EFFECT OF Hrm PRESSURE ON AQUEOUS EuSOa Table 1x1 : Derived Constants
n 78.3b 78.16 77 I75 77.15 75.20 12.37 65.20 64.90 60 10 54 1.2 49.40 43 I33" I
~
is
A0
L40.73 rt 0 . 1 138.78rt0.03 135.19zk0.04 130.19kQ.09 118.14f0.1 98.25 k 0.05 63.63rtO.06 63.0510.08 46.48i-0.03 31.165 :F- 0.008 2E..287'=k0.004 10.760 rt 0.001
KA
d
0.98 i 0.04 0.99 f 0.01 0.93 =t0.02 0.79 i 0.09 (0.41f0.24) (0.19 I 0.03) ( 0 . 0 rt 0.07) (0.12i0.10) (0.34 5 0.05) 1.64 rt 0.04 3.95 rt 0.01 9.86 I 0 . 0 3
3.3 3.3 3.5 3.8
6.2 5.2 3.9
rT
0.01 0.005 0.008 0.03 0.09 0.01 0.05 0.08 0.05 0.02 0.04 0.07
Values at 30°, see ref 12.
account the influence on the association of the specific ion-solvent interactions connected t o the solvent strucSure.
I n order t o investigate the dependence of ionic solvation on the solvent composition, the volumetric behavior of water-sulfolane mixtures was derived from the density values given in Table I. 'The results are shown in Figure 2 where the molar volume exccss in per cent [(AV/V)lOO] is plotted against the mole fraction of sulfolane ( N z ) . As can be seen, a negative volumc excess is found as sulfolane is added to pure water. Assuming that the increased ~ ~ c k density ~ n g in the water-rich mixtures enhances the preferential solvation of ions by water, the observed decrease of ~ ~ ~ ~ association of potassium perchlorate can he ~ considering the increased screening effect 01 the d v a tion shell on the ion-ion interaction. A further comment should be made, finally, about the postulated increase of ionic solvation caused by the water structure modification. If such a process occurs, a decrease OC ionic mobility must be observed in the water-rich region. The behavior of Walden product shown in Figure 3 seems t o confirm, &o from the hydrodynamic point of view, the above ~ ~ ~ s ~ ~
igh Pressure on the Formation of Aqueous EuSO,+ at 25" by Clarence F. Hale and F. H. Spedding" Ames Laboratory, U , S. Atomic Energy Commission and Department of Chemistry, Iowa State University, Ames, Iowa 60010 (Received March 30,1973) Publication costs assisted by Ames Laboratory, Iowa State University, Ames, Iowa
The formation of aqueous EuS04' was studied a t various pressures from atmospheric to 2040 atm a t 25" using uv absorption spectrophotometry. Data were gathered a t a constant ionic strength of 0.046 m and as a function of ionic strength from 0.010 to 0.046 m. The formation constants were found to be independent of wavelength from 240 to 250 mh. The plots of log K and log K O vs. pressure were found to exhibit distinct quadratic behavior. For the infinitely dilute solution, AVO of formation was calculated to be 25.6 and 12.0 ml/mol ab atmospheric pressure and 2040 atm, respectively. The large AVO value a t atmospheric pressure when compared to those from similar studies and, from theories on ion-pair formation provides overwhelming ~ ~ +calculated to evidence that EuS04+ is an inner-sphere complex in dilute aqueous solution. j Y ' ~ ~ s was be -44 ml/mol a t 1 atm and 25'. I
Introduction An earlier investigation from this laboratory employed differential uv absorption spectrophotometry' to study the association of aqueous E ~ 3 -and t s042-ions as a function of dilute ionic strength, temperature, and wavelength. Analysis of the resulting AH" and AS" data provided strong evidence that EuSO4-t- in dilute aqueous solution at 25" existJsprimarily in the innersphere form; i.e., the ions are in mutual contact with no solvent molecules separating them as in t,he Case for
the outer-sphere type. Since the change in the partial molal volumes, A v o , for E u S O ~ +formation should also be m x d i v e t o the type of complex formed,2it was decided t o make a similar investigation of this system as a function of pressure. Other studies made on the formation of aqueous com(1) C. F. Hale and F. H. Spedding, J . Phv5. Chem., 76, 188 (1972). Pressure Physics and Chemistry,,7 vel. 2, (2) R.s. Bradley, Academic Press, New Y o r k , N. Y . , 1963, PP 131-162.
The Journal of PJ~ysicalChemistru, Vol. 76. A-0. 20,1972
plex iomi as 2~ furnotiorx of pressure have been rather wan^^ 7 Di~:ci~siorib 01those pertinent t o the present stig~,tion v i l l i be m d e later in this paper.
It was cornposed of a movable Teflon plu contained in B stainless steel jrickek having 811 inner of HasteTZoy-C. The pres~uww m ~ ~ ~ by ~ ~ H ourdon t i a h type gauges on the pump side of the separator and t,wo on the optical cell side. 'Jhem ~ ~ ~ ~ 'TIE rrwdmck cmpioyed in the volumetric preparation provided an acaiiracy of atm u~9i o 680 atrn anid OS Lhc europiar nra ~ ~ sodium perchlorate, ~ and I ~ ~ ~ ~ ~ A27~ a h flb01Xl680 2040 ah"l. XII sull"ritertoek ~ ~ ~and~sample ~ and t ~reference o ~ ~ The s o p l i c ~cell l was ~ ~ ~ o r i~i ~) huwith ~ gd ~~ ~ ~~ ~ t ~ ~ iiiis m r e iticiaiausl with those in the earlier temwater before using and the reiere e ~ ~ s e a ~ t 240, ~ n ~ s 245, and '250 ~ m pwere checked a,nd PP&, The ~~~~s~~~~~~~~~~~ of n sirnglt test ~ ~ l u t i o c n sured ut theae three wav t o 3040 atm. After l l i e ~ e at ~ ~ ~ ~ i sure bS" setumed to d lbtm and chcclted. If any significant differ %>ereploy^^ at each pressure P studies made at variable ionic greater than ~ . ~ ~ ~ ~smnitsl 0~ Lbr~r run ~was re~ ~ c paabed after 00061tirg and ~ o tiire ~ ~ ~ ~~ ~e ~ er~chsample had an identical ~ ~ l z n t iexcept ! ~ i thae it contained In addition, a t the corrcluslon ot 8, daj B workythe optical cell was B~ms?hedwith diatiXlrd ~ r oea' l 21-d Ute hwsrtlines r~chccked t h range studied was low, the Since only onc ~ ~ ~ ~ ~ ~o~~~~~~~ p r ~e ds vir&s s uu ~ e rrtrations with pressure were absorbancy readings were ~mctde tm A.r. Thc mlng that the densities of the unlike Lhe previous s i udj on this ey3tcni1 where the more accurate ~ e t of hdifferential ~ ~ ~s ~ ~ ~o ~ ~ ~ ~t ~ ~~ r of t h T~i!st* ~ O l ~ ~ ~ oAn Cary s. Model 14 e ~ e r soEli~o~ c e ~ reeordnng ~ ~ ~equipped~ with a ~thermo- ~ was employed, ~ ~the absorbancies ~ ~of the ~ A tions had t o Ise ~ ~ i ~ ~ r ~froin c t ~h t me ai~kke~ nt, supplied from an external sample solutiom :iO.i", was employed to meaEquations and Definition of Terms. The molar ther'flie a ~ ~ - Q i ~~ ~e ~~ ~~ ~ ~epump, l~ ~ -316-stainless ~ n ~ e d modynamic equilibrium constant K ' for the association of e u r o p i ~ and ~ ~sulfate ( ~ ~ions ~ ~as expressed by eq Z is ing, v:dve~,g ~ i g e s and , high-pressure optical the product of ils formation ~~~~R~~~~~~ R and activity sapphii c T i n ~ l o ' j vwere ~ supplied by the Americoefficient factor ( Y + ) * can dnstrumtnt 420. and :ire (all listed in their commercial catslug. jrlo~v2'a~er,some minor modifications were Eu3-t -1 scB*2-G ELt8C94" (1) made "Jl'he pLI I"p 13 adapted t o use distilled water uid, ' h e path length of the optical K [EuSO,'*]/( [1Eua+j[sO,'-J) (24 $%.trim f 0 Lo 2.0 cm while its overall K" = R{aY~u,,,"/((r,,.l')IYsoaz-))t 1%) so &at it would fit into the standard the unknown activity co cell ~ ~ ~ ~of a, ~C'ary) 14.~ The ~ optical ~ ~cell iwas ~ ~Fore thist invcstigation ~ ~ cient factor was assumed t o have been invariant at each also provicBI:dl Yjlil"1l 11 Har iloy-C liner t o inhibit corropressureforthosestudiesmade at constant ionic strength. sion a d special 0 r i n rwutaining ~ a high percmtage of For maximum clarity the hydration spheres of the ions ~~~~~~1 0 rings were found t o discharge a have not been shown, y, relalive to that of the test Equation 4 which assumed that ~ e e r - ~ ~ , m law ~ert'~ I tolerate, These modificaand the law of mass action were applicable over the d u d its pressrrre rating to experimental conditions employed was used to evaiuate ~~~,~~~~~ psi !rom psi. K and (e1 - e o ) from the experimental absorbancy data. 01" the low-experimental absorbancies (less than TB 2 ) h e ce, d a r bhort path length of 2.0 c q 8 the noa.mr,l slidv iviw replaced with one which ex(3) S. D. I-Iamann, 1'. d. Pearce, and W. Straws, J . Phys. Chem., y scale by a factor of 10. All 68, 375 (1964). neuunily at each wavelength and (4) F, N. Fisher and D. F. Davies, ibid., 69, 2595 (1965), (5) F. R. Fisher and D. F. Davies, ibid., 71, 819 (1967). p of Ihe spectra. The reference (6) It. A. Horne, B. R. Myers, and 6. R. Frysinger, IFnorg. Chem., o excessive attenuation of 3, 452 (1964). e narrow aperture of the high~~~~~~~~~
~~~~~~~~~~
~~~~~~~~~~
the test solutions with the oilalter used by the pump, a sepathe pump and optical cell.
( 7 ) F. € Fisher, I. J . I'hgs. Chem., 66, 1607 (19fi2). (8) The analogous 1,emperature study previously made on this system' employed optical cells having path lengths of 10 cm. Also, unlike the previous study which utilized differential spectrophotometrj-, the reference iioliitions which had very low absorbancies bad to be measured separately.
EP~FECT OF HIGW 'PEESSUREON AQUEOUS EuS04
2027
It contains a term t o correct for the presence of NaS04i o n pairs.
The derivation of this equation without the NaSO4- modification is well known and therefore will not be given h e m g Light absorption by sodium sulfate was found to be insignificant a t the concentrations and wavelengths eniployed. As in the previous temperature study 011 this system,l the formation of bisulfate ion was safely ignored, Due t o the inability t o obtain scccurate Kz and (e2 -- a") values a t pressures significantly above ~ t ~ ~ ~ sno~corrections h ~ ~ r were ~ c made , for the presenc~of the Eu(SOJ2- complex.
[EuS04'] = ( A , - A,)/(L(€l-
e"))
[SO?-] = S -- [EuS04+] - [NaS04-] [Eu3+] = E K
=
c/([(ea
1 = 6 ( E - [EuSO4+]]
-
- €">
(5) (6)
[EuS04+]
(7)
-
(8)
a"][S042-])
+ 35 + N - Z[NaSOa-I
(9)
where 6 = ( A , - A,)/ISL, a" = (A, - &)/EL, E = molar concentration Eu(GlO.&, 8 = molar concentration Na2S04, N = molar concentration NaC104, L = path length in em, A , = absorbancy of sample solution, A, = absorbancy of reference solution, eo = molar cient of Eu3+, el = molar extinction coefficient of EuSOd+, [XI = molar concentration of x a t equilibrium. log K" - (AZ2AD)I (10) where A Z 2 -- ZZ2(products) - ZZ2(reactants), Z = charge on ion, A = Debye-Hueckel constant (pressure and temperature dependent), D = constant. Determination of the Formation Constants. For the investigations a t constant ionic strength K and (a1 - E " ) were obtained from eq 4 in conjunction with eq 38, 5, 6, and 7 , in that order, by initially setting [Eu3*] = E and [Sod2-] = S. An iterative process was then employed using refined values for [S04z-], [Eu3+],and [;C\'aS04-], until the change in K was less than 0.1%; this took four to five cycles. For &, the formation constant of NaS04- as defined by eq 8, thevalue of 5.0 at infinite dilution as determined by Jenkins and a t 25" was used. Its pressure dependence was estimated from the equation for ionpair association proposed by Fuoss.ll For these calculations Owen and rinkley's12 analysis of Kyropou1osI3measurement,s on the dielectric constant of water at high pressures was e m p l ~ y e d . ' ~Also the value of 4.8 calculated for 9 a t 1 atm and 2.5" was assumed t o be
independent of pressure. Q was found to decrease from 5.0 at 1 atm to 4.3 a t 2040 atm at 25'. The ionic strength dependence of Q was obtained from eq 10 after 0.3, as recommended by D a ~ i e s . ' ~ first setting D The adequacy of this value for D for such an extrapolation was discussed previously.1 For those studies made at various ionic strengths, R was calculated directly from eq 8 after assuming that the (€1 - a") values obtained in the constant ionic streiigth invesligation for any one wavelength and pressure remained constant over the entire ionic strength range studied; i.e., 0.046-0.010 m. First an approximate ionic strength for a single sample solution was determined from eq 9 and 5 by ignoring the presence of lajaS04-- ion pair. A value for Q was then calculated for this approximate ionic strength as described above, after which the initial jNaS04-l Concentration was obtained from eq 3n by first setting [S042-] = S . Then [SQ42-] wa8 calculated from oq 5 and 6, which in turn was used in eq 8 and 9 to obtain K and a new ionic strength. After this pros:css was repeated for all the sample solution^, the resulting R values were then extrapolated t o infinite dilution by using eq 70 to obtain the initial molar thermodynamic formation constant K" . This procedure was repeated, using progressively more accurate [Sodz- ] concentrations, until the change indr'" was lew than 0.1%; generally only three cycles were required. Due t o the prezlsure dependence oE the molar concentration scale, these molar formation constants had to be corrected to the moial concentration scale before accurate AV and AV" values could be determined. 'This was accomplished by multiplying the final R and K" values by the density of pure water a t that pressure. To distinguish the formation constants based on the molal scale from those on the molar scdc, the molal formation cornstants have been written 8s K and K O . The IC' t o K" corivemioiiE mere exact, b,ut thosc for K t o IE were not. T-Iowever, due to the low-ionic strength of 0.046 nz, the resulting error in K is negligible. Also, in the Ab' calculations It is the change in density with prcssure thal is important and not its ttbsoluti: value. The method 01 least squares was exnployed for all the data fittnng. The experimental points17 were weighted I
(9) C. B. ;Monk, "'Electrolytic Dissociation," 1st ed, Academic Press, London, 1961, p 186. (10) I. L. Jenkins and C . B. Monk, J . Amer, Chem, shc., 72, 2695 (1950). (11) R. A. Robinson and R. H. Stokes, "EAectrolyte Solutions," Butterworths, London, 1959, p 551. (12) 18. B. Owen and S. R. Brinkley, Jr., Phys. Eeu., 64, 32 (1943). (13) S. Kyropoulos, Z. Phys., 40, 507 (1926). (14) The more recent data of Owen, Miller, Milner, and Cogan15 are probably more accurate but, unfortunately, only extend to 1000 atm. (15) B. B. Owen, R. C, Miller, C. E. Milner, and 'IT. L. Cogan, J . Phys. Chem., 65, 2068 (1961). (16) e. 'IV. Davies, "Ion Association," 1st ed, Butterwortha, London, 1962, p 41. The Journal of Physical Chemistrlil,Vol. 76: N o . 20,1972
ed by YVolberg.l8 Any points confidence level were rejected. l9 T i %L poimt WEM wjeeikd, that particular set of iterations ~"B I qm,Led *ram the laeginning. All the calculations v~ereexecuted by an i M Xodel360 digital computer.
The final R and K" values t ~ g ~ twilh h i ~Cheir standard deviations are reported in Table [IT, Thew molar furmation constants were calculate age of the three given at each prcsn uncertainties were determined in the same manner, al-
Table 1x1 : Final Molar and Molal Formation Constanl,s for Aqueous EuSOat at, 25' 57z 517 444 397 353 324 268 222 186 155 142
567 504 453 398 358
1 ]I 38 272 408 545 BMiCI 953 1225 1497 1770 2040
3117 261 211 182 182 139
73.66 71.24 70.21 67.95 66 36 63.87 59.48 55.93 53.02 51.32 47.73
564 506 443 405 353 320 25.5 213 186 1.62 127
~
62.02 59.95 58.71 56.20 54 * 94 53.04 49.96 46.41 43.18 40.69 40.59
_p_l.__I
The variatble ionic btrength studies were made from 0.0 i l t o 01.046 m at the same pressures and wavelengths above. 'The resulting molar thermodynamic formation constarits KO1 obtained after extrapolation to infinite elilulion, ®iven in Table 11. Again no trend with wavelength was noted within the standard devialion8 which a-crcrsgetd about 1.5 to 2.5% over the entire presslire range _n___.._______^l_(_(I_X_..__
-
-
~
-
~
able II: R" for Aqueous EuS04+ Formation a t 25'
K"
x
10-3 x, ma--------
~
_.-.---.---------O.
Pressure,
046 m---
Ioiiio strength.---------r-------O KO
atrn
IC
1 136 272 408 545 680 983 1225 1497 1770 2040
x
10-2
5.64 & 0.15 5.09 k 0.12 4.47 & 0.11 4.00 f 0.11 3.55 I 0.10 3.20 0.08 2.61 d: 0.07 2.15 rt 0.07 1.85 i0.08 1.56 rt 0.07 I .36i:0.12
x
IO -2
5.62 5.10 4 50 4.05 3.61 3.28 2.70 2.25 1.95 i.66 1.46
m-----'10
IC0
x
15-3
4.76 i 0.07 4.25 0.06 3 . j 7 -c 0.09 3.18 0.06 2.17& 0.07 2.44 f 0.05 1.94 rt: 0.05 1.59 I O . 0 5 1.29 rt: 0.03 1.08 A : 0.02 0,94 & 0.aa
x
15-3
16.74 4.25 3.59 3.22 2.83 2.50 2,Ol 1.66 1.36 1,24 9.01
When log K and log K O were plotted vs. pressure, a plot which exhibited distinct quadratic beha,vior 'vvas obtained. The following equations were found to best represent the data over the entire pre~surerange. The accompanying uncertainties are the standard tions obtained from the least-squares fit of the dat log
K
=
2.755 ~3.821 1W4P-t 4.48 X d
-8.P
Li--o.0022
1 I 1
Pressure, atm
1 1.36 272
408 545 680
053 ii 225
1497 1x70 2040
240
245
250
4.57 4.12 3.56 3.12 2.79 2 40 1.34 I 53
4.93 4.34 3.62 3.17 2.77 2.49 1.98 1.66 1.31 I .07 0.98
4.78 4.29 3.53 3.24 2.76 2.44 1.91 1.58 1.32
1.24 1 05
0.96
1.11
0.89
(17) The raw absorbancy data were far to numerous t o be included in this paper. Therefore, all the A , -. A r values for the best solu.tions at all the ionic strengths, wavelengkhs, and pressures employed will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemical Society, 1155 Sixteenth St., N.W., Washington, D. C. 20036, by referring Lo code number JPC-72-2925. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche. (18) J. R. Wolberg, "Prediction Analysis," Van Nostrand, Pjew York, N. Y . , 1967. (19) W. Chauvenet, "Spherical and Practical Astronomy," Vol. V, Lippincott+ Philadelphia, Pa., 1868, p 558. (20) The importance of K being constant as a function of wavelength was discussed fully in an earlier paper.'
EFFECT OF EIGEI FIFESSURE OM AQUEOUS EuSOa log
KO
= 3.682
2929
-- 4.540 X 10-4P
+ 5.89 X
10-8P2
10.0044
The desired AV and AV" values were obtained from eq 16 and are reported in 'Table IV. Table IV: AV arid AV" for Aqueous EuS04-'-Formation a t 28' ,--Ionic strength---0 . 0 4 6 TIZ
I'ressure, atm
1
136 272 408 545 680 953 1225 1497 1770 2040
4 0m
Av,
AVO,
ml/mol
ml/mol
21.5 20.8 20.2 19.5 18.8
25.6 24.7 23.8 22.9 22.0 21.1 19.3 17.4 15.6 13.8 12.0
18.1
16.7 15.3 14.0 12.6 11.2
(RTb In K ' / ~ P=) ~-AVO
Since the AZ2 for EuS04+ formation lies between that of MgS04 and LaFe(CN)a,one would expect its AVO to be 5-9 ml/mol at 25" and 1 atm if EuS04* were of the outer-sphere type. Instead, the much higher value of 25.6 ml/niol was obtained. This three- to five fold increase in AVO from that predicted by theory for outersphere ion pairs could only be reasonably explained by assuming that EuS04f exists as an innersphere complex in dilute aqueous solution. Table V: AVO of Formation for Some Aqueous Complex Ions a t 25" and 1 atm Complex
MgS04 MnSOr LaFe( CN)o La804 +. Ed304 +
(11)
Discussion The association of two ions to form an outer-sphere complex should be accomplished by only a slightly positive AV", because the primary hydration sheaths and surrounding solvenx molecules of both ions are but little affected. However, a large positive AVO would be expected for inner-aphere complex formation where mutual contact of the ions would lead to significant liberation of the solvent molecules due to the disruption of the hydration sheaths and the greater cancellation of charges. Previous investigations concerning the effects of high pressure on the formation of complex ions have been rather scarce in the literature. Those which have a bearing on the present study are listed in Table V. PTamann, I'earce, and Strauss3found AV" = 8.0 ml/ mol for the formation of aqueous lanthanum ferricyanide ion pairs at 2.5" and 1 atm. They compared this value and that of 7 . 3 ml/mol from Fisher's' study on MgS04 with those calculated from the theories on ion association as proposed by Bjerrum21 and FuossII and found good agreement. This led the authors to conclude that these two salts form true outer-sphere complexes in dilute aqueous solutions.
AVo
Ref
7.3 7.4 8.0 21-26 25.6
18 2
3 5 This study
The only previous high-pressure investigation made on an aqueous rare earth-sulfate complex was that on Laz(S04)3by Fisher and Daviese5 They studied the electrical conductance of La2(S04)sat various pressures up to 2000 atm at 25" and reported 21.2-26.2 ml/mol a t atmospheric pressure and 6.8-11.8 ml/mol at 2000 atm for AV" of association. They employed three different equations in their calculations and found that each gave different AV" values. This and the fact that their values were also concentration dependent precluded their reporting a single AVO for each pressure. Nevertheless, their results over the entire pressure range agrce very well with those from this i n v e s t i g a t i ~ n . ~This ~ is particularly noteworthy since they used completely different experimental and analytical methods as compared t o those employed in this study. (21) See ref 10, p 393. (22) The IC1 values calculated in this study actually represent the sum of the formation constants for the inner- and outer-sphere species. Merely making the spectroscopic studies at various wavelengths does not by itself enable one t o separate Ki into its component parts. (23) Due to the effective shielding of the 4f orbitals by the 5s and 5p orbitads aqueous rare earth(II1) ions display many similar chemical properties. Therefore, since the partial molar volumes of aqueous lanthanum and europium salts are very similar,24 e.g., V ' O L ~ ~=T -42.0 and = -44.5 ml/mol, it would be expected that their AVO values for monosulfate complex ion formation should also be similar. (24) F. H. Spedding, M. J. Pikal, and B. 0. Ayers, J. Phys. Chem., 70, 2550 (1966).
The Journal of Physical Chemistry, Vol. 76, N o . 20, 1978
