Standard Buffer of N,N-Bis(2-Hydroxyethyl)-2-Aminoethanesulfonic Acid (Bes) for Use in the Physiological pH Range 6.6 to 7.4 Rabindra N. Roy, Erik E. Swensson, Guilio LaCross, Jr., and Charles W. Krueger Department of Chemistry, Drury College, Springfield, MO 65802
Three buffer solutions containing N,N-bis(2-hydroxyethyl)2-amlnoethanesulfonic acid (known as Bes) and its sodium salt, are proposed to be useful as secondary pH standards and for the control of acidity in the physiologically important pH range of 6.6 to 7.4. Conventional paH values for three buffer solutions consisting of Bes and its sodium salt (sodl0.02m sodium Besate) with compositions of 0.03m Bes 0.02m sodium Besate, and O.lm um Besate, 0.02m Bes Bes O.lm sodium Besate, have been assigned from 5 to 55 O C by means of emf measurements made on hydrogen/ silver bromide cells without liquid Junction.At 37 'C, the assigned value of paH for an equimolal buffer of Bes (0.1 mol kg-') and Na Besate (0.1 mol kg-') is 6.97, whereas for 0.02 mol kg-' Bes and 0.02 mol kg-' Na Besate, It is also 6.97; and finally for 0.03 mol kg-' Bes and 0.02 mol kg-' Na Besate, the paH is 6.76.
+
+
+
The standardization of p H and control of acidity in the physiologically important p H range is rendered difficult by the rarity of weak acid-base systems with pK between 6 and 8. Phosphates, borates, and tris(hydroxymethy1)aminomethane (Tham or Tris) have been shown to be useful biochemical buffers in the pH range of 7 to 9 (1-5). I t has been found that borate forms stable complexes with many hydroxy organic compounds. I t is also known that phosphates are not well suited to studies in physiological media because of side reactions with proteins, carbohydrates, and certain blood constituents. Moreover, the p H temperature coefficient (-0.0015 p H unit/"C) of the phosphate buffer does not adequately approximate blood p H variations (-0.015 p H unit/OC). In addition, Tris has poor buffering capacity below a p H of 7.5. I t is a primary aliphatic amine of considerable reactivity and has an undesired inhibitory effect on biological reactions (6). Because of these shortcomings, attention has recently been focused on the hydroxymethyl derivative of glycine; that is tris(hydroxymethy1)methylglycine (tricine), which, with a pK2 of 8.135 ( 7 ) ,promises to make possible the control of paH between 7.6 to 8.1 a t 25 "C (8). In their selection of buffer substances useful in the clinical and biological region of p H (6 to 8), Good et al. (6) called our attention to N,N-Bis(2-hydroxyethyl)-2-aminoethanesulfonic acid (Bes) from a listing of 1 2 new or seldomly used hydrogen ion buffers which are compatible with biological media (6). In spite of the uncertain effect of ampholytes upon the ionic strength, glycine has long been used for the control of acidity in the pH range 8.2 to 10.1 (9).The pK2 of glycine a t 25 "C is 9.780 ( I O ) , whereas that of Bes [one of the buffer components recommended by Good and his associates (611, is 7.193 ( 1 2 ) a t that same temperature. Hence, the tertiary amino group of Bes is a comparatively weaker base than the primary amino group of its parent compound, glycine. Bes is therefore better suited for
p H control in the buffer region of biochemical interest. It has the following formula
and exists in a zwitterionic form similar to that of glycine itself. I t is soluble to the extent of 3.2M a t 0 "C (6)and can be easily purified from aqueous alcohol. Conventional paH values have been calculated by the methods of Bates et al. (8, 121, for three standard solutions of Bes and sodium Besate buffer obtained by the addition of strong alkali. Two equimolal buffer solutions consist of Bes and sodium Besate, each a t a molality of 0.02 mol kg-' and 0.1 mol kg-l, respectively, while the third has the composition: Bes with molality of 0.03 mol kg-', and sodium Besate with a concentration equal t o 0.02 mol kg-l. The conventional pa^ values for these three solutions are assigned a t intervals of 5 "C from 5 to 55 OC, including 37 "C (human body temperature).
EXPERIMENTAL A commercial sample of Bes (Sigma Chemical Co.), was recrystallized twice from 70% ethanol and was dried a t room temperature under vacuum in a desiccator. The sample was powdered and then stored in a desiccator over Drierite (CaS04) until used. The product was assayed a t 99.96% (standard deviation 0.1%) when titrated with the same standard solution of sodium hydroxide that was subsequently used to prepare the buffer solutions. The titration was carried out under carbon dioxide-free conditions, either to a calculated end point of pH equal to 9.44 (0.05M solution), or to a n equivalence point read from the differential plot of ApH/AV vs. volume (V) of the standard alkali solution. The end point was established by glass electrode measurements of the pH change. Reagent-grade potassium bromide (Fisher ACS Certified) was crystallized from water. The buffer solutions were prepared from purified Bes and a standard solution of carbonate-free sodium hydroxide and carbon dioxide-free deionized water having a conducohm-' cm-'. Three different buffer tivity of less than 1 X concentrations were studied. Potassium bromide was added in different amounts to four different portions of each buffer solution. All weighings were corrected to vacuum. The solutions were deoxygenated by bubbling hydrogen for about one-half hour before the cells were filled with solution to prevent contamination of the solutions with oxygen and carbon dioxide. The preparation of the hydrogen electrodes, the cell design (131, the preparation of the solutions, the purification of the hydrogen gas, and other experimental details have been described previously (1). The silver-silver bromide electrodes were of the thermal type (14) formed by heating a t 580 "C a paste consisting of 10% (by weight) of silver bromate and 90% (by weight) silver oxide. The bias potentials of the electrodes in 0.05M HBr solution were always less than 0.05 mV. The emf measurements were made a t intervals of 5 O from 5 to 55 OC. The emf a t 25 OC was measured a t the beginning, in the middle, and a t the end of each run. The emf a t 37 "C was recorded twice; namely, in the middle and a t the end of the run. The maximum differences among the three measurements a t 25 OC were always within 0.04 mV, and a t 37 "C, the difference was 0.05 mV, demonstrating the excellent stability of the cells. Duplicate cells of type I were always prepared using each of the cell solutions. The emf readings of the ANALYTICALCHEMISTRY, VOL. 47, NO. 8 , JULY 1975
1407
l &
duplicate cells on the average agreed well within 0.05 mV. The emf was measured with a Leeds and Northrup type K-3 potentiometer, standardized with an Eppley standard cell in conjunction with a Leeds and Northrup electronic null detector (model 9829), employing a sensitivity of 25 1 V . The temperature of the bath in which the cells were immersed was regulated to within 0.02 K by means of a Sargent-WelchThermonitor Model ST.
I
+ KBr,
AgBr;Ag
(I)
the silver-silver bromide electrode has been found to be highly reproducible and stable ( 8 ) ; moreover, the lower solubility of silver bromide as compared with silver chloride makes the silver-silver bromide electrode more reliable for use in solutions of nitrogen bases. However, a correction to the molality of the chloride ion would be necessary if the silver-silver chloride electrode were used. The standard emf of cell I is known in the temperature range under investigation (17, 18). Preliminary measurements for 0.01 mol kg-l .HBr over the temperature range gave values of E o which are in satisfactory accord (within 0.04 mV) with those of Harned, Keston, and Donelson (17), and hence these values of E o were used in the present calculations. The average values of the emf and the compositions of the solutions are given in Table I. The acidity function ~ ( u H ~ Bwas ~ ) derived from the measured emf of the cell according to the equation
0 0 0 0
0 0 0 0 0
m - m w
s"" ?
w m m m
v w m m v m o - m w w w
o m m t m m w m w v m v 0 3 m v w w w w
r r m a w o r w m m m w w t - r w 0 3 m w m w w w w o
0,
0 0 0 0
0 0 0 0
0 0 0 0 0
m c - m m
o m t - t - v
8
The method used for the assignment of standard ~ U values follows closely the same procedure on which the NBS standard pH scale is based (15, 16). The fundamental difference between the NBS procedure and the procedure adapted here lies in employing a cell with a siIver-silver bromide electrode instead of the corresponding cell with a silver-silver chloride electrode. The emf measurements were made on electrochemical cells without transference, of the type:
0 0 0 0
d
METHOD AND RESULTS
Pt;H,(g, 1 atm); Buffer
Q
.->
H
u
G
U
m w d m w m m m
(r
m o - e l
v o r m m o d o o r r m w w w w w
w m 0 w
0 0 0 0
0000
0 0 0 0 0
m w d m r a m m m c o a o m m w
mmfficm w v w
w m r m m v a v m m m m o 3 m t w w w o
0
NO+^
m C u
m w w w
I
cd
v m m w 3 e l w w
o m w w
a m w o
N
-E y Y
L-
2 -
Y
5
where E o is the standard emf of the cell and (RT In 1O)lF is the Nernst slope. When the quantity on the left side of Equation 1 was plotted vs. the molality of the bromide ion, mBr-, a linear form of nearly horizontal slope was obtained. The graphical extrapolation to mBr- = 0 gave the intercept, p(u~y~,)O The . deviation of the straight line plot, introduced by this extrapolation, was well within 0.002. Convenvalues for the bromide-free buffer solutions tional ~ U H were computed by the equation:
Zo P= fl"
In Equation 3, A is the Debye-Huckel limiting slope on the scale of molality, I is the total ionic strength of the buffer solution, and p is the product of the Debye-Huckel constant B and the ion-size parameter ao. The value of p was taken to be 1.6 a t all temperatures and the values of the constant A a t all temperatures are listed elsewhere (19). The justification for the choice of p = 1.6 for the bromide ion has been given by Bates et al. ( 8 ) , in great detail. The p H of all the cell solutions was close to neutrality, and therefore no correction for hydrolysis was deemed necessary; the zwitterionic form of Bes, B was presumed to be1408
ANALYTICAL CHEMISTRY, VOL. 47, NO. 8, JULY 1975
m o m m m m w m 0 . i ~m m w w w m
2
0 0 0 0
0000
0 0 0 0 0
$ E "
r w m m w w moo w m 0 m m w
m h m a m
m r m o m r o m w w
t - m m m m m m m o w m m m o m a o d m t m w w w o
0 0 0 0
0 0 0 0
0 0 0 0 0
g -
-..
0 0 0 0
0 0 0 0
0 0 0 0 0
' i
0 0 0 0
0 0 0 0
0 0 0 0 0
-
-i
_ L 2
e -
2
.L
where an expression for 7 ~ is ~given - by the equation
w m o m w
m m r 3 w
o o o o w
8
g Q)
-7 5
.-G
_
E
>
m
m
m
m
m
m
0
N 3 3 0
0 0 0 0
m - 3 0 3
0 0 0 0
0000'Ll
0 0 0 0
0 0 0 0
0 0 0 0
m m m m
m m m m
0 0 0 0
0 0 0 0
C
J
4
3
E
m 9
2
C I
0
s ;."
E-
0 0 0 0
0 0 0 0
h d r r d 0 0 0 0
"
E
Table 11. ~ U Values H of Bes (HB): Sodium Besate (NaB) Ratio of 1.5: 1 at a Sodium Besate (NaB) Molality of 0.02 from .i to 55 "C P ( n H Y B I. 1
f
CJ
5 10 15 20 25 30 35 37 40 45 50 55
Doti
V ~ K R ~
7.344 7.262 7.182 7.105 7.031 6.962 6.893 6.866 6.826 6.762 6.700 6.642
7.343 7.259 7.181 7.105 7.031 6.960 6.893 6.865 6.826 6.762 6.700 6.642
7.342 7.257 7.179 7.103 7.031 6.959 6.893 6.864 6.826 6.761 6.699 6.642
7.341 7.253 7.178 7.102 7.031 6.958 6.892 6.863 6.825 6.761 6.699 6.641
7.341 7.250 7.177 7.101 7.030 6.956 6.892 6.862 6.825 6.760 6.699 6.641
7.284 7.193 7.119 7.043 6.972 6.897 6.832 6.802 6.765 6.700 6.637 6.579
7.505 7.418 7.342 7.262 7.193 7.122 7.055 7.029 6.986 6.928 6.862 6.805
7.448 7.361 7.284 7.204 7.134 7.063 6.995 6.969 6.926 6.866 6.800 6.743
Table 111. ~ U Values H of Bes (HB): Sodium Besate (NaB) Ratio of 1: 1 a t a Sodium Besate (NaB) Molality of 0.02 from .5 to 55 "C m
D ( ~ H r)
5 10 15 20 25 30 35 37 40 45 50 55
7.510 7.429 7.349 7.274 7.201 7.131 7.064 7.038 7.000 6.934 6.873 6.813
7.509 7.426 7.348 7.271 7.199 7.129 7.061 7.035 6.996 6.933 6.870 6.811
7.507 7.424 7.345 7.268 7.197 7.127 7.059 7.033 6.993 6.930 6.867 6.809
7.506 7.421 7.344 7.266 7.195 7.125 7.057 7.032 6.990 6.929 6.865 6.807
Table IV.~ U Values H of Equimolal Bes (HB) and Sodium Besate ( N a B ) Solutions at a Sodium Besate (NaB)Molality of 0.1 from 5 to 55 "C P(
5 10 15 20 25 30 35 37 40 45 50 55
7.570 7.483 7.400 7.320 7.246 7.174 7.104 7.077 7.036 6.971 6.907 6.847
7.568 7.481 7.399 7.320 7.245 7.173 7.103 7.076 7.036 6.971 6.907 6.847
a H r Br )
7.566 7.479 7.398 7.320 7.244 7.173 7.103 7.076 7.036 6.970 6.907 6.846
have as an uncharged species and hence was considered to produce no change in the ionic strength. In other words, the ionic strength of each bromide-free buffer solution was taken to be equal to that of sodium Besate itself. Tables 11, 111, and IV list the values of p ( u ~ y ~ , ) , p ( u ~ y ~ , ) and O , ~ U for H a Bes:sodium Besate ratio of 1.51
7.565 7.477 7.397 7.319 7.242 7.172 7.103 7.076 7.036 6.970 6.906 6.846
7.563 7.475 7.395 7.319 7.241 7.172 7.102 7.076 7.035 6.970 6.906 6.846
7.459
7.370 7.290 7.213 7.134 7.064 6.993 6.966 6.925 6.858 6.794 6.733
a t a sodium Besate molality of 0.02 mol kg-'; and for two equimolal buffer ratios of Bes and sodium Besate a t a total molality of 0.02 and 0.1 mol kg-l, respectively. The PUH values are described as a function of temperature in the range of 5 to 55 "C by the following equation: 0.03m Bes, 0.02m sodium Besate: ANALYTICALCHEMISTRY, VOL. 47, NO. 8, JULY 1975
1409
pa,
= 6.9696 - 0.01451 ( t - 25)
+
0.0000498 ( t - 25)' and 0.02m Bes, 0.02m sodium Besate: pa,
(4)
= 7.1338 - 0.01453 ( t - 25) t 0.0000509 ( t
- 25)' (5)
and O.lm Bes, O.lm sodium Besate: pa, = 7.1366 - 0.01494 ( t - 25)
+
0.0000508 ( t
was standardized a t 25 "C by means of the primary aqueous phosphate standard (L3.51, composed of KHzP04 ( m = 0.008695) and NaZHP04 ( m = 0.03043). The p H of this solution is 7.413 ( 2 2 ) a t 25 "C. After equilibration of the cell for an hour, the emf of the solution was measured by forming a liquid junction in a 1-mm vertical capillary tube. The phosphate buffer was then replaced by the equimolal buffer a t a Bes-sodium Besate molality of 0.1 mol kg-l, and the emf reading was taken. The temperature of the two solutions and their barometric pressures were identical during both determinations. The operational definition of pH is given by (24)
- 25)' (6)
where t is the temperature in "C. The standard deviations for regression for these three equations are 0.0023, 0.0020, and 0.0016, respectively.
DISCUSSION The Bes-sodium Besate buffers should prove useful in controlling p H near the neutral point for equilibrium and kinetic studies, as well as in the determination of dissociation constants by the spectrophotometric method. The listH in Tables 11,111,and IV clearly indied values of ~ U given cate that the more desirable characteristics of Bes buffers, such as the dilution or concentration effects, the temperature coefficient, etc., are quite compatible with those of whole blood. For example, the temperature coefficient, ApHlAt, of whole blood is -0.015 (20), whereas for the buffer pair of 0.02 mol kg-l Bes and 0.02 mol kg-I sodium Besate, it is approximately -0.013 p H unit per degree Celsius, and for the system composed of 0.1 mol kg-l Bes and 0.1 mol kg-' sodium Besate, the value equals -0.016 pH unit per degree Celsius. All of these values refer to the region near body temperature as well as near room temperature. Similar orders of magnitude are obtained in the other temperature regions. The uncertainty in conventional ~ U values H stems from the deviations in E, E " , and the natural constants upon , The convenwhich the acidity function, ~ ( U H Y B ~is) based. tion to which these assigned ~ U values H are referred is considered to be exact by definition. From a consideration of the standard deviation of the data from which the value of E" was determined ( 1 5 ) , as well as the reproducibility of the emf data given in Table I, the total error in the ~ U H values is estimated to be on the order of 0.003 pH unit. This is due to an error of 0.001 unit in the emf measurements and 0.002 unit due to extrapolation of ~ ( U X ~ B ,to) ~ ( u H ~ B , The ) ~ . highest uncertainties are those a t the two extreme temperatures of 5 and 55 "C. I t has been mentioned in the previous section that Bes behaves as a neutral species (21) or a dipolar ion ( 2 2 ) .The evidence that a zwitterionic compound such as Bes does not make any contribution to the total ionic strength has been elaborately discussed for the case of tricine by Bates, Roy, and Robinson (8). Finally, we have investigated the residual liquid-junction potential for an equimolal buffer a t a Bes-sodium Besate molality of 0.1 mol kg-l using a p H cell assembly with liquid junction. The design of the cell has been given elsewhere (23). The customary p H cell with a liquid junction (indicated in the cell below by the vertical line) Pt; H,(g, 1 atm); solution 13.511.1KC1 (aq); Calomel electrode (II)
1410
ANALYTICAL CHEMISTRY, VOL. 47, NO.
8, JULY 1975
where X denotes the unknown buffer (Bes-sodium Besate) and S refers to a reference solution of known pH. The emf of the Bes buffer was 0.66809 and that of the phosphate buffer was 0.68615 a t 25 "C. Hence, the pH(X) a t 25 "C was 7.108, which is lower by 0.029 than the value calculated by Equation 6 (i.e., 7.137). I t appears, therefore, that the p H meter readings (Le., the operational pH), should be in. creased by 0.029 to yield the actual values of ~ U H Hence, the ~ U values H presented in Tables 11,111,and IV should be considered as secondary standards for pH measurements.
ACKNOWLEDGMENT The authors thank L. N. Roy for the preliminary calculations and J. J. Gibbons for his valuable suggestions and careful reading of the manuscript. LITERATURE CITED (1) R. G. Batesand V.E. Bower, Anal. Chem., 28, 1322 (1956). (2) R. G. Bates and R. A. Robinson, Anal. Chern., 45, 420 (1973). (3) V.E. Bower, M. Paabo, and R. G. Bates, Clin. Chem., 7, 292 (1961). (4) V. E. Bower, M. Paabo, and R. G. Bates, J. Res. Nat. Bur. Stand., Sect. A, 66, 267 (1961). (5) R. A. Durst and E. R. Staples, Clin. Chem., 18, 206 (1972). (6) N. E. Good, G. D. Winget. W. Winter, T. N. Connoliy, S. izawa. and R. M. M. Singh. Biochemistry, 5, 467 (1966). (7) R. N. Roy, R. A. Robinson, and R. G. Bates, J. Am. Chem. SOC., 95, 8231 (1973). (8) R. G. Bates, R. N. Roy, and R. A. Robinson, Anal. Chern., 45, 1663 (1973). (9) S. P. L. Sorenson, C. R. Trav. Lab. Carlsberg, 8 , 1. 396 (1909): Biochem. Z.,21, 131, 201 (1909): 22, 352 (1909). (10) E. J. King, J. Am. Chem. SOC.,73, 155 (1951). (11) R. N. Roy, G. LaCross, Jr., C. W. Krueger, and J. J. Gibbons, unpublished measurements. (12) R. G. Bates, J. Res. Naf. Bur. Stand., Sect. A, 66, 179 (1962). (13) R. Gary, R. G. Bates, and R. A. Robinson, J. Phys. Chem., 68, 1186 (1964). (14) R. N. Roy, R. A. Robinson, and R. G. Bates, J. Chem. Thermdyn., 5, 559 (1973). (15) R. G. Bates and E. A. Guggenheim, Pure Appl. Chem., 1, 163 (1960). (16) R. G. Bates, "Determination of pH", 2nd ed.. Wiley. New York, NY, 1973, Chap. 4. (17) H. S. Harned, A. S . Keston, and J. G. Donelson, J. Am. Chem. SOC.,5 8 , 989 (1936). (18) H. E. Hetzer, R. A. Robinson, and R. G. Bates, J. Phys. Chem., 66, 1423 (1962). (19) Reference 14, p 449. (20) T. E. Rosenthal, J. Biol. Chem.. 173, 25 (1948). (21) M. Randall and C. F. Failey, Chem. Rev., 4, 291 (1927). (22) E. J. Cohn and J. T. Edsall, "Proteins, Amino Acids and Peptides", Reinhold, New York, NY, 1943, Chap. 4 and 12. (23) Reference 14, p 56. (24) Reference 14, p 253.
RECEIVEDfor review February 3, 1975. Accepted April 7, 1975.
