A buffer contains 0.30 mol of propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)\( and \)0.25 \mathrm{~mol}$ of potassium propionate \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOK}\right)\) in 1.80 L. (a) What is the pH of this buffer? (b) What is the pH of the buffer after the addition of \(0.10 \mathrm{~mol}\) of \(\mathrm{NaOH}\) ? \((\mathbf{c})\) What is the \(\mathrm{pH}\) of the buffer after the addition of \(0.10 \mathrm{~mol}\) of \(\mathrm{HCl}\) ?

(In this exercise, the propionic acid (C₂H₅COOH) and potassium propionate (C₂H₅COOK) are the conjugate acid-base pair. We need to find the Ka expression, knowing that the dissociation of propionic acid (HA) is written as: HA ⇌ H⁺ + A⁻ The Ka expression is: Ka = [H⁺][A⁻]/[HA])

(Given the moles and volume of the buffer, we can find the initial concentrations: Initial concentration of C₂H₅COOH: 0.30 mol / 1.80 L = 0.167 M Initial concentration of C₂H₅COOK: 0.25 mol / 1.80 L = 0.139 M)

(Now we can use the Henderson-Hasselbalch equation to find the pH of the initial buffer: pH = pKa + log([A⁻]/[HA]) First, we will need the pKa value, which can be found in a textbook or online source. For propionic acid, the pKa value is 4.88. Substitute the molarities into the equation: pH = 4.88 + log(0.139/0.167) pH ≈ 4.68)

(When we add 0.10 mol of NaOH to the buffer solution, it will react with the propionic acid according to: C₂H₅COOH + OH⁻ → C₂H₅COO⁻ + H₂O Calculate the new moles of propionic acid and potassium propionate after the reaction: Moles of propionic acid = 0.30 mol - 0.10 mol = 0.20 mol Moles of potassium propionate = 0.25 mol + 0.10 mol = 0.35 mol Now, find the new concentrations of each component in the buffer: New concentration of C₂H₅COOH: 0.20 mol / 1.80 L = 0.111 M New concentration of C₂H₅COOK: 0.35 mol / 1.80 L = 0.194 M Find the new pH using the Henderson-Hasselbalch equation: pH = 4.88 + log(0.194/0.111) pH ≈ 5.23)

(When we add 0.10 mol of HCl to the buffer solution, it will react with the potassium propionate: C₂H₅COO⁻+ H⁺ → C₂H₅COOH Calculate the new moles of propionic acid and potassium propionate after the reaction: Moles of propionic acid = 0.30 mol + 0.10 mol = 0.40 mol Moles of potassium propionate = 0.25 mol - 0.10 mol = 0.15 mol Now, find the new concentrations of each component: New concentration of C₂H₅COOH: 0.40 mol / 1.80 L = 0.222 M New concentration of C₂H₅COOK: 0.15 mol / 1.80 L = 0.083 M Find the new pH using the Henderson-Hasselbalch equation: pH = 4.88 + log(0.083/0.222) pH ≈ 4.34) As a summary: a) The initial pH of the buffer is approximately 4.68 b) The pH of the buffer after the addition of NaOH is approximately 5.23 c) The pH of the buffer after the addition of HCl is approximately 4.34