Which of the following is incorrect?

Options

A. `wedge_m ^@ NaCl - wedge_m ^@ NaBr = wedge_m ^@ KCl - wedge_m^@ KBr`
B. `wedge_m ^@ H_2O = wedge_m ^@ HCl + wedge_m ^@ NaOH - wedge_m^@ NaCl`
C. `wedge_m ^@ NaI - wedge_m ^@ NaBr = wedge_m ^@ NaBr - wedge_m^@ KBr`
D. `wedge_m ^@ NaCl - wedge_m ^@ KCl = wedge_m ^@ NaBr - wedge_m^@ KBr`

Answer

To solve the question of identifying the incorrect statement among the given equations related to molar conductance at infinite dilution, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Molar Conductance at Infinite Dilution**:
- Molar conductance at infinite dilution (\( \lambda_m^0 \)) is the conductance of an electrolyte when it is completely dissociated into its ions. According to Kohlrausch's Law, the molar conductance of an electrolyte can be expressed as the sum of the molar conductances of its constituent ions.

2. **Analyzing the First Equation**:
- The equation states:
\[ \lambda_m^0 \text{(NaCl)} = \lambda_m^0 \text{(Na}^+) + \lambda_m^0 \text{(Cl}^-) \]
- This equation is correct as it follows the principle of complete dissociation of NaCl into Na\(^+\) and Cl\(^-\).

3. **Analyzing the Second Equation**:
- The equation states:
\[ \lambda_m^0 \text{(H}_2\text{O)} = \lambda_m^0 \text{(H}^+) + \lambda_m^0 \text{(OH}^-) \]
- This equation is also correct as it represents the dissociation of water into H\(^+\) and OH\(^-\), and it matches with the dissociation of strong acids and bases.

4. **Analyzing the Third Equation**:
- The equation states:
\[ \lambda_m^0 \text{(NaI)} - \lambda_m^0 \text{(Na}^+) - \lambda_m^0 \text{(I}^-) = \lambda_m^0 \text{(Na}^+) + \lambda_m^0 \text{(Br}^-) - \lambda_m^0 \text{(KBr)} \]
- Breaking it down:
- Left side: \( \lambda_m^0 \text{(NaI)} = \lambda_m^0 \text{(Na}^+) + \lambda_m^0 \text{(I}^-) \)
- Right side: \( \lambda_m^0 \text{(KBr)} = \lambda_m^0 \text{(K}^+) + \lambda_m^0 \text{(Br}^-) \)
- After cancellation, we find that the two sides do not equate, indicating that this equation is incorrect.

5. **Analyzing the Fourth Equation**:
- The equation states:
\[ \lambda_m^0 \text{(NaCl)} - \lambda_m^0 \text{(KCl)} = \lambda_m^0 \text{(Na}^+) - \lambda_m^0 \text{(K}^+) \]
- Breaking it down:
- Left side: \( \lambda_m^0 \text{(NaCl)} = \lambda_m^0 \text{(Na}^+) + \lambda_m^0 \text{(Cl}^-) \)
- Right side: \( \lambda_m^0 \text{(KCl)} = \lambda_m^0 \text{(K}^+) + \lambda_m^0 \text{(Cl}^-) \)
- After cancellation, both sides equate, indicating that this equation is correct.

### Conclusion:
The only incorrect equation is the third one involving sodium iodide and sodium bromide. Therefore, the answer is that option number 3 is incorrect.