A buffer solution contains 0.0200 M acetic acid and 0.0200 M sodium acetate. What is the pH after 2.0 mmol of NaOH are added to 1.00 L of this buffer? pKa = 4.75 for acetic acid.

The correct answer is 4.84

Explanation:

We use the Henderson Hasselbach's equation to calculate the pH of a buffer solution:

pH = pKa = log ( [conjugate base]/[weak acid])

In this case:

conjugate base: acetate ⇒ [conjugate base] =  [acetate] = 0.0200 M

weak acid: acetic acid ⇒ [weak acid] =  [acetic acid] = 0,0200 M

pH = pKa + log ([acetate]/[acetic acid])= pKa + log (0.0200 M/0.0200 M)

When a strong base- such as NaOH- is added, the acid reacts with OH⁻ to form the conjugate base. So, the conjugate base is increased while the acid is decreased. Thus, in 1 liter of solution we have:

acetate = (0,0200 mol/L x 1 L) + (2.0 mmol x 1 mol/1000 mmol) = 0.022 mol

acetic acid= (0,0200 mol/L x 1 L) - (2.0 mmol x 1 mol/1000 mmol) = 0.018 mol

Finally, we calculate the pH:

pH = 4.75 + log (0.022 mol /0.018 mol )= 4.84