Buffer Standards of Tris(Hydroxymethyl)methylglycine (“Tricine”) for the Physiological Range pH 7.2 to 8.5 Roger G. Bates, Rabindra N. Roy,’ and R. A. Robinson Department of Chemistry, University of Florida, Gainesville, Fla. 3260 1
Tris(hydroxymethyl)methylglycine, known as “tricine,” is one of the series of buffer materials chosen by Good et a/. for their compatibility with biological media and their high buffer capacity in the pH range of physiological interest. Conventional pa^ values at temperatures from 5 to 50 “C have been assigned to two buffer solutions composed of tricine and its sodium salt by the method used to establish the NBS primary pH standards. Cells without liquid junction were employed, with hydrogen electrodes and silver-silver bromide electrodes, and the convention for the single ion activity coefficient was modified appropriately to apply to bromide ion instead of chloride. The compositions of the buffer solutions selected were 0.05m tricine 4- 0.05rn sodium tricinate and 0.06m tricine + 0.02m sodium tricinate. The paH of the latter at 37 “C (7.407) matches closely the pH of blood.
The standardization of p H and control of the acidity in the p H range 7 to 9 are of special importance in biological and clinical chemistry and in oceanography. Phosphates and borates, common constituents of buffers in this region, interact unfavorably with biological media. Phosphates, for example, precipitate many polyvalent cations and may also act as an inhibitor to enzymatic processes. Borate forms stable complexes with many hydroxy compounds. In the words of Good et al. ( I ) , “It is impossible even to guess how many exploratory experiments have failed, how many reaction rates have been depressed, and how many processes have been distorted because of the imperfections of the buffers employed.” In 1966,Good and his coworkers ( I ) offered a partial solution to this problem by seleciing 12 new or little used hydrogen ion buffers which are, for the most part, compatible with common biological media. The nine criteria used to evaluate these materials included high solubility in water, minimal salt effects and temperature effects. stability in solution, and absence of absorption bands in the visible and ultraviolet regions of the spectrum. Although the preparation and properties of these buffer substances were described, the pH values of solutions of these compounds have not, in general, been determined. One exception is tris(hydroxymethy1)aminomethane (“tris,” “THAM”), buffer solutions of which have been studied extensively both in water and in sodium chloride solutions of ionic strength 0.16 ( 2 - 4 ) . As has been po’nted out earlier ( I ) , however, tris is an aliphatic amine of considerable reactivity and sometimes has an undesired inhibitory effect on biological reactions. There ib alsc ?vidence of an abnormal liquid-junction potential when refOn leave 1971-73 from Drury College,
Springfield,
Mo.
(1) N. E. Good, G. D. Winget, W. Winter, T. N. Connolly, S . Izawa, and R. M. M . Singh, Biochemistry, 5 , 467 (1966). (2) R. G. Batesand V . E. Bower. Ana/. Chem., 28, 1322 (1956). (3) R. A . Durst and B. R. Staples, Clin. Chem., 18, 206 (1972). (4) R. G. Bates and R. A. Robinson, Ana/. Chem., 45, 420 (1973).
erence electrodes with asbestos fiber junctions are used in tris buffer solutions ( 5 ) . It is not yet known, however. whether a similar effect exists with other buffer materials of related structure. Glycine has long been favored for the control of pH in the range 8.2 to 10.1 (6). The secondary amino group of N-tris(hydroxymethy1)methylglycine (“tricine”), one of the buffer materials in the list of Good et al. (I), is a considerably weaker base than the primary amino group of glycine itself, with a pK, value of 8.135 at 25 “C (7) as compared with 9.780 for the parent glycine a t the same temperature (8). Buffer solutions of pH closely matching that of human blood are readily prepared from tricine and a strong alkali. Furthermore, tricine is soluble to the extent of 0.8M at 0 “C ( I ) , is stable in solution, and is easily purified. The compound exists in a zwitterionic form. Conventional ~ U values H have now been determined, by the method used at the National Bureau of Standards ( 9 ) , for t a ( J standard solutions of tricine and its sodium salt. One of these consists of tricine and sodium tricinate, each at a molality of 0.05 mol kg-1. The other, which matches closely the pH of blood a t 37 “C, has the composition: tricine, molality = 0.06 mol kg-1; sodium tricinate, molality = 0.02 mol k g - l . The pa^ values have been assigned to these two solutions a t intervals of 5 “C from 5 to 50 “C and for the second solution also at 37 “C.
METHOD AND RESULTS The details of the method by which ~ C Z H values on the NBS conventional standard scale of hydrogen ion activity are assigned have been given elsewhere (IO). The proceH for tricine buffers difdure used to determine ~ U values fered only in employing a cell with silver-silver bromide electrode, Pt;HZ(g, 1 atm), Buffer
+ KBr, AgBr;Ag
instead of the corresponding cell with a silver-silver chloride electrode. Silver bromide electrodes are highly stable in many solutions of nitrogen bases where the elevated solubility of silver chloride makes the silver-silver chloride electrode unreliable. Furthermore, the standard emf of cell I is well known over a considerable temperature range (11, 12). The compositions of the solutions and the average values of the emf are given in Table I. At 25 “C, the emf at the beginning, middle, and end of the temperature se( 5 ) C. C. Westcott and T. Johns, Appl. Res. Tech. Rep., No. 5 4 2 , Beckman Instruments, Inc., Fullerton, Calif. ( 6 ) S. P. L. S#rensen. Compt. Rend. Lab. Carlsberg, 8, 1. 396 (1909): biocnem. Z , 21. 131. 201 (1909); 22, 352 (1909). 17) R . N. Roy. R. A . Robinson, and R. G. Bates, unpublished rneasurements (8) E. J. King, J. Amer. Chem. SOC.,73, 155 (1951). (9) R. G.Bates, J. Res. Mat. Bur. Stand., Sect. A, 66, 179 (1962). (10) R. G. Bates, “Determination of pH,” 2nd ed., Wiley, New York, N.Y., 1973, Chap. 4. (11) H. S. Harned, A . S. Keston, and J. G. Donelson. J. Amer. Chem. SOC.,58, 989 (1936). (12) H. 8. Hetzer, R . A . Robinson, and R. G. Bates, J. Phys. Chem., 66, 1423 (1962)
A N A L Y T i C A L C H E M I S T R Y , VOL. 45, NO. 9, A U G U S T 1973
1663
Table II. paH Values of Equimolal Tricine (HT) and Sodium Tricinate (NaT) Solutions from 5 to 50 "C
0 ul 0
pa H
P(aHYBr)
mKRr
=
mHT
0
mNaT
In 9
t("C) 0 0 0 0 0 0 0
0 P 0
0 IC
m
5 10 15 20 25 30 35 40 45 50
0.016029 0.009547 0.005654
0
0.04875
0.04761
0.04572
0.04444
0.05
8.562 8.454 8.350 8.251 8.157 8.066 7.980 7.896 7.817 7.740
8.564 8.456 8.352 8.254 8.161 8.069 7.984 7.900 7.821 7.744
8.565 8.457 8.353 8.255 8.162 8.071 7.985 7.901 7.823 7.747
8.566 8.458 8.356 8.257 8.165 8.074 7.988 7.905 7.826 7.751
8.485 8.375 8.271 8.175 8.079 7.988 7.902 7.817 7.740 7.663
0 0 0 0
Table Ill. paH Values for the Solution of Tricine (0.06m) and Sodium Tricinate (0.02m) from 5 to 50 "C 0
p(aH?'Br)
pal{
ul
m
0 0 0 0 0 0 0
m
~
~ 0.015 r
0.01
0.005
0
8.088 7.980 7.877 7.778 7.684 7.593 7.507 7.473 7.423 7.344 7.266
8.085 7.977 7.873 7.775 7.682 7.590 7.501 7.470 7.419 7.339 7.262
8.080 7.974 7.871 7.771 7.680 7.587 7.497 7.467 7.416 7.336 7.259
t("C) 0
m 0 0 0 0 0 0 0 0
0 N ul
0 N 0
0 0 0 0 0 0 0
0 ul r
0 0 0 0 0 0 0
5 10 15 20 25 30 35 37 40 45 50
8.093 7.983 7.879 7.781 7.686 7.596 7.510 7.475 7.426 7.346 7.269
ries was averaged. Duplicate cells usually gave readings within 0.04 mV of the recorded average, while the change in emf from the beginning to the end of the runs was usually considerably less than 0.1 mV. Values of the acidity function p(aHyBr) were derived at each temperature from the emf ( E ) ,the molality of bromide ( m H r - ) ,and the standard emf (EO)by the equation P ( ~ H Y B ~=)
0 0
r
0 0 0 0 0 0 0
0 ul
0 0 0 0 0 0 0
E - E@ -_ ( R T In 10)lF
+ log mBr-
A I"*
mr-ct
o m w
c wT momom -
T 2 ~
0 0 0 0 0 0
0 0 0 0 0 0
P
-
E
1664
-
A N A L Y T I C A L C H E M I S T R Y , VOL.
(1)
When the values for each buffer solution were plotted as a function of m B r - straight lines of small slope were obtained, and intercepts, namely p(aHyBr)', a t mBr- = 0 were easily obtained by graphical extrapolation. The uncertainty introduced in this step appeared to be less than 0.002. Finally, paH for the bromide-free buffer solutions was calculated by introducing a convention for Y B r - : PaH = p(aHyB~)@ - 1+
N b m
8.023 7.916 7.813 7.713 7.621 7.527 7.437 7.407 7.355 7.275 7.197
p ~ 1 / 2
(2)
In Equation 2 , A is the slope constant of the DebyeHuckel theory (scale of molality), I is the ionic strength of the buffer solution, and the value of p was taken to be 1.6 a t all temperatures. The ionic strength of each bromidefree buffer solution was taken to be the same as the molality of tricinate; hydrolysis of the buffer species is negligible, and the zwitterion form of tricine was assumed to make no contribution to the ionic strength. It will be noted in Table I1 that the value of p ( a ~ y ~ , ) O derived by extrapolation of the data for the equimolal buffer solution to mBr- = 0 corresponds to a buffer molality of 0.04444 mol kg-1 instead of 0.05 mol kg-1. This is because the buffer molality was not held constant but varied with the bromide molality in this series of mea-
45, N O . 9, AUGUST 1973
surements. The only effect of a n increase from 0.04444 to 0.05 mol kg--l without altering the buffer ratio would be to increase the last term of Equation 2 by 0.003 unit at each temperature. This correction has been made in order to obtain paH for the solution in which both tricine and sodium tricinate are present a t a molality of 0.05 mol kg-1. The values of p(aHyH,) and paH are summarized in T a bles I1 and III. The paF3values for the two buffer solutions are represented by the following equations: 0.05rn tricine, 0.05rn sodium tricinate: patI = 8.0789 - 0.01861(t - 25)
+
0.000080(t - 25)'
(3)
and 0.06rn tricine, 0.02m sodium tricinate: pa, = 7.6189 - 0.01870(t - 25)
+
0.000074(t
- 25)'
(4)
where t, the temperature in "C, lies between 5 and 50 "C. The standard deviations for regression of the "observed" results from these two equations are 0.0014 and 0.0013, respectively.
EXPERIMENTAL Tricine, obtained from Sigma Chemical Co., was recrystallized from 70% ethanol and dried in vacuum a t room temperature. An assay of 99.97% was obtained by titration of tricine with the same standard alkali subsequently used to prepare the buffer solutions. Reagent-grade potassium bromide was recrystallized from water. The solutions were deaerated with bubbling hydrogen after preparation, and air was excluded during the filling of the cells. The cell design ( 1 3 ) and the preparation of the hydrogen electrodes (14) have been described earlier. The silver-silver bromide electrodes, of the thermal type, were prepared by decomposition of a paste of silver oxide and silver bromate on helices of platinum wire at 580 "C. Measurements of test cells with hydrogen and silver-silver bromide electrodes in an HBr solution of molality 0.01 mol kg-l gave results consistent with earlier data from which the standard emf of the cell was determined (11, 12). The data a t six temperatures from 5 to 50 "C differed from those of Harned, Keston, and Donelson ( 1 2 ) by an average of only 0.04 mV. The buffer solutions were prepared from purified tricine and a standard solution of carbonate-free sodium hydroxide. Potassium bromide was added in different amounts to three different portions of each buffer solution. Duplicate cells of type I were prepared from each of the six cell solutions so obtained.
DISCUSSION In the foregoing treatment, tricine, a zwitterion, was presumed to make no contribution to the ionic strength, as would be the case with a neutral molecule. The validity of this procedure is confirmed by indirect lines of evidence. The emf data from which pK for the dissociation process H T = H f T - (where H T represents tricine) was determined (7) enable the activity coefficient terms ) be derived. When plotted as a funclog Y H T ( ~ H ~ - / ~ T - to tion of m f j r - + mT-, these values are found to yield straight lines of small slope, as indeed would be expected if ( y ~ ~ - / y , r . is . ) unity and H T behaves as a neutral species (2.5) or a dipolar ion ( 1 6 ) . If, on the other hand, the species H T were behaving as two individual ions, curvature should be observed, and it would then appear that the tricine makes a contribution to the ionic strength of the solution.
+
(13) R. Gary, R . G . Bates, and R. A . Robinson, J. Phys. Chem., 68, 1186 (1964). (14) R. G . Bates, "Determination of pH," 2nd ed., Wiley, New York, N.Y., 1973, Chap. 10. (15) M. Randall and C. F. Failey. Chem. R e v . , 4, 291 (1927). (16) E. J. Cohn and J. T. Edsall, "Proteins. Amino Acids and Peptides." Reinhold. New York, N Y . , 1943, Chap. 4and 12.
An examination of the data in Table I leads to similar conclusions. For the six solutions for which data at 25 "C are given in Table I, one obtains the following values of
1%
?"T(YHr-
/?T-
ml
1: m3
log ? w r ( ? t $ r - / ? r
Series 1 ( m , = m2) 0.04~5 0.04761 0.04572
0.016 0 2 9
-0.022
0.009547 0.005654
- 0 025 -0.027
Series 2 (ml = 3 m 2 ) 0.06 0.06 0.06
0.015 0.01 0.005
-0.028 -0.026 -0.024
If the tricine (molality r n l ) were behaving as a 1:l electrolyte instead of as a neutral molecule, the DebyeHuckel equation would lead one to expect an activity coefficient term eight to ten times as large as is actually found. Although the activity coefficient of tricine in salt solutions has not been measured, data are available for the closely related compound glycine in solutions of sodium chloride (17). Values of log y for glycine vary nearly linearly with ionic strength at I < 0.1 in sodium chloride solutions, closely resembling the behavior of the nonelectrolyte urea in salt solutions ( 1 8 ) . The value of log y for glycine at a molality of 0.05 mol kg-I in a 0.05m solution of sodium chloride is estimated to lie between -0.01 and -0.02. The choice of p = 1.6 was based on the following considerations. The p H convention (19), adopted for the purpose of deriving pa^ of standard reference solutions from p(uHiycl)derived from the emf of cells with hydrogen and silver-silver chloride electrodes, prescribes a value of 1.5 for p in the calculation of log y r l . The quantity p represents Be, the product of the Debye-Huckel B constant and an ion-size parameter 6 , and would therefore be expected to be slightly larger than 1.5 for bromide ion and still larger for iodide ion. Bates (20) has determined p(aE5yx)0for phosphate buffer solutions, where X is chloride, bromide, or iodide. It is evident that pat{ must have the same value regardless of which set of data is :]sed to derive it. When the Bates-Guggenheim convention (19) is used, the pat3 of the equimolal phosphate buffer solution is 7.065 a t I = 0.01 and 6.862 at I = 0.1. To match these values with data for p ( a t ~ y ~ ~ p) Omust , be about 1.6; if p ( a ~ y l ) Ois used, p must be about 1.75. Wit,h these values of p , pa^ from the bromide data is found t o be 7.064 and 6.860, respectively, at these two ionic strengths; from the iodide data, pa^ is found to be 7.064 and 6.859, respectively. The tricine buffer solutions may be properly regarded as standards of assigned puk1 and should find use when solutions of known conventional paH are needed. as, for example, in the determination of dissociation constants by the spectrophotometric method. They are also suitable secondary standards of pH. They cannot, however. be considered as primary standards for pH until it is shown that the liquid-junction potential arising with their use matches that of the uniform set of primary standards by which the practical scale of pH is presently defined. (17) E. E. Schrier and R . A . Robinson, J. Biol. Chem., 246, 2870 (1971). (18) V. E. Bower and R. A. Robinson,J . Phys. Chem.. 67, 1524 (1963) (19) R. G . Bates and E. A. Guggenheim. Pure Appl. Chem., 1 , 163 (1960). (20) R. G. Bates. J. Res. Nat. Bur. Stand.. 39. 411 (1947)
A N A L Y T I C A L C H E M I S T R Y , VOL. 45. NO. 9. A U G U S T 1973
1665
This comparison of the ~ u Hassigned to the solution of tricine (0.06m) and sodium tricinate (0.02m) with the primary pH standards was made as follows. The emf of a cell with hydrogen gas electrode, 3.5M calomel reference electrode, and liquid junction formed in a 1-mm vertical capillary tube was determined when the cell contained the 1:3.5 phosphate standard composed of KHzPO4 ( m = 0.008695) and NazHP04 ( m = 0.03043). The phosphate standard was then replaced by the tricine buffer and the measurement repeated. The barometric pressure and the temperature (26.3 "C) were the same for the two measurements, and the emf for the tricine buffer was higher than that for the phosphate standard by 0.01056 V. At 26.3 "C,
therefore, the pH of the tricine buffer was 0.178 unit higher than that of the phosphate standard [7.409 a t this temperature (IO)]or 7.587. This value is 0.009 unit lower than 7.596 calculated by Equation 4 of this paper. Thus, the residual liquid-junction potential is probably not so large as to exclude tricine from consideration as a primary standard for pH measurements. Received for review February 16, 1973. Accepted April 6, 1973. Work supported in part by the National Science Foundation under Grant GP-14538 and by the donors of the Petroleum Research Fund, administered by the American Chemical Society.
Ionic Hydration and Single Ion Activities in Mixtures of Electrolytes with a Common Unhydrated Anion R. A. Robinson and Roger G. Bates Department of Chemistry, University of Florida, Garnesville, Fla. 32607
In earlier papers, a hydration convention permitting single ion activities to be derived from mean ionic activities of unassociated electrolytes has been outlined. This convention has now been combined with the thermodynamic theory of electrolyte mixtures to obtain single ion activity coefficients for the three ions in mixtures of two electrolytes with a common unhydrated anion. The method is illustrated with data for mixtures of potassium chloride and sodium chloride at a total molality of 4 mol kg-' and for hydrochloric acid and sodium chloride at a total molality of 3 mol kg-l.
Ion-selective electrodes responsive to a considerable variety of ions are now available. Thermodynamics leads one to expect that the potentials of these electrodes are a function of ion activities instead of concentrations, and this conclusion is supported by experimental evidence (1-4). Ion-selective electrodes are therefore capable of measuring ionic activity relative to a standard in which the activity of the ion is known or assigned. Inasmuch as thermodynamic theory can offer no unique definition of the activity of any single ionic species, no consistent standard scales of ionic activity yet exist. The problem is compounded by the common use of ion-selective electrodes at high ionic strengths, where marked specific differences among the activity coefficients of ions of like charge become apparent. As a result, a chaotic situation is rapidly developing. A conventional scale of hydrogen ion activity ( 5 ) has proved very satisfactory for the standardization of glass pH electrodes. The convention on which it is based (6) re-
lates the activity coefficient. of chloride ion to ionic strength (0 in the region 0 < I < 0.1. Other simple conventions would have served equally well in this dilute range. The problem of establishing scales for a variety of ions a t higher ionic strengths is, however, of considerably greater complexity. The scales that will eventually be adopted for single ion species must be consistent with the measurable thermodynamic constants for pairs or other combinations of ions. Accordingly, they must take account of specific ionic properties of which differences in the interaction of ions with the solvent are probably the most important. In earlier papers (7, 8) we have suggested that the hydration number h can be used to characterize ionic specificity of the latter type. In 1948, Stokes and Robinson (9) put forth a hydration theory combining ion-ion interaction with ion-solvent interaction and showed that the mean activity coefficients (r*)of strong electrolytes can be expressed accurately by an electrostatic (DebyeHuckel) term dependent on the ion size, together with a hydration number and the solvent activity. We have introduced (7) a conventional method (based on hcl- = 0) to derive ionic hydration numbers from the hydration number for the electrolyte and have shown that thermodynamics then leads to a formula for separating the mean activity coefficient into the activity coefficients of the component ions. For a uni-univalent electrolyte ( u = 2) at molality m , the equations for the cation (+) and anion ( - ) are logy+ = logy, 0.00782(h+ - h-)m$ (1)
+
and logy- = logy,
(1) p. Schindler and E. Walti, Helv. Chim. Acta, 51, 539 (1968). (2) A. Shatkayand A. Lerman,AnaL Chem., 41, 514 (1969). (3) J. N. Butler, in "Ion-Selective Electrodes," R. A. Durst, Ed., Nat. Bur. Stand. Spec. Pub., 314, Washington, D.C., 1969, Chap. 5. (4) R. G. Bates and M. Alfenaar, Nat. Bur. Stand. Spec. Pub/., 314, Chap. 6. (5) R. G. Bates, J. Res. Nat. Bur. Stand., 66A, 179 (1962). (6) R . G. Bates and E. A. Guggenheim. Pure Appl. Chem., 1, 163 (7960).
1666
+
0.00782(h- - h+)m$
(2)
where 4 is the osmotic coefficient, (-ln a,)/0.018 u r n . (7) R. G. Bates, B. R. Staples, and R. A. Robinson. Anal. Chem., 42, 867 (1970). (8) R. A. Robinson, W. C. Duer, and R. G. Bates, Anal. Chem., 43, 1862 (1971). 70, 1870 (9) R. H. Stokes and R. A. Robinson, J. Amer. Chem. SOC.. (1948).
A N A L Y T I C A L C H E M I S T R Y , VOL. 45, NO. 9, AUGUST 1973
