Making use of the assumptions we ordinarily make in calculating the \(\mathrm{pH}\) of an aqueous solution of a weak acid, calculate the pH of a \(1.0 \times 10^{-6}-\mathrm{M}\) solution of hypobromous acid \(\left(\mathrm{HBrO}, K_{\mathrm{a}}=2 \times 10^{-9}\right) .\) What is wrong with your answer? Why is it wrong? Without trying to solve the problem, explain what has to be included to solve the problem correctly.

The pH of a \(1.0 \times 10^{-6}-\mathrm{M}\) solution of hypobromous acid (\(\mathrm{HBrO}\), \(K_{\mathrm{a}} = 2 \times 10^{-9}\)) can be calculated using the standard assumption, which gives an approximate pH of 7.85. The problem with this answer is that it suggests the solution is slightly alkaline, which contradicts the fact that hypobromous acid is acidic. The issue lies in the assumption that made it easier to solve for the concentration of H+ ions by ignoring the contribution of water's auto-ionization. To correctly calculate the pH, we need to consider the dissociation of hypobromous acid and auto-ionization of water, and calculate equilibrium concentrations of all species before finding the pH.