Question

Suppose you have 1.00 L of an aqueous buffer containing 60.0 mmol acetic acid (pKa = 4.76) and 40.0 mmol acetate. The pH of this buffer is 4.58. What volume of 4.00 M NaOH would be required to increase the pH to 4.93?

Answer 1

A buffer is any type of substance that will resist pH change when H+ or OH- is added.

This is typically achieved with equilibrium equations. Both type of buffer will resist both type of additions.

When a weak acid and its conjugate base are added, they will form a buffer

The equations:

The Weak acid equilibrium:

HA(aq) <-> H+(aq) + A-(aq)

Weak acid = HA(aq)

Conjugate base = A-(aq)

Neutralization of H+ ions:

A-(aq) + H+(aq) <-> HA(aq); in this case, HA is formed, H+ is neutralized as well as A-, the conjugate

Neutralization of OH- ions:

HA(aq) + OH-(aq) <-> H2O(l) + A-(aq) ; in this case; A- is formed, OH- is neutralized as well as HA.

Now,

initially

pH = pKa + log(A / HA)

4.58 = 4.76 + log(40 / 60 )

which makes sene

in order to increase pH:

mmol of base added = MV = 4*V, V is in mL

mmol of acetic acid decreases, since it gets neutralized by base = 60 - 4*V

mmol of Acetate will increase, due to neutralization = 40 + 4*V

substitute

4.93 = 4.76 + log(40 + 4*V/ 60 - 4*V )

10^(4.93 -4.76) = (40 + 4*V/ 60 - 4*V )

1.47910(60-4V) = 50 + 4V

1.47910*60 - 4*1.47910*V = 50 + 4*V

(4+4*1.47910)*V = 1.47910*60-50

V = 38.746/(4+4*1.47910)

V = 3.9072 mL of NaOH required