Question

You are preparing a buffer consisting of acetic acid and sodium acetate with a total of acetic acid and sodium acetate concentration of 250 mM and a PH of 5.0. What concentration of acetic acid and sodium acetate should you use?

Answer 1

From Henderson Hasselbalch equation

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

Given that pH = 5.0

pKa = 4.76

concentration of buffer solution = 250 mM = 0.25 M

For acetate-acetic acid buffer,

pH = pKa + log [acetate]/[acetic acid]

4.5 = 4.76 + log [acetate]/[acetic acid]

log [acetate]/[acetic acid] = 5.0-4.76

log [acetate]/[acetic acid] = 0.24

[acetate]/[acetic acid] = 10^0.24

[acetate]/[acetic acid] = 1.74

[acetate] = [acetic acid] x 1.74 -- Eq (1)

From given data, concentration of buffer solution = 0.25 M

i.e [acetate]+ [acetic acid] = 0.25 M ----Eq (2)

From Eq (1), [acetate] = [acetic acid] x 1.74

Substitute this acetate value in Eq (2)

Then Eq (2) becomes, [acetic acid] x 1.74 + [acetic acid] = 0.25 M

[acetic acid] { 1.74+1 } = 0.25 M

[acetic acid] { 2.84} = 0.25 M

[acetic acid] = 0.25 M / 2.84

= 0.088 M

[acetic acid] = 0.088 M

[acetate]+ [acetic acid] = 0.25 M ----Eq (2)

then, [acetate]+ 0.088 M = 0.20 M

  [acetate] = 0.25 M - 0.088 M

= 0.162 M

[acetate] =  0.162 M

Therefore, [acetic acid] = 0.088 M

[Sodium acetate] =  0.162 M