The relationship between equivalent conductance `(A_(eq))`, specific conductivity (K) and normality (xN) of a solution is:

Options

A. `k=(1000xx x)/(wedge_(eq))`
B. `wedge_(eq)=(1000xx k)/x`
C. `wedge_(eq)=k/(1000xx x)`
D. `k=(wedge_(eq))/(1000xx x)`

Answer

To derive the relationship between equivalent conductance (A_eq), specific conductivity (K), and normality (xN) of a solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equivalent Conductance**:
- Equivalent conductance (A_eq) is defined as the conductance of an electrolyte solution containing 1 gram equivalent of the electrolyte. It can be denoted as:
\[ A_{eq} = \frac{K \times 1000}{xN} \]
- Here, K is the specific conductivity, and xN is the normality of the solution.

2. **Defining Specific Conductivity (K)**:
- Specific conductivity (K) is a measure of how well a solution conducts electricity. It is defined as the conductance of a solution of a certain volume and is expressed in units of S/cm (Siemens per centimeter).

3. **Understanding Normality (xN)**:
- Normality (xN) is defined as the number of gram equivalents of solute per liter of solution. It can also be expressed in terms of volume:
\[ xN = \frac{\text{Number of gram equivalents}}{\text{Volume of solution in liters}} \]

4. **Relating the Units**:
- The unit of specific conductivity (K) is S/cm, which can also be expressed as:
\[ K = \frac{1}{R} \cdot \frac{A}{L} \]
- Where R is the resistance in ohms, A is the area of the electrodes in cm², and L is the distance between the electrodes in cm.

5. **Substituting Units**:
- When substituting the units into the equation for equivalent conductance, we can express K in terms of its units:
\[ K \text{ (in S/cm)} = \frac{\text{cm}^{-1}}{\text{ohm}^{-1}} = \text{cm}^{-1} \cdot \text{ohm}^{-1} \]
- Normality (xN) has units of equivalents per liter, which can be converted to equivalents per cm³:
\[ xN = \frac{\text{equivalents}}{1000 \text{ cm}^3} \]

6. **Final Relationship**:
- By substituting the units of K and xN into the equation for A_eq, we can derive the relationship:
\[ A_{eq} = \frac{K \times 1000}{xN} \]
- This shows that equivalent conductance is directly proportional to specific conductivity and inversely proportional to normality.

### Conclusion:
The relationship between equivalent conductance (A_eq), specific conductivity (K), and normality (xN) of a solution is given by:
\[ A_{eq} = \frac{K \times 1000}{xN} \]