Final answer:
To calculate the pH of a 0.320 mol L-1 pyridine solution, use the pKb value to find the pKa of the conjugate acid, then determine [OH-] through the base ionization equilibrium, calculate pOH, and then use pH + pOH = 14 to find the pH.
Step-by-step explanation:
To determine the pH of a 0.320 mol L-1 solution of pyridine, we must consider the base ionization in water. Pyridine (C₅H₅N) reacts with water to form pyridinium ion (C₅H₅NH⁺) and hydroxide ion (OH⁻). The given pKb of pyridine is 8.75, from which we can calculate the pKa of the conjugate acid (pyridinium ion) using the formula pKa + pKb = pKw, where pKw is the ion product constant of water, which is 14.00 at 25°C.
Using the provided pKb value, we find:
pKa = pKw - pKb = 14.00 - 8.75 = 5.25
Since we are dealing with a weak base, the Henderson-Hasselbalch equation can be used for estimating the pH. However, in a solution of pyridine, we do not have initial concentrations of the pyridinium ion. Therefore, to find the pH, we need to calculate the concentration of hydroxide ions produced by the ionization of pyridine in water. Using the formula pOH = pKb + log([base]/[OH⁻]), we can calculate pOH and then pH using the relationship pH + pOH = 14.
Typically, in the absence of added pyridinium ion, the ionization of pyridine will be minimal due to its weak base nature. This implies that the initial concentration of pyridine will be approximately equal to the equilibrium concentration of the base, and the concentration of hydroxide ions will be low. The concentration of hydroxide ions can be determined using the Kb expression for the base ionization equilibrium.
Once [OH⁻] is found, calculate the pOH:
pOH = -log [OH⁻]
And finally, calculate the pH:
pH = 14 - pOH