1922
ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
Buffers for the Physiological pH Range: Thermodynamic Constants of 3-( N-Morpholino)propanesulfonic Acid from 5 to 50 "C Munessar Sankar' and Roger G. Bates" Department of Chemistry, University of Florida, Gainesville, Florida 326 7 1
The pK2 values for the dissociation of the NH' charge center of the ampholyte 3 4 N-morphollno)propanesulfonic acid (MOPS) have been determined at 10 temperatures from 5 to 50 OC by measurements of the emf of cells without liquid junctlon, utilizing hydrogen electrodes and silver-silver bromide electrodes. The pKz was found to be 7.184 at 25 O C , confirming the expectation that the NH' group In the substituted propanesuifonic acid Is weaker than that in the correspondlng ethanesulfonic acid prevlously studied. Enthalpy and entropy values for the dissoclatlon process were derlved from the temperature coefficient of pKz, and MOPS was shown to be useful for pH control in the region close to that of blood serum.
T h e buffer substances recommended by Good ( I ) have proved useful for p H measurement and control in t h e physiological region of p H 7 to 9. These compounds, primarily protonated amines or N-substituted amino acids, are compatible with many media of biochemical importance. An inconsistency earlier observed between the p H of certain of these buffers in saline media of ionic strength equal to 0.16 and the NBS standard p H scale has recently been attributed to abnormal liquid-junction potentials ( 2 ) . Four substituted aminoethanesulfonic acids, designated MES, BES, TES, and HEPES, were the subject of an earlier communication (3). [N.B. A hydrogen atom has been omitted from the nitrogen atom in the formula for TES given on p 1293 of reference 3.1 T h e pK2 values of BES, TES, and HEPES at 37 "C fall in the useful range 7 to 7.5(near the p H of blood serum), b u t t h a t of MES, 2-(N-morpholino)ethanesulfonic acid, is near 6.15. Since morpholinium ion itself has a pK, near 8.2 a t 37 "C ( 4 ) , it is clear that substitution of -(CH2)$03- on the nitrogen atom of morpholine increases the acidity of the NH' group. This enhancement should fall off as n becomes greater, thus providing a means of tailoring a buffer substance with pK2 in the desired range. T h e ampholyte 3-(N-morpholino)propanesulfonicacid, known as MOPS,
(n
\H+ N-C,H,SO I
EXPERIMENTAL MOPS, purchased from the Sigma Chemical Co., was recrystallized twice from 80 w t % redistilled ethanol. It was dried under vacuum for 4 h at 80 OC and stored over Drierite. The purified compound was assayed by titration with a carbonate-free solution of NaOH; the resulh obtained for two samples were 100.05 and 99.97%. Reagent-grade NaBr was crystallized twice from conductivity water. It was heated slowly t o 140 OC in vacuum and maintained at this temperature for 5 h. The salt was stored over Drierite. Reagent-grade HBr solution was purified by distillation. Two stock solutions were prepared by weight methods from MOPS, NaBr, and standard NaOH solution in such amounts that the molalities of MOPS, NaMOPS, and NaBr were equal in each. Additional solutions for the cell measurements were prepared by adding weighed amounts of C0,-free water. Other details of the emf techniques have been described elsewhere (3).
RESULTS The values of the emf ( E ) of the cell Pt;H,(g, 1 atm)IMOPS(m), N a M O P S ( m ) , NaBr(m)( AgBr;Ag (A) where m is molality, from 5 to 50 "C are summarized in Table I. T h e standard emf ( E " ) of the cell was determined by measuring the emf (Es) of the cell Pt;H2(g, 1 a t m ) J H B r ( m = 0.Ol)IAgBr;Ag by the equation
E" = E,
-
4k
+ 2k log y*(HBr)
(1)
In Equation 1, k is written for (RT In 10)/F ( 5 ) ,and r*(HBr) is the mean ionic molal activity coefficient of HBr, molality 0.01 mol kg-'. Values of the latter a t 0, 25, and 50 O C were taken from the work of Hetzer et al. (6), and values a t the other temperatures were interpolated. The values of E" given at the foot of Table I are the means derived from the emf (E,) of 12 cells a t each of the 10 temperatures. T h e p H of the buffer solutions of MOPS and its sodium salt is so close to neutrality that hydrolysis is negligible, even in the most dilute buffers included in this study. Furthermore, the molalities of MOPS, NaMOPS, and NaBr were equal, and hence an apparent pK2, designated pK{, is defined by
C2H4 would be expected to have a pK, value somewhat higher than that of MES. T h e thermodynamic constants for the second dissociation of MOPS have now been determined a t intervals of 5 "C from 5 t o 50 "C, and the pK2 has indeed been found t o be 7.184at 25 "C and 7.041 a t 37 "C. T h e p H of a MOPS solution (buffer ratio 1:l)in a saline medium of Z = 0.16 has been determined a t 25 and 37 "C.
where yM and yM-represent the activity coefficients of the ampholyte MOPS and its anion, respectively. As in the earlier study (3), pK4 was found to vary linearly with ionic strength (0,and the limit (pK2) at Z = 0 was readily found by linear regression analysis: pK2' = pK2
leave from the University of Durban-Westville,South Africa, 1977-78. I On
+ CUI
(3)
The values of pK2 and a are summarized in Table 11, together
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
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Table I. Electromotive Force (E) and Standard Emf ( E " ) , in Volts from 5 t o 50 "C, of the Cell: Pt;H,(g, 1 atm)lMOPS(m), NaMOPS( rn ), NaBr( m )lAgBr f i g m 5 "C 10°C 15°C 20°C 25°C 30°C 35°C 40°C 45°C 50°C 0.004880 0.007331 0.009786 0.012251 0.014721 0.019679 0.02467 0.02962 0.03472 0.03979 0.04488 0.05000
0.61844 0.60891 0.60224 0.59702 0.59292 0.58627 0.58131 0.57723 0.57390 0.57091 0.56844 0.56613
0.62245 0.61278 0.60594 0.60066 0.59642 0.58970 0.58457 0.58046 0.57699 0.57399 0.57142 0.56909
0.62624 0.61633 0.60941 0.60397 0.59971 0.59280 0.58762 0.58336 0.57987 0.57675 0.57417 0.57173
0.62985 0.61974 0.61271 0.60715 0.60281 0.59576 0.59049 0.58613 0.58257 0.57937 0.57673 0.57423
0.63328 0.62296 0.61580 0.61015 0.60571 0.59855 0.59313 0.58868 0.68508 0.58182 0.57912 0.57659
0.63652 0.62600 0.61870 0.61296 0.60842 0.60114 0.59561 0.59109 0.58741 0.58409 0.58133 0.51876
0.63961 0.62887 0.62146 0.61559 0.61099 0.60356 0.59794 0.59332 0.58958 0.58618 0.58339 0.58074
0.64250 0.63157 0.62404 0.61807 0.61339 0.60583 0.60010 0.59538 0.59157 0.58811 0.58526 0.58256
0.64522 0.63410 0.62645 0.62037 0.61562 0.60791 0.60209 0.59727 0.59341 0.58987 0.58698 0,58422
0.64779 0.63649 0.62872 0.62253 0.61768 0.60986 0.60392 0.59904 0.59509 0.59149 0.58853 0.58574
E":
0.07986
0.07795
0.07587
0.07362
0.07122
0.06869
0.06605
0.06324
0.06030
0.05725
Table 11. pK, Values for MOPS from 5 to 50 "C. Constants of Equation 3. ti"C PK, CY (J (PK, )" 5 10
15 20 25 30 35 40 45 50 a
0.699 0.671 0.640 0.611 0.589 0.569 0.547 0.526 0.509 0.491
7.442 7.376 7.310 7.247 7.184 7.123 7.064 7.006 6.949 6.893
0.0007 0.0006 0.0007 0.0007 0.0006 0.0005 0.0005 0.0005 0.0006 0.0005
Standard deviation of the intercept.
with the standard deviation of the intercept, u(pK,).
DISCUSSION The values of pK2 a t the 10 temperatures fitted extremely well an equation of the form suggested by Harned and Robinson (7): 0.0038661T
(4)
where T i s the thermodynamic temperature ( t "C + 273.15). T h e standard deviation for regression was only 0.0002. T h e standard thermodynamic quantities for the process M O P S + H+
+ MOPS-
(5)
a t T = 298.15K, calculated from the constants of Equation 4, are as follows: AGO, 9801 cal mol-'; AH", 5000 cal mol-',
and AS", -16.10 cal K-' mol-', while AC," is estimated to be 10.5 cal K-' mol-'. The standard deviations in these quantities can be estimated from the standard deviation of pK, (0.0006) by the method described by Please (8). They are as follows: u(AG") = 0.4 cal mol-'; a(AHo) = 6 cal mol-'; u(AS") = 0.02 cal K-' mol-'; and u(ACp0) = 1 cal K-' mol-'. I t is evident from a comparison of the thermodynamic constants for the dissociation of MOPS (N-morpholinopropanesulfonic acid) with those of M E S (N-morpholinoethanesulfonic acid) that lengthening of the chain has, as expected, decreased the acidity of the NH+ group. At the same time, the enthalpy of dissociation has increased from 3.5 to
5.0 kcal mol-', yet the change in ASo (from -17.0 to -16.1 cal K-' mol-') is small and no change in IC," is apparent. T h e usefulness of MES and related ampholytes for p H control in the physiological region has been pointed out by Good ( I ) . I t rests in part on the fact t h a t these substances do not, in general, form stable complexes with metal ions and other compounds common to biological media. In addition, they may provide suitable secondary reference solutions a t I = 0.16 for the standardization of p H measuring equipment close to the p H of blood and plasma ( 2 ) . I t was therefore considered worthwhile to ascertain whether the p H of MOPS buffer solutions ( I = 0.16) is consistent with the pH(S) based, like the NBS primary standards, on the emf of cells without liquid junction. Our earlier work ( 2 )has shown that inconsistencies are most likely to arise from failure to match the ionic strength of the buffers being compared. I t was suggested t h a t a suitable reference solution for pH measurements in isotonic saline and media of similar composition is a phosphate/NaCl solution of I = 0.16 having the composition (in molality units); KH2P04,0.005217; Na2HP04,0.018258; NaC1,O.l. The pH(S) of this reference solution was shown i;o be 7.323 a t 25 "C and 7.297 a t 37 "C. A buffer solution with the composition: MOPS, 0.04 molal; NaMOPS, 0.04 molal; NaCl, 0.12 molal, was prepared. T h e emf of cell (B) Pt;H,(g, 1 a t m ) l M O P S / N a C l solnlAgC1;Ag
(B)
was measured at 25 and 37 "C and values of pH(S) calculated a t these two temperatures ( 5 ) . In addition, the p H of the MOPS/NaCl solution was determined in a cell with liquid junction, Hg;Hg2C12,3.5M KClllBuffer solnlH,(g, 1 a t m ) ; P t
(C)
standardized with the phosphate/NaCl reference solution. T h e results of these measurement,s of cells B and C are summarized in Table 111. T h e p H of the MOPS/NaCl solution based on a cell with liquid junction is the same as the assigned pH(S) at 25 "C but differs by 0.005 a t 37 "C. Although the difference at 37 "C is larger than those for buffers of MES and T E S under similar circumstances ( 2 ) ,it is evident that MOPS buffers may prove to be useful secondary pH standards in the range of physiological interest.
Table 111. Comparison of pH(S) from Cell B with pH from Cell C at 25 and 37 "C t, "C
EBQ
EB
P W )
Ec(std.)b
25 37
0.70628 0.70847
0.22255 0.21453
7.128 6.976
- 0.67989 - 0.69068
EC -0.66837 -0.67125
PH 7.1 28 6.981
a Emf for both cells in volts. * Cell standardized with phosphate/NaCl solution having the following composition (in molalities): KH,PO,, 0.005217; Na,HPO,, 0.018258; NaC1, 0.1.
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
LITERATURE CITED (11 . . N. E. Good. G. D. Wimet. W. Winter. T. N. Connollv. S. Izawa. and R. M. M. Singh, Biochernkk, 5 , 467 (1966). (2) R. G. Bates, C. A. Vega, and D. R. White, Jr., Anal. Chem., 50, 1295 (1978). (3) C. A. Vega and R . G. Bates, Anal. Chern., 48, 1293 (1976). (4) H. B. Hetzer, R. G.Bates, and R. A, Robinson, J. Phys. Chem.,70, 2869 (1966). (5) k. G. Bates, "Determination of pH", 2nd ed.,Wiley, New Ywk, N.Y., 1973, Chap. 4 and appendix, table 1. (6) H. B. Hetzer, R. A. Robinson, and R. G. Bates, J. Phys. Chem., 66, 1423 (1962).
(7) H. S. Harned and R. A. Robinson, Trans. Faraday SOC..36. 973 (1940). (8) N. W. Please, Biochem. J . , 56, 196 (1954).
RECEIVED for review July 21,1978. Accepted August 14, 1978. Work supported in part by the National Science Foundation under Grant CHE76 24556. M.S. thanks the following organizations in the Republic of South Africa for financial assistance: the C*S.l.R*,Ernest Oppenheimer and Sentrachem Ltd.
Instrumental Approach to Potentiometric Stripping Analysis of Some Heavy Metals Daniel Jagner Department of Analytical Chemistry, University of Gothenburg, Fack, S-402 20 Goteborg, Sweden
The method is based on the potentiostatic reduction and amalgamation of analytes and the subsequent registration of the potential-time curve when the reduced metals are reoxidized by means of mercury(I1) ions. Potentiostatic reduction Is achieved by means of a simple battery-operated potentiostat, equipped with a timerhwitcher unit facilitating semiautomatic analysis. The time-potential curves are registered by means of a pH-meter and/or an x-f recorder. Analytical procedures for bismuth, cadmium, thallium, lead, copper, and zinc ions in different media are reported. The relative precision is approximately 0.06.
T h e increasing need for trace metal analysis, in particular for the determination of lead and cadmium, is well documented. Consequently, there is also a need for simple analytical instrumentation suitable for this purpose. T h e hitherto simplest instrumental approach to trace metal analysis is that of ion-selective electrodes, a general purpose p H meter being the main instrumentation. Unfortunately ion-selective electrodes are not selective and sensitive enough for metal analysis in the concentration range below lo4 M ( I ) , which is that of most interest. The majority of the most important trace metals do, however, dissolve readily in mercury. This has been utilized in a large number of analytical procedures based on anodic stripping voltammetry ( 2 ) . Advanced instrumentation, e.g., for differential pulse anodic stripping voltammetry, has been designed for this purpose (3). Such dedicated instrumentation is, however, normally expensive since it does not consist of equipment usually available in the chemical laboratory. This paper describes an instrumental technique, which combines the simplicity of the ion-selective electrode instrumentation with the selectivity and sensitivity of anodic stripping voltammetry.
PRINCIPLE If a working electrode, consisting of material insoluble in mercury and with a high hydrogen overvoltage, is held potentiostatically a t a sufficiently reductive potential in a deaerated sample containing Hg(I1) ions and mercury soluble metal ions M(n) the reactions 0003-2700/78/0350-1924$01 .OO/O
+ 2eM(n) + ne-
Hg(I1)
-
--
Hg(1)
M(Hg)
will occur simultaneously. If the hydrodynamic conditions at the working electrode surface are kept constant, e.g., by rotating the electrode or by stirring the sample, the rate of reduction of M(n) ions will be constant until a significant fraction of these ions has been reduced. By keeping the electrode surface small the decrease in M(n) concentration will occur only very slowly. If, a t unchanged hydrodynamic conditions, the potentiostatic circuitry is disconnected and at the same time the working and the reference electrodes remain connected to a high input impedance voltmeter (e.g., a p H meter) the potential changes due to the reactions
+ iHg(I1)
+
M(n) + nHg(1) 2
can be observed. The experimental curve thus registered, potential vs. time, consists of a normal redox titration curve superimposed on a capacitance background. If the background contribution is accounted for, the time elapse between two consecutive equivalence points will be proportional to the amount of the particular metal in the mercury phase. Analogous to anodic stripping voltammetry, the amount of amalgamated metal is proportional to the concentration of metal ions M(n) in the sample and to the time of pre-electrolysis (plating). Consequently. the potential-time curve can be made the basis for quantitative analysis, either by the use of a calibration plot, a n internal standard, or by using a standard addition procedure. The principle of potentiometric stripping analysis has been described previously by the author in connection with more complicated instrumentation ( 4 , 5 ) .
EXPERIMENTAL Instrumentation. The only instrumentation required for potentiometric stripping analysis is a potentistatic circuitry and a pH meter, the latter being used both for the adjustment of an adequate plating potential and for the registration of the stripping curves. In all experiments, the same potentiostat was used but three different ways of registering the potentiometric stripping analysis curves were investigated. In the first method, which is G 1978 American Chemical Society
