The equation that is incorrect is:

Strategy: Use Kohlrausch's law to expand each equation into its ionic components. An equation is correct if the anions/cations can\cel out to form an identity.

Evaluating Option (a): LHS: $(\Lambda_m^0)_{\ce{KBr}} - (\Lambda_m^0)_{\ce{NaCl}} = (\lambda_{\ce{K}^+}^0 + \lambda_{\ce{Br}^-}^0) - (\lambda_{\ce{Na}^+}^0 + \lambda_{\ce{Cl}^-}^0)$ RHS: $(\Lambda_m^0)_{\ce{KBr}} - (\Lambda_m^0)_{\ce{KCl}} = (\lambda_{\ce{K}^+}^0 + \lambda_{\ce{Br}^-}^0) - (\lambda_{\ce{K}^+}^0 + \lambda_{\ce{Cl}^-}^0) = \lambda_{\ce{Br}^-}^0 - \lambda_{\ce{Cl}^-}^0$ Sin\ce LHS $\neq$ RHS (LHS has extra $\lambda_{\ce{K}^+}^0 - \lambda_{\ce{Na}^+}^0$), this equation is incorrect.

Other options:

• (c): Water $= \ce{H^+} + \ce{Cl^-} + \ce{Na^+} + \ce{OH^-} - (\ce{Na^+} + \ce{Cl^-}) = \ce{H^+} + \ce{OH^-}$. (Correct)
• (d): $\ce{Na} - \ce{Na}$ can\cels $\implies \ce{Br} - \ce{I} = \ce{K} - \ce{K}$ can\cels $\implies \ce{Br} - \ce{I}$. (Correct)

$\boxed{\text{Answer: (a)}}$