Units of the properties measured are given below. Which of the properties has not been matched correctly?

Options

A. molar conductance `= Sm^2 mol^(-1)`
B. Cell constant =`m^(-1)`
C. Specific conductance = S `m^2`
D. Equivalent conductance =S `m^2 (g eq)^(-1)`

Explanation

To solve the question about which property has not been matched correctly with its unit, we will analyze each property and its corresponding unit step by step.

### Step 1: Understand the Properties and Their Formulas

1. **Resistance (R)**:
- Formula: \( R = \frac{\rho L}{A} \)
- Units: Ohm (Ω)

2. **Conductance (G)**:
- Formula: \( G = \frac{1}{R} \)
- Units: Siemens (S)

3. **Cell Constant (g*)**:
- Formula: \( g^* = \frac{L}{A} \)
- Units: Meter inverse (m⁻¹)

4. **Specific Conductance (κ)**:
- Formula: \( κ = \frac{1}{\rho} \)
- Units: Siemens per meter (S/m)

5. **Molar Conductance (λm)**:
- Formula: \( λ_m = \frac{κ \times 1000}{C} \)
- Units: Siemens meter square per mole (S m² mol⁻¹)

6. **Equivalent Conductance (λequiv)**:
- Formula: \( λ_{equiv} = \frac{κ \times 1000}{N} \)
- Units: Siemens meter square per gram equivalent (S m² g-equiv⁻¹)

### Step 2: Analyze the Given Options

Now, let's analyze the units given in the options:

1. **Molar Conductance**:
- Given: Siemens meter square per mole (S m² mol⁻¹)
- Correct: Siemens meter square per mole (S m² mol⁻¹) - **Correct**

2. **Cell Constant**:
- Given: Meter inverse (m⁻¹)
- Correct: Meter inverse (m⁻¹) - **Correct**

3. **Specific Conductance**:
- Given: Siemens meter square (S m²)
- Correct: Siemens per meter (S/m) - **Incorrect**

4. **Equivalent Conductance**:
- Given: Siemens meter square per gram equivalent (S m² g-equiv⁻¹)
- Correct: Siemens meter square per gram equivalent (S m² g-equiv⁻¹) - **Correct**

### Step 3: Conclusion

From the analysis, the property that has not been matched correctly is **Specific Conductance**, which is incorrectly stated as having the unit of Siemens meter square (S m²) instead of the correct unit, which is Siemens per meter (S/m).

### Final Answer

The property that has not been matched correctly is **Specific Conductance**.

---