Question 8.11: Buffer pH Calculation What is the pH of a solution if you mi...

First we must find the p K_{ a }, which we see from Table 8.5 is 7.55. Then we must calculate the ratio of the conjugate base to the acid. The formula calls for the concentration, but in this situation, the ratio of the concentrations will be the same as the ratio of the moles, which will be the same as the ratio of the volumes, because both solutions had the same starting concentration of 0.2 M. Thus, we can see that the ratio of base to acid is 2 : 1 because we added twice the volume of base.

Notice that we did not have to know anything about the structure of HEPES to work out this example.

TABLE 8.5 Acid and Base Forms of Some Useful Biochemical Buffers
Acid Form		Base Form	pKa
\text {TRIS}- H ^{+}	N—tris [hydroxymethyl]aminomethane (TRIS)	TRIS*	8.3
(protonated form) \left( HOCH _{2}\right)_{3} CNH _{3}^{+}	\rightleftharpoons	(free amine) \left( HOCH _{2}\right)_{3} CNH _{2}
^-TES – H ^{+}	N—tris [hydroxymethyl]methyl-2-aminoethane sulfonate (TES)	^-TES	7.55
(zwitterionic form) + \left( HOCH _{2}\right)_{3} CNH _{2} CH _{2} CH _{2} SO _{3}{ }^{-}	\rightleftharpoons	(anionic form) \left( HOCH _{2}\right)_{3} CNHCH _{2} CH _{2} SO _{3}^{-}
^-\text {HEPES}- H ^{+}	N—2—hydroxyethylpiperazine-N’-2-ethane sulfonate (HEPES)	^-HEPES	7.55
(zwitterionic form)	\rightleftharpoons	(anionic form)
^- MOPS – H ^{+}	3—[N—morpholino]propanesulfonic acid (MOPS)	^-MOPS	7.2
(zwitterionic form)	\rightleftharpoons	(anionic form)
{ }^{2-} PIPES – H ^{+}	Piperazine—N,N’-[2-ethanesulfonic acid] (PIPES)	{ }^{2}{ }^{-} \text {PIPES }	6.8
(protonated dianion)	\rightleftharpoons	(dianion)
*Note that TRIS is not a zwitterion.