[TheExibo]

1. The problem statement, all variables and given/known data

Using sodium citrate and citric acid, create a buffer solution that will withstand an addition of 20ml of 0.1mol/L HCl or NaOH solution without a significant increase in pH (+/-2). Bonus marks for using the smallest amount of buffer solution.

2. Relevant equations

Reaction: H3C6H5O7 ↔ 3H+ + C6H5O7

ka of Acetic Acid = 7.4x10^(-4)

pka of Acetic Acid = 3.13

ph = pka + log[A-/HA]

3. The attempt at a solution

I'm not sure where to begin. The Henderson-Hasselbalch equation above might be needed, but our teacher never showed us it, so most likely we have to create this solution without it. My understanding is that a solution needs to be created with the same concentration of hydronium ions from the citric acid as with the concentration of citrate, the conjugate base.

Also, citric acid apparently is triprotic, losing 3 hydrogens in water. However, it is a weak acid, meaning it does not ionize completely. What is my first step in solving this overall question?

[TheExibo]

Update:

I used the H-H equation after receiving info that the pka and pH in buffer solutions must be equal. Making the two equal, I calculated that the concentration of acid divided by the concentration of its conjugate base must equal 1. How can I do this step in the lab? How do I make the ratio equal to 1?

[Borek]

To be honest, this looks like an insanely difficult problem for students that were not even shown HH equation. Especially if you are asked to use triprotic weak acid.

I am baffled, I have no idea how to help you, especially when the question is so incomplete. What does it mean "amount of the buffer" - volume of the solution? Number of moles of the substances used to prepare the buffer?

Citric acid has three relatively close dissociation steps. In general I would aim for a pH=pKa2 buffer, as the buffering effects of the pKa1 and pKa3 woudl help keeping the pH at bay after the strong acid/base was added, but if you are told to use citric acid and monosodium citrate (or is it something else?) you may be forced to use pH=pKa1.

I used the H-H equation after receiving info that the pka and pH in buffer solutions must be equal.

Yes, that will guarantee the maximum buffer capacity.

Making the two equal, I calculated that the concentration of acid divided by the concentration of its conjugate base must equal 1. How can I do this step in the lab? How do I make the ratio equal to 1?

You have to assume concentration of one of them to be something and calculate how much of the other to add.

For what it is worth - while I know how to approach this problem to get an "exact" solution, it would require solving a set of fifth degree polynomials. Not something you want to try at home. The best approach I can think of is to download the Buffer Maker (there is a 30 days free trial), learn how to use it, and play with numbers to see what can be done.