[GoGoGadget]

I'm working on a prelab for my Biochem lab course and one question I had was:

If Hepes is given in basic form and if you need to make a buffer of pH 8, will you have to add HCl or NaOH? Why?

I stated that because Hepes has a pKa of 7.55, that you would need to add NaOH in order to raise the pH level to 8 so that H ions will dissociate from the acidic form of Hepes and form more of the conjugate base form of Hepes.

Is this the correct way to think about this question? Thanks for reading!

[trinitrotoluene]

I think the question is stating that you are given deprotonated hepes. Something like Hepes-Na. I would use the Henderson-Hasselbalch equation to find the pH of the solution if you just dumped it in, then adjust the pH with acid or base accordingly. The pKa is the pH at which the acid and base exist in equal amounts, but if you just dump a bunch of Na-Hepes into water, the pH might not be at the pKa value.

[Borek]

you would need to add NaOH in order to raise the pH level to 8 so that H ions will dissociate from the acidic form of Hepes and form more of the conjugate base form of Hepes

As tnt already suggested, you are given solution that contains conjugate base only, so adding NaOH won't change amount of the base.

[GoGoGadget]

Thank you both for your input, I do appreciate it.

I ended up emailing one of the TAs for the course and was told to use this equation, which makes sense as the problem states that hepes is given in a basic form.

pH = (pKa + log[base]/2

Because the pKa of hepes is 7.55, and if I were to use a concentration of 0.1 M I would end up a pH of 7.05 in using this equation. I know that it was mentioned that adding NaOH wouldn't change the pH by much but I'm not sure I understand then how HCl would raise the pH since it would become more acidic and thus lower the pH in the end?

[GoGoGadget]

Although I went back to take a look at the equations listed again in my lab manual, I saw that the actual equation for weak bases is pH = pKa + 14 + log[base]/2. If this is what I actually need to use then, I end up with a pH of 10.3 so in this case, adding HCl to reach a pH of 8 would make sense. The pH of 10.3 would then make sense too as it reflects hepes in a basic form.

[magician4]

welcome to the land of confusion: this, in my opinion, is an example of  "teaching pH-calculation in biochemistry at its worst"

HEPES is a molecule constructed from a piperazine system and an ethylsulfonic acid part when it comes to pH-relevant substructures
Hence, there should be (and in fact are) 2 pKb's and one pKa  : approx pKb(I) 4 , pKb(II) 6.5 and pKa ~ - 3  (estimated from the respective stem substances)

as in this form, in a waterbased solution the strongest acid and the strongest base would (next to) cancel each other out, we'd have the anion ethyl-SO₃^- (which is irrelevant to pH) and the protonated form of the first aminoelement of the piperazine system (with the respective pKa value of the conjugated form: pKa (R₂NH₂⁺)= 14 - 4 = 10 )
...and , of course, the "untouched" second amino group - where the pKa of the conjugated form (!) would be 14-6.5 = 7.5

  so, THIS value most probably is given to you

as in this situation,  pKa of the protonated amine >> pKb of the non-protonated amine, the pH-bahaviour of HEPES would , in good approximation, be ruled by this very second (!) unprotonated amine (of which the pKa of its conjugated species is given to you)

... and this information is completely USELESS if we'd start with the "basic form" of HEPES, i.e. something like the sodium salt thereof, as in this moment, the pKb of the still untouched first aminogroup (of which i did estimate pKb ~ 4 , but which is NOT given to you) would rule the game

  the information given in this problem is incomplete, confusing and contradicting, as it is suggested that the basic form of HEPES should be considered to be a monoprotic acid of pKa 7.55 - when it is anything but

... and the hint of your TA person that allegedly pH = 0.5 (pKa + log[base]) really is that wrong and ignorant, it makes me want to cry


regards

Ingo

[GoGoGadget]

Thanks so much for your input, magician4. In reading more about HEPES, I saw that it is a buffer that exists as a Zwitterion, where I read that internal transfers of protons can take place within the solution. I can definitely see now that my professor provided this as a pre-lab question I suppose to get students to think more in depth about it. Is it possible to think whether if either HCl or NaOH would make much of a difference in raising the overall pH level if different substructures will contain different pH levels?

[magician4]

having said all the above - which remains true - I would like to tell you why this problem still is worthy consideration, and what is meant , and why this type of substances is nicknamed "good buffers"

imagine you had NH₃ , NH₄⁺Cl^- at equal (starting) concentrations : clearly this is a buffer, having it's buffer point at pH = pKa(NH₄⁺) = 9.25

at "the buffering moment" you hence have 2 eq. of ammonia present: one which is protonated, and the other that is not, and all that  per one eq. of chloride
... i.e. 1 eq. anion of a strong acid , one eq. protonated form of a weak base, one eq. of the non-protonated form of named base = "buffer"

now, imagine that you'd replace the "non-protonated form" of the weak base with another substance (of not identical, but quite near pKa ) : what would the outcome , the behaviour of such a system be?
well , the closer the pKb- values, the more it would seem like you in fact still had a homogeneous buffer, maybe "a bit off" in buffer point, but in general: still a buffer

  you could regard such an alternative composition as "in good approximation a buffer, too, denoted by named "a bit off" buffer point "

this system would in , for example , a titration look pretty much like those curves you're familiar with from "normal buffers"
...and in fact that's exactly what normal (!) HEPES does, being composed of*⁾ the anion of a strong acid (the ethyl sulfonic acid anion part) , the protonated form of the one amino group , and the nonprotonated form of the other at a 1:1 starting ratio, , with the two of them being close enough in pKb ) , and that's what the resulting pH-curve would look like:

(HEPES titration , from :  link)

  you don't make a relevant mistake if you treat HEPES as "a buffer at optimum buffer composition" with a virtual(!!!)  pKa of the virtual conjugated (i.e.protonated) form of a virtual weak base belonging to ( that's what the pKa = 7.55 mentioned in fact IS : a virtual, but nontheless of practical relevance, value)

so, in HEPES all components for a buffer are chemically united in one molecule right from the start - which is a good idea: no handling of strong acids and badly smelling bases , no scaling and measuring ... just add it, and have the desired result instantaneously.
besides, having a virtual pKb of 7.55 = for real pH , i.e. next to neutral, next to always is a desired situation in biochemistry.
... and having a molecule that doesn't form complexes with the usual suspects (i.e. Ca²⁺ , Mg²⁺ and so on) is a nice benefit, too

and hence, those substances that unite all these properties, in biochemistry are named "Good buffers"

In reading more about HEPES, I saw that it is a buffer that exists as a Zwitterion,(...)

well, that's true, but is not the point with HEPES : you have to bring the parts "united with the non- protonated form of a similar, weak base" and " at equimolar ratios" into the picture, too, to understand the real value of this system


with respect to your original problem: you could ask if a respective calculation of the pH of an anionic solution of , for example , a 0.1 M [HEPES]^- Na⁺ would be possible using the virtual pKa reported.
such a system would have as pH relevant concentrations 0.2 M of this "virtual" base ( pls. try to figure out why I doubled the conc. !) , and it follows that
pH = 14 - 0.5*( pKb - log 0.2 ) = 7 + 0.5*( pKa + log 0.2 )
(again, pls. figure out how this equation came about)
compare this to the experimental data (here: given by, for example, Sigma Aldrich ) and decide for yourself if the approximation would be a good one

... and the rest of the original problem you should be able to figure out all by yourself by now, I take it


regards

Ingo





*⁾
to clarify which of the two nitrogens of the piperazine system becomes protonated first, i.e. has the "stronger" pKb:

(from : link )