Article pubs.acs.org/jced
Interactions in the Quaternary Systems H2O−Er(NO3)3 −La(NO3)3 − Pr(NO3)3, H2O−Er(NO3)3 −La(NO3)3 −Nd(NO3)3, and H2O−Er(NO3)3 − Pr(NO3)3 −Nd(NO3)3 to Very High Concentrations Biao Li† and Mei He*,‡ †
Department of Criminal Science and Technique, China Criminal Police University, Shenyang 110854, P. R. China Department of Applied Chemistry, Shenyang University of Chemical Technology, Shenyang 110142, P. R. China
‡
ABSTRACT: The ionic interactions have been investigated from the isopiestic measurements on the quaternary systems H 2O−Er(NO3) 3−La(NO3)3−Pr(NO3)3, H 2 O−Er(NO 3 ) 3 −La(NO 3 ) 3 −Nd(NO 3 ) 3 , and H 2 O−Er(NO 3 ) 3 −Pr(NO 3 ) 3 − Nd(NO3)3 at 298.15 K to near saturation. The isopiestic measurements can be represented by a modified Pitzer ion-interaction model extending to C(3) within the experimental uncertainty over a full concentration range. In addition, the Zdanovskii−Stokes−Robinson model or partial ideal solution model is obeyed by all of the systems within isopiestic accuracy, indicating zero exchange energy between the unlike salts, which is consistent with the nature of rare earth elements.
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INTRODUCTION The Pitzer ion-interaction model, 1−3 which contains a Debye−Hückel limiting law parameter and the empirically determined β(0), β(1), and Cϕ parameters, has widely been used in the representation of thermodynamic properties of aqueous electrolyte solutions and their mixtures to moderate ionic strengths. Recently, various modifications to the Pitzer ion-interaction model extending either to β(2), C(2), or D(2) have been introduced for highly soluble 1−1, 2−1, and 2−2 electrolytes4−7 and their mixtures.8,9 However, all of them cannot fit the highly soluble and highly unsymmetrical electrolytes very well, particularly for rare earth nitrites, chlorides, and perchlorates, where their standard deviations are significantly higher than the experimental errors of the precise isopiestic measurements of Spedding et al.10 and Rard et al.11−17 We18 found this problem could simply be solved by introducing a C(3) parameter into the Pitzer ion-interaction model, which can quantitatively represent these literature isopiestic10−17 measurements up to the maximum saturate or supersaturate concentrations available. Ionic interactions in the 3−1 actinide and lanthanide ions may follow a similar ion-interaction trend due to the similarity of actinides and lanthanides, but the actinides can hardly be manipulated at high concentrations due to their radioactivity. Therefore, thermodynamic properties from infinite dilution to saturation (or supersaturation) are of fundamental importance for the pure and mixed aqueous solutions containing 3−1 rare earth electrolytes. On the other hand, based on the Zdanovskii−Stokes− Robinson (ZSR) model19−23 for aqueous solutions, we have developed a partial ideal solution model 24−29 for every kind © 2012 American Chemical Society
of the multicomponent systems A−B−C−...−Z with zero interchange energies among B, C, ..., Z related to their binary subsystems A−B, A−C, ..., A−Z at constant activity of the common component A. The partial ideal solution model has been verified by the experiments of organic mixtures, aqueous and nonaqueous solutions, alloys, molten salt mixtures, slags, and nonstoichiometric solid solutions. However, for aqueous electrolyte mixtures, the model testing is normally available only to moderate ionic strengths. It is therefore interesting to examine whether the new isopiestic measurements for quaternary mixed rare earth electrolyte solutions to very high concentrations still follow the ZSR model (or the partial ideal solution model). In this paper, we tried to extend the isopiestic measurements to the quaternary systems H2O−Er(NO 3) 3−La(NO 3 ) 3 −Pr(NO 3 ) 3 , H 2 O−Er(NO 3 ) 3 −La(NO 3 ) 3 −Nd(NO 3 ) 3 , and H 2 O−Er(NO 3 ) 3− Pr(NO 3 ) 3 −Nd(NO 3 ) 3 to near saturation and to represent the new measurements by the new simple modified ion-interaction model, the ZSR or partial ideal solution model, and other empirical equations.
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EQUATIONS For highly soluble and highly unsymmetrical electrolytes (MX) such as aqueous rare earth nitrates, perchlorates, and chlorides and their mixtures (MX−NX−...) with the same Received: October 6, 2011 Accepted: December 14, 2011 Published: January 6, 2012 513
dx.doi.org/10.1021/je201079a | J. Chem. Eng.Data 2012, 57, 513−520
Journal of Chemical & Engineering Data
Article
Table 1. Isopiestic Results of Quaternary Systems H2O−Er(NO3)3−La(NO3)3−Pr(NO3)3, H2O−Er(NO3)3−La(NO3)3− Nd(NO3)3, and H2O−Er(NO3)3−Pr(NO3)3−Nd(NO3)3 at 298.15 K mref
mB
mC
mD
mol·kg−1
mol·kg−1
mol·kg−1
mol·kg−1
2.1019 {H2O−NaCl}
1.0019 0 0 0.3358 0.5819 0.1535 1.8338 0 0 0.6462 0.9025 0.5121 2.6019 0 0 0.9117 1.3125 0.7054 3.4031 0 0 1.2234 1.7735 0.8626
4.1889 {H2O−NaCl}
2.9589 {H2O−CaCl2}
3.7112 {H2O−CaCl2}
2.1073 {H2O−NaCl}
4.1038 {H2O−NaCl}
2.9893 {H2O−CaCl2}
3.6343 {H2O−CaCl2}
2.1176 {H2O−NaCl}
4.1181
1.0039 0 0 0.3355 0.5821 0.1522 1.8002 0 0 0.6383 0.8932 0.4952 2.6337 0 0 0.9202 1.3205 0.7096 3.3179 0 0 1.1971 1.6994 0.8078 1.0082 0 0 0.3367 0.5832 0.1539 1.8053
Δ
(1) H2O(A)−Er(NO3)3(B)−La(NO3)3(C)−Pr(NO3)3(D) 0 0 1.1692 0 0 1.1497 0.3895 0.3811 −0.0002 0.2453 0.2402 −0.0005 0.3432 0.6362 0.0001 0 0 2.2094 0 0 2.1484 0.7107 0.6989 −0.0006 0.5565 0.5502 0.0001 0.5508 1.0125 −0.0002 0 0 3.1453 0 0 3.0438 1.0065 1.0033 0.0000 0.7722 0.7596 −0.0005 0.7421 1.4995 −0.0003 0 0 4.1019 0 0 3.9650 1.2979 1.2854 0.0001 0.9678 0.9621 −0.0003 0.9931 1.9996 −0.0001 (2) H2O(A)−Er(NO3)3(B)−La(NO3)3(C)−Nd(NO3)3(D) 0 0 1.1717 0 0 1.1415 0.3891 0.3806 −0.0003 0.2458 0.2401 0.0000 0.3427 0.6348 0.0002 0 0 2.1680 0 0 2.0743 0.6895 0.6793 0.0001 0.5377 0.5308 0.0001 0.5252 1.0001 −0.0005 0 0 2.1837 0 0 3.0241 1.0108 1.0074 0.0000 0.7840 0.7617 −0.0005 0.7468 1.5005 0.0002 0 0 4.0013 0 0 3.7985 1.2518 1.2401 0.0001 0.9521 0.9493 0.0001 0.9625 1.9601 0.0000 (3) H2O(A)−Er(NO3)3(B)−Pr(NO3)3(C)−Nd(NO3)3(D) 0 0 1.1574 0 0 1.1466 0.3853 0.3816 −0.0003 0.2441 0.2415 0.0000 0.3387 0.6363 0.0002 0 0
514
ϕexp
ϕcalc
Δϕa
1.041 0.892 0.907 0.943 0.977 0.921 1.292 1.072 1.103 1.153 1.179 1.142 1.498 1.239 1.280 1.334 1.370 1.323 1.687 1.400 1.448 1.509 1.551 1.490
1.040 0.891 0.906 0.944 0.978 0.921 1.291 1.072 1.102 1.153 1.181 1.142 1.497 1.238 1.280 1.335 1.371 1.323 1.687 1.399 1.448 1.511 1.552 1.491
0.001 0.001 0.001 −0.001 −0.001 0.000 0.001 0.000 0.001 0.000 −0.002 0.000 0.001 0.001 0.000 −0.001 −0.001 0.000 0.000 0.001 0.000 −0.002 −0.001 −0.001
1.042 0.893 0.916 0.947 0.980 0.926 1.282 1.065 1.113 1.150 1.177 1.143 1.506 1.246 1.311 1.350 1.384 1.341 1.669 1.384 1.458 1.501 1.538 1.485
1.041 0.892 0.915 0.947 0.980 0.926 1.282 1.064 1.112 1.151 1.178 1.142 1.505 1.245 1.311 1.351 1.384 1.342 1.668 1.383 1.457 1.503 1.539 1.485
0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.001 0.001 −0.001 −0.001 0.001 0.001 0.001 0.000 −0.001 0.000 −0.001 0.001 0.001 0.001 −0.002 −0.001 0.000
1.043 0.909 0.917 0.953 0.984 0.932 1.284
1.042 0.908 0.916 0.953 0.985 0.932 1.283
0.001 0.001 0.001 0.000 −0.001 0.000 0.001
dx.doi.org/10.1021/je201079a | J. Chem. Eng.Data 2012, 57, 513−520
Journal of Chemical & Engineering Data
Article
Table 1. continued mref
mB −1
mol·kg
mol·kg
{H2O−NaCl}
0 0 0.6405 0.8957 0.4976 2.6405 0 0 0.9231 1.3247 0.7126 3.4341 0 0 1.2322 1.7676 0.8487
2.9966 {H2O−CaCl2}
3.7391 {H2O−CaCl2}
a
mC −1
mD −1
mol·kg
mol·kg−1
Δ
(3) H2O(A)−Er(NO3)3(B)−Pr(NO3)3(C)−Nd(NO3)3(D) 2.1148 0 0 2.0802 0.6722 0.6802 −0.0004 0.5214 0.5355 0.0001 0.5125 1.0032 0.0002 0 0 3.0884 0 0 3.0317 0.9953 0.9952 0.0001 0.7610 0.7643 0.0002 0.7191 1.5069 −0.0002 0 0 4.0004 0 0 3.9295 1.2796 1.2619 −0.0002 0.9628 0.9584 −0.0007 0.9881 1.9885 0.0002
ϕexp
ϕcalc
Δϕa
1.096 1.115 1.164 1.188 1.152 1.508 1.289 1.313 1.367 1.397 1.355 1.694 1.454 1.480 1.542 1.577 1.521
1.095 1.114 1.163 1.188 1.152 1.507 1.288 1.312 1.367 1.398 1.354 1.693 1.454 1.480 1.543 1.577 1.523
0.001 0.001 0.001 0.000 0.000 0.001 0.001 0.001 0.000 −0.001 0.001 0.001 0.000 0.000 −0.001 0.000 −0.002
Δϕ = ϕexp − ϕcalc.
Table 2. Parameters and Standard Deviations of the Modified Pitzer Model for Fitting Literature Osmotic and Activity Coefficients of Aqueous Pure Nitrates from Infinite Dilution to the Maximum Ionic Strengths Available at 298.15 Ka,b nitrates
(3/2)β(0)
(3/2)β(1)
(3/2)β(2)
(33/2)C(0)
(33/2)C(1)
(33/2)C(2)
(33/2)C(3)
103σ
maximum I
Er(NO3)3 La(NO3)3 Pr(NO3)3 Nd(NO3)3
0.4597 0.3129 0.3342 0.3436
8.41 8.15 7.80 7.32
−7.15 −5.13 −4.07 −2.51
−0.02212 −0.01028 −0.01166 −0.01230
0.3805 0.3138 0.3420 0.3763
−0.2866 −0.3629 −0.4790 −0.5732
1.1361 1.1857 1.2981 1.3968
2.0 0.9 1.6 1.8
44 51 46 38
Given αB1 = 1.8 kg1/2·mol−1/2, αB2 = 6.0 kg1/2·mol−1/2, αC1 = 0.15 kg·mol−1, αC2 = 0.25 kg·mol−1, and αC3 = 0.35 kg·mol−1. bGiven β in kg·mol−1, C in kg2·mol−2, and I in mol·kg−1.
a
Table 3. Mixing Parameters and Standard Deviations of the New Modified Pitzer Model for Fitting Osmotic Coefficients of the Aqueous Mixtures H2O−Er(NO3)3−La(NO3)3, H2O−Er(NO3)3−Pr(NO3)3, H2O−Er(NO3)3−Nd(NO3)3, H2O−La(NO3)3− Pr(NO3)3, H2O−La(NO3)3−Nd(NO3)3, and H2O−Pr(NO3)3−Nd(NO3)3 at 298.15 K
a
mixtures
θcc′a
ψcc′ab
σ (with θ and ψ)
σ (without θ and ψ)
H2O−Er(NO3)3−La(NO3)3 H2O−Er(NO3)3−Pr(NO3)3 H2O−Er(NO3)3−Nd(NO3)3 H2O−La(NO3)3−Pr(NO3)3 H2O−La(NO3)3−Nd(NO3)3 H2O−Pr(NO3)3−Nd(NO3)3
−0.02225 −0.01475 −0.01371 −0.001929 −0.007020 −0.005430
0.002170 0.001618 0.001397 0.0000824 0.0006041 0.0005768
0.0016 0.0010 0.0009 0.0011 0.0013 0.0008
0.0027 0.0018 0.0017 0.0013 0.0015 0.0010
Given in kg·mol−1. bGiven in kg2·mol−2. ln γMX = − |zMzX|A ϕ[I1/2/(1 + bI1/2)
anion X, the new simple modified ion-interaction model for the osmotic coefficient (ϕ) and activity coefficient (γ) may simply be given by18
+ (2/b)ln(1 + bI1/2)] + (νMν X /νMX)mT γ [2BMX + (νMν X)1/2 mTCMX ]
+
∑ (νcνX /νc X)mc X mT[(νcνX)1/2 CcγX ] c
γ + (νMν X /νMX)mMX mT[(νMν X)1/2 CMX ]
ϕ − 1 = (2/ ∑ mi){− A ϕI 3/2/(1 + bI1/2)
+ [(νM/νMX) ∑ mc (2θMc + mX ψMc X)
i
+
c
∑ mcmX (BcϕX + ZCc X)
+ (ν X /νMX)∑ ∑ mc mc ′ψcc ′ X
c
+
∑∑ c
