Equivalent conductivity of `Fe_(2)(SO_(4))_(3)` is relative to molar conductivity by the expression `:`

Options

A. `Lambda_(eq)=Lambda_(m)`
B. `Lambda_(eq)=lambda_(m)//3`
C. `Lambda_(eq)=3Lambda_(m)`
D. `Lambda_(eq)=Lambda_(m)//6`

Explanation

To find the relationship between the equivalent conductivity and molar conductivity of \( \text{Fe}_2(\text{SO}_4)_3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- **Molar Conductivity (\( \Lambda_m \))**: It is defined as the conductivity of an electrolyte solution divided by its molar concentration. It indicates how well an electrolyte conducts electricity in solution.
- **Equivalent Conductivity (\( \Lambda_{eq} \))**: It is defined as the conductivity of an electrolyte solution divided by its equivalent concentration. It indicates the conductivity per equivalent of the solute.

2. **Determine the Number of Ions**:
- The formula \( \text{Fe}_2(\text{SO}_4)_3 \) dissociates in solution to give:
- 2 Fe\(^{3+}\) ions
- 3 SO\(_4^{2-}\) ions
- Therefore, the total number of ions produced from one formula unit of \( \text{Fe}_2(\text{SO}_4)_3 \) is \( 2 + 3 = 5 \) ions.

3. **Relating Molar Conductivity and Equivalent Conductivity**:
- The molar conductivity can be expressed in terms of equivalent conductivity as follows:
\[ \Lambda_m = n \cdot \Lambda_{eq} \]
where \( n \) is the number of equivalents produced from one mole of the solute.

4. **Calculating the Number of Equivalents**:
- For \( \text{Fe}_2(\text{SO}_4)_3 \), since it produces 5 ions, we can say that:
\[ n = 5 \]

5. **Substituting into the Equation**:
- Now substituting \( n \) into the relationship:
\[ \Lambda_m = 5 \cdot \Lambda_{eq} \]

6. **Finding Equivalent Conductivity**:
- Rearranging the equation to find \( \Lambda_{eq} \):
\[ \Lambda_{eq} = \frac{\Lambda_m}{5} \]

### Final Expression:
Thus, the equivalent conductivity of \( \text{Fe}_2(\text{SO}_4)_3 \) is related to its molar conductivity by the expression:
\[ \Lambda_{eq} = \frac{\Lambda_m}{5} \]