pH solving for buffer

Question

Calculate the pH of a buffer solution made by combining 20.00 mL of 1.0 M NaOH with

2.00 mL of 17.5 M acetic acid (HC2H3O2, pKa = 4.74) and then enough DI water to obtain a final volume of 200.0 mL.

Answer 1

Since acetic acid is a weak acid, when you add a strong base such as NaOH, you will form a buffer consisting of acetic acid and sodium acetate:

HC₂H₃O₂ + OH^- ==> C₂H₃O₂^- + H2O (Na⁺ is a spectator)

To find the pH of a buffer we can use the Henderson Hasselbalch equation; pH = pKa + log [salt]/[acid]

To use this, we must first find [salt] and [acid]. This can be done with an ICE table:

2.00 ml x 1 L/1000 ml x 17.5 mol/L = 0.035 moles acetic acid

20.00 ml x 1 L/1000 ml x 1.0 mol/L = 0.02 moles NaOH

HC₂H₃O₂ + OH^- ==> C₂H₃O₂^- + H2O

0.035............0.02.............0..............Initial

-0.02...........-0.02............+0.02.......Change

0.015..............0...............0.02..........Equilibrium

pH = pKa + log [salt]/[acid]

pH = 4.74 + log (0.02/0.015)

pH = 474 + log 1.33

pH = 4.74 + 0.12

pH = 4.86