Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.
Solution and Explanation
Conductivity of a solution is defined as the conductance of a solution of 1 cm in length and area of cross-section 1 sq. cm. The inverse of resistivity is called conductivity or specific conductance. It is represented by the symbol κ. If àis resistivity, then we can write:
\(\kappa = \frac{1}{\rho}\)
The conductivity of a solution at any given concentration is the conductance (G) of one unit volume of solution kept between two platinum electrodes with the unit area of cross-section and at a distance of unit length.
\(G = \kappa \frac{a}{l} = \kappa.1 = \kappa\)
i.e.,
(Since a = 1, l = 1)
Conductivity always decreases with a decrease in concentration, both for weak and strong electrolytes. This is because the number of ions per unit volume that carry the current in a solution decreases with a decrease in concentration.
Molar conductivity: Molar conductivity of a solution at a given concentration is the conductance of volume V of a solution containing 1 mole of the electrolyte kept between two electrodes with the area of cross-section A and distance of unit length.
\(\land_m = \kappa \frac{A}{l}\)
Now, l = 1 and A = V (volume containing 1 mole of the electrolyte).
∴\(\land_m = \kappa V\)
Molar conductivity increases with a decrease in concentration. This is because the total volume V of the solution containing one mole of the electrolyte increases on dilution.
The variation of \(∧_m\) with \(\sqrt{c}\) for strong and weak electrolytes is shown in the following plot:
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Concepts Used:
Conductance
What is conductance?
Conductance is an expression of the ease with which electric current flows through materials like metals and nonmetals. In equations, an uppercase letter G symbolizes conductance. The standard unit of conductance is siemens (S), formerly known as mho.
What is conductance in electricity?
Conductance in electricity is considered the opposite of resistance (R). Resistance is essentially the amount of friction a component presents to the flow of current.
The conductivity of electrolytic solutions is governed by the following factors:
- Interionic attraction
- Solvation of ions
- The viscosity of the solvent
- Temperature