[Strike]

Hello (wasn't 100% sure which forum buffer solutions belong in so I chose Analytical..),

I'm trying to prepare a 1L buffer of 0.2M and pH = 2.5. The pKa values given for the three COOH groups of citric acid are 3, 5 and 6.5.

The question is how many moles of HCl should be mixed with trisodium citrate to prepare the buffer?

I tried using pH - pKa = log [A-]/[HA]

2.5 - 3 = log [COO-]/[COOH] (where COO- is the deprotonated citrate and COOH is the pronated citric acid)

10^-.5 = log [COO-]/[COOH]

0.316 = [COO-]/[COOH]

0.316[COOH] = [COO-]

and now I'm stuck..

I wasn't even sure if I should be using the H-H equation.

[Pradeep]

Take the concentration as 0.2 M. Then use mass balance equations to balance protons.


Total [H+] = 3 [COOH] + 2 [COO-]

Can you do the rest ?

[Borek]

You start with Citrate^3-. You have to protonate it all the way to H₂Citrate^- and partially to H₃Citrate. This is simple stoichiometry - and you are right about using HH equation to calculate [H₂Citrate^-]/[H₃Citrate] ratio. Just remember [H₂Citrate^-]+[H₃Citrate] = 0.2M.

Check Buffer Maker - buffer calculator, it was designed to help in this type of calculations with much higher accuracy you can obtain with just pen & paper.

[Strike]

I think I calculated the solution having 0.1519M of the H3Citrate and 0.048M H2Citrate- but I'm still not sure how many moles of HCl I need to protonate it.

[Pradeep]

Since your solution doesn't have protons, you have to add them externally, to convert Citrate 3- to H3Cit and H2Cit-.


3 * 0.1519 + 2 * 0.48 = Is the number of protons should be added.

So the amount of HCl should added can be calculated.

[Strike]

Ah, that makes complete sense, thank you very much Pradeep and Borek.

I also tried your buffer calculator, Borek. It came up with about 7.72g of HCl to use which comes out to ~0.211 moles but my calculations gave me 0.5511 moles.

[AWK]

I think I calculated the solution having 0.1519M of the H3Citrate and 0.048M H2Citrate- but I'm still not sure how many moles of HCl I need to protonate it.

If these above data are correct do simple stoichiometric calculations (these can be done know even without calculator and result is correct). Firstly write down a stepwise reaction of citrate with HCl.

[Borek]

I also tried your buffer calculator, Borek. It came up with about 7.72g of HCl to use which comes out to ~0.211 moles but my calculations gave me 0.5511 moles.

Not knowing how you did it I can't comment - the most obvious approach to use Buffer Maker gives the answer in terms of volume of 1M solution, not in terms of the mass of HCl. Also please note that by default Buffer Maker calculates result using different pKa values (widely accepted 3.128, 4.761, 6.396), so the result can't be identical. These values can be easily changed. Attached image contains results of the calculations done for these values. It shows you need 0.5548 moles of HCl - both 0.5548 and 0.5519 yield the same final pH of 2.50.

3 * 0.1519 + 2 * 0.48 = Is the number of protons should be added.

While this is correct (although see the next paragraph), I find it rather confusing. The way I see it it is much simpler to follow obvious stoichiometry of the reactions involved. First you need to completely protonate Citrate^3- to H₂Citrate^- - which means 2*0.2 mole of H⁺, and then protonate 0.1519 mole of the H₂Citrate^- to H₃Citrate. That yields the same 0.5519 moles of H⁺, but it is much more obvious why you need 2*0.2 than why you need 2*0.1519+2*0.048 to get to H₂Citrate^- stage.

Please note there is a typo in what you wrote, which makes the result completely off. Should be 2*0.048.

[Pradeep]

Since stoichiometric calculation method was too time consuming I am used to use mass balance. I thought you are an analytical chemist and you have the potential to understand the calculation. Can't you Strike?

Buffer calculators are electronic programs developed by people like you and me. If you are interesting, having the programming ability and having the necessary knowledge in chemistry, you can make a buffer calculator your self. It is a very basic computational chemistry program.

 

[Borek]

You are missing the point. We are read by students who are learning how to do this stuff. The less confusing the approach, the better the chance they will understand what they are doing.

You have never defined what you mean by [COOH] and [COO^-], which doesn't help (and no, it is not obvious what you mean, [COOH] can be both concentration of COOH from the last protonation step and total concentration of all protonated groups). Also, you have never explained where you got 3 and 2 from - it doesn't help either. Stoichiometric approach means it is enough to follow protonation reactions stoichiometry, it doesn't require use of cryptic symbols and coefficients.

[Pradeep]

Strike asked the question. He has used the terms HA, HA-, COOH and COO-. So I used same terms to answer him.

I am not a teacher. I am an analytical chemist. I was focusing only to help to solve his problem. I thought spending my time to help these will be good for them.  I apologize  about my poor practice.

[Borek]

I was focusing only to help to solve his problem. I thought spending my time to help these will be good for them.

That's what we all try to do. Just remember in most cases you are helping students, not your peers.