c340 Buffers Key

Key for Exercise on Buffers
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Table 1. Weak Acids and Their pK_a's
Acid	pK_a	Acid	pK_a
acetic	4.76	H₃PO₄	2.14
H₂CO₃	3.77	H₂PO₄^-	6.86
HCO₃^-	10.2	HPO₄^2-	12.4
citrate^2-	5.80	TRIS	8.16

2. pH = pK_a+ log ([A^-]/[HA])
a. 3.77 = 3.77 + log ratio                           log ratio = 0
    ratio = 1, so the concentration of HCO 3 - = 0.75 M
b. 4.5 = 3.77 + log ratio                            0.73 = log ratio
    ratio = 5.37
c. Total buffer concentration = 1.5 M (0.75 + 0.75)
    [A^-] = 5.37 [HA]                                    [A^-] + [HA] = 1.5 M
    5.37 [HA] + [HA] = 1.5 M                    6.37 [HA] = 1.5 M
    [HA] = 0.235 M = 0.24 M

3. a. H₃PO₄ and NaH₂PO₄
b. 1:1 (equal concentrations)
c. Add NaOH, which increases the concentration of A^-
d. NaH₂PO₄ and Na₂HPO₄
e. 6.5 = 6.86 + log ratio - 0.36 = log ratio 0.44 = ratio
f. 6.5 = 2.14 + log ratio 4.36 = log ratio ratio = 22,900

Table 2. Buffers for different pH's
pH	Acid	Higher concentration	pH	Acid	Higher concentration
3.5	H₂CO₃	HA	7.0	H₂PO₄^-	A^-
4.0	H₂CO₃	A^-	8.0	TRIS	HA
5.0	acetic	A^-	9.0	TRIS	A^-
6.0	citrate^2-	A^-	10.0	HCO₃^-	HA

Choose the acid with the closest pK_a. If the pH is higher than the pK_a, [A^-] should be higher than [HA].

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