Anal. Chem. 1980, 52, 2409-2412
Table 111. Calibration Stability Data ( 2 2 6 F'pm H, in Oil) no. of days from calibration
analytical result, ppm
0
225
42
224 218 2 15
82 112 112 142
216 210
error, %
0.4 0.9 3.5 4.9
2409
of 5 months. A full glass syringe is known to keep its hydrogen content unaltered for long periods ( 2 , 4 )but no tests have been reported to ascertain this constancy for syringe uncompletely filled. This test shows that the analyzer can be used for a t least 2 months without the need for a new calibration.
ACKNOWLEDGMENT The authors thank MM. G . Trudel, R. Jacques, and L. Laroche for their technical assistance.
4.4
7.1
Stability of t h e Calibration. For the user, the stability of the calibration is another important factor that had to be established. T o obtain such data, we used a 50-mL glass syringe with a definite concentration (226 ppm) as determined by the conventional chromatographic analysis of a sample obtained from the same source and the syringe was kept in the dark a t 24 f 2 "C for the duration of the test. Every month, a 5-mL sample of this oil was injected into the analyzer. In Table 111, we show that after 5 months, the Calibration gradually shifted from 226 to 210 ppm, an error of 7.1%. This observation presumes that the concentration in the glass syringe remained constant throughout this period
LITERATURE CITED Waddington, F. B.; Albn, D. J. E k t r . Rev. (London)1969, 23,751-755. Dlnd, J. E.; Daoust, R.; RQgis, J.; Morgan, J. Minutes of the 38th International Conference of Doble Clients 1971, 6 , 1101-1 113. Dornenburg, E.; Strittmatter, W. BBC-Nachr. 1974, 5 , 238-241. Dind, J. E.; R6gis, J . Pulp Pap. Can. 1975, 76, 61-64. Pugh, D. R. Minutes of me 4w1 International Conference of Doble Cllents 1973, 10, 401-412.
BClanger, G.;Duval, M. IEEE Trans. Electr. Insul. 1977, €I- 12, 334-340. Niedrach, L. W.; Alford, H. R. J . Nectrochem. SOC. 1965, 112. 117-124.
RECEIVED for review June 9, 1980. Accepted September 3, 1980.
Second-Stage Dissociation Constants of Piperazine-N, N'-bis(2-ethanesulfonic acid) Monosodium Monohydrate and Related Thermodynamic Functions in Water from 5 to 55 "C Rabindra N. Roy," James J. Gibbons, Jorge
L. Padron,
and James Moeller'
Department of Chemistry, Drury College, Springfield, Missouri 65802
The thermodynamic second-stage dissociation constants of piperazine-N,N'-bis(2-ethanesulfonic acid) monosodium monohydrate (PIPES), Pi, have been determined at 12 temperatures from 5 to 55 O C including 37 O C from emf measurements in cells without liquid junction using hydrogen and silver-silver bromide electrodes. The pK,s (for the process P* e P- 4- H') are given as a function of the thermodynamic temperature I by the equation pK2 = -458.29/T+ 12.184 0.01236 T. Standard thermodynamic functions associated with the acidic dissociation process have also been calculated. For example, at 25 O C AGO = 9497 cai mol-l, AHo = 2930 cal mol-', A S o = -22.0 cal K-' mol-', and ACpo = 34 cal K-' mol-'. These quantities are compared with those of structurally related compounds (e.g., N-substituted taurines).
-
T h e control of pH in the physiologically important range of acidities ([H+]= 10-6-10-8) is sometimes not possible because of the lack of weak acid-base systems with pKs lying between 6 and 8. Considerable interest has been shown to the acid-base behavior of the simplest aminoethanesulfonic acid, taurine (1)and its N-substituted derivatives, as recomPresent address: Indiana University Medical School, Bloomington, IN 47401.
mended by Good and his associates ( 2 ) . These compounds are all ampholytes (with zwitterionic strudures:l and are useful buffers compatible with most media of physiological interest for the pH range from 6 to 8. In earlier studies of biochemical buffers, the pK values and related thermodynamic quantities of N-substituted glycine [that is, N-tris(hydroxymethy1)methylglycine (Tricine) (3,4)]and N-substituted taurine [that is, N,N-bis(2-hydroxymethyl)-2-aminoethanesulfonicacid (BES) (5, S)] have been determined. Other substances along this line that have been studied, mostly by Bates and his co-workers (7,8),include N,N-bis(2-hydroxymethyl)glycine (Bicine) (7), tris(hydroxymethy1)aminoethane (TRIS) (8,9), and very recently four N-substituted aminoethanesulfonic acids (10). At present, we have extended our studies of the acid-base equilibria and thermodynamic quantities for the second dissociation step of N-substituted taurine [that is, piperazine-N,N'-bis(2-ethanesulfonicacid) monosodium monohydrate (PIPES)] chosen from the list of Good et al. ( 2 ) . Conventional paH values for equimolal buffers (0.02,0.03,0.05, and 0.1 mol kg-') of PIPES and NaPIPESate from 5 to 55 "C including 37 "C have recently been reported (11). In this work, we present the values of pK2 and associated thermodynamic AS", and AC,") at 12 temperatures quantities (AGO, AH", from 5 to 55 "C, including 37 " C by measuring the emf of cells without liquid junction of the type Pt;H,(g,:L atm)lP*(rnl), NaP(m2),KBr(m2),KBr(m,)lAgBr,Ag, where m is molality.
0003-2700/80/0352-2409$01.00/00 1980 American Chemical Society
2410
ANALYTICAL CHEMISTRY, VOL. 52, NO. 14, DECEMBER 1980
Table I. Electromotive Force ( E , in Volts) of the Cell Pt;H, (8, 1atm) IPIPES ( m ), NaPIPESate ( m 2), KBr (m,)iAgBr,Ag from 5 to 55 " C m,/mol kg-' m,/mol kg"
m,/mol kg-'
0.099 93 0.100 00 0.099 13
0.090 08 0.090 00 0.089 32
0.080 08 0.080 00 0.080 11
0.060 05 0.060 00 0.060 06
0.030 06 0.030 00 0.030 05
0.020 07 0.020 00 0.020 13
0.010 04 0.010 00 0.010 1 7
0.556 33 0.560 56 0.564 9 1 0.569 06 0.572 94 0.576 79 0.580 02 0.581 28 0.583 08 0.585 87 0.588 30 0.590 45
0.565 0,570 0.574 0.579 0.583 0.587 0.590 0.592 0.594 0.597 0.599 0.601
0.582 01 0.587 02 0.592 03 0.596 25 0.601 27 0.605 30 0.609 10 0.610 50 0.612 64 0.616 03 0.618 94 0.621 53
E
t, "C 5 10 15 20 25 30 35 37 40 45 50 55
0.040 08 0.040 00 0.039 89
0.529 99 0.533 51 0.537 37 0.540 68 0.543 65 0.546 52 0.549 28 0.550 26 0.551 75 0.553 92 0.555 1 9 0.556 56
0.531 97 0.535 62 0.539 33 0.542 73 0.546 4 1 0.549 07 0.551 85 0.552 82 0.554 30 0.55648 0.558 28 0.559 74
0.534 20 0.538 01 0.541 70 0.545 20 0.548 1 9 0.551 62 0.554 48 0.555 49 0.556 98 0.559 22 0.561 04 0.562 51
EXPERIMENTAL SECTION Commercial samples of PIPES (United States Biochemical Co.) were purified by recrystallization (twice) from 80% ethanol and dried at 70 "C under a heated vacuum desiccator. It was then finely powdered and stored in a desiccator over Drierite (CaSO,). It assayed 99.98% (standard deviation = 0.02%) when titrated under C02-freeconditions with a standard solution of sodium hydroxide to a calculated end point of pH equal to 9.75 (that of a 0.05 M solution of PIPES). The glass electrode was used for these pH measurements. Reagent grade potassium bromide (Fisher ACS certified) was recrystallized from water. For the determination of pK,, eight different cell solutions (buffers) containing an approximately 1:l molar ratio of PIPES to its sodium salt (NaPIPESate) were prepared by mixing accurate amounts of PIPES, standard solution of C02-freeNaOH doubly distilled deionized water, and KBr. The molality range of the buffer solutions varied from 0.1 to 0.01 mol kg-'. Buoyancy corrections were applied to all weighings. Purified hydrogen gas was swept through each solution to remove dissolved air before the cells were filled. The design of the cells (12), the method of the preparation of the hydrogen electrodes (13),and the silver-silver bromide electrodes (14, 15) have been previously reported. The constant-temperature bath was controlled to within 0.02 "C. The constant-temperature bath was controlled to within 0.02 "C. The emf measurements were made with a Leeds and Northrup Type K-5 potentiometer standardized with an Eppley standard cell. A n d l detector (Leeds and Northrup Model 9829) with a sensitivity of 25 FV was employed. The detailed procedure for the preparation of solutions and other experimental details are presented elsewhere (5). The cells displayed excellent stability and the initial, middle, and final emf readings at 25 "C agreed to within 0.05 mV on the average.
PROCEDURE Thermodynamic Dissociation Constant (pK2). The zwitterionic structure of piperazine-N,"-bis(2-ethanesulfonic acid) monosodium monohydrate (PIPES) is written as
and abbreviated as P'. The second acidic dissociation constant of PIPES, namely
P* e P-
+ H+
takes place in weakly alkaline solutions, making this a useful buffer system for controlling p H in biochemical studies. The pK2 was determined by the measurement of emf using cell I with a 1:l ratio between the zwitterion (P') and the buffer ion (P-). The emf values for the eight different buffer solutions in the molality range 0.01-0.1 mol kg-' from 5 to 55 OC are
0.540 1 7 0.544 1 8 0.548 00 0.551 75 0.555 57 0.559 09 0.561 57 0.562 64 0.564 26 0.566 68 0.569 23 0.570 89
0.54949 0.553 53 0.558 23 0.562 21 0.565 43 0.569 28 0.572 9 1 0.573 5 1 0.575 82 0.578 42 0.580 67 0.582 56
86 36 93 31 39 36 89 20 09 11 71 99
Table 11. Acidic Dissociation Constant ( p K , ) of PIPES from 5 to 55 "C t, "C 5 10 15 20 25 30 35 37 40 45 50 55
PK, (exptl)
std devu
P (slope)
PK, (calcd)b
7.103 7.063 7.030 6.993 6.960 6.928 6.890 6.892 6.851 6.812 6.772 6.729
0.004 0.004 0.004 0.003 0.005 0.002 0.003 0.004 0.003 0.003 0.002 0.002
-0.2453 -0.2089 -0.1728 -0.1527 -0.1050 -0.0665 -0.0501 -0.0512 -0.0313 -0.0160 0.0212 0.0440
7.098 7.066 7.032 6.997 6.962 6.925 6.888 6.894 6.850 6.811 6.772 6.731
a Standard deviation of the intercept. from eq 7 .
Calculated
listed in Table I, after being corrected to a partial pressure of 1 atm. The pKz was evaluated by extrapolating the values of the "apparent" thermodynamic dissociation constant, p K i , to zero ionic strength, I (which is equal to m2 m3). The pertinent equation is (2) PK2' = PK2 - log [yP+YBr-/YP-l
+
pK2' = ( E - E o ) F / ( R TIn 10) + log (mlrn3/m2)(3) where E" is the standard electrode potential of the Ag-AgBr electrode in HzO (16). Since the paH of the cell solutions (for example, 0.1 m PIPES + 0.1 m NaPIPESate) a t 25 "C is 6.487 ( I I ) , any hydrolysis corrections for Pi and P- in this neutral region are unnecessary. If y p + is assumed to be unity, the last term of eq 2 should be directly proportional to the ionic strength, I . Thus, the simplified form of eq 2 is expressed as (4) pK2' = pK2 - PI where 0 is the slope parameter of the linear fit. The values of pK2 (the least-squares estimate of the intercept of the linear regression) and the slope parameter 0,together with the standard deviation of regression, are entered in Table 11. The pK2 value reported in Table I1 (6.993) a t 20 " C is slightly higher than the 6.96 value for a 0.01 M solution quoted by Good et al. (2). In order to be consistent with our earlier studies, we have selected an equation of the form proposed by Harned and Robinson (17)to express the pKz as a function of the thermodynamic temperature T, with the final form becoming pK2 = A / T B C T (5)
+ +
ANALYTICAL CHEMISTRY, VOL. 52, NO. 14, DECEMBER 1980
DISCUSSION
Table 111. Thermodynamic Functions (on the Molal Scale) for the Dissociation of PIPES in Water from 5 t o 5 5 O c a
t, 'C
cal mol-'
5 15 25 35 45 55
9034 i 9271 i 9497 2 9712t 9915 c 10107 i
a
AH",
AGO,
AS", cal K - ' mol-'
cal mol-'
5 3 3
227825992930i 32732 3627 t 3993 i
3
3 5
1 3 3 -24.3 i 0.5 86 .-23.2 I0.3 45 -22.05 0.2 48 - 2 0 . 9 i 0.2 94 - 1 9 . 8 ~0.3 1 4 8 -18.6 * 0.5
ACP",
cal K-' mol-' 32i 33 i 34 * 35i 36i
5 5 5 6 6 3 7 i. 6
1 thermochemical calorie = 4.184 J.
The following empirical equation is also in common usage by other investigators (18)
P K ~= A / T
+ B + Clog T
2411
(6)
Vega and Bates (IO)have recently confirmed that eq 5 and 6 are equally applicable for studies of this type. T h e experimental values of pK2 were then fitted to eq 5 to produce the temperature dependency equation pK2 = -458.29/T 12.184 - 0.012362' (7)
+
T h e standard deviation of a single value of pK2 from eq 7 is 0.0026. Derived T h e r m o d y n a m i c Quantities. The changes in Gibbs free energy (AGO), enthalpy ( A H o ) ,entropy (ASo), and heat capacity ( A C p o )for the dissociation process represented by eq 1 were calculated in the usual manner from the change of pK2 with temperature as given in eq 7 . The results are summarized in Table 111. The uncertainties in these values were estimated by application of the method of propagation of errors, as described by Please (19). These estimated uncertainties are also given in Table 111. The pK2 and thermodynamic functions for the dissociation of PIPES are compared in Table IV with the corresponding values for other compounds (taurine and N-substituted taurines) structurally related to PIPES.
In each of the zwitterions listed in Table IV, the positive and negative charge centers are separated by two methylene groups. This table also shows that the acidic strength increases from the parent compounds (taurine) to its derivatives (Nsubstituted taurines). This decrease in pK2 in the series is probably due to the inductive effect of the oxygen atom and the steric effects of the bulky hydrophobic ethylene or hydrophilic hydroxyethyl groups on the nitrogen atom (20). The ampholytes HEPES (N-Z-hydroxyethylpiperazine-N'-2ethanesulfonic acid) and PIPES, in addition to normal zwitterionic forms, contain an extra basic nitrogen, which may complicate the acid-base behavior and associated thermodynamic quantities. It is highly interesting to note the contrary variations of ASo (negative) and ACpo (positive), apparent in Table IV, for both HEPES and PIPES. In general, electrostatic interactions with charged species, such as P- and Hffrom PIPES, tend to cause an orientation of polar solvent molecules (water) in the proximity of these ions, and thus both the entropy and the heat capacity should decrease. Although the actual quantitative nature of these interactions is not yet known, according to Cox et al. (21),other "hydrophobic interactions" between uncharged species (the hydrocarbon position of P') and water molecules may lead to both a lowering of entropy and an increase in heat capacity, as is the case in the present study (PIPES), as well as for HEPES. It is also evident from Table IV, that the lowering of pK2 is accompanied by a decrease in AH" and increases in -AS" and ACpo (with the exceptions of HEPES and PIPES in the series). This anomaly was caused by the structural similarities between these latter two compounds. T h e decrease in pK2 with subsequent decrease in AH" is due to hydroxyethyl (22) or ethylene substitution on the nitrogen atom of the parent compound (taurine). Conventional paH values for buffer solutions prepared from PIPES and sodium hydroxide have been reported (11) and these solutions are considered as secondary standards for the control of pH range of physiological interest.
Table IV. Thermodynamic Functions (on the Molal Scale) at 25 "C for the Dissociation of a Series o f Structurally Related Compounds in Watera
compound
PK, 9.061
-O,SCH,CH,NH,+ (TAURINE) CH,CH,
11
\
+\
I
-O,SCH, CH,N
NCH,CH,OH (HEPES)
AH"/ cal mol-'
As"/
cal K - ' mol-'
Ac:po/l
cal K mol-'
ref
10000
-7.9
--8
2 :1
7.565
4870
-18.3
3.1
10
7.550
7680
-8.8
--4
10
7.187 7.187
5780 5830
-13.5 -13.3
-- 1
1:2 10
6.960
2930
-22.0
34
6.270
3490
-17.0
1
CH,CH2 H
+I
-O,SCH,CH,NC(CH,OH), (TES) H -O,SCH,CH,NH(C,H,OH),
(BES)
,CH,CH, \ + NHCH,CH,SO; \ I CH,CH, CH,CH, +I \ -O,SCH,CH, NH /O W E S ) \ CH,CH, NaO,SCH,CH,N
a
1 thermochemical calorie = 4.184 J.
(PIPES)
0
this work
10
Anal. Chem. 1980, 52, 2412-2416
2412
ACKNOWLEDGMENT
(12) Cary, R.; Bates,R. G.; Robinson, R. A. J. Phys. Chem. 1964,68,1187. (13) Bates, R. G. “Determination of pH”, 2nd ed.; Wiley: New York, 1973; Chapter 10. (14) Roy, R. N.; Robinson, R. A,; Bates, R. G. J . Chem. Thermodyn. 1973, 5 , 559. Roy, R. N.; Swensson, E. E.; LaCross. G., Jr. J . Chem. Thermodyn. 1975, 7 , 1015. Harned, H. S.;Keston, A. S.; Donelson, J. G. J. Am. Chem. SOC. 1936, 58 989. Harned, H. S.;Robinson, R. A. Trans. Faraday SOC. 1940,36, 973. Ives, D. J. G.; Moseley, P. G. N. J. Chem. SOC.,Faraday Trans. 11976, 72, 1132. Please, N. W. Biochem. J . 1954,56, 196. Paabo, M.; Bates, R. G. J. Phys. Chem. 1970, 7 4 , 702. Cox, M. C.;Everett, D. H.; Landsman, D. A,; Munn, R. J. J. Chem. SOC. Bl968, 1373. Timimi, B. A.; Everen, D. H. J. Chem. SOC. B 1968, 1380.
The authors thank John Rogers for performing preliminary work in the recrystallization PIPES.
LITERATURE CITED King, E. J. J. Am. Chem. SOC. 1953, 75, 2204. Good, N. E.; Winget, G. D.; Winter, W.; Connoiy, T. N.; Izawa, S.; Singh, R. M. M. Biochemistry 1966,5 , 467. Roy, R. N.;Robinson, R. A.; Bates, R. G. J. Am. Chem. Soc.1973,95, 8231. Bates, R. G.;Roy, R. N.; Robinson, R. A. Anal. Chem. 1973,45. 1663. Roy, R . N.;Swensson, E. E.: LaCross, G., Jr.; Krueger, C. W. Anal. Chem. 1975, 47, 1407. Roy, R. N.; Gibbons, J. J.; Krueger, C. W.; LaCross, G., Jr. J . Chem. Thermodyn. 1977, 9 , 325. Dana, S.P.; Grzybowski, A. K.; Bates, R. G. J. Phys. Chem. 1964,68, 275. Bates. R. G.; Hetzer, H. B. J . Phys. Chem. 1961, 65,667. Dana, S.P.; Grzybowski, A. K.; Weston, B. A. J . Chem. SOC. 1963, 792. Vega, C. A.; Bates, R. G. Anal. Chem. 1976, 48, 1293. Roy, R. N.: Gibbons, J. J.; Padron, J. L.; Buechter, K.; Faszholz, S. Clin. Chem. ( Winston-Salem, N.C.), in press.
RECEIVED for review July 3, 1980. Accepted September 12, 1980. The authors wish to acknowledge the National Institutes Of for their partial support in the form Of research Grant NIH 1 R01 GM 26809-01 BMT.
Response of Fluoride Ion Selective Electrode in Organic Solvents J. F. Coetzee” and M. W. Martin DepaHment of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania
The response of the single-crystal lanthanum fluoride electrode was evaluated in both direct potentiometry and potentiometric titrations in a variety of alcohols and dipolar aprotic solvents and in their mixtures with water. Response in direct potentiometry In “anhydrous” solvents tends to be somewhat super-Nernstlan, especially for unbuffered fluoride ion activitles in the 10-5-10-6 M range. The response becomes more ideal when some water is added or when solutions are otherwise buffered. Possible reasons for this behavior are discussed in terms of existing hypotheses for the response mechanism of the electrode. Solubility product constants of lanthanum fluoride and other metal fluorides were determined in several organic solvents and their mixtures with water. By addition of organlc solvents to aqueous samples, the sendtlvity of direct potentiometry in unbuffered solutions can be improved by up to 1 decade, while for potentiometric titrations the Improvement is from 2 to 3 decades.
Since a change in solvent may cause profound changes in thermodynamic as well as kinetic properties of analyte ions and also of other ions present and of exchange sites in ionselective membranes, it is to be expected that such properties of ion-selective electrodes as their sensitivity, selectivity, and response time may be strongly solvent dependent. Little is known about such solvent dependence at present, yet it would be of both fundamental and applied interest to obtain such information. One example of fundamental aspects of the field of ion-selective electrode potentiometry that are incompletely understood is the response mechanism of several classes of electrodes. The availability of response data in solvents other than water should, a t the very least, broaden perspectives on the relative significance of various factors thought to con-
15260
tribute to electrode response, including the solubility of the membrane, adsorption of analyte ions and/or other species on the membrane, and formation of gel layers on the membrane. One example of potential benefits of an applied nature to be derived from studies in solvents other than water would be if the sensitivity and/or selectivity of an electrode could be improved by modifying the solvent medium in a practicable manner. Since most (although not all) samples of analytical interest for ion-selective electrode methodology are aqueous solutions, and since replacement of “all” water in such samples by other solvents is a tedious process, the properties of mixtures of water with other solvents would be of more practical interest than the properties of essentially anhydrous solvents. The addition of water-miscible solvents, such as ethanol or acetone, to aqueous samples has of course been a long-standing expedient of improving the sensitivity of analytical procedures, e.g., both gravimetric and volumetric procedures based on precipitation of lead sulfate. However, little has been done to improve analytical procedures by optimization of the solvent in those cases where the solvent dependence is complex and the benefits, if any, of changing the solvent are not immediately predictable. This paper is concerned with the response of the singlecrystal lanthanum fluoride electrode for fluoride ion ( 1 ) in a variety of organic solvents and their mixtures with water. The response of this electrode in different solvents is of particular interest for a number of reasons. First, solvent effects for fluoride ion, which is the “hardest” known ligand (21, are expected to be particularly large, but little is known (because of experimental problems) about its properties in solvents other than water, especially dipolar aprotic solvents. Second, the response mechanism of the electrode seems to be especially complex; in particular, the relative importance of such factors as the solubility of the membrane, adsorption of fluoride ion
0003-2700/80/0352-2412$01.00/0C2 1980 American Chemical Society
