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The concept of pH is a measure of the acidity or basicity of a solution. In this case, the solution contains pyridine, a weak base. The pH of a solution is defined as the negative logarithm of the hydrogen ion concentration ([H^+]), which can be expressed as: \[ \text{pH} = -\log_{10}([H^+]) \].For basic solutions, we often work with pOH instead, where \[ \text{pOH} = -\log_{10}([OH^-]) \]. Knowing that \[ \text{pH} + \text{pOH} = 14 \], we can calculate pOH if we have the pH. In this exercise, with \text{pH} = 8.5, the pOH is calculated as \text{pOH} = 14 - 8.5 = 5.5.This pOH value helps us find the hydroxide ion concentration using the expression:\[ [\text{OH}^-] = 10^{-\text{pOH}} = 10^{-5.5} \approx 3.16 \times 10^{-6} \text{ M} \].Understanding how to convert between pH, pOH, and [OH^-] concentration is crucial when analyzing weak base equilibria in chemistry.

A weak base, like pyridine, does not completely ionize in water. Instead, it establishes an equilibrium between its non-ionized and ionized forms. The chemical reaction for pyridine when it reacts with water is:\[ \text{C}_5\text{H}_5\text{N} + \text{H}_2\text{O} \rightleftharpoons \text{C}_5\text{H}_5\text{NH}^+ + \text{OH}^- \].For weak bases, the equilibrium lies more on the side of the unreacted base. Unlike strong bases, weak bases have a smaller equilibrium constant (K_b), indicating less dissociation.In this problem, the weak base pyridine also has a conjugate acid. The equilibrium position can be altered if enough of the conjugate acid, \text{C}_5\text{H}_5\text{NH}^+, is present.The extent of ionization and the concentration of key species in a weak base solution depend heavily on the base dissociation constant K_b. This constant is determined using the expression:\[ K_b = \frac{[\text{C}_5\text{H}_5\text{NH}^+][\text{OH}^-]}{[\text{C}_5\text{H}_5\text{N}]} \].

The equilibrium expression is a fundamental aspect of analyzing chemical equilibria, and it helps quantify the concentrations of reactants and products in a solution at equilibrium. For pyridine, the equilibrium involves:\[ \text{C}_5\text{H}_5\text{N} + \text{H}_2\text{O} \rightleftharpoons \text{C}_5\text{H}_5\text{NH}^+ + \text{OH}^- \].To quantify this reaction, we rely on the base dissociation constant K_b which is derived from the ratio of the concentrations of products to reactants:\[ K_b = \frac{[\text{C}_5\text{H}_5\text{NH}^+][\text{OH}^-]}{[\text{C}_5\text{H}_5\text{N}]} \].In our example, where pyridine has a small K_b (calculated from its related K_a of the conjugate acid), we assume that the product concentrations are equal. This leads us to:\[ K_b = \frac{(3.16 \times 10^{-6})\times (3.16 \times 10^{-6})}{[\text{C}_5\text{H}_5\text{N}]} \approx 1.59 \times 10^{-9} \].Rearranging this expression allows us to solve for the concentration of unreacted pyridine, showing the power of equilibrium expressions in understanding chemical systems.