A 250.0-mL buffer solution is 0.250 M in acetic acid and 0.250 M in sodium acetate. a. What is the initial pH of this solution? b. What is the pH after the addition of 0.0050 mol of HCl? c. What is the pH after the addition of 0.0050 mol of NaOH?

Verified step by step guidance

1. <insert step 1> Identify the components of the buffer solution: acetic acid (CH₃COOH) and sodium acetate (CH₃COONa). Note that acetic acid is a weak acid and sodium acetate is its conjugate base.
2. <insert step 2> Use the Henderson-Hasselbalch equation to find the initial pH of the buffer solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant of acetic acid, \( [\text{A}^-] \) is the concentration of acetate ion, and \( [\text{HA}] \) is the concentration of acetic acid.
3. <insert step 3> For part b, calculate the change in moles of acetic acid and acetate ion after adding 0.0050 mol of HCl. HCl will react with the acetate ion to form more acetic acid: \( \text{CH}_3\text{COO}^- + \text{HCl} \rightarrow \text{CH}_3\text{COOH} + \text{Cl}^- \).
4. <insert step 4> Use the Henderson-Hasselbalch equation again to find the new pH after the addition of HCl, using the updated concentrations of acetic acid and acetate ion.
5. <insert step 5> For part c, calculate the change in moles of acetic acid and acetate ion after adding 0.0050 mol of NaOH. NaOH will react with acetic acid to form more acetate ion: \( \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O} + \text{Na}^+ \). Use the Henderson-Hasselbalch equation to find the new pH after the addition of NaOH.