Complexation of Cu ( I I) by Polyrnethacrylic Acid
References and Notes (1) (a) Presented in part at the Xth International Conference on Coordination Chemistry, Tokyo and Nikko, Japan, Sept 1967. (b) Abstracted in part from a dissertation submitted to the Faculty of the Graduate School of the State University of New York at Buffalo by W. M. Anspach in partial fulfillment of the requirements for the degree of Master of Arts, 1968. (2) J. A. Marinsky, "Equations for the Evaluatlon of Formation Constants of Complexed ion Species In Polyelectrolyte Systems," in "Ion Exchange and Solvent Extraction-A Series of Advance," Voi. IV, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, N.Y., 1973, Chapter 5. (3) H. P. Gregor, L. B. Luttinger, and E. M. Roebl, J. Phys. Chem., 59, 366 (1955). (4) M. Mandel and J. C. Leyte, J. Polym. Sci., Part A-2, 2663 (1964). (5)F. J. C. Rossotti and H. Rossotti, "The Determination of Stability Constants," McGraw-Hili, New York, N.Y., 1961.
439 (6) G. Scatchard and W. T. Yap, J. Amer. Chem. SOC., 86, 3434 (1964). (7) J. A. Marinsky, "ion Exchange," Vol. I, J. A. Marinsky, Ed., Marcel Dekker, New York, N.Y., 1966, Chapter 9. (8) L. Travers and J. A. Marinskv. J. Polvm. Sci.. Part C. Svmoosium No. 47, in press. G. Schwarzenbach, "Compieximetric Titrations," interscience, New York, N.Y., 1957. C. Eger, J. A. Marinsky, and W. M. Anspach, J. lnorg. Nucl. Chem., 30, 1889 (1966). I. M. Kolthoff and J. J. Lingaine, "Polarography," Vol. 11, 2nd ed., Interscience, New York, N.Y., 1952, D. Olander and A. Holtzer, J. Amer. Chem. SOC.,90, 4549 (1968). R . Arnold and J. Th. G. Overbeek, Recl. Trav. Chem. Pays-Bas, 69, 192 (1950). T. 0. Denney and C. B. Monk, Trans. Faraday SOC.,47,992 (1951). C. W. Davies, J. Chem. SOC.,2093 (1938).
- .
Complexation of Copper(l1) by a Polymethacrylic Acid Gelia J. A. Marinsky* and W. M. Anspachlb Chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214 (Received June 28, 1974)
The complexing of Cu(I1) by a polymethacrylic acid gel has been investigated. Potentiometric, polarographic, spectral, and magnetic susceptibility measurements have been employed to facilitate the experimental program. The spectral and magnetic data indicate that metal-metal interaction occurs at low degrees of neutralization. The stability constant of the CuAz species, predominant in the higher neutralization range, i s shown to be comparable in magnitude with the stability constant reported in the literature for copper (acetate)z. The quantitative evaluation of the stability constant is made possible by correcting for cornplication arising from the large and variable electric field at the surface of the polyelectrolyte in the polyion domain and by expressing the concentration of polymer species in terms of the measurable volume of the gel phase.
Introduction In recent s t u d i e ~ it~ has - ~ been shown that for the correct interpretation of complex formation of metal ions with the ionized functional groups of weakly acidic polymers it is necessary to (1) correct for deviation from ideality of these metal ions a t the highly charged surface of the reaction site and when more than a single ligand attaches to the metal ion to (2) express ion concentrations of polymer-contained species in moles/total volume, u, of the polymer which exists as a separate phase in the equilibrated system. The first of these requirements is satisfied by experimental measurement of such deviation from ideality by potentiometric study of the competing equilibrium between HCion and the functional group attached to the polymer's matrix. The potential difference between the surface of the polyion arid the region in which the potential vanishes is measured during pH measurement in the course of neutralization of the metal ion-containing polyacid and is the source of such information, the deviation from ideality of mobile H+ ions a t the site of the reaction being given by the well-known equation
where $(a) corresponds to the potential at the surface of the polyion, z is the charge of the proton, K , is the intrinsic
dissociation constant of the acid, and [A-] and [HA] correspond to the concentration of dissociated and undissociated acid.6 Since the free, mobile metal ions are exposed to the same field their deviation from ideality a t the reaction site, accounting for the valence, 2, of the metal ion, is equal to exp(-ZeJ.(a)lkT). In the metal-bound systems, however, the value of [A-] is not easily a ~ a i l a b l e ~and , ~ , only ~ the term [A-] exp( -tJ.(a)/hT)is accurately known. The second requirement is not easily resolvable because of inaccessibility of the domain volume of charged polymers in solution. The unavailability of such information has frequently led to the use of the incorrect concentration unit, moles per solution volume, V, for all species of the equilibrium solution. The resolution of formation constants based on such expression of the concentration of all species in these two phase systems has as a consequence interfered with a valid analysis of complexation in these systems. Only in the situation where the dominant complex species of the metal, polyacid system is an ion pair, MAZ-l, does this aspect become unimportant with use of this concentration unit. In this situation the volume dimension of the concentration unit cancels in the mass-action expression for PI, the ion-pair formation ~ o n s t a n t . ~When - ~ an additional species such as MA2Z-2 forms, however, use of the accessible but inappropriate concentration unit usually leads to sizable variation in the value of Pz with experimenThe Journal of Physical Chemistry, Vol. 79, No. 5 , 1975
440
J. A. Marinsky and W . M . Anspach
mequiv of .H) were completely neutralized with standard NaOH. These resin samples were equilibrated at 24 f 2 O for a minimum of 40 days in 100.0 ml of solution 0.05 M in Na2S04 and either 0.005, 0.00025, or 0.00166 M Cu(1I)SOd. The Cu(I1) concentration was chosen to correspond respectively to M, v4, and yc of the resin molarity in the three series of experiments that were performed. The presence of a sufficient predetermined quantity of H2SO4 in these solutions prior to contact with the resin assured the desired dissociation of the PMA gel at equilibrium while preventing the precipitation of basic oxides of Cu. Such precipitation was encountered with the direct addition of acid-free solution to resin samples neutralized earlier with standard base to the selected association values. The pH of the equilibrated samples was measured with a glass-saturated calomel electrode system at the ambient temperature using a Radiometer Model 4 pH meter. Preliminary calibrations of the glass electrode with standard buffer solutions were refined by the potentiometric titration method of Eger, Anspach, and M a r i n ~ k y . ~ c Methods used to minimize the presence of COP in these systems are detailed in the earlier paper.4 Polarographic Analyses. The equilibrium concentrations of Cu(I1) ion remaining in solution above the gel samples were determined polarographically with a Radiometer polariter P04. The samples were adjusted to a pH of -10 with disodium iminodiacetate in 0.1 M KN03 ( E 1 1 2 ~=~ 0.35) to facilitate the analysis.9 Spectral Investigation. Several resin samples that were used in the potentiometric investigation were separated from the equilibrated mixture (Cu(1I):HA = 1:6) by filtration. They were rinsed with deionized water, air dried, and prepared for spectral examination in a Cary Model 14 recording spectrophotometer as follows. The dried resins were ground with a mortar and pestle until the product passed through a standard 80 mesh screen. A small piece of blotting paper which had an oval window (y4 in. X y8 in.) punched into its center was then placed on the bottom half of a flat steel die. The oval window was filled with the minimum amount of powder required to cover the opening completely and was covered with the top half of the steel die. The die was then extended in a hand-pumped hydraulic KBr press a t a pressure of 30,000 psi for 1 min. The resulting samples were transparent, held to the blotter form, and were fairly resistant to shock. Samples of the hydrogenform resin were prepared in a similar manner and were used in the reference beam. The samples were placed in the reference sample holder and screening was inserted between the reference and the light source to reduce the intensity of the reference beam. The maximum possible wavelength interval (220 to 1050 mp) was scanned. Matched pairs of quartz glass window cylindrical cells (1, 5, and 10 cm) were used to facilitate a parallel spectral exExperimental Section amination of CuSO4 added to the linear PMA analog of the gel. The complete neutralization range of a solution 0.004 Chemicals. Most of the chemicals used in this study have M in PMA, 0.000667 M in CuSO4, and 0.05 M in NazS04 already been listed together with a description, where per(Cu(1I):PMA = 1:6) as well as few selected samples of 0.004 tinent, of their preparation andlor purification prior to use, in an earlier paper4 detailing study of Ni(I1) and Co(I1) M PMA containing 0.001 and 0.002 M CuSO4 (Cu(1I):PMA = 1:4 and 1:2) in 0.05 M Na2S04 were investigated. binding by the cross-linked PMA gel. The CuS04, a Baker Magnetic Susceptibility Measurements. Several gel Analysed Reagent, KN03, a Fisher Certified Reagent, and samples were prepared in a manner identical with that disodium iminodiacetic acid, from the Aldrich Chemical used for the potentiometric investigation, a Cu(I1) to acid Co., employed in this research, but not a part of the earlier molar ratio of 1:6 being employed at the different degrees study, were used as received. of neutralization that were selected for study. After equiliPotentiometric Titrations. A number of 0.100 f 0.0005 g samples of the hydrogen form of the PMA gel ( ~ 1 . 0 0 bration, these samples were filtered, washed with deionized tal conditions. The direction and magnitude of variation that may be observed, however, provides an accurate estimate of the change in the relative volume of the polymer domain since the apparent value of 0 2 is inversely related to the true constant value by vlV. Constancy in /32 has been observed only when the dimensions of the polymer are insensitive to experimental conditions. This situation has been encountered with Cu(I1) bound to polyacrylic acid (PAA). During the formation of CuAz in PAA, when the initial equivalents of Cu(I1) are not significantly smaller than the' equivalents of PAA, such dimensional stability of the polymer has been indicated by the constancy of It was, in fact, this observation of polymer volume stability in such Cu(I1)-crowded systems that demonstrated unambiguously the inverse relationship of f12(app) to initial polymer concentration when the concentration unit is based on the total solution volume. As polymer concentration was increased in a parallel series of experiments, care being taken to provide sufficient Cu(I1) ion to assure formation of the dimensionally stable CuA2 complex, the value of /32 decreased pr~portionately.~ One can, in principle, avoid these complications by expressing the concentration of polymer species in mole fraction terms. With this approach, however, the estima.te of species concentrations will be uncertain if both MA+ and MA2 form. The total number of moles in the polymer phase will change with the quantity of MA2 formed in the various systems studied and cannot be assessed with accuracy. The use of equivalent fractions to eliminate this problem leads to improper application of the mass-action law. In any case the use of these Concentration units are not amenable to the objectives of this research program and have not been employed. It was an important objective of this research program to make accessible a fairly accurate assessment of the concentration of polymer species within the polymer domain. A cross-linked polymethacrylic acid (PMA) gel of definable volume and relatively high inflexibility was used. Potentiometric measurements (pH) provided information with respect to deviation from ideality of the Cu(I1) ion a t the site of reaction. Assay of the free, mobile Cu(I1) ion in the equilibrium mixture was accomplished polarigraphically. With this approach a meaningful stability constant /32 for the CuAz complex that forms was expected to be resolved. Since it has been demonstrated previously that the physical chemical properties of cross-linked gels duplicate these properties in their linear polyelectrolyte analog^,^ the resolution of data expected from this experimental program should lead from measurements of / 3 ? ~ ( to ~ ~a ~method ) for estimate of the absolute volume of the linear polyelectrolyte analog in any Cu(I1)-PMA experimental situation where CuA2 is the dominant complex species.
The Journal of Physical Chemistry, Vol. 79, N o . 5, 1975
Complexation of Cu(l I ) by Polymethacrylic Acid water, and air dried. They were then ground with a pestle and mortar, the powdered product being in a convenient form for reproducible sampling in glass Gouy-balance tubes. Measurements were made at the ambient temperature of 25 f lowith a Gouy-balance assembly consisting of an Alpha Model 7500 air-cooled electromagnet, a 7500 PS filtered power supply, a 7500 R series current regulator, and a chain analytical balance. The equipment constant (% HZA, where H i s the field strength and A the cross-sectional area of the sample), determined for the experimental assembly by employing the measured magnetic deflection of a standard NiCl2 solutionlo (16.35 wt %), was reproduced by a similar analysis of solid CuSO4 5H20." With this apparatus constant, the volume susceptibility (Xv)of representative gel samples was evaluated. These numbers were converted to gram susceptibilities (X,) and the Weidermann mixture equation12 was used to compute the gram susceptibility of the copper complex. From the net molar susceptibility of CuA2 a corrected molar susceptibility, X M , was obtained by employing a diamagnetic correction for closed electron shells in the complex and a permanent temperature-independent correction for the paramagnetism of the Cu(I1) ion. The value of the sum of these two terms was taken to be -12 X 10-6 after Figgis and Martin.13 In computing the effective magnetic moment (peff) the Curie constant, 0, was assumed to be negligible as is the case with most Cu(I1) compounds.ll
-
Results The potentiometric data that were obtained were employed in eq 1 to evaluable the term [A-] exp(-t+(a)/k.T). In this equation [HA] and [H+] were calculable. A value of K, equal to 1.48 X was obtained by extrapolation of potentiometric data obtained for the linear PMA analog of the gel in 0.05 M Na2S04 as described previ~usly.~ This value is in excellent agreement with the dissociation constant reported for isobutyric acid, the repeating monomer unit of this polymer. The fraction of total Cu, ao, present as free, mobile Cu(I1) ion in the various equilibrium mixtures was obtained directly from polarographic analysis of the supernatant solution as described in the Experimental Section. These data permitted evaluation of the term, (1 - ao)/ u~AK-~[A-] where AK-l = exp(-t$(a)/kT). This composite expression of the binding data is equal to Zn,~P,AK-'[A]n-l where Pn is the apparent overall stability constant of the nth complex of the system when concentration of all species in the system is expressed as moles/V where Vis the total volume of the solution. The results of the computations are presented in Table I and have been plotted in Figure 1. The open points represent data obtained at neutralization values >0.35 and fall on a straight line which intercepts the ordinate axis at zero; the solid points, representing data obtained at 01 values C0.30, fall above the straight line. The deviation from the straight line for each set of data points in this neutralization range, though of a similar pattern, becomes more pronounced and extensive as the concentration ratio of Cu(I1) to PMA gel decreases from $ to yS. In this lower neutralization region a gel expansion of -300% is indicated if the changing slope of Figure 1 is attributed to volume change in the gel. This result does not correlate with the pattern of expansion (minimal) with neutralization that is observed in this polymer by Gustafson and Lurio.14
441
TABLE I: Analysis of Potentiometric and PolarographicDataa 103[A']AICi
a,
(1 - ao)/ ao[A-]AICi (IO-')'
CY
pH
0.10 0.20 0.30 0.40 0.50 0.60 0.80
3.877 4.110 4.310 4.503 4.678 4.863 5.065 5.283
A,/Cu(IIC) = 2 0.97 0.858 1.40 0.777 2.09 0.680 2.80 0.615 3.51 0.526 4.31 0.425 5.14 0.336 5.67 0.251
1.71 2.05 2.26 2.23 2.57 3.14 3-84 5.26
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
3.877 4.007 4.157 4.295 4.420 4.553 4.675 4.810 4.961 5.140
A,/cu(II) 1.027 1.33 1.78 2.31 2.89 3.69 4.54 5.73 7.44 1.023
2.10 2.11 2.43 3.51 3.11 3.80 3 -83 4.70 5.58 7.79
0.70
=
4 0.823 0.782 0.699 0.552 0.527 0.417 0.365 0.271 0.194 0.111
A,/Cu(II) = 6 2.17 1.19 0.794 2.97 1.64 0.672 2.25 0.556 3.54 3.02 0.469 3 -74 4.34 4.29 0.350 5.60 5.85 0.234 8.82 0.129 7.66 11.51 0.054 11.55 a 1.00 mequiv PMA gel; 1.00 meguiv NaOH: 0.05 M NazS04; total volume 100.00 ml after addition of 0.100 "2S04. 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
3.940 4.099 4.259 4.411 4.588 4.752 4.962 5.237
A-Cu/PMA=
'4
1-a. 800-
aoAK-'[A-]
-
600 -
002
004
006
008
010
012
014
016
A K - ' [A-I
Figure 1. Graphical analysis of polarographic study of the Cu(II)-PMA gel system.
and potentiometric
The source of this discrepancy with predicted behavior is believed to be identified by the spectral and magnetic studies. Representative spectral data that were obtained for the Cu(I1)-PMA (linear) system (0.0040 M PMA, 0.00667 M CuS04,0.05 M Na2S04) are presented in Figure 2. The absorption peak shifts from about 810 to 717 mfi when PMA is added to the CuS04-NazS04 solution and the molar exThe Journal of Physical Chemistry, Vol. 79, No. 5, 7975
J. A. Marinsky and W. M . Anspach
442
L-L._LIJI_I___I_LIL/J 400 500 600 700
300
ma
Flgure 3. The effect of neutralization on the absorption spectrum of a Cu-PMA gel mixture: Cu/AT = 1/6. mP
Figure 2. The effectof neutralization on the absorption spectrum af a CU-PMA mixture: Cu/AT = 1/6;p = 0.15 (Na2S04). tinction coefficient increases from about 12 (in the absence of PMA) to a maximum value of approximately 170 (in the presence of PMA) a t a = 0.6. As the neutralization of acid proceeds from a N 0 to a = 0.6, the wavelength of maximum absorption shifts from 717 to -688 mp and a shoulder a t -370 mp, just before the charge transfer band dominates the situation, is observed to first increase in magnitude and then decrease as a approaches a value of 0.6. Beyond an CY value of 0.6, the 688-mp peak decreases in magnitude and shifts slightly to 692 mp while the shoulder at 370 mp disappears. An isosbestic point a t -800 mM appears when a > 0.5. These data, presented previously in a brief summary of this work,la have since been substantiated in a more comprehensive study by Leyte, Zuiderweg, and Van Reisen.15 Our earlier tentative assignment of the absorption shoulder at 370 mp to Cu-Cu interaction that was based on the interpretation of similar results obtained with the Cu(I1) acetate system16 is now fully supported and in fact much clarified by their scholarly analysis of a more detailed examination of the spectral (uv and ir) properties of the Cu(I1)PMA system. The disappearance of the shoulder and the decrease in absorptivity together with a slight shift of the absorption maximum at -692 mp and the appearance of an isosbestic point at neutralization values of 5 and greater indeed appears to be associated with reduction of Cu-Cu interaction in the increasing presence of A-. By attributing the property of dimerization to the CuA2 species in the PMA gel over the neutralization range 0 < a < 0.35 a reasonable rationalization of the observed deviation in the gel system from linearity of the binding data is provided. The solid state absorption spectrum for the Cu(1I)-PMA gel system (l/6 molar ratio) is presented in Figure 3. The relative peak heights are of no importance in this type of study, due to variations in sample thickness and consistency. The apparent downswing of the CY = 0.6 curve in the ultraviolet region is not real, but rather a function of the sample thickness, which resulted in the spectrophotometer slits being wide open. As a consequence evidence of dimerization could not be forthcoming. The fact that the wavelengths of maximum absorption, as well as the general shape of the spectrum, are comparable is significant, however, and supports the estimate that dimerization also occurs in the gel in the low a region. The overall shape of the solid state spectra are quite similar to those obtained with the Cu(I1)-PMA (linear) system. However, unlike this sysThe Journal of Physical Chemistry, Vol. 79, No. 5, 1975
tem, in which the wavelength of maximum absorption shifts toward lower wavelengths as a increases beyond 0.6, the solid state spectrum exhibits a maximum absorption at -680 mp (instead of 688-717 mp) and shows little, if any, change with a. The apparent absence of evidence for sizeable conformational change in the less flexible gel may be due to the use of solvent-depleted sample sources but is not unexpected on the basis of resin rigidity and the volume expansion studies of Gustafson. Additional support for the rationalization of the binding data in the low neutralization range with the dimerization of Cu is provided by the results of the magnetic susceptibility measurements that are summarized in Table 11. The low moments calculated for the a = 0.2 and 0.4 samples parallel the low values obtained for crystalline copper acetate,l7Js and are attributable to dimer formation. It has been proposed that the low moments result from exchange that occurs between the copper atoms uia an overlap of the d,z -- y z orbitals forming a CT bond.ll This result demonstrates the parallel behavior of the gel and its linear polyelectrolyte analog. The persistence of dimerization beyond an a value of 0.35 may be a consequence of solvent removal during air drying of samples in the source preparation. Discussion On the basis of these results it is concluded that the dominant complex species in the CuSO4-PMA gel-NazSOd system is CuA2 over the neutralization range of 0.35 < a < 0.80. The value of /32(app) obtained for this species from the slope of the straight line that is drawn in Figure 1 through the data points compiled in this neutralization region is 7.85 X lo4. The line intercepts the ordinate axis at a point very near zero. An accurate estimate of the value of the intercept (PI) from the graph is not possible, however, and the following approach to the assignment of a reasonable 81 value for CuA+ seems appropriate. Froneaus a t a fixed experimental condition has measured the value of & for the (nickel acetate+) and (copper acetate+) ion pair to be 4.7 and 44,respectively. A value of unity has been determined for the NiA+ ion pair in the NiS04-PMA gel-NazS04 system a t the same experimental conditions employed in this study4 and by presuming the same ratio in /31 values that is observed with the acetate system PICuA+ is -10. In the neutralization range 0 < CY < 0.35 the disturbance of the linear correlation of the data points in Figure 1 has been attributed to Cu-Cu interaction that involves neighboring CuA2 entities. Spectral and magnetic susceptibility are the basis for this interpretation of these discordant results. From the gel water content measurements of Gustafson and I,urio14 it is observed that the change in volume of
Complexation of Cu ( I I) by Polymethacrylic Acid
443
TABLE 11: Magnetic Susceptibilities and Moments of Cu(I1)-PMA Gel Systems (M/AT = 1/6) -Sample
a @PA(10-6) 106Xv (complex) peff
H’ form resin Cu resin Cu resin Cu resin
1.041 1.041 1.061 1.061
0.20 0.40 0.60
1.3183 1.0358 1.6467 0.0000
133.6 300.5 790.0
0.506 0.848 1.365
a PMA gel with Cu(I1) content is too small to have a noticeable effect on the experimental value of ,62(app)CUA2 that has been measured. The apparent molar volume of approximately 90 ml that is estimated for the polymer has been employed in eq 2 to obtain P2(U)CUA2.
= 7.0 X 10‘
This value of &,)CUA2 is in reasonable agreement with the value of &cU) that can be derived from the experimental studies of Gustafson and Lurio. In their program the exchange of 4.63 mmol of Cu(NO3)z in 100 ml of 1M NaN03 with 9.26 mmol of PMA gel (a concentration level 9.26 times larger than in this experimental program) was studied as a function of the degree of neutralization of the polyacid with standard base. At 50% neutralization an equilibrium pH of 4.06 was measured by them; the molar concentration of HA, Cu(II), and CuAz was approximately 0.046, 0.023, and 0.023 M, respectively. The mass action expression for the reaction is given by eq 4 where AK-l, the 2HA
+
Cu(I1)
a CuA, +
[CuA ][H+I2
1=- 1
2H’ CuAZ
=
(3)
(4)
nonideality term for H+ and Cu(I1) ions at the surface of the polyion, cancel. When the molar concentration of all species are based upon the solution volume
By resorting to gel species concentrations expressed relative to gel volume CUA
p2(”)
2
V
= ,92(app) = 1.64 x
= 1.37
X
lo4 (0.0083)
10’
These values of 7.0 X lo1 and 1.37 X lo2 for &,)CUA2 compare with a P2Cu(Ac)2 value of 4.4 X lo2 measured by Froneausl9 for the copper(I1) (acetate)z complex in 1 M NaC104. The stoichiometric concentration of free, mobile Cu(I1) ion was used in the computation of PZ for the biligated copper in these systems and the difference between the & values reported above could be at least in part due to differences in the unaccounted for excess free energy of the Cu(I1) in these systems (PMA gel, 0.05 M NaZS04, M CuSO4; PMA gel, 1.0 M NaN03, M Cu(N03)~;and HAC (acetic acid), 1 M NaC104, M Cu(C104)~).In 0.05 M NazS04 the Cu(I1) is competitively complexed by S042-; in addition electrostatic interaction of the ionized species
needs to be taken into account. When this is done y+cU N 0.084 in 0.05 M N a ~ S 0 4 The . ~ mean molal activity coefficient published for Cu(NO& and Cu(C104)2 at M E 1 is 0.437 and 0.568, respectively.20 With these correction terms P2(U)CUA2 values of 830 (SO,-), 340 (NOS-), and 780 (C104-), respectively, are resolved. Considering the uncertainty in the estimate of the excess free energy of the Cu(I1) in these systems the reasonably good correlation of the stability constant of CuAz that is affected provides supporting evidence for the validity of the model that has been developed for the computation of the formation constants of complex species in charged polyelectrolytes. First it has been demonstrated that appropriate expression of concentration of species in charged polymer systems is based on the volume of the polymer domain. Only with this treatment of the data can the experimental results obtained in this research be correlated with those of Gustafson and Lurio who employed a quantity of resin approximately tenfold greater than was used in the studies reported in this paper. Second, the observation that the stability constant of copper ( a ~ e t a t eis ) ~quite close to that of the CuA2 species formed in polymer systems with a chemically similar ligand group ( P K H ~ B ~PKHAJis of fundamental importance as well. It is believed, on the basis of this result and earlier result^^-^ that when the functional group of the polymer is chemically equivalent to that of a model monomer system the complexation behavior to be expected of the polymer after proper attention to polyelectrolyte effects can be deduced from study of the monomer itself. The use of insolubilized cross-linked polymer models of linear polymer systems of scientific interest to provide easy access to the volume of polyion domains as a function of experimental conditions offers an experimental approach to the study of all types of linear polymeric systems. With appropriate design of experiments the volume of these linear systems become accessible at any experimental situation. With such knowledge of the thermodynamic and physical properties of complex polymeric systems analyzable in this manner calorimetric studies of these systems can become much more meaningful than they presently are. The application of the experimental approach that has been well documented by this and earlier studies should be extremely advantageous for the study of biopolymeric systems. Acknowledgment. Financial support through Contract No. AT(30-1)-2269 with the United States Atomic Energy Commission is gratefully acknowledged.
References and Notes (1) (a) Presented in part at the Xth International Conference on Coordination Chemistry, Tokyo and Nikko, Japan, Sept 1967. (b) Abstracted in part from a dissertation submitted to the Faculty of the Graduate School of the State University of New York at Buffalo by H.M. Anspach in partial fulfillment of the requirements of the degree of Master of Arts, 1968. (2) J. A. Marinsky, “Equations for the Evaluation of Formation Constants of Complexed Ion Species in Polyelectrolyte Systems,” in “Ion Exchange and Solvent Extraction, A Series of Advances,” Vol. IV, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, N.Y., 1973, Chapter 5. (3) C. Travers and J. A. Marinsky, J. Polm. Sci., Part C, Symposia (1974). ( 4 ) W. M. Anspach and J. A. Marinsky, submitted for publication in J. Phys. Chem. ( 5 ) N. Imai, M. C. Lim, and J. A. Marinsky, Isr. J. Chem., 11, No. 6 (1973). (6)G. Torrence, S. Amdur, and J . A. Marinsky, J. Phys. Chem., 75, 2144 (1971). (7) M. Reddy, J. A. Marinsky, and A. Sarkar, J. Phys. Chem., 74, 3891 (1970). The Journal of Physical Chemistry, Vol. 79, No. 5, 1975
Ted B. Flanagan and James F. Lynch
444 (8)C. Eger, J. A. Marinsky, and W. M. Anspach. J. lnorg. Nucl. Chem., 30, 1889 (1968). (9)I. M. Kolthoff and J. J. Lingaine, "Polarography," Vol. 11, 2nd ed, Interscience, New York, N.Y., 1952. (IO) D. P. Shoemaker and C. W. Garland, "Experiments in Physical Chemlstry," McGraw-Hill, New York, N.Y., 1962. (11)8. N. Figgis and J. Lewis in "Progress in Inorganic Chemistry," Vol. VI, F. A. Cotton, Ed., Interscience, New York, N.Y., 1964. (12)R. L. Martin and A. Whitley, J. Chem. SOC., 1394 (1958). (13)B. N. Figgis and R. L. Martin, J. Chem. Soc., 3837 (1956).
(14)R: L. Gustafson and J. A. Lurlo, J. Phys. Chem., 69, 2849 (1965). (15)J. C. Leyte, L. H. Zuiderweg, and M. Van Reisen, J. Phys. Chem., 72, 1127 (1968). (16)S. Yamada, H. Nahamura, and Tsuchlda, Bull. Chem. SOC.Jap., 30,953 (1957). (17)M. Kondo and J. Kubo, J. Phys. Chem., 62,468(1958). (18)R. L. Martin and A. Whitley, J. Chern. SOC., 2960 (1958). (19)S.Froneaus, Acta Chem. Scand., 5,859 (1951). (20)R . A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworths, London, 1959.
Thermodynamics of a Gas in Equilibrium with Two Nonstoichiometric Condensed Phases. Application to MetaVHydrogen Systems l e d 6. Flanagan* and James F. Lynch Chemistry Department, University of Vermont, Burlington, Vermont (Received September 19, 1974) Publication costs assisted by the Petroleum Research Fund
For many metal/Hz systems values of d(ln p112)/d(1/57) are approximately constant over wide temperature ranges for regions of hydrogen contents where two nonstoichiometric condensed phases coexist with the gas. This near constancy is surprising in view of the change in the hydrogen compositions of the two condensed phases with temperature and the dependence of the relative partial molar enthalpies of solution of hydrogen upon the contents of the pure condensed phases. Previous treatments of such systems have not lead to an understanding of the origin of this constancy. In the present research, two approaches are developed for the understanding of the temperature invariance of d(ln p1/2)/d(l/57). One is based on the enthalpy of solution of hydrogen in each of the pure phases adjacent to the phase boundaries and the change of the phase boundaries with temperature. The other approach estimates the heats of desorption a t various temperatures for the reaction metal hydride -+ 1/2H2 metal (H saturated) from the relative partial molar enthalpies of desorption. Both approaches are employed in detail for the Pd/H2 system and illustrate the origin of the temperature invariance of d(ln p1/2)/d(l/T).
+
Introduction The phase rule predicts that the equilibrium pressure of hydrogen in equilibrium with two H-containing condensed phases should be invariant at a given temperature. For metal/Hz systems the two condensed phases are generally the metal saturated with hydrogen and a metal hydride phase. Both are nonstoichiometric. From the temperature dependence of the pressure over the two condensed phases, the plateau pressure, a value of AH may be derived. Generally, for metal/Hz systems, the value of AH derived from R[d(ln p1/2)/d(l/57)] has been found to be independent of temperature over a wide range. This derived value of AH is generally assumed to correspond to the reaction metal (Hsatd)
+ */?H2-+ metal hydride
(1)
It is surprising that the values of AH derived in this manner are constant with temperature because the nature of reaction 1 changes appreciably with temperature as the nonstoichiometric compositions of metal (H satd) and metal hydride change over the temperature range where d(ln p1I2)/d(l/T) has been evaluated. For example, Figure 1 shows the variation of the phase boundaries with temperature for the classical metal/Hz system: Pd/H2. The marked change in the nature of reacThe Journal of Physical Chemistry, Vol. 79, No. 5, 1975
tion 1 can clearly be seen from Figure 1. Besides the change in compositions of the two phases, the relative partial enthalpies of absorption of hydrogen vary with composition of the pure phases. Figure 2 shows for the Pd/H2 system the (calculated) variation of the relative partial molar enthalpy of absorption, &H, with hydrogen content. It is very surprising therefore to find the degree of linearity observed in plots of In p112against 1/57 (Figure 3). The temperature dependence of the plateau pressure has been discussed for metal/Hz systems by Speiserl and less explicitly by Darken and Gurry.2 One form of the equation given by Speiser for hydrogen in equilibrium with the hydrogen-saturated metal and the metal hydride is
where the composition of the nonstoichiometric hydride is M1-,H, and the composition of the H-saturated metal is M1-,H,. The double-primed symbols refer to the gas phase, the single-primed symbols to the nonstoichiometric metal hydride phase, and the unprimed symbols to the Hsaturated metal. Speiser has pointed out1 that this equa-
