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Buffer capacity (β) is defined as the amount of a strong acid or a strong base that has to be added to 1 liter of a buffer to cause a pH change of 1.0 pH unit: ...
Typology: Lecture notes
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By Dr. Jan Pláteník
Principle of buffering
A buffer solution is a solution that resists changes in pH either when diluted or when limited amounts of acid or base are added to it. Such a solution can be prepared by combining a weak acid and its salt with a strong base (conjugated base) or, analogously, a weak base and its salt with a strong acid (conjugated acid).
For example:
Acetate buffer : CH 3 COOH (the weak acid) + CH 3 COONa (the salt, conjugated base)
Phosphate buffer : NaH 2 PO 4 (the weak acid) + Na 2 HPO 4 (the salt, conjugated base)
Tris buffer:
(Tris: Tris [2-amino-2-(hydroxymethyl)-propan-1,3-diol)] , an organic base)
The Henderson-Hasselbalch equation describes the behavior of such a buffer and for the mixture of a weak acid and its salt with a strong base (conjugated base) it has the form:
pKa negative logarithm of the dissociation constant for the weak acid, cs substance concentration of the salt (conjugated base), cac substance concentration of the weak acid (conjugated acid).
Graphically the Henderson-Hasselbalch equation plotted as the acid : conjugated base ratio vs. pH of buffer actually constitutes the titration curve of the weak acid (see figure on the next page).
Note also that for the acid : base ratio 1:1 the pH of buffer just equals the pKa (this is valid for uni-univalent systems, e.g., CH 3 COOH/CH 3 COONa, NaH 2 PO 4 /Na 2 HPO 4 ).
ac
s a (^) c
c pH = pK + log
The equation for a weak base and its salt with a strong acid (conjugated acid) has the form:
pKb negative logarithm of the dissociation constant for the weak base, cb substance concentration of the base, cs substance concentration of the salt (conjugated acid), pKw = 14 = − log 10-14^ (ionic product of water).
added to 1 liter of a buffer to cause a pH change of 1.0 pH unit:
The buffer capacity depends on the amounts of substance of the weak acid and its conjugated base in the buffer. It is in fact directly related to the first derivative of the buffer titration curve, or, in other words, the slope of the titration curve. As the slope of the titration curve is the smallest at the acid : base ratio 1:1, the buffer capacity is maximal at the same point (the second derivative of the titration curve is equal to zero at the same point).
s
b w b c
c pH = pK − pK + log
pH
c pH
c (^) b ac ∆
9:1 8:2 7:3 6:4 1:1 4:6 3:7 2:8 1:
5
6
7
8
9
10
Titration curve of sodium phosphate buffer
pH = pKa = 7.