DISSOCIATION CONSTANT OF PIPERAZINIUM ION
2081
Dissociation Constants of Piperazinium Ion and Related Thermodynamic Quantities from 0 to 50" by Hannah B. Hetzer, R. A. Robinson, and Roger G. Bates National Bureau of Standards, Washington, D . C. 30334 (Received October 30, 1067)
1
The two thermodynamic dissociation constants of piperazinium ion at 11 temperatures from 0 to 50' have been determined from emf measurements of hydrogen-silver chloride cells without liquid junction. The first (acidic) dissociation constant (K1)for the process P Z H ~ ~ +H20 = H30+ PzH+ is given as a function of T("K) by the equation -log K1 = 952.11/T 4.3919 - 0.007555T. At 25", -log K 1 is 5.333, AH" is 31,080 J mol-', ASo is 2.2 J deg-1 mol-', and AC," is 86 J deg-1 mol-1. The second (acidic) dissociation constant (Ka) for the process PzH+ HzO = HsO+ Pz is given by the equation -log K 2 = 1656.59/T 6.1316 0.006556T. At 25O, -log K 2 is 9.731, AH" is 42,870 J mol-1, AS" is -42.6 J deg-1 mol-', and AC," is 75 J deg-1 mol-]. The results are compared with those for other protonated bases of similar structure.
+
+
+
P t ; H2 (g, 1 atm), Pz92HC1 (ml),
Introduction The measurement of the dissociation constant of piperidine has already been described. The dissociation constants of pyrrolidine2 and morpholine3 have also been determined. This paper reports a determination of the two dissociation constants of piperazine (hexahydro-1,4-diazine), The structures of piperazine and some related nitrogen bases are shown in Scheme I. Scheme I
Piperidine
+
+ +
Pyrrolidine Morpholine
.Piperazine
NH ?2
hH2 "2'
1,2-Diaminoethane
N,N'-Dimethyl-l,2diaminoethane
The piperazinium ion (PzH22f) dissociates in two stages
+ HzO PzH+ + H2O
PzHz2+
+ PzH+ Ha0+ + PZ
HaO+
Hence, one can study the effect of both the NH2+ group and the NH group on the dissociation of the other NH2+ group. A compilation of earlier values for the dissociation constants of piperazine has been made by P e ~ i n . ~
Method The method was essentially the same as that used in the study of m ~ r p h o l i n e . ~The two types of cells studied can be represented by
Pz.HC1 (m2),NaCl (0 or m2),AgCl; Ag (I) and P t ; H2 (g, 1 atm), Pz.HC1 (m2),Pz (ma), NaCl (0 or rn2
+ 2ms), AgCl; Ag
(11)
Solutions for cell I were prepared by two different methods. One (series 1 in Table I) was by adding a solution of hydrochloric acid to a solution of piperazine in such amount as to produce a mixture of the dihydrochloride and the monohydrochloride. In these solutions the molality of sodium chloride was zero. The other method (series 2 of Table I) was by adding a solution of carbonate-free sodium hydroxide to a solution of piperazinium dihydrochloride; for these solutions, the molality of sodium chloride was m2. Solutions for cell I1 were also prepared in two ways. I n one method (series 1in Table II), a solution of hydrochloric acid was added to a solution of piperazine in an amount sufficient to produce a mixture of the monohydrochloride and the free base; for these solutions, the molality of sodium chloride was zero. I n the other method, sodium hydroxide solution was added to the dihydrochloride to produce a mixture of the monohydrochloride and the free base; for these solutions, the molality of sodium chloride was (mz 2m3). None of the three usual corrections to the emf of the cell, one for the partial pressure of the amine, the second for the solubility of silver chloride as a result
+
(1) R. G. Bates and V. E. Bower, J. Res. Nat. Bur. Stand., 57, 163 (1956). (2) H. B. Hetzer, R. G. Bates, and R. A. Robinson, J. Phus. Chem., 67, 1124 (1963). (3) H. B. Hetzer, R. G. Bates, and R. A. Robinson, ibid., 70, 2869 (1966). (4) D. D. Perrin, "Dissociation Constants of Organic Bases in Aqueous Solution," Butterworth and Co. Ltd., London, 1966.
Volume 7.9, Number 6 June 1068
H. B. HETZER,R. A. ROBINSON, AND R. G. BATES
0d00000000
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+
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+
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3
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-
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6
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' I
8
8
b.
000000000000 The Journal of Physical Chemistry
DISSOCIATION CONSTANT OF
2083
PIPERAZINIUM I O N
of complex-ion formation, and the third for hydrolysis, was required for the solutions in cell I. Corrections were made for the third of these effects in the solutions of cell 11. The largest, at 50", was 0.015 pK unit. The amount of complex-ion formation from piperazine and silver ion was estimated from the work of Schwarzenbach, et a l l 5 and the correction to the chloride ion concentration was found to be negligible. Materials. Piperazine dihydrochloride was recrystallized twice from 50% ethanol and dried overnight at 103". The chlorine content was determined gravimetrically as silver chloride (calcd, 44.58; found, 44.57). The majority of the cell solutions were prepared from this material. Anhydrous piperazine was recrystallized three times from absolute ethanol. The colorless product was dried in a stream of dry nitrogen at room temperature, since any yellow color present in the ethanol solutions has been observed to deepen on heating above 50". The melting point (in a capillary tube) was 111"; that expected for 100% purity is 111.4°.6 Gas chromatographic analysis indicated 99.3% purity as compared with 97.3% before recrystallization. Potentiometric titration with standard hydrochloric acid to the first inflection point, pH 7.7 for a 0.16 m solution, gave an assay of 99.50/,.
Results First Dissociation Constant. The emf values of cell I for 15 solutions from 0 to SO", corrected to 1 atm hydrogen pressure, are given in Table I. The first (acidic) dissociation constant of piperazinium ion
K1 =
an +mP.H +YP.H mpm+ Y m w
+
(1)
+
is related to the emf of cell I by the equation pK1 = ( E
- E " ) / k + log ~ log ml/mz
+
C I -
+ log
(YPnHaa+YCI-/YPsH+)
(2)
where E" is the standard potential of the silver-silver chloride electrode' and IC is (RT In 10)/F. An approximation to pK1 is given by the equation pK1' = ( E - E")/IC
+ log mcl- + log ml/mz - 4AI'Ia (3)
where A is the Debye-Huckel slope constant (on the molal scale) and I = (3ml mz) for series 1 or (3ml 2m2) for series 2. Equation 3 utilizes the DebyeHuckel limiting law and thus implies a zero value for the ion-size parameter of the Debye-Huckel formula. An equation of this sort has been found to give a useFigure ful extrapolation of the data for other 1 shows values of pK1 calculated from the data at 25" in series 2 of Table I (the pK1 values have been raised by 0.02 unit in the figure). A linear extrapolation
+
+
PK:
0
0.05
0 , IO
I Figure 1. Extrapolation of P K ' ~to I = 0 a t 25': a, data of series 1, Table I; 0, data of series 2, Table I. (These points have been displaced upward by 0.02 unit.)
seems to be justified, and pK1 was calculated by means of the equation pK1 = pK1'
+ aI
(4)
using the method of least squares. The pK1' values at 25" calculated from the data in series 1 of Table I are also shown in Figure 1. It is not immediately obvious that the pK1' values from the data in series 1 are lower than those calculated from series 2, because the latter have been displaced upwards by 0.02. Nevertheless, if the data are plotted using the same scale of ordinates, it is evident that series 1 gives pK1 values lower than those from series 2 by about 0.008. This is not unexpected; indeed, there is no reason to believe that the activity coefficient term in eq 3 should be the same for the solutions in two series, when one contained sodium chloride and the other did not. A straight-line extrapolation through the five points for series 1 (using eq 4) gives PK1 = 5.325 at 25", which is lower than that derived from series 2. However, an inspection of Figure 1 suggests that the points from series 1 are not quite linear. This means that a better straight-line extrapolation would be obtained if the ion-size parameter were not taken to be zero. A similar situation is presented by the protonated form of tris(hydroxymethy1)aminomethane, where a nonzero value of the ion-size. (5) G. Schwarzenbach, B. Maissen, and H. Ackerman, Helv. Chim. Acta, 23, 2333 (1952). (6) C. R. Witschonke, Anal. C h m . , 26, 562 (1954). (7) R. G. Bates and V. E. Bower, J. Res. Nat. BUT.Stand., 53, 283 (1954).
Volume 7.9, Number 6 June 1968
H. B. HETZER,R. A. ROBINSON, AND R. G. BATES
2084 parameter was needed for solutions which contained potassium chloride* while a zero value was satisfactoryg for solutions without added salt. Instead of introducing an adjustable ion-size parameter, an alternative, and equivalent, method of treating the data of series 1 was adopted. The v a r i e tion of pK1' with I was expressed by the equation
+ a I + b12
pK1 = pK1'
(5)
allowing for the slight curvature seen in Figure 1. With the aid of this equation, again using the method of least squares, the data from series 1 gave an extrapolated value of pK1 = 5.333, identical with that obtained from series 2. The agreement was not as good at other temperatures; the two series differed on the average by 0.002 in pK1. Five solutions were studied in series 1 and ten solutions in series 2. It was decided, therefore, to weight the extrapolated pK1 values from the two series in the ratio 1:2. The final pK1 values at temperatures from 0 to 50" are given in Table 111. The standard deviation was 0.001 at all temperatures except 40", where it was 0.002. Table I11 also lists pKl values calculated by means of the equationlo pK
=
A1/T - A2
+ A3T
(6)
with A1 = 952.11, A2 = -4.3919, and A3 = -0.007555; T("K) = t("C) 273.15.
+
Table I11 : Dissociation Constants of Piperaeinium Ion from 0 to 50"
0 5 10 15 20 25 30 35 40 45 50
5.816 5.712 5.614 5.518 5.424 5.333 5.246 5.153 5.066 4.981 4.896
10.407 10.259 10.126 9.996 9.864 9.731 9.609 9.485 9.367 9.252 9.142
5.814 5.713 5.615 5.519 5.425 5.333 5.242 5.154 5.066 4.981 4.897
+
a p K ~ = 952.11/T 4.3919 0.0018. 'pK2 = 1656.59/T dev = 0.0031.
+
-
10.406 10.264 10.126 9.992 9.861 9.733 9.609 9.487 9.369 9.253 9.139
0.007555T. Std dev = 6.1316 0.006556T. Std
-
Second Dissociation Constant. The emf values of cell I1 for 15 solutions from 0 to 50", corrected to 1 atm hydrogen partial pressure, are given in Table 11. The emf of cell I1 is related to the second (acidic) dissociation constant of piperazinium ion K2
=
UH +mPzYPe mPzH"YPaH +
The Journal of Physical Chemistry
(7)
by means of the equation
+
pK2 = ( E - E")/,% log mcllog (m2
+
+ moH-)/(ms - moH-) + 1% (YPzH+'Y'CI-/YPz) (8)
A useful extrapolation function (again based on the Debye-Huckel limiting law) is
+
+
pKz' = ( E - E")/,% logmcllog (m2 mo~-)/(m3- OH-)
+
- 2AI"'
(9)
where I = m2 for those solutions which contained no sodium chloride and I = (2m2 2m3) for the remainder. The thermodynamic pK2 was obtained by extrapolating these values of pK2', again using the method of least squares, to I = 0. The standard deviation in pK2 was 0.005 at 10, 15, 20, and 25", 0.006 at 0, 5 , 30, 45, and 50", 0.007 at 35", and 0.008 at 40". It is our usual practice to measure the emf at 25" at least twice in the course of a run over a temperature range. When this was done, good agreement was found for the data pertaining to cell I, as has been the case with other With cell 11, on the other hand, the final value at 25" differed, in some instances, from that found earlier in the run by amounts exceeding 0.5 mV. When this happened, the results at all temperatures were rejected and are not included in Table 11. This behavior suggests some instability of piperazine in alkaline solution, which seems to be accentuated at higher temperatures. 11t12 For the 15 solutions of Table 11, the largest difference between the final emf at 25" and that measured earlier in the run was 0.4 mV (equivalent to 0.007 in pK2). The smallest difference was 0.04 mV, and the average was 0.2 mV. Nevertheless, the possibility of a slight decomposition of piperazine cannot be excluded even in these "well-behaved" solutions. It will be noted that the standard deviation in pK2 is considerably greater than that for pK1. Although the values of pK2 are given to three decimal places in Table 111, the rather large standard deviation (0.0031) should not be overlooked. Table I11 also contains values of pK2 calculated by means of eq 6 with A1 = 1656.59, A2 = -6.1316, and A3 = -0.006556.
+
Discussion A comparison of the present results with previous determination~5*~~,~3-~5 of pK1 and pK2 is given in (8) S.P. Datta, A. K. Grzybowski, and B. A. Weeton, J . Chem. SOC., 792 (1963). (9) R. G. Bates and H. B. Hetaer, J . Phys. Chem., 65, 667 (1961). (10) H. S. Harned and R. A. Robinson, Trans. Faraday Soc., 36, 973 (1940). The constants of eq 6 were obtained with the use of OMNITAB.
(11) See also M. E. Smith and L. B. Smith, Biol. Bull., 96, 233 (1949). (12) F. R. Greenbaum, Am. Pharm. J . , 109, 550 (1937). (13) J. M. Pagano, D. E. Goldberg, and W. C. Fernelius, J . Phya. Chem., 6 5 , 1062 (1961).
DISSOCIATION CONSTANT OF PIPERAZINUM
2085
ION
Table IV. Earlier values are listed as well as the differences between these pK values and those recorded in Table 111. The difference is taken as positive if the value in Table I11 is the lower. It will be seen that the pK2 data reported here are in fair agreement with earlier work. In general, our values are about 0.03 unit lower than previous ones. On the other hand, our values of pKl are on the average 0.22 lower than other published results. However, an examination of the literature shows that, in most cases, pK1 had been measured by means of a cell with liquid junction, using a solution of total ionic strength about 0.01,and it is not always certain that allowance for the activity coefficient term of eq 2 has been properly made. It may be noted that for a solution of ionic strength 0.01 the term 4AI"2 in eq 3 amounts to 0.20,which is close to the difference, A,, shown in Table IV. I n one instance at least,ll measurements were made over a range of concentrations and apparent pK1 values extrapolated to zero ionic strength. The extrapolated value obtained in this way is in good agreement with ours. Table I V : Comparison of pK Values t,
Pagano, et al.'s Pagano, et al. Schwarzenbach, et aL6 Pickett, et al.14 Smith and Smith" Paoletti, et al.16 Pagano, et al. Pagano, et al. a
OC
pKi
10 20 20 23.5 25 25 30 40
5.85 5.63 5.69 5.56 5.32 5.60 5.54 5.37
Aia
pKa
0.24 10.12 -0.01 0.03 0.21 9.89 0.26 9.82 -0.04 0.06 0.23 9.83 -0.01 9.70 -0.03 9.72 -0.01 0.27 0.07 0.29 9.68 0.11 0.30 9.48
- (pK1 from Table 111). (pK2 from Table 111).
Al = (pK1 cited)
cited)
-
A*b
AZ = (PKa
Table V summarizes the three thermodynamic quantities, AH", AS", and AC," for the dissociation of piperazinium ion and some related compounds, including the ethylenediammonium ion16 and the N,N'dimethylethylenediammonium ion. l7 Estimates of the standard errors of the thermodynamic quantities for the first dissociation of piperazinium ion a t 25" (based on the method of Pleasel*) are as follows: AH", 50 J mol-'; AS", 0.2 J deg-' mol-'; ACpo,8 J deg-l mol-'. For the second dissociation step, the estimated standard errors are about twice these figures. It may be noted that the change in heat capacity is positive for these dissociation processes, all of which are of the type
+
BH22+ HzO
H30+
+ BH+
or
BH+
+ H2O L_ H30+ + B
Table V : Thermodynamic Quantities for the Dissociation of Piperazinium Ion and Related Compounds a t 25" AS',
Piperazinium ion First stage Second stage Morpholinium ion8 Piperidinium ion1 Pyrrolidinium ion2 Ethylenediammonium ion16 First stage Second stage N,N '-Dimethylethylenediammonium ion17 First stage Second stage
ACpo,
AHo,
J
J
J mol-'
deg-1
mol-1
deg-1 mol-'
31 ,080 42,870 39,030 53,390 54,470
2.2 -42.6 -31.7 -33.9 -33.7
86 75 48 88 68
6.838 45 , 480 9.960 49,450
21.3 -24.3
73 40
30 -71
... ...
5.333 9.731 8.492 11.123 11.305
7.47 10.29
51,600 37 ,400
I n contrast, a dissociation of the type HA
+ HzO
H30+
+A
is usually, if not always, accompanied by a decrease in heat capacity. Examples can be taken from the data for the dissociation of acetic acid,19 for which AC," is -142 J deg-l mol-', and for the three stages of dissociation of citric acid,20 for which AC," = -130, - 184,and -251 J deg-l mol-l. It can also be seen that, if there are two stages of dissociation, the entropy change is positive for the first stage and negative for the second. This is true for the three examples cited in Table V and also for the tetramethylenediammonium ion2' (+7.7, - 15.0 J deg-' mol-') and for the hexamethylenediammonium ion16 (+3.2, -17.0 J deg-' mol-'). Positive values for the first stage of dissociation and negative values for the second stage for the N-methyl- and l-methylethylenediammonium ions (in 0.5 m potassium nitrate solution) have been reported recently.22 It would be interesting to know if this relationship is also valid for the hydrazinium ion, NH3+.NH3+. Unfortunately, (14)L. W.Pickett, M. E. Corning, G. M. Wieder, D. A. Semenov, and J. M. Buckley, J. Am. Chem. Soc., 75, 1618 (1953). (15) P. Paoletti, M. Ciampolini, and A. Vacca, J . Phys. Chem., 67, 1065 (1963). (16) D.H.Everett and B. R. W. Pinsent, Proc. Roy. SOC.(London), A215, 416 (1952). (17) Calculated using the pK values at 0 and 25O of F. Basolo, R. K. Murmann, and Y . T. Chen, J . Am. Chem. Xoc., 75, 1418 (1 953). (18) N. W.Please, Biochem. J., 56, 196 (1954). (19) H.8. Harned and R. W. Ehlers, {bid., 55, 652 (1933). (20) R. G.Bates and G. D. Pinching, J . Res. Nat. Bur. Stand., 71, 1274 (1949). (21) From values of the parameters of eq 6 quoted by R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," revised ed, Butterworth and Co. Ltd., London, 1965, p 521, using pK data provided by Professor D. H. Everett. (22) A. Vacca and D. Arenare, J. Phys. Chem., 71, 1495 (1967). Volume 78, Number 6 June 1968
2086
J. GUION,M. BLANDER, D. HENGSTENBERG, AND K. HAGEMARK
there seem to be no data from which the entropy change for the first stage can be calculated, but pK2 valueszs at 15, 25, and 35" suggest that ASo for the second stage in the dissociation Of ion has a negative value (- 32 J deg-l mol-l).
Acknowledgment. The authors are indebted to William D. Dorko for performing the gas chromatographic examination of the DiDerazine. ~- (23) G, Ware, J. B. Spulnik, and E, C. Gilbert, 58, 1605 (1936).
J,
Am. Chem, ~ o c , ,
Thermodynamic Treatment and Electromotive Force Measurements of the Ternary Molten Salt Systems Silver Chloride-Sodium Chloride-Potassium Chloride and Silver Chloride-Sodium Chloride-Cesium Chloride by J. Guion, M. Blander, D. Hengstenberg, and K. Hagemark North American Aviation Science Center, Thousand Oaks, California 91860 (ReceivedOctober 81, 1967)
Partial molar excess free energies of mixing of silver chloride have been determined in the binary systems AgCl-NaCl, AgC1-KC1, and AgC1-CsCl and in the ternary systems AgCl-NaCl-KC1 and AgC1-NaC1-CsC1 by an electromotiveforcetechnique using the reversible formation cell Ag-AgC1 alkali chlorides-Clz, graphite. The excess free energies for AgCl in the binary systems could be represented by the expression A ( l - N A g C J 2 . The parameter A is 900 cal/mol for the AgC1-NaC1 system, -1500 cal/mol for the AgC1-KC1 system, in accord with prior measurements, and - 3450 cal/mol in the AgC1-CsCl system which had not been measured previously. A convenient thermodynamicformalism for the ternary systems is introduced in which the excess free energies are related to weighted sums of the excess free energies of the three binary systems and a, ternary term (eq 8). The small ternary terms calculated from our measurements are consistent with calculations of this term from the quasi-lattice theory and illustrate a significant property of ternary systems.
+
Introduction The thermodynamic properties of multicomponent systems are significant in many important metallurgical and chemical processes. The concentration dependence of the chemical potentials of components in ternary systems has not been thoroughly investigated. This concentration dependence often has a profound effect on the extent of chemical reactions with components as well as on the phase behavior of ternary systems. I n several papers, values of thermodynamic functions for ternary systems have been approximated in a simple manner from a knowledge of the binary subsystems. The purpose of this paper is first to obtain expressions for the difference between such approximations and an exact formulation and to investigate these differences experimentally in a simple system. Our calculations are based in part on Darken's general treatment of ternary systems.z The derived expressions suggest a rational method of making measurements used in our electromotive force measurements on the ternary systems AgCI-KCI-NaC1 and AgC1CsCl-NaCl. Furthermore, in a forthcoming paperS The Journal of Physical Chemistry
the quasi-chemical approximation has been applied to the ternary metal alloy systems Cd-Sn-Bi, Cd-Bi-Pb, and AI-Bi-Pb. The same treatment is also applicable to ternary ionic salt systems with a common anion (or cation), provided that the cations (or anions) have the same charge. The nearest neighbor interaction parameters used in the alloy systems have to be replaced by the next nearest neighbor interaction parameters for the cations (or the anions). Our measurements for AgC1alkali chloride systems provide a test for the theory. The binary systems AgC1-NaC1, AgC1-KC1, and AgCI-CsC1 have been previously investigated by calorimetric means4 and by an electromotive force technique for the first two system^.^^^ Calorimetric (1) For example, see G. W. Toop, Trana. Met. SOC.A I M E , 233, 850 (1965). (2) L.S. Darken, J . Amer. Chem. SOC.,7 2 , 2909 (1950). (3) K. Hagemark, J. Phge. Chem., in press. (4) L. S. Hersh and 0. J. Kleppa, J. Chem. Phys., 42, 1309 (1965). (5) M. B. Panish, F. F. Blankenship, W. R. Grimes, and R. F. Newton, J. Phys. Chem., 62, 1325 (1958). (6) I. G.Murgulescu and S. Sternberg, Rev. Chim. Acad. Rep. Populaire Roumaine, 2 , 251 (1957).
