Anal. Chem. 1983, 65, 1084-1087
1084
Second Dissociation Constant of 3-(I\CMorpholino)-2-hydroxypropanesulfonic Acid and pH of Its Buffer Solutionst Y. C. Wu, P. A. Berezansky, Darning Feng, and W. F. Koch' National Institute of Standards and Technology, Inorganic Analytical Research Division, Gaithersburg, Maryland 20899
3-( KMorphoilno)-2-hydroxypropanesuifonic acid (MOPSO) has been recommendedas a second pH standard in the range of phydoiogicai application. The pH values for this buffer system, at Ionic strengths matchlng those In physldogicai fluids, have been determined at temperatures from 0 to 50 O C by the emf method. The liquid junction potentials between the M e r solutions of MOPSO and saturated KCI soiutlon of the calomel electrode at 25 O C have been evaluated by measurement with flowing junction so that the operational pH values can be ascertained. The second dl6sociationconstant of MOPSO at various temperatures has been determined and is 6.829 f 0.004 at 25 OC. The related thermodynamlc properties have been calculated.
INTRODUCTION Though phosphate buffer has been widely used as a physiological pH standard, it is not an ideal pH standard for physiological use. (The reason of which will be discussed later.) In response to the need for new physiological pH standards, we have determined the p K 2 ~of N-(2-hydroxyethy1)piperazine-N'-ethanesulfonicacid (HEPES) and the pH values of its buffer solutions a t temperatures from 0 to 50 "C by the emf method.' The National Institute of Standards and Technology has certifieded HEPES (SRM 2181)and its sodium salt, NaHEPESate (SRM 2182),as new Standard Reference Materials, This zwitterionic buffer system is intended as an alternative to the physiological phosphate buffer standard (pH 7.415 at 25 OC) for clinical pH measurements.2 We now propose a second zwitterionic physiological pH standard, 3-(N-morpholino)-2-hydroxyprcpanesulfonic acid (MOPSO), as a substitute to the equimolal phosphate buffer (pH 6.863at 25 "C) for two-point calibration in pH measurement for physiological application. In order to establish MOPSO as a pH standard, its p K 2 ~ values are needed. Using the titration method, Ferguson et al.3 and Kitamura and Itoh4 both reported that the p K 2 ~of MOPSO was 6.88 at 25 "C. Dasgupta and Nara5 obtained a P K ~ value A of 6.625 f 0.157 a t 24 f 1 "C by measuring the conductance of 10-3 m NaMOPSOate solution before and
* Author to whom correspondence should be addressed.
Certain commercial equipment, instruments, or materials are identified in this report to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified is necessarily the best available for the purpose. (1)Feng, D.; Koch, W. F.; Wu, Y. C. Anal. Chem. 1989,61, 1400. (2)Certificate of Analysis: Standard ReferenceMaterials, 2181 HEPES and 2182 HEPES Sodium Salt; National Institute of Standards and Technology, 1989. (3) Ferguson, W. J.; Braunschweiger, K. I.; Braunschweiger, W. R.; Smith, J. R.; McCormick, J. J.; Wasmann, C. C.; Janis, N. P.; Bell, D. H.; Good, N. E. Anal. Biochem. 1980, 104,300. (4) Kitamura, Y.; Itoh, T. Solution Chem. 1987, 16, 715. (5)Dasgupta, P. K.; Nara, 0. Anal. Chem. 1990, 62, 1117. +
after passage through an H+-form exchanger. Popsbhal, Deml, and BoEek6 reported a p K 2 ~value of 6.79 f 0.06 at 0.006m ionic strength by using a capillaty isotachaphoresispH measurement. All these values are not the true thermodynamic dissociation contant since they do not include the activity coefficients. Furthermore, they are not accurate enough for our purpose of establishing a pH standard. In this work, the p K 2 ~of MOPSO at temperatures from 0 to 50 "C was determined based on measurements of the emf of the following cell without liquid junction: Pt, H, (1 atm)/MOPSO ( m J , NaMOPSOate (m2),NaCl (m,)/AgCl,Ag where NaMOPSOate is the sodium salt of MOPSO and m is the concentration in molality. The pH values at the same temperature ranges have been evaluated and assigned to two MOPSO buffer solutions, 0.05 equimolal MOPSO-NaMOPSOate and 0.08equimolalMOPSO-NaMOPSOateNaC1; the ionic strength of the latter matches that of physiologicalfluids. The theory and the experimental method of determining the p K 2 ~and pH for the two MOPSO buffers are the same as those for the HEPES system. There is one exception: in this work the mutual influence of MOPSO on the activity coefficient of NaCl and vice versa is evaluated from the work done in this laboratory? while for HEPES system,this mutual influence between NaCl and HEPES was not yet known. In addition, the compatibility of the three physiological buffers, viz., phosphate, HEPES, and MOPSO, is tested with the liquid junction potential by means of the flowing junction method.
THEORY MOPSO, when dissolved in water, is in the form of a zwitterion, a dipolar molecule (Z*). The second dissociation constant of this molecule may be expressed as8
where a is activity, and y is the molal activity coefficient. By definition, pH = -log U H , we have PH = P K ~ A + log (m,J+,*) log (TzJTzl) (2) If mz- = mp, and the activity coefficient term is neglected, PKZAis approximately equal to pH. For accurate determination of p K z and ~ pH, the emf measurement of the following cell was performed: Pt, H,(1atm)/MOPSO (ml), NaMOPSOate (m,), NaCl (m,)lAgCl,Ag (6)Pospichal, J.; Deml, M.; BoEek, P. J. Chromatogr. 1987,390, 17. (7)Wu, Y. C.; Feng, D.; Koch, W. F. J.Res. Natl. Zmt.Stand. Technol. 1991, 96,757. (8) Cohn, E.
J.; Edsall, J. T. Proteins, Amino Acids and Peptides; Hafner Publishing Co.: New York, 1965;Chapter 4.
This article not subject to US. Copyright. Published 1993 by the American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 65, NO. 8, APRIL 15, 1993
Thus
E = E" - k log u H u C ~ E" - k log UH - k log mclycl (3) where Eo is the standard potential of Ag,AgCl electrode, and k is the Nernst slope, R T In 1O/F. The charges on H+ and C1- are dropped for convenience. The substitution of eq 2 into eq 3 with rearrangement yields
( E - E o ) / k + log mcl - log (m,/m,)
= pKzA
-
E' = (E - E o ) / k+ log ma
+ log m,,
data in the literature about the influence of HEPES on the activity coefficient of NaC1. So we had to assume that this influence was the same as that of glycine.' Later, the influence of HEPES and MOPSO on the activity coefficient of NaCl was determined using a sodium ion-selective electrode? and the data were used to evaluate the log (yNaCI/Y"NaCI) term in this study.
+
log (rzlrzt)- log YCI (4) Because the second dissociation of MOPSO is small ( p K 2 ~ 7), mZ*and mz- are set to be equal to the initial concentrations of Zfand 2-in the cell, i.e., mz* = ml,mz- = m2; therefore, all quantities in the left-hand side of eq 4 are known. Let E' represent the left-hand side of eq 4, then
- log mZ.
(5) = PK~A- log YZ+ + log (YZ-IYC~) To obtain P&A, an evaluatiori for the y terms in eq 5 is necessary. It has been found that the activity coefficient of a dipolar molecule in a salt solution is a function of its own concentration and the ionic strength of the solution and can be expressed as follows:~-" -log yz, = amZt + 61 + {f (6) where I is the ionic strength of the solution; a,6, and { are adjustable parameters. Since Z-ion and C1- ion both have a charge of -1, the first term in the extended Debye-Huckel equation for activity coefficient is assumed to be the same, and any difference is lumped to the linear term, thus
EXPERIMENTAL SECTION Apparatus. The cells studied were the following: Pt-H2(g,1atm)/MOPSO (ml), NaMOPSOate (m2), NaCl (m3)/AgC1,Ag (1) Pt-H2(g,1atm)/MOPSO (ml), NaMOPSOate (m2), NaCl (m,)//KCl (satd),Hg,Cl,,Hg (11) Pt-H,(g, 1atm)/phosphate buffer//KCl (satd), Hg2C12,Hg (111) where "//" denotes a liquid junction. All the electrodes and the setup have been described in the previous paper.' An Orion 701A pH meter and an Orion 91-02 combination glass electrode were used for the pH titration of MOPSO. Materials. MOPSO and NaMOPSOate were obtained from Sigma Co. (St. Louis, MO). A portion of MOPSO was recrystallized twice from 70% ethanol solution. Both purified and unpurified materials were dried in a vacuum oven at 2-3 Pa and 50 "C for 24h and were assayed by titration with standard sodium hydroxide. The analyses of unpurified and purified MOPSO averaged 99.70 and 99.99% pure, respectively. NaCl was ACS reagent grade and was dried at 110 "C for 4 h before use. All mass measurements were made with an accuracy of 0.03 mass percent, and air buoyancy correctionswere applied for all masses used. The laboratory distilled water used in this experiment was passed through a deionizing column and had a conductivity of less than 1 &cm.
log (rz./rc1) = @I (7) where 0 is also a adjustable parameter.' By substituting eqs 6 and 7 into eq 5, we obtain
E' = pKzA+ amZt + (@+ 6)I + {f (8) By plotting E' vs I a t each mz* and extrapolating to I = 0 through a least-squares method, we obtain P K ~ A + a m p as the intercepts and the parameters j3 + 6 and { as the parameters
of the quadratic equation. A plot of ~ K Z+A a m p extrapolated to mz* = 0 will yield p K 2 from ~ the intercept and a from the slope. After p K 2 ~ is known, pH values for the buffer solutions can be obtained as follows. Substituting eqs 6 and 7 into eq 2 and rearranging, we have PH = pKzA+ log (mz./mz,) - log yzt +
1% (rzJrc1) + log Y a = pKzA + log (mz,/mz+) + amZt + (0 + 6)I + tf + log Yc1 (9) Since there is no known method to determine single ion activity, we have to assume that YCI = YNaCI. Then, log y a in eq 9 may be calculated using the following equation: (lo) log YCI = log YNaCl = log y"NaC1 + log (YNaCdY'NaCI) where ~ " N ~ is C Ithe activity coefficient of NaCl in pure NaCl ~ activity ~ 1 coefficient of NaCl in the buffer solution; 7 ~is the represents solution. The last term of eq 10,log (YN~cI/Y"N~c~), the influence of MOPSO on the activity coefficient of NaCl. When we were studying the HEPES system, there was no (9) Scatchard, G.; Kirkwood, J. G . Phys. 2. 1932,33, 297. (10) Robert, R. M.; Kirkwood, J. G. J. Am. Chem. SOC.1941,63,1373. (11) Feng, D.; Koch, W. F.; Wu,Y. C. J . Solution Chem. 1992,21,311.
1085
RESULTS Second DissociationConstant (p&) of MOPSO. The emf values at seven temperatures are listed in Table I, where each emf value is a mean of a t least two runs. The values of E" in eq 3 were taken from previous work done in this laboratory.12 A typical plot of E' vs I and p K z ~+ am1 vs ml a t 25 "C is illustrated in Figure 1. As seen from Figure 1,the curves of E' vs I for the MOPSO system are not straight lines, as they are for HEPES system. However extrapolation to I = 0 can be obtained with a least-squares method. The p K z ~ values so obtained are listed in Table I1 and are shown in Figure 2. The thermodynamic properties relatedto the second dissociation of MOPSO are also obtained and listed in Table 11. They are similar to the corresponding values of HEPES (1).
pH Values for 0.05 Equimolal MOPSO-NaMOPSOate and 0.08 Equimolal MOPSO-NaMOPSOate-NaC1 Buffer Solutions. pH values for the buffer solutions were calculated from eq 9. For the two equimolal buffer solutions, mz- = mz*; log y c ~ can be obtained from eq 10, where values I interpolated from tabulated data13 and for log ~ " N ~ Cwere values for log ( Y N ~ C ~ / Y " N ~ C were I) taken from our previous report7 The adjustable parameters a,@,6, and lwere obtained through the quadratic equation by a least-squares method for the curves in Figure 1. The pH values at 12 temperatures thus obtained were fitted to the polynomial
pH = 1137.6/T + 3.5690 - 0.0017360T (11) for equimolal 0.05 MOPSO-NaMOPSOate buffer solution, (12) Wu, Y. C.; Koch, W. F. J. Solution Chem. 1986, 15, 481. (13) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths Scientific Publications: London, 1959; p 481.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 8, APRIL 15, 1993
Table I. emf Values of the Cella E. V ml
m2 = m3
0.02 0.02 0.02 0.02 0.02 0.05 0.05 0.05 0.05 0.05 0.08 0.08 0.08 0.08 0.08
0.01 0.02 0.04 0.06 0.08 0.01 0.02 0.04 0.06 0.08 0.01 0.02 0.04 0.06 0.08
10 "C 0.72938 0.72994 0.73088 0.73150 0.73212 0.70740 0.70811 0.70898 0.70959 0.71026 0.69622 0.69706 0.69800 0.69860 0.69926
5 "C 0.72762 0.72818 0.72913 0.72976 0.73040 0.70606 0.70678 0.70765 0.70828 0.70896 0.69512 0.69596 0.69690 0.69752 0.69818
15 "C 0.73094 0.73148 0.73244 0.73306 0.73366 0.70855 0.70927 0.71012 0.71072 0.71138 0.69712 0.69798 0.69892 0.69951 0.70015
20 "C 0.73232 0.73286 0.73382 0.73442 0.73500 0.70956 0.71024 0.71108 0.71170 0.71233 0.69782 0.69871 0.69964 0.70024 0.70087
25 "C 0.73353 0.73405 0.73500 0.73562 0.73619 0.71026 0.71102 0.71186 0.71249 0.71310 0.69832 0.69925 0.70019 0.70084 0.70138
37 "C 0.73576 0.73634 0.73724 0.73780 0.73836 0.71150 0.71228 0.71308 0.71366 0.71426 0.69909 0.69996 0.70089 0.70148 0.70203
50 "C 0.73714 0.73772 0.73862 0.73916 0.73972 0.71182 0.71260 0.71340 0.71399 0.71456 0.69886 0.69974 0.70066 0.70124 0.70181
Pt-Hz (1 atm)/MOPSO (ml), NaMOPSOate (mz), NaCl (m3)/AgCl, Ag for evaluation of p K 2 ~ .
Na2HP04)and saturated KC1 solution at 25 OC is found to be 2.5 mV.l For the system in cell I11
't
E, = ~ P H-, E ' d o m e l + Ejs (14) where the subscript s denotes the physiological phosphate standard. The combination of eqs 13 and 14 yields k(pH - pH,) + Ej- Ej, (15) Substituting E,, = 2.5 and pH, = 7.415 into eq 15,the liquid junction potential between a buffer solution and saturated KC1 solution a t 25 OC can be evaluated as follows:
E - E,
Ej = ( E - E , )
+ 59.16(7.415- pH) + 2.5
(16) The results are listed in Table IV, together with the liquid junction potentials of HEPES buffer solutions for comparison. Some other buffer properties of the HEPES and MOPS0 buffer solutions are listed in Table V.
DISCUSSION
6.92
1 I
I
0
I
0.04
I
, 0.08
I
I
I
I
0.12
0.16
ionic strength (mol/kg) Figuro 1. Evaluation of pK2 at 25 OC: 0 , pK'vs I at ml = 0.02; 0, ~ K ' v sI at ml = 0.05; A, PK'vS I at ml = 0.08; + t PK2 ffm, VS ml
.
+
and the polynomial pH = 1312.O/T+ 2.4699 - 1.7835 X 10-5T (12) for equimolal 0.08 MOPSO-NaMOPSOateNaCl buffer solution, where Tis the temperature in Kelvin. The smoothed pH values are listed in Table 111. Liquid Junction Potentials of Two Buffer Solutions. The liquid junction potentials between the two buffer solutions and saturated KCl solution of the calomel electrode were obtained from cells I1 and 111. The emf of cell I1 can be expressed as
E = kpH - E'domel+ Ej (13) where Ej is the liquid junction potential, and E'cdomel is the electrode potential of the saturated calomel electrode. Equation 13 shows that if the pH is known, the liquid junction potential Ej can be obtained. Thus, Ej between the physiological phosphate buffer (0.008695m KH2P04 - 0.03043 m
In 1961, the (formerly) National Bureau of Standards certified the physiological phosphate pH buffer for use in the physiological range of interest between pH 7.3 and 7.5. Since then, this buffer has been widely accepted and used in clinical laboratories as a primary pH standard. However, there are some disadvantages concerning this buffer: phosphates precipitate some polyvalent cations in the blood, such as Ca2+ and Mg*+, and may also act as an inhibitor to enzymatic processes; its temperature coefficient (-0.0028pH unit/OC) does not adequately approximate that of whole blood (-0.015 pH unit/OC) and plasma (4.01pH unit/OC).15 In this work and our previous work,l we have provided four buffer solutions based on zwitterionic buffer systems for clinical pH measurements: 0.05 equimolal HEPES-NaHEPESate, 0.05 equimolal MOPSO-NaMOPSOate, 0.08equimolal HEPESNaHEPESateNaCl, and 0.08equimolal MOPSO-NaMOPSOate-NaC1. These four buffer solutions are compatible with the constituents of physiological fluids, and their temperature coefficients (see Table V) more closely approximate that of whole blood and plasma than the temperature coefficient of phosphate. The 0.05 equimolal HEPES-NaHEPESate and 0.05 equimolal MOPSO-NaMOPSOate buffer solutions (pH = 7.364 and 6.699a t 37 "C, respectively) can be used as pH standards in two-point calibrations for solutions with low ionic strength. As seen from Table IV, the liquid junction potentials between each of the 0.05 equimolal HEPESNaHEPESate, 0.05 equimolal MOPSO-NaMOPSOate, phys(14)Wu, Y.C.;Koch, W. F.; Marinenko, G.J . Res. Natl. Bur. Stand. 1984, 89,395.
(15)Durst, R. A,; Staples, B. R. Clin. Chem. 1972, 18, 206.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 8, APRIL 15, 1993
Table 11. Second Dissociation Constants and Related Thermodynamic Properties of MOPSO temp, "C 5 10 15 20 25 7.076 7.001 6.929 7.231 7.153 PKZA 39.30 39.56 38.78 39.04 AGO, kJ/mol 38.51 24.05 24.14 23.96 23.78 23.87 AHo, kJ/mol 52.3 52.0 51.7 53.0 52.6 -ASo, J/(mol.K) 18.2 18.5 18.8 17.5 17.8 ACPo, J/(mol.K)
37 6.766 40.17 24.37 51.0 19.5
1087
50 6.599 40.83 24.63 50.1 20.4
Table V. Some Buffer Properties of Four Buffer Solutions of HEPES and MOPSO dilution buffer temp solution value value coeff 0.05 m HEPES-NaHEPESate -0.054 0.061 -0.011 0.05m MOPSO-NaMOPSOate -0.087 0.091 -0.014 -0.026 0.107 -0.012 0.08 m HEPES-NaHEPESate-NaC1 0.08 m MOPSO-NaMOPSOate-NaC1 -0.012 0.105 -0.016
I 0
I
I
I
1
I
10
30
30
40
50
tl
OC
Ftgure 2. pKZAat different temperatures.
Table 111. Smoothed pH Values of 0.05 Equimolal MOPSO-NaMOPSOate and 0.08 Equimolal MOPSO-NaMOPSOate-NaC1 Buffer Solutions temp, "C pH, 0.05 m pH, 0.08 m 0 7.260 7.268 5 7.176 7.182 10 7.095 7.098 15 7.017 7.018 20 6.941 6.940 25 6.867 6.865 30 6.795 6.792 35 6.726 6.722 37 6.699 6.695 40 6.658 6.654 45 6.592 6.588 50 6.528 6.524 Table IV. emfs and Liquid Junction Potentials in Cell Pt-Hz/Solution//KCl (satd). Ha,Ch.Ha at 25 O C _____ solution E,V pH E,,mV physiological phosphate 0.68178 7.415 2.5 0.05m MOPSO-NaMOPSOate 0.64978 6.867 2.9 0.05m HEPES-NaHEPESate 7.503 2.2l 0.08 m MOPSO-NaMOPSOate-NaC1 0.64787 6.865 1.1 0.08 m HEPES-NaHEPESate-NaC1 7.516 0.V ______
iological phosphate buffer, and the saturated KC1 solution are relatively close to each other (2.2,2.9, and 2.5 mV, respectively). These three buffer solutions are intercomparable for pH measurements. For physiological fluids, the ionic strength is about 0.16 m. A major constituent of physiological fluids is sodium chloride which will decrease the liquid junction potential between a solution and saturated KCl solution significantly.
The 0.08 equimolal HEPES-NaHEPESate-NaC1 and 0.08 equimolal MOPSO-NaMOPSOate-NaC1 buffer solutions (pH = 7.373 and 6.694 a t 37 "C, respectively) are specially designed as pH standards in two-point calibrations of pH measurement systems used with physiologicalfluids. These two buffer solutions have approximately the same ionic strength as the physiological fluids, and the liquid junction potentials between them and saturated KC1solution (0.5 and 1.1 mV, respectively) are expected to be close to those of physiological fluids. Therefore, using these two buffer solutions as pH standards will minimize the error in pH measurements involving the physiological fluids. If ordinary pH standards are used in this kind of measurement, it is estimated that the residual liquid junction potentials will result in errors of about 0.03 in pH. Because of the difference in liquid junction potentials, the two 0.08 m buffer solutions will not give equivalent results when compared with the physiological phosphate buffer during pH measurements. Estimation of uncertainties: The maximum difference observed among our set of Pt,H2 electrodes is 0.020mV and is an insignificant component of uncertainty. The standard potential of the Ag,AgCl electrodes is accurate to 0.1 mV, corresponding to an uncertainty about 0.002 in pH. The uncertainty for p K 2 ~based on twofold standard deviation of the intercept is about 0.004,corresponding to a component of uncertainty in the pH for the buffer solutions of 0.004.The component of uncertainty in the pH resulting from the uncertainties of the adjustable parameters is estimated to be 0.004 for the 0.05 equimolal MOPSO-NaMOPSOate solution and 0.01for the 0.08equimolalMOPSO-NaMOPSOate-NaC1 solution. In the evaluation of assigned pH values to buffer standards, the assumptions for the assignment of the activity coefficient of the chloride ion are the major source of Uncertainty. Since there is no known method to determine single ion activity, we assume that YCI- = Y N ~ += Y N ~ C I . We have assigned an uncertainty of 0.004in log y,corresponding to approximately 0.25 mV, due to this extrathermodynamic assumption for 0.05 equimolal MOPSO-NaMOPSOate buffer solution, and 0.3-0.4 mV, or about 0.006 in pH, for the 0.08 equimolal MOPSO-NaMOPSOate-NaC1. The overall uncertainty for the pH values were estimated by combining the above systematic uncertainties with the random component (0.002 in pH) by the method of root-sum-squares. Accordingly, referring to the values in Table 111, for the 0.05 equimolal MOPSO-NaMOPSOate buffer solution, the estimated uncertainty in the pH is 0.010,and for the 0.08 equimolal MOPSO-NaMOPSOateNaCl buffer solution, the estimated uncertainty in the pH is 0.015.
RECEIVED for review June 17, 1992. Accepted January 11, 1993.
