sented by the cross-square diagram given below. KC1 (2)-NazS04 (3). â'TVT. The six possible mixtures are obtained by going around the sides and across both ...
J. Chem. Eng. D8f8 1986, 31, 470-472
470
PVT Properties of Concentrated Aqueous Electrolytes. 7. The Volumes of Mixing of the Reciprocal Salt Pairs KCI, K2S04,NaCI, and Na2S04at 25 OC and I = 1.5 m Frank J. Mlllero’ and Sara Sotolongo Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33 149- 1098
The densities of mixtures of the six possible comblnatlons of the salts KCI, NaCI, K$04, and Na,S04 have been determined at constant lonlc strength ( I = 1.5 m ) and 25 ‘C. The results have been used to determine the volume of mlxlng (AV,) for these salts. The values of AV, have been flt to equatlons of the form AV, = yzy312[v0 v,( 1 2 y 3 ) ]where y, Is the lonlc strength fraction of salt I , and v o and Y , are parameters related to the lnteractlon of like charged Ions. The cross-square rule was found to hold wlthln the experlmental error of the measurements.
Table I. Relative Densities (Ap = p - po, g ~ m - of ~ the ) Mixtures at 25 “C and I = 1.5 m mixture NR 1 0 3 ~ ~ NaCl (2)-KC1 (3) 0 57.831
+
-
KCl (2)-KzS04 (3)
I ntroductlon
In recent papers ( 7 , 2) we have been interested in determining the excess volume and compressibility properties of the major components of natural waters. These results have been used to study the interactions of like charged ions and to estimate the PVT properties of natural brines (3). In the present paper we will report on the volume of mixing the salts NaCI, KCI, Na2S04,and K,SO, which are the components of many natural waters. Experimental Sectlon The densities of NaCI, KCI, Na2S04,and K2SO4 and their mixtures were measured at 25 OC by using a Picker vibrating flow densimeter ( 4 ) . The instrument was calibrated with the known densities of water (5)and seawater (6). The temperature of the densimeter was controlled to fO.OO1 OC with a Hallikainen thermotrol. The temperature was set and monitored with a Hewlett Packard quartz crystal thermometer calibrated with a platinum resistance thermometer and a G-2 Mueller bridge (IPTS-68). All the solutions were made by weight with reagent-grade (Baker) chemicals and degassed ion+xchanged water (Millipore Super Q). The molalities of the stock solutions were checked from density measurements using the equations of state for these salt solutions (7, 8).
NaCl (2)-NazS04 (3)
NaCl (2)-KzS04 (3)
Results and Calculations The six possible mixtures of the salts studied can be represented by the cross-square diagram given below KC1 (2)-NazS04 (3)
“ T ‘V T The six possible mixtures are obtained by going around the sides and across both diagonals. The relative densitiis (p - po, g ~ m -of~ these ) mixtures were measured at a constant ionic strength of 1.5 m and 25 OC. The results are given in Table I as a function of the ionic strength fraction Cy3 = 13/(12 13),
+
0021-9568/86/173 ~-047Q$Q1.50/0
0.1972 0.3932 0.4923 0.6959 0.7978 1.0 0 0.1019 0.2042 0.3032 0.4050 0.5049 0.6065 0.7051 0.8030 0.9021 1.0 0 0.1016 0.2036 0.3019 0.4015 0.5050 0.6036 0.7014 0.8007 0.9007 1.0 0 0.1021 0.2035 0.4048 0.5039 0.6040 0.7038 0.8013 0.9008 1.0 0 0.1010 0.2015 0.3024 0.4028 0.5030 0.6029 0.7019 0.8015 0.9010 1.0 0 0.1031 0.2056 0.3083 0.4077 0.5100 0.6069 0.7062 0.8061 0.9042 1.0
59.295 60.744 61.473 62.964 63.704 65.169 65.078 65.058 65.048 65.032 65.039 65.057 65.097 65.146 65.204 65.284 65.372 65.447 64.936 64.425 63.940 63.430 62.925 62.434 61.951 61.473 60.965 60.472 57.820 58.024 58.232 58.680 58.929 59.194 59.465 59.762 60.067 60.399 57.428 58.171 58.916 59.677 60.459 61.256 62.064 62.888 63.728 64.594 65.464 64.895 64.347 63.828 63.311 62.821 62.328 61.862 61.404 60.980 60.567 60.204
where subscripts 2 and 3 refer to different solutes and 1 is water). 0 1986 American Chemical Society
Journal of Chemical and Engineering Data, Vol. 31, No. 4, 1986 471 0.20
I
Table 11. Parameters vo a n d v1 for the Eq AV, + Vl(1 - 2Y3)l mixtures una Ut" 0.0070 0.0050 NaCl (2)-KC1 (3) 0.3097 -0.0377 NaCl (2)-Na2S04 (3) KC1 (2)-KzS04 (3) 0.2738 -0.0327 0.0365 0.0206 K2SOI (2)-Na2S04 (3) 0.3171 -0.0173 NaCl (2)-KzS04 (3) 0.3979 -0.1056 KCl (2)-NazS04 (3)
---.
NoCI+NoISO,
K,SO,+No,SO,
o'oo
04 u,
02
0.6
0.8
= y9312[v0 Sb
0.001 (1) 0.005 (6) 0.005 (6) 0.005 (6) 0.005 (6) 0.007 (8)
"The units of uo and u1 are cm3 kg H20 mol-2. bThe standard error in AV,,, for eq 4, cm3 kg-' HzO. The errors in density (lo6 g ~ m - are ~ ) given in parentheses.
I
Table 111. Verification of the Cross-Square Rule 0.241
common ion mixtures NaC1-KCl Na2S04-K2S04 NaC1-Na2S04 KCl-KzSO4
KCI +No,
A V,(max) 0.004 f 0.001 0.022 f 0.005 0.175 f 0.005 0.164 f 0.005
0.365 f 0.02 uncommon ion mixtures NaC1-K2SO4 KC1-Na2S04 Flgwe 1. Values of the volume of mixing (AV,) for the Na, K, CI, SO4 system at I = 1.5 m and 25 OC vs. the ionic strength fraction Cy3, where 3 is the second electrolyte).
AVJmax) 0.182 f 0.05 0.217 f 0.007 Y .
0.399 f 0.01 comparison of
=
X 0.365 f 0.02 0.399 f 0.01
For ternary mixtures of electrolyte (2) of molality m 2 and electrolyte (3) of molality m,, the mean apparent molal volume, @,,(2,3), is given by
where p and po are, respectively, the densities of the solution and pure water, M , = (M,m, M,m,)/(m, m,) and the total molality mT = m 2 m3 (M, is the molecular weight of solute i). The apparent molal volumes & ( i ) of the binary solutions were calculated from the measured densities
+
+,(i) =
+
+
W/W,/P)- [IO3 (P - Po)/Pom,l
(2)
The volumes of mixing, AV, for each mixture were determined from the experimental values of & ( i ) and @.,(2,3)by using the equation Avm
= mT@v(293)-
m2
6 v ( 2 ) - m34v(3)
(3)
The values of AV, (cm3kg-' H20)for the various mixtures are shown in Figure 1 as functions of the ionic strength fractions, y , = w,m3/(w2m, w,m,), where w, are ionic strength factors ( w = 1 for 1-1 electrolytes and 3 for 2-1 electrolytes). The values of AV, for the side mixtures are related to the interactions of like charged ions. The largest values are found for the common cation mixtures for CI-SO, interactions. The interactions between Na and K are quite small. These findings are in agreement with the heats of mixing for these mixtures
+
0.034 f 0.03
NaS0,- upon addition of KCI (see Figure 1). The volumes of mixing for the Na-K-CI-SO, solutions can be used to examine the cross-square rule (9)which states that the sum of the volumes of mixing the common ion mixtures is equal to the cross mixtures
En = Ex
Avm
were fit to equation of the form (IO)
= YZY3z2[v0 +
vl(l - 2Y3)1
(4)
where v , and v 1 are parameters related to ionic interactions ( v , to cation-cation and anion-anion interactions and v 1 to triplet interactions, cation-anion-cation). The values of v o and v 1 for the various mixtures are given in Table 11. With the exception of the KCI Na,SO, mixture the values v , are quite small and v , is directly related to the maximum value of A V, (=vo X 0.25 X 1.5'). The skew in the KCI Na2S04system toward Na,SO, may be related to changes in the ion pair
+
+
(5)
where E O
= AV,(NaCI+KCI)
+ AV,
AV,(K,S04+Na,S0,)
+
(KCI+K,SO,) AV,(Na,SO,+NaCI)
(6)
+ AV,(KCI+Na,SO,)
(7)
+
and
EX =
AV,(NaCI+K,SO,)
The verification of the cross-square rule for this mixture is shown in Table 111. Within the experimental errors of the measurements the cross-square rule holds for the Na-K-CISO, system at I = 1.5 m and 25 OC. The PVT properties of the NaCl K2S04and KCI Na2S04 solutions can be used to examine use of the equations of Wood and Reilly ( 7 1 ) to estimate the densities of solutions Na-KCI-SO,. The mean apparent equivalent volume of a mixture is given by
+
+
@,
(9). The values of AV,
I
= ECEME,d),(MX) M X
AV,/eT
(8)
where E, is the equivalent fraction of ion i, $,(MX) is the apparent equivalent volume of MX at the ionic strength of the mixture, AV, is the volume of mixing the various components, and eT is the total equivalents of the mixture. The volume of mixing term (AV,/e,) has been formulated by Wood and Reilly ( 7 7 ) using the cross-square rule Av,/eT
= ( ~ T / ~ ) [ C E , E , E , V , ( M , N+ ) ~C E x E y E ~ v o ( x , y ) (9) ~]
where v,(M,N)' and v,(X,Y)~are the volume of mixing interaction parameters for mixing, respectively, the cations M N
+
472
J. Chem. Eng. Data 1886, 3 1 , 472-474
of the equation of Wood and Reilly ( 7 7 ) for solutions of known composition formed by unknown natural processes.
Table IV. Maximum Errors in Density for the Cross-Square Mixtures Obtained by Using the Equations of Wood and Reilly (I1 ) 1066p, g cm-3 mixture
w i t h o u t AV,,,
w i t h AVm
+ K2S04 K C l + Na2S04
238 171
72 90
NaCl
Reglstry No. KCI, 7447-40-7; NaCi, 7647-14-5; K,SO, Na,SO,, 7757-82-6.
7778-80-5;
Literature Cited (1) Millero, F. J.; Connaughton, L. M.; Vinokurova, F.; Chetirkin, P. V. J . Solution Chem. 1985, 14(12), 837-851. (2) Millero, F. J.; Lampreia, M. J. Soiuf/on Chem. 1985, 14(12), 853-864. (3) Millero, F. J. Pure Appi. Chem. 1985, 57, 1015. (4) Picker, P.; Tremblay, E.; Joiicoeur, J. J. Solution Chem. 1974, 3 , 377. (5) Kell, G. S.J . Chem. Eng. Data 1975, 2 0 , 97. (6) Miilero, F. J.; Poisson, A. Deep-Sea Res. 1881, 28, 625. (7) Millero, F. J. I n Activity Coefficients in €/ectro/yte Solutions; Pytkowicz, R. M., Ed.; CRC Press: Boca Raton, FL 1979; pp 63-151. (8) Millero, F. J.; Sotoiongo, S.Universlty of Miami, Miami, FL, unpublished results, 1983. (9) Anderson, H. L.; Wood. R. H. I n Water; Franks, F., Ed.; Plenum: New York, 1973; Vol. 111, Chapter 2. (IO) Friedman, H. L. Ionic Solution Thewy; Wiley-Interscience: New York, 1962; Vol. 3, p 265. (11) Wood, R. H.; Reilly, P. J. Annu. Rev. Phys. Chem. 1970, 21, 387. (12) Young, T. F. Rec. Chem. Prog. 1951, 12, 81.
+
in the presence of the common anion X and the anions X Y in the presence of the common cation M. This equation attempts to account for cation-cation and anion-anion interactions and neglects higher order triplicate interactions ( 1I). A summary of the maximum errors in density obtained by using the estimate 9,(eq 8) and
are given in Table I V (M = CEiMi is the mean equivalent weight of the mixture). The use of the volume of mixing term reduces the maximum errors by 2-3 times compared to use of Young's ( 72) simple addiiie rule (the first term in eq 8). The ~ ) still higher than the maximum errors (90 X lo-' g ~ m - are maximum errors (12 X lo-' g ~ m - obtained ~ ) for the original solutions and the full A V , equation but demonstrate the utility
Received for review December 13, 1985. Accepted June 30. 1986. We acknowledge the support of the Office of Naval Research (N00014-80-C00424) and the Oceanographic (OCE-8120659) and Geochemical (EAR8210759) sections of the National Science Foundatlon for this study.
Concentrated Phosphoric Acid Media: Acid-Base, Oxidation-Reduction, and Solvation Properties Claire Louis' and Jacques Besslere Laboratoire de Chimie Electrochimie Analytique, Facult6 des Sciences, Universitg de Nancy 7, B.P. 239 54506 Vandoeuvre Les Nancy Cedex, France PO4 media (1-14 mol/L) giving the R,(H) acidity function ( 2 ) , and the R0(H2P04-),R,(HPO?-), and Ro(PO4*) functions ( 3 , 4 ) characterizing phosphate anion activities and solvation transfer coefficients of solutes ( 2 - 4 ) especially those which are significant in the hydrometallurgy field. Along with water activities they allow us to explain the changes with acid concentration of oxidation-reduction, precipitation reactions, and extraction processes.
H,O-H,PO, media (1-14 moi/L) are characterized by means of the R,(H) acidity function and the R,(H2P04-), R,(HPO,'-), and R,( PO:-) functions whlch represent their ability to give up the proton and the H2P04-, HPOt-, and PO-: particles, respectively. Their solvation properties are characterized by means of the soivatlon-transfer activity coefficients of the solutes which are calculated from the normal potential values of the corresponding redox systems or from soiubUlty product values. The significance of the parameter water activity Is underlined.
Results 7 . R , ( H ) Acldity Functlon. The R,(H) acidity function ( 2 - 4 ) is determined from the variation with the acid concentration of the H+/H2(hydrogen electrode) and the 1,Cbenzoquinone/hydroquinone (Q/QH2) redox system potentials (Ea,+/, and Eaas/w2s, respectively) referred to the ferrocenium/ferrocene (Fc+/Fc) comparison system (Table I) according to the relations
I ntroductlon Phosphoric acid solutions produced in the industrial processing of phosphate ores are about 5.5 and 11.5 mol/L (30% and 50% P,O,). They contain valuable species such as uranium in the presence of iron, sulfate, and fluoride (hexafluoroand others silicate essentially) at fairly high concentrations (I) such as cadmium and arsenic which must be eliminated. Provisions for improving the successive stages in the industrial processes are possible from a thermodynamical point of view by using such data as acidity level, phosphate anion activities, water activity, and solvation properties. The data concerning concentrated phosphoric media existing in the literature nevertheless do not allow us to describe thoroughly their properties: studies dealing with a limited acid concentration range or carried out under peculiar conditions (e.g., in the presence of sulfate) give unreliable results because of incompletely defined reference systems. We present in this paper the results of a study by electrochemical methods of H20-H30021-9568/86/1731-0472$01.50/0
R&H)
(EOWH+/H2
- Ea,+,,2)/o.058
with E,WH+ln2 = -0.400 V vs. Fc+/Fc (1)
-
with EWOs/w*s ROW) = ( E W a s i ~ ~-2Eaas/aH2s)/0.058 s i-0.316 V vs. Fc+/Fc (2) (The Superscript a corresponds to the acidic medium and the superscript w to water.) 2 . H 2 P O 4 - p HP042-, and P043- Anlon Actlvltles. By analogy with the R,(H) acidity function, H2P04-,HP0,2-, PO -: anion activities are characterized by the R,(H2P04-), R,(HPO?-), and R0(P043-)functions. R,(HP042-) = -log aHp0,2-and R,-
0
1986 American Chemical Society
