the number of ions per unit volume that carries the current in a solution decrease on dilution. The molar conductivity of a solution at a given concentration is the conductance of volume V of the solution containing one mole of electrolyte kept between two electrodes with an area of cross-section A and distance of unit length.

Ʌm = К/c

Here, c = concentration in moles per volume, К = specific conductivity and Ʌm = molar conductivity. As the solution contains only one mole of electrolyte, the above equation can be modified as:

Ʌm = КV

### Browse more Topics under Electrochemistry

Learn more about the Working and setup of Galvanic Cells here.

## Change in Molar Conductivity

Molar conductivity increases with a decrease in concentration. This happens because the total volume, V, of the solution containing one mole of electrolyte also increases. Upon dilution, the concentration decreases. Furthermore, when the concentration approaches zero, the molar conductivity of the solution is known as limiting molar conductivity, Ë°m. Variation of molar conductivity with concentration is different for both, strong and weak electrolytes.

### Variation of Molar Conductivity with Concentration of Strong Electrolytes

For strong electrolytes, the molar conductivity increases slowly with the dilution. The plot of the molar conductivity and $$\sqrt{c}$$ is a straight line having y-intercept equal to Ë°m. The value of limiting molar conductivityË°m can be determined from the graph or with the help of Kohlrausch law.

For strong electrolytes, the molar conductivity increases slowly with the dilution. Thus, the plot of the molar conductivity and c1/2 is a straight line having y-intercept equal to Ë°m. The general equation for the plot is:

Ʌm = Ë°m  A(\sqrt{c}\)

Where A is a constant equal to the slope of the line. Furthermore, the value of “A” for a given solvent depends on the type of electrolyte at a particular temperature. Hence, it differs from solution to solution.

What are Electrochemical Cells?

### Variation of Molar Conductivity with Concentration for Weak Electrolyte

For weak electrolytes, the graph plotted between molar conductivity and (\sqrt{c}\)  (where c is the concentration) is not a straight line. This is because weak electrolytes have lower molar conductivities and lower degrees of dissociation at higher concentrations which increases steeply at lower concentrations. Hence, we use Kohlrausch law of independent migration of ions for determining to limit molar conductivity, Ëm° of weak electrolytes.

## Solved Example for You

Question: How does the concentration of a solution affect its specific conductivity?

Answer: Specific Conductivity decreases with a decrease in concentration. Since the number of ions per unit volume that carry current in a solution decrease on dilution. Hence, concentration and conductivity are directly proportional to each other.

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