The equation that is incorrect is :

Options

A. `(Lambda_(m)^(0))_(H_(2)O)=(Lambda_(m)^(0))_(HCl)+(Lambda_(m)^(0))_(NaOH)-(Lambda_(m)^(0))_(NaCl)`
B. `(Lambda_(m)^(0))_(KCl)-(Lambda_(m)^(0))_(NaCl)=(Lambda_(m)^(0))_(KBr)-(Lambda_(m)^(0))_(NaBr)`
C. `(Lambda_(m)^(0))_(NaBr)-(Lambda_(m)^(0))_(NaCl)=(Lambda_(m)^(0))_(KBr)-(Lambda_(m)^(0))_(KCl)`
D. `(Lambda_(m)^(0))_(NaBr)-(Lambda_(m)^(0))_(Nal)=(Lambda_(m)^(0))_(KBr)-(Lambda_(m)^(0))_(NaBr)`

Answer

To determine which equation is incorrect based on Coulomb's law, we need to analyze each option given in the question. Coulomb's law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductance of its cations and anions.

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
- Recall that at infinite dilution, the equivalent conductivity (Λ) of an electrolyte is the sum of the conductance of its cations (λ+) and anions (λ-).
- Mathematically, this can be expressed as:
\[ Λ = λ^+ + λ^- \]

2. **Analyzing the First Option**:
- The first equation is \( H_2O = H^+ + OH^- \).
- This equation is correct as water dissociates into hydrogen ions and hydroxide ions.
- Therefore, this option is not incorrect.

3. **Analyzing the Second Option**:
- The second equation is \( KCl - NaCl \).
- Breaking down:
- \( KCl \) dissociates into \( K^+ + Cl^- \).
- \( NaCl \) dissociates into \( Na^+ + Cl^- \).
- The equation becomes:
\[ (K^+ + Cl^-) - (Na^+ + Cl^-) = K^+ - Na^+ \]
- This shows that the equation holds true. Thus, this option is also correct.

4. **Analyzing the Third Option**:
- The third equation is \( KBr - NaCl \).
- Breaking down:
- \( KBr \) dissociates into \( K^+ + Br^- \).
- \( NaCl \) dissociates into \( Na^+ + Cl^- \).
- The equation becomes:
\[ (K^+ + Br^-) - (Na^+ + Cl^-) = K^+ + Br^- - Na^+ - Cl^- \]
- This does not simplify to a valid equality. Thus, this option is incorrect.

5. **Analyzing the Fourth Option**:
- The fourth equation is \( Na^+ + Br^- - Na^+ - K^+ + Br^- \).
- Breaking down:
- The equation simplifies to:
\[ Br^- - K^+ \]
- This does not yield a valid equality either. Thus, this option is also incorrect.

### Conclusion:
After analyzing all the options, we find that the third equation \( KBr - NaCl \) is the incorrect equation based on Coulomb's law.