The unit of equivalent conductance is :

Options

A. `"ohm"^(-1)cm^(2)"equiv"^(-1)`
B. `"ohm"^(-1)cm^(2)g^(-1)`
C. `"ohm cm"^(2)"equiv"^(-1)`
D. `"ohm"^(-1)"mol"^(-1)`

Answer

To determine the unit of equivalent conductance, we can follow these steps:

### Step 1: Understand Equivalent Conductance
Equivalent conductance (Λ) is defined as the conductance of a solution containing one gram equivalent of an electrolyte in one cubic meter (m³) of solution.

### Step 2: Know the Formula for Equivalent Conductance
The formula for equivalent conductance is given by:
\[ \Lambda = \frac{\text{Conductivity} (\kappa)}{\text{Normality} (N)} \]

### Step 3: Identify Units of Conductivity
The unit of conductivity (κ) is the reciprocal of resistivity. Therefore, the unit of conductivity is:
\[ \text{Unit of Conductivity} = \frac{1}{\text{Ohm}} \cdot \text{cm}^{-1} = \text{Ohm}^{-1} \cdot \text{cm}^{-1} \]

### Step 4: Identify Units of Normality
Normality (N) is defined as the number of equivalents of solute per liter of solution. The unit of normality is:
\[ \text{Unit of Normality} = \text{equivalents} \cdot \text{L}^{-1} = \text{equivalents} \cdot \text{cm}^{-3} \]

### Step 5: Substitute Units into the Equivalent Conductance Formula
Now, substituting the units of conductivity and normality into the formula for equivalent conductance:
\[ \Lambda = \frac{\text{Ohm}^{-1} \cdot \text{cm}^{-1}}{\text{equivalents} \cdot \text{cm}^{-3}} \]

### Step 6: Simplify the Units
When we simplify this expression, we get:
\[ \Lambda = \text{Ohm}^{-1} \cdot \text{cm}^{-1} \cdot \frac{\text{cm}^{3}}{\text{equivalents}} = \frac{\text{cm}^{2}}{\text{Ohm} \cdot \text{equivalents}} \]

### Step 7: Final Unit of Equivalent Conductance
Thus, the unit of equivalent conductance can be expressed as:
\[ \text{Unit of Equivalent Conductance} = \frac{\text{cm}^2}{\text{Ohm} \cdot \text{equivalent}} = \text{per Ohm cm}^2 \text{ per equivalent} \]

### Conclusion
The correct option for the unit of equivalent conductance is:
**Per Ohm Centimetre Square Per Equivalent.**