[Sidge85]

Hello, first time poster, apologies if I'm posting in the incorrect forum.

I would like to get some assistance with the calculation of a Citrate buffer. I have done all the calculations myself however I'm not sure if I have done them correctly. I work in a biology based job however I need to make buffers from time to time. I know that there are pH calculators out there, however I wanted to get some practice in actually working out the ratios myself. If someone good essentially mark my work that would be great. I've set myself the goal of preparing a 50mM Citrate buffer at pH 4.0

Ok so I started on wikipedia and found that Citric acid has 3 pKa values 3.09, 4.75 amd 5.41. I am familiar with the henderson-hasselbalch eqn. I have seen somewhere that using this equation you should hope to get a a [base]/[acid] ratio as close to 1 as possible. After plugging in the three different pKa values I got ratios of 8.128, 0.178 and 0.039. Using the idea that I want to be as close to 1 as possible I went with the pKa of 4.75 ([base]/[acid] ratio of 0.178). This idea makes sense as the pKa value is the one closest to the pH I want to achieve

Since I'm using pKa2, I assume that would mean that I would be using Monosodium hydrogen citrate as the acid and disodium hydrogen citrate as the conjugate base.

Since the [acid] + [base] must = 0.05 (50mM buffer) and be in the ration of 0.178base:acid I worked through that [acid] should be 0.042M and [base] should be [0.008]

From that point of I used the monosodium hydrogen citrate MW as 214.11g/mol and the disodium hydrogen citrate MW as 236.09g/mol to get

monosodium hydrogen citrate required a 8.99g/L
and disodium hydrogen citrate required at 1.89g/L

Is this correct? If I have gone wrong somewhere I'd really appreciate being put on the right track.

Thanks in advance

[Borek]

I have not checked the number, just skimmed over what you wrote. Your approach - finding ratio and themn solving system of two equations - is in general correct. However, it may not work for citrate.

Citric buffers are quite difficult to calculate. Problem is, all three pKa values are very close, so you can't ignore two others and select the one you like. As a rule of thumb you may remember that if the distance between pKa value you use and the other pKa value is below 2 (even safer 3) you can't assume the other dissociation step doesn't interfere with your calculations.

See discussion od Henderson-Hasselbalch equation for some more details.

Note: even some of the buffer calculators available on the web will be not able to deal correctly with citric acid. My Buffer Maker takes all pKa values into account, so it gives reasonably good answers.

[AWK]

Note, in the intermediate results round all numbers to at least 3-4 significant digits. In your case 0.008/0.042 is 0.190 and not 0.178 and just this rounded numbers you used for mass calculation of reagents. Assumming that 0.042 is exact, The calculated mass of disodium hydrogen citrate has  an error greater than 0.1 g.

[Sidge85]

Thank you for your replies. They both contain handy tips.

Borek, thank you for the link, it is very interesting.