Buffer system- addition of base

Question

create 25.0 mL of a 0.50M citrate buffer at a pH of 3.2, using Dihydrogen citrate (Ka=1.8x10^-5). For the buffer to work for the purpose needed it must be able to withstand the addition of 1.0 mL of 2.0 M HCl and not change the pH by more than 0.3 units.

Answer 1

Not entirely sure of how the question is being posed, but based on the title, it is assumed we are to use base and dihydrogen citrate to prepare the buffer. That being the case, we would have

H₂Cit^- + OH- ==> HCit^-2 + H2O

Using the Henderson Hasselbalch equation where H₂Cit^- is the acid and HCit^2- is the conjugate base...

pH = pKa + log [conj.base]/[acid]

3.2 = 4.74 + log [conj.base]/[acid]

log [conj.base]/[acid] = -1.54

[conj.base]/[acid] = 0.0285

[H₂Cit^-] + [HCit^2-] = 0.50 M

[HCit^2-] / [H₂Cit^-] = 0.0285 ---> HCit^2- = 0.0285 H₂Cit^-

[H₂Cit^-] + 0.0285 ]H₂Cit^-] = 0.50

[H₂Cit^-] = 0.486 M

[HCit^2-] = 0.014 M

0.486 mol / L x 0.025 L = 0.01215 mols H₂Cit^-

0.014 mo / L x 0,025 L = 0.00035 mols HCit^2-

Place 0.0125 mols H₂Cit^- in 20 mls ddH₂O

Add 0.00035 mols NaOH (use concentrated NaOH so volume is minimal)

Bring volume to 25.0 mls

Result should be 25 mls of solution containing 0.01215 mols H₂Cit^- + 0.00035 mols HCit^2- @ pH 3.2

Unfortunately, this buffer would not handle the addition of 1.0 ml of 2.0 M (0.002 moles) of HCl and still keep the pH within 0.3 units of the original pH.