Final answer:
To determine the pH when ethylamine is mixed with its conjugate acid, we calculate the pKa from the given Kb and use the Henderson-Hasselbalch equation with the molarities of the base and conjugate acid after mixing.
Step-by-step explanation:
To calculate the pH of the resulting solution when 165.0 mL of 0.12 M C₂H₅NH₂ is mixed with 280.0 mL of 0.21 M C₂H₅NH₃Cl, we must first understand that C₂H₅NH2 (ethylamine) is a weak base and C₂H₅NH₃Cl is its conjugate acid. The reaction between the weak base and its conjugate acid will form a buffer system. To calculate the pH of a buffer system, you would typically use the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base and [HA] is the concentration of the acid.
To find pKa, we use the given Kb of C₂H₅NH₂, which is 5.6×10⁻⁴. The relationship between Kb and Ka is given by Kw = Ka × Kb, where Kw is the ion-product constant for water at 25°C (1.0×10⁻ⁱ⁴). Thus, Ka = Kw/Kb, and pKa = -log(Ka).
Once we have pKa, we can find the molarities of the base (C₂H₅NH₂) and its conjugate acid (C₂H₅NH³⁺) after mixing, by using the initial concentrations and volumes. Then, we can use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution.