Question

Define conductivity and molar conductivity for a solution of an electrolyte. Why does the conductivity of a solution decrease with decrease in concentration?

Hint:

Conductivity ($\kappa$) always decreases with dilution, but Molar Conductivity ($\Lambda_m$) always increases with dilution.

Answer 1

Step 1: Define conductivity ($\kappa$).
Conductivity is the conductance of a unit cube ($1$ cm $\times$ $1$ cm $\times$ $1$ cm) of an electrolyte solution. Its unit is S cm$^{-1}$ (siemens per centimetre).
Step 2: Define molar conductivity ($\Lambda_m$).
Molar conductivity is the conducting power of all ions produced when one mole of an electrolyte is dissolved in a given volume $V$ (cm$^3$) of solution. It is related to conductivity by $\Lambda_m = \kappa \times V$, where $V$ is the volume containing one mole. Its unit is S cm$^2$ mol$^{-1}$.
Step 3: Explain why conductivity decreases on dilution.
Conductivity depends on the number of ions available per unit volume to carry electric current. When the solution is diluted (concentration decreases), the same number of moles of ions are now distributed over a larger volume, so the number of ions per cubic centimetre decreases.
Step 4: Conclusion.
Fewer ions per unit volume means fewer charge carriers passing a cross-section per unit time, so conductivity decreases as the concentration decreases.