Which one of the following graphs between molar conductivity `(A_(m))` versus `sqrtC` is correct?

Options

A.
B.
C.
D.

Explanation

To determine the correct graph between molar conductivity (Λm) and the square root of concentration (√C), we need to analyze the behavior of strong electrolytes according to the Debye-Hückel-Onsager equation.

### Step-by-Step Solution:

1. **Understanding Molar Conductivity**:
Molar conductivity (Λm) is a measure of how well an electrolyte conducts electricity in solution. It is influenced by the concentration of the electrolyte.

2. **Debye-Hückel-Onsager Equation**:
For strong electrolytes, the molar conductivity can be described by the equation:
\[ \Lambda_m = \Lambda_m^0 - B \sqrt{C} \]
where:
- \( \Lambda_m^0 \) is the molar conductivity at infinite dilution,
- \( B \) is a constant that depends on the nature of the electrolyte,
- \( C \) is the concentration of the electrolyte.

3. **Graphing the Relationship**:
Rearranging the equation gives:
\[ \Lambda_m = \Lambda_m^0 - B \sqrt{C} \]
This indicates that if we plot \( \Lambda_m \) (y-axis) against \( \sqrt{C} \) (x-axis), we will get a straight line with a negative slope (-B).

4. **Identifying the Characteristics of the Graph**:
- The y-intercept will be \( \Lambda_m^0 \).
- As concentration increases (√C increases), molar conductivity decreases, leading to a downward slope.

5. **Comparing Different Electrolytes**:
- For different strong electrolytes like KCl and NaCl, the slopes of the graphs will be the same if they are of the same type (1:1 electrolytes).
- However, the initial molar conductivity (y-intercept) will differ based on their ionic mobility in solution.

6. **Conclusion**:
The graph for KCl will be higher than NaCl at zero concentration because K+ ions are larger and have better mobility compared to Na+ ions due to differences in hydration. Therefore, the graph of KCl will start higher on the y-axis compared to NaCl.

### Final Answer:
The correct graph will show a straight line with a negative slope, starting higher for KCl than for NaCl.