Uric acid, \(\mathrm{HC}_{5} \mathrm{H}_{3} \mathrm{O}_{3} \mathrm{~N}_{4}\), can accumulate in the joints. This accumulation causes severe pain and the condition is called gout. \(K_{\mathrm{a}}\) for uric acid is \(5.1 \times 10^{-6} .\) For a \(0.894 M\) solution of uric acid, calculate (a) \(\left[\mathrm{H}^{+}\right]\) (b) \(\left[\mathrm{OH}^{-}\right]\) (c) \(\mathrm{pH}\) (d) \% ionization

The calculation of pH is a critical concept in chemistry, particularly in the field of acid-base reactions. pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It is defined as the negative logarithm of the concentration of hydrogen ions (\text{H}^{+}) in a solution. The formula for calculating pH is quite straightforward:
\(pH = -\text{log}[H^+]\)
Where \([H^+]\)is the concentration of hydrogen ions in moles per liter (Molarity). In the context of uric acid in the given exercise, once the concentration of hydrogen ions is found from the acid ionization constant (\(K_a\)), pH can be determined using this formula. Lower pH values correspond to higher acidity, and higher pH values indicate basicity. The pH scale typically ranges from 0 to 14 for most common solutions, with 7 being neutral (pure water). It's important for students to remember that pH is a dimensionless quantity and is a measure of the activity of the hydrogen ion in the solution.

Percent ionization is a concept that helps us understand the extent to which an acid or base dissociates in a solution. For acids, it represents the fraction of the original acid that has donated \(H^+\)ions to form the conjugate base. The percent ionization is especially significant for weak acids and bases, which do not fully dissociate in solution. The higher the percent ionization, the stronger the acid or base. The formula to calculate percent ionization is given by:
\(% \thinspace Ionization = \frac{[H^+]}{[Acid]_0} \times 100\%\)
Here \([H^+]\)is the concentration of ionized hydrogen ions at equilibrium (calculated from the \(K_a\)expression), and \([Acid]_0\)is the initial concentration of the acid. In the uric acid example, finding the concentration of hydrogen ions allows us to calculate what percentage of the initial uric acid has ionized. This can give insights into the strength of the acid and the reaction's dynamics at equilibrium.

Acid-base equilibrium refers to the state of balance between the forward and reverse reactions in an acid-base ionization process. In the case of a weak acid like uric acid, the acid (\(HA\)) partially dissociates into its conjugate base (\(A^-\)) and hydrogen ions (\(H^+\)) in solution:
\(HA \rightleftharpoons A^- + H^+\)
At equilibrium, the rates of the forward and reverse reactions are equal, and the concentrations of the reactants and products remain constant. The equilibrium constant (\(K_a\) for acids or \(K_b\) for bases) quantifies the position of the equilibrium. This principle is essential for understanding reaction tendencies, calculating concentrations at equilibrium, and making predictions about the pH of a solution. For weak acids, the value of \(K_a\)is a measure of their tendency to donate hydrogen ions to the solution. Small \(K_a\)values indicate a lower degree of ionization and a weaker acid.

The \(K_a\) expression is a mathematical representation of the equilibrium condition for the ionization of an acid in water. It specifically characterizes the strength of an acid in terms of its ability to donate protons (\(H^+\)) to the solution. The expression for the acid ionization constant, \(K_a\), for a generic acid \(HA\) can be presented as:
\(K_a = \frac{[A^-][H^+]}{[HA]}\)
Here, \([HA]\)is the concentration of the undissociated acid, and \([A^-]\)and \([H^+]\)are the concentrations of the conjugate base and hydrogen ions, respectively, at equilibrium. The square brackets denote concentrations in moles per liter (Molarity). A large \(K_a\)value indicates a stronger acid, as it signifies a greater extent of ionization. In the context of the exercise on uric acid, applying the \(K_a\)expression allows students to calculate the unknown concentrations at equilibrium, further leading to pH calculations and determination of other related values such as percent ionization.