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Question
Discuss the variation of conductivity and molar conductivity with concentration.
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Solution
Both conductivity and molar conductivity change with changes in the concentration of the electrolyte. Conductivity always decreases as the concentration of both weak and strong electrolytes decreases. This can be explained by the fact that with dilution, the number of ions carrying electric current per unit volume decreases. The conductivity of a solution at any concentration is the conductivity of a unit volume of the solution placed between two platinum electrodes having a unit cross-sectional area and situated at a unit distance from each other.
This is clear from the following equation:
C = `(kappa A)/l` = κ ...(Both A and l are in appropriate units m or cm)
The molar conductivity of a solution at a given concentration is the conductivity of volume (V) of the solution containing one mole of electrolyte dissolved in it and placed between two electrodes of cross-sectional area (A), located at a unit distance from each other. So,
Plot of c1/2 versus molar conductivity for potassium chloride (a strong electrolyte) in aqueous solution.
∧m = `(kappa A)/l` = κ
Since l = 1 and A = V (volume in which one mole of electrolyte is dissolved)
∧m = κ V
Molar conductivity increases with decreasing concentration. This is because the total volume (V) in which one mole of electrolyte is present also increases. It has been found that, upon dilution of the solution, the increase in volume is much greater than the decrease in κ.
Strong Electrolytes: For strong electrolytes, the value of ∧m increases gradually with dilution, and it can be represented by the following equation:
∧m = `Lambda_m^0 - Ac^(1//2)`
It can be seen that if ∧m is plotted against c1/2, we get a straight line with intercept A and slope equal to ‘A’. The value of constant ‘A’ at a given solvent and temperature depends on the type of electrolyte, i.e., on the charges of the cation and anion produced on dissociation of the electrolyte in solution. Thus, NaCl, CaCl2, and MgSO4 are known as 1-1, 2-1 and 2-2 electrolytes, respectively. The value of ‘A’ is the same for all electrolytes of the same type.
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