For a dilute solution of a strong electrolyte, the variation of molar conductivity with concentration is given by

Options

A. `wedge_(m)=wedge^(@)._(m)+Ac`
B. `wedge_(m)=wedge^(@)._(m)-Ac`
C. `wedge_(m)=wedge^(@)._(m)+Asqrt(c)`
D. `wedge_(m)=wedge^(@)._(m)-Asqrt(c)`

Explanation

To solve the question regarding the variation of molar conductivity with concentration for a dilute solution of a strong electrolyte, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Molar Conductivity**:
Molar conductivity (λm) is defined as the conductivity of an electrolyte solution divided by its molar concentration. It is a measure of how well an electrolyte conducts electricity in solution.

2. **Debye-Hückel Equation**:
For a dilute solution of a strong electrolyte, the variation of molar conductivity with concentration can be described by the Debye-Hückel equation. The equation is given by:
\[ \lambda_m = \lambda_m^0 - A \sqrt{c} \]
where:
- \( \lambda_m \) is the molar conductivity at concentration \( c \),
- \( \lambda_m^0 \) is the molar conductivity at infinite dilution,
- \( A \) is a constant that depends on the nature of the electrolyte,
- \( c \) is the concentration of the electrolyte.

3. **Interpreting the Terms**:
- \( \lambda_m^0 \): This value represents the maximum conductivity of the electrolyte when it is fully dissociated and at infinite dilution.
- \( A \sqrt{c} \): This term accounts for the decrease in molar conductivity as the concentration of the electrolyte increases. The square root relationship indicates that as concentration increases, the effect on conductivity is not linear.

4. **Conclusion**:
The relationship provided by the Debye-Hückel equation shows that for a dilute solution of a strong electrolyte, the molar conductivity decreases with increasing concentration due to interactions between ions.

### Final Expression:
Thus, the variation of molar conductivity with concentration for a dilute solution of a strong electrolyte is given by:
\[ \lambda_m = \lambda_m^0 - A \sqrt{c} \]