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 NH
3 , NH
4+Cl
- at equal (starting) concentrations : clearly this is a buffer, having it's buffer point at pH = pKa(NH
4+) = 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. Ca
2+ , Mg
2+ 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 )