The relationship `lambda_(m)=lambda_(m)^(0)-BsqrtC` will not hold good for the electrolyte?

Options

A. HCl
B. KCl
C. `BaCl_(2)`
D. HCN

Explanation

To determine which electrolyte does not follow the relationship \( \lambda_m = \lambda_m^0 - B\sqrt{C} \), we need to analyze the given relationship and the nature of the electrolytes provided in the options.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
- The equation \( \lambda_m = \lambda_m^0 - B\sqrt{C} \) describes the molar conductivity (\( \lambda_m \)) of weak electrolytes, where \( \lambda_m^0 \) is the molar conductivity at infinite dilution, \( B \) is a constant, and \( C \) is the concentration of the electrolyte.
- This relationship indicates that as the concentration of a weak electrolyte increases, its molar conductivity decreases due to ion interactions.

2. **Identifying Electrolytes**:
- We need to evaluate the nature of the electrolytes provided in the options:
- **Option 1: HCN (Hydrogen Cyanide)** - This is a weak electrolyte because it does not completely dissociate in solution.
- **Option 2: KCl (Potassium Chloride)** - This is a strong electrolyte as it completely dissociates into \( K^+ \) and \( Cl^- \) ions in solution.
- **Option 3: BaCl2 (Barium Chloride)** - This is also a strong electrolyte, completely dissociating into \( Ba^{2+} \) and \( 2Cl^- \) ions.
- **Option 4: HCl (Hydrochloric Acid)** - This is a strong electrolyte, fully dissociating into \( H^+ \) and \( Cl^- \) ions.

3. **Determining the Correct Answer**:
- The relationship \( \lambda_m = \lambda_m^0 - B\sqrt{C} \) does not apply to strong electrolytes because they fully dissociate in solution, and their conductivity does not follow the same pattern as weak electrolytes.
- Therefore, the electrolytes that do not follow this relationship are the strong electrolytes: KCl, BaCl2, and HCl.

4. **Conclusion**:
- Since the question asks for the electrolyte for which the relationship does not hold, we can conclude that the answer is any of the strong electrolytes listed. However, since the question seems to imply a single answer, we can choose one strong electrolyte, such as **KCl**.

### Final Answer:
The relationship \( \lambda_m = \lambda_m^0 - B\sqrt{C} \) will not hold good for strong electrolytes like KCl, BaCl2, or HCl.

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