Question 8.E.J: (a) Find the pH of a solution prepared by dissolving 1.00 g ...
(a) Find the pH of a solution prepared by dissolving 1.00 g of glycine amide hydrochloride (Table 8-2) plus 1.00 g of glycine amide in 0.100 L.
(b) How many grams of glycine amide should be added to 1.00 g of glycine amide hydrochloride to give 100 mL of solution with pH 8.00?
(c) What would be the pH if the solution in part (a) were mixed with 5.00 mL of 0.100 M HCl?
(d) What would be the pH if the solution in part (c) were mixed with 10.00 mL of 0.100 M NaOH?
(e) What would be the pH if the solution in part (a) were mixed with 90.46 mL of 0.100 M NaOH? (This is exactly the quantity of NaOH required to neutralize the glycine amide hydrochloride.)
| TABLE 8-2 Structures and pK_{a} values for common buffers^{a,b,c,d} | |||||
|
Name |
Structure |
pK_{a}^{e} μ = 0 μ = 0.1 M |
Formula mass |
\Delta (pK_{a})/\Delta T
(K^{-1}) |
|
| N-2-Acetamidoiminodiacetic acid
(ADA) |
 |
—(CO_{2}H) | 1.59 | 190.15 | — |
| N-Tris(hydroxymethyl)methylglycine
(TRICINE) |
(HOCH_{2})_{3}C\overset{+}{N}H_{2}CH_{2}CO_{2}H | 2.02 (CO_{2}H) | — | 179.17 | −0.003 |
| Phosphoric acid | H_{3}PO_{4} | 2.15 (pK_{1}) | 1.92 | 98.00 | 0.005 |
| N,N-Bis(2-hydroxyethyl)glycine
(BICINE) |
(HOCH_{2})_{2}\overset{+}{N}HCH_{2}CO_{2}H | 2.23 (CO_{2}H) | — | 163.17 | — |
| ADA | (see above) | 2.48 (CO_{2}H) | 2.31 | 190.15 | — |
| Piperazine-N,N′-bis(2-ethanesulfonic
acid) (PIPES) |
 |
—(pK_{1}) | 2.67 | 302.37 | — |
| Citric acid | HO_{2}CCH_{2}\overset{\begin{matrix} OH \\ \mid \end{matrix} }{\underset{\begin{matrix} \mid \\ CO_{2}H \end{matrix} }{C}}CH_{2}CO_{2}H | 3.13 (pK_{1}) | 2.90 | 192.12 | −0.002 |
| Glycylglycine | H_{3}\overset{+}{N}CH_{2}\overset{\begin{matrix} O \\ \parallel \end{matrix} }{C}NHCH_{2}CO_{2}H | 3.14 (CO_{2}H) | 3.11 | 132.12 | 0.000 |
| Piperazine-N,N′-bis(3-propanesulfonic
acid) (PIPPS) |
 |
—(pK_{1}) | 3.79 | 330.42 | — |
| Piperazine-N,N′-bis(4-butanesulfonic
acid) (PIPBS) |
 |
—(pK_{1}) | 4.29 | 358.47 | — |
| N,N′-Diethylpiperazine
dihydrochloride (DEPP-2HCl) |
 |
—(pK_{1}) | 4.48 | 215.16 | — |
| Citric acid | (see above) | 4.76 (pK_{2}) | 4.35 | 192.12 | −0.001 |
| Acetic acid | CH_{3}CO_{2}H | 4.76 | 4.62 | 60.05 | 0.000 |
| N,N′-Diethylethylenediamine-N,N′-
bis(3-propanesulfonic acid) (DESPEN) |
^{- }O_{3}S(CH_{2})_{3}\overset{+}{\underset{\begin{matrix} \mid \\ CH_{3}CH_{2} \end{matrix} }{N}}HCH_{2}CH_{2}H\overset{+}{\underset{\begin{matrix} \mid \\ CH_{2}CH_{3} \end{matrix} }{N}}(CH_{2})_{3}SO_{3}^{- } | —(pK_{1}) | 5.62 | 360.49 | — |
| 2-(N-Morpholino)ethanesulfonic acid
(MES) |
 |
6.27 | 6.06 | 195.24 | −0.009 |
| Citric acid | (see above) | 6.40 (pK_{3}) | 5.70 | 192.12 | 0.002 |
| N,N,N′,N′-Tetraethylethylenediamine
dihydrochloride (TEEN·2HCl) |
Et_{2}\overset{+}{N}HCH_{2}CH_{2}H\overset{+}{N}Et_{2}\cdot2Cl^{- } | —(pK_{1}) | 6.58 | 245.23 | — |
| l,3-Bis[tris(hydroxymethyl)methyl-
amino] propane hydrochloride (BIS-TRIS propane-2HCl) |
(HOCH_{2})_{3}C\overset{+}{N}H_{2}(CH_{2})_{3}\overset{+}{\underset{\begin{matrix} \mid \\ (HOCH_{2})_{3}C \end{matrix} }{N}}H_{2}\cdot2Cl^{- } | 6.65 (pK_{1}) | — | 355.26 | — |
| ADA | (see above) | 6.84 (NH) | 6.67 | 190.15 | −0.007 |
a. The protonated form of each molecule is shown. Acidic hydrogen atoms are shown in bold type. pK_{a} is for 25°C.
b. Many buffers in this table are widely used in biomedical research because of their weak metal binding and physiologic inertness (C. L. Bering, J. Chem. Ed. 1987, 64, 803). In one study, where MES and MOPS had no discernible affinity for Cu^{2+}, a minor impurity in HEPES and HEPPS had a strong affinity for Cu^{2+} and MOPSO bound Cu^{2+} stoichiometrically (H. E. Marsh, Y.-P. Chin, L. Sigg, R. Hari, and H. Xu, Anal. Chem. 2003, 75, 671). ADA, BICINE, ACES, and TES have some metal-binding ability (R. Nakon and C. R. Krishnamoorthy, Science 1983, 221, 749). Lutidine buffers for the pH range 3 to 8 with limited metal-binding power have been described by U. Bips, H. Elias, M. Hauröder, G. Kleinhans, S. Pfeifer, and K. J. Wannowius, Inorg.
Chem. 1983, 22, 3862.
c. Some data from R. N. Goldberg, N. Kishore, and R. M. Lennen, J. Phys. Chem. Ref. Data 2002, 31, 231. This paper gives the temperature dependence of pK_{a}.
d. Temperature and ionic strength dependence of pK_{a} for buffers: HEPES—D. Feng, W. F. Koch, and Y. C. Wu, Anal. Chem. 1989, 61, 1400; MOPSO—Y. C. Wu, P. A. Berezansky, D. Feng, and W. F. Koch, Anal. Chem. 1993, 65, 1084; ACES and CHES—R. N. Roy, J. Bice, J. Greer, J. A. Carlsten, J. Smithson, W. S. Good, C. P. Moore, L. N. Roy, and K. M. Kuhler, J. Chem. Eng.
Data 1997, 42, 41; TEMN, TEEN, DEPP, DESPEN, PIPES, PIPPS, PIPBS, MES, MOPS, and MOBS—A. Kandegedara and D. B. Rorabacher, Anal. Chem. 1999, 71, 3140. This last set of buffers was specifically developed for low metal-binding ability (Q. Yu, A. Kandegedara, Y. Xu, and D. B. Rorabacher, Anal. Biochem. 1997, 253, 50).
e. See marginal note on page 166 for the distinction between pK_{a} at μ = 0 and at μ = 0.1 M.
| TABLE 8-2 (continued) Structures and pK_{a} values for common buffers^{a,b,c,d} | |||||
| Name | Structure |
pK_{a} μ = 0 μ = 0.1 M |
Formula mass |
\Delta (pK_{a})/\Delta T (K^{-1}) |
|
| N-2-Acetamido-2-aminoethane-
sulfonic acid (ACES) |
H_{2}N\overset{\overset{O}{\parallel } }{C} CH_{2}\overset{+}{N}H_{2}CH_{2}CH_{2}SO_{3}^{- } | 6.85 | 6.75 | 182.20 | −0.018 |
| 3-(N-Morpholino)-2-hydroxy-
propanesulfonic acid (MOPSO) |
 |
6.90 | — | 225.26 | −0.015 |
| Imidazole hydrochloride |  |
6.99 | 7.00 | 104.54 | −0.022 |
| PIPES | (see above) | 7.14 (pK_{2}) | 6.93 | 302.37 | −0.007 |
| 3-(N-Morpholino)propanesulfonic
acid (MOPS) |
 |
7.18 | 7.08 | 209.26 | −0.012 |
| Phosphoric acid | H_{3}PO_{4} | 7.20 (pK_{2}) | 6.71 | 98.00 | −0.002 |
| 4-(N-Morpholino)butanesulfonic
acid (MOBS) |
 |
— | 7.48 | 223.29 | — |
| N-Tris(hydroxymethyl)methyl-2-
aminoethanesulfonic acid (TES) |
(HOCH_{2})_{3}C\overset{+}{N}H_{2}CH_{2}CH_{2}SO_{3}^{- } | 7.55 | 7.60 | 229.25 | −0.019 |
| N-2-Hydroxyethylpiperazine-N′-2-
ethanesulfonic acid (HEPES) |
 |
7.56 | 7.49 | 238.30 | −0.012 |
| PIPPS | (see above) | —(pK_{2}) | 7.97 | 330.42 | — |
| N-2-Hydroxyethylpiperazine-N′-3-
propanesulfonic acid (HEPPS) |
 |
7.96 | 7.87 | 252.33 | −0.013 |
| Glycine amide hydrochloride | H_{3}\overset{+}{N}CH_{2}\overset{\overset{O}{\parallel } }{C}NH_{2}\cdot Cl^{- } | — | 8.04 | 110.54 | — |
| Tris(hydroxymethyl)aminomethane
hydrochloride (TRIS HCl) |
(HOCH_{2})_{3}C\overset{+}{N}H_{3}\cdot Cl^{- } | 8.07 | 8.10 | 157.60 | −0.028 |
| TRICINE | (see above) | 8.14 (NH) | — | 179.17 | −0.018 |
| Glycylglycine | (see above) | 8.26 (NH) | 8.09 | 132.12 | −0.026 |
| BICINE | (see above) | 8.33 (NH) | 8.22 | 163.17 | −0.015 |
| PIPBS | (see above) | —(pK_{2}) | 8.55 | 358.47 | — |
| DEPP 2HCl | (see above) | —(pK_{2}) | 8.58 | 207.10 | — |
| DESPEN | (see above) | —(pK_{2}) | 9.06 | 360.49 | — |
| BIS-TRIS propane·2HCl | (see above) | 9.10 (pK_{2}) | — | 355.26 | — |
| Ammonia | NH_{4}^{+} | 9.24 | — | 17.03 | −0.031 |
| Boric acid | B(OH)_{3}^{+} | 9.24 (pK_{1}) | 8.98 | 61.83 | −0.008 |
| Cyclohexylaminoethanesulfonic
acid (CHES) |
 |
9.39 | — | 207.29 | −0.023 |
| TEEN·2HCl | (see above) | —(pK_{2}) | 9.88 | 245.23 | — |
| 3-(Cyclohexylamino)propanesulfonic
acid (CAPS) |
 |
10.50 | 10.39 | 221.32 | −0.028 |
| N,N,N′,N′–Tetraethylmethylene-
diamine·2HCl (TEMN·2HCl) |
Et_{2}\overset{+}{N}HCH_{2}H\overset{+}{N}Et_{2}\cdot 2Cl^{- } | —(pK_{2}) | 11.01 | 231.21 | — |
| Phosphoric acid | H_{3}PO_{4} | 12.35 (pK_{3}) | 11.52 | 98.00 | −0.009 |
| Boric acid | B(OH)_{3}^{+} | 12.74 (pK_{2}) | — | 61.83 | — |
