Which of the following is the unit of eq. conductance ?

Options

A. mho
B. mho `cm^(2)`
C. mho `cm^(-1)`
D. mho `cm^(-2)`

Answer

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

### Step-by-Step Solution:

1. **Understand Equivalent Conductance**:
Equivalent conductance (Λ) is a measure of the ability of an electrolyte solution to conduct electricity. It is defined as the conductance of the solution divided by the concentration of the electrolyte in equivalents per liter.

2. **Formula for Equivalent Conductance**:
The formula for equivalent conductance is given by:
\[ \Lambda = \frac{\kappa \times 1000}{C} \]
where:
- \( \Lambda \) is the equivalent conductance,
- \( \kappa \) is the specific conductance (conductivity),
- \( C \) is the concentration in equivalents per liter.

3. **Identify Units**:
- The unit of specific conductance (\( \kappa \)) is siemens per meter (S/m) or ohm⁻¹m⁻¹.
- The concentration \( C \) is measured in equivalents per liter (eq/L).

4. **Substituting Units into the Formula**:
Substituting the units into the formula for equivalent conductance:
\[ \text{Unit of } \Lambda = \frac{\text{S/m} \times 1000}{\text{eq/L}} \]

5. **Simplifying the Units**:
- The term \( 1000 \) is a conversion factor and does not affect the unit type.
- Rearranging the units gives:
\[ \text{Unit of } \Lambda = \frac{\text{S/m}}{\text{eq/L}} = \text{S} \cdot \frac{L}{m \cdot eq} \]

6. **Converting to Common Units**:
Since \( 1 \text{ S} = 1 \text{ ohm}^{-1} \), we can express the unit as:
\[ \text{Unit of } \Lambda = \text{ohm}^{-1} \cdot \frac{L}{m \cdot eq} \]
- To convert \( m \) to \( cm \), we note that \( 1 \text{ m} = 100 \text{ cm} \), thus:
\[ \text{Unit of } \Lambda = \text{ohm}^{-1} \cdot \frac{L \cdot 100^2}{cm^2 \cdot eq} = \text{ohm}^{-1} \cdot \frac{10000 \text{ cm}^2}{cm^2 \cdot eq} \]

7. **Final Unit of Equivalent Conductance**:
Therefore, the final unit of equivalent conductance is:
\[ \text{Unit of } \Lambda = \text{ohm}^{-1} \cdot \text{cm}^2/\text{eq} \]

### Conclusion:
The unit of equivalent conductance is **ohm⁻¹ cm²/eq**.