# Thermodynamics vs apparent ka

CSA

## Homework Statement

I am preparing a phosphate and a bicarbonate buffer at pH 7.4. I am not using the tradition of making a "rough" buffer and then adjusting the pH to the desired value as I want to target a certain value of osmolarity in both buffers. As such I just want to do all calculations beforehand to determine the exact amounts of the compounds I would need in the solution. I think I should be able to do that, except I want to accurately determine that ratio of the acid and conjugate base, accounting for the effect of temperature on pka. But the only values for the pka I could find were the generally quoted values which I believe are at 20 Celsius. Is this known as the thermodynamic pka? How do I account for the effect of temperature on the pka into my calculations? Or is not required to do so? And what is the difference between thermodynamic ka and apparent ka anyways? Greatly appreciate any help!

## Homework Equations

bicarbonate buffer: H2CO3 <--> HCO3- + H+
Phosphate buffer: H2P04- <--> HPO42- + H+
Pka = ([H+][A-])/([HA])

## The Attempt at a Solution

I found a buffer calculator (http://www.biomol.net/en/tools/buffercalculator.htm) that allows you to input the temperature. When the recipe is produced, it also gives an apparent pka value. So is safe to simply use this apparent value in my calculations? Or are there any other considerations i must make such as ionic strength? But I don't fully understand what ionic strength is and how it affects the buffer.

Mentor
I am afraid you won't be able to deal with calculations without understanding at least the very rudimentary concepts of the Debye-Huckel theory (at least at the level outlined here).

At the moment temperature is probably the least of your worries, as it is ionic strength of the solution changing the Ka value that is the main problem you will be facing initially.

As far as I can tell "apparent pKa" typically refers to the value adjusted for the ionic strength, changes with the temperature are much lower. Ka values listed in tables are valid only for infinitely diluted solutions.

You can try another buffer calculator, which does make corrections for both temperature and ionic strength. Note, that these theoretical values are almost always a bit off, theories we use are quite good for diluted solutions, but for concentrations higher that 0.1 M they start to fail. There are theories using experimental coefficients that work for higher concentrations, but typically you will find required correction coefficients were not determined yet.

CSA
CSA
Alright, thanks for the help.

Homework Helper
Gold Member
Harder to advise when we don't completely know what do you are trying to do and achieve. For example is it trying to observe the specific effects of bicarbonate or phosphate on some system and to be sure effects are not just something secondary to do with ionic strength or osmolarity?

Would it be possible to while doing the best you can with these calculations, to smother the uncertainties by making the main ionic strength or osmolarities due to something else like NaCl or Na2SO4 ?

Since you think these things are significant then when you report your results you should state the actual composition of your solutions and any pH measurements you made (stating the conditions and any standardisations) in case anyone should want to repeat or interpret your experiments, otherwise anyone reading it will be no wiser than we are now.