What is the pH of a solution if you mix 100. mL of 0.20 M HEPES in the acid form with 200. mL of 0.20 M HEPES in the basic form?

Question

Strategy
To use the Henderson-Hasselbalch equation, you need the ratio of the conjugate base to weak acid forms of the buffer. Since the HEPES solutions have equal concentrations, the ratio of the volumes will give you the ratio of the moles used. Divide the volume of the conjugate base form by the volume of the weak acid form. Take the log of the ratio and add it to the [latex]pK_a[/latex] for HEPES

Accepted Answer

Solution
First, we must find the [latex]pK_a[/latex], which we see from Table 8.6 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 0.20 M. Thus, we can see that the ratio of base to acid is 2 : 1 because we added twice the volume of base.

pH = [latex]pK_a[/latex]+ log ( [ [latex]A^- [/latex] ]/ [HA]) = 7.55 + log (2) = 7.85

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

Table 8.6 Acid and Base Forms of Some Useful Biochemical Buffers

Acid Form		Base Form	pKa
TRIS—[latex]H^+[/latex] (protonated form) ([latex]HOCH_2)_3CNH_3^+[/latex]	N— [hydroxymethyl] aminomethane (TRIS) [latex]\rightleftharpoons [/latex]	TRIS* (free amine) ([latex]HOCH_2)_3CNH_2[/latex]	8.3
[latex]^–TES—H^+[/latex] (zwitterionic form) ([latex]HOCH_2)_3C\overset{+}{N}H_2CH_2CH_2SO_3^-[/latex]	N—tris [hydroxymethyl]methyl-2-aminoethane sulfonate (TES) [latex]\rightleftharpoons [/latex]	[latex]^–T[/latex]ES (anionic form) ([latex]HOCH_2)_3CNHCH_2CH_2SO_3^–[/latex]	7.55
[latex]^–HEPES—H^+[/latex] (zwitterionic form)	N—2—hydroxyethylpiperazine-N’-2-ethane sulfonate (HEPES) [latex]\rightleftharpoons [/latex]	[latex]^–HEPES[/latex] (anionic form)	7.55
[latex]^–MOPS—H^+[/latex] (zwitterionic form)	3—[N—morpholino]propanesulfonic acid (MOPS) [latex]\rightleftharpoons [/latex]	[latex]^–[/latex]MOPS (anionic form)	7.2
[latex]^{2–}PIPES—H^+ [/latex] (protonated dianion)	Piperazine—N,N’- bis [2-ethanesulfonic acid] (PIPES) [latex]\rightleftharpoons [/latex]	[latex]^{2–}[/latex]PIPES (dianion)	6.8

*Note that TRIS is not a zwitterion.

Question 8.11: What is the pH of a solution if you mix 100. mL of 0.20 M HE...

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