Question

Define conductivity.

Hint:

Conductivity is the reciprocal of resistivity, that is, the conductance of a unit cube of solution.

Answer 1

Step 1: Understanding the Concept:
A solution of an electrolyte carries current because its ions move. How well it does this is measured by its conductance and its conductivity.

Step 2: Start from resistance:
The resistance of a conductor of length \( l \) and cross-section area \( A \) is \( R = \rho \dfrac{l}{A} \). Here \( \rho \) is the resistivity.
Conductivity is the reciprocal of resistivity.
\[ \kappa = \frac{1}{\rho} = \frac{1}{R} \times \frac{l}{A} \]

Step 3: State the definition:
Conductivity \( \kappa \) is the conductance of a solution of 1 cm length and 1 cm\(^2\) cross-section. In other words, it is the conductance of a unit cube of the solution.
Its SI unit is \( \mathrm{S\ m^{-1}} \). It is also written as \( \mathrm{S\ cm^{-1}} \).

Step 4: What affects it:
Conductivity of an electrolyte falls on dilution, because fewer ions are present per unit volume.

Final Answer:
Conductivity is the reciprocal of resistivity, or the conductance of a unit cube of the solution. \[ \boxed{\kappa = \frac{1}{\rho}} \]