Apparent Molal Volumes of Aqueous Rare Earth ... - ACS Publications

Article pubs.acs.org/jced

Apparent Molal Volumes of Aqueous Rare Earth Salts Fit to the Pitzer Equation Carmen Rodriguez, Kaitlan Prugger, and Frank J. Millero* Rosenstiel School of Marine and Atmospheric Science University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149, United States ABSTRACT: The apparent molal volumes (Vϕ) of the trivalent rare earth (La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu and Y) chlorides, nitrates and perchlorates have been calculated from the density measurements at 25 °C and (5 to 80) °C and 0.02 − 4 m. The values of Vϕ have been fitted to the Pitzer equations, Vϕ = V̅ 0 + (AvI/(1.2m) ln(1 + 1.2I0.5) + 2RTm(βV(0) + βV(1) g(y) + mCV), where V̅ 0 is the infinite dilution partial molal volume, Av is the DebyeHückel slope, I is the ionic strength, and g(y) = (2/y2)·[1 − (1 + y) exp(−y)] where y = 2(I0.5). The Pitzer volume parameters βV(0), βV(1) and CV are functions of temperature. The values of V̅ 0, βV(0), βV(1), and CV for most of the rare earth chlorides are similar orders of magnitude. These results should be useful in estimating the effect of pressure on the equilibria of rare earths in natural waters over a wide range of temperature.

1. INTRODUCTION The Pitzer1 equations have been successfully used to examine the thermodynamic properties of electrolytes in aqueous solutions. May et al.,2 for example, have recently used these equations to examine the activity coefficients, enthalpies, heat capacities, and volumes of 200 electrolytes at 25 °C. Krumgalz et al.3−7 have used the Pitzer equations to fit the volumes of a number of monovalent and divalent electrolytes from (0 to 100) °C. The Pitzer equations have been used to estimate the effect of pressure on processes in natural waters6,8 and the density9,10 and compressibilities of seawater.10 At the present time studies on the use of the Pitzer equations for the volume of trivalent metal electrolytes are limited.2,11,12 The recent Pitzer equations results of May et al.2 for the rare earths were only made at 25 °C. In this paper we have used the Pitzer equations to examine the effect of temperature on the volumes of rare earth chlorides from (0 to 80) °C using the published densities of Spedding and coworkers.13−18 These results will be useful in examining the effect of pressure on the reactions of the rare earths in the deep ocean waters and natural brines.

Table 1. Values of the Infinite Dilution Partial Molal Volumes (V̅ i0 cm3 mol−1) for the Rare Earths at 25 °C Used in This Studya mean V̅ i0

3+

−39.17b −42.16 −42.73 −41.77 −41.15 −40.38 −40.29 −40.79 −41.42 −42.19 −43.84 −44.28 −45.51

La Pr3+ Nd3+ Sm3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+ Lu3+ a

The infinite dilution volumes for the rare earths were determined by additivity using the following sequence: assuming V̅ i0(H+) = 0 cm3 mol−1, V̅ i0(Cl−) is determined from V̅ i0(HCl)5 = 17.824 cm3 mol−1; V̅ i0(Na+) is determined from V̅ 0(NaCl)24 = 16.681 cm3 mol−1; V̅ i0(NO3−) is determined from V̅ 0(NaNO3)5 = 28.007 cm3 mol−1; V̅ i0(ClO4−) is determined from V̅ 0(NaClO4)5 = 43.14 cm3 mol−1; V̅ i0 of the rare earths are calculated from the average volumes of the Cl− and NO3− salts. bV̅ i0(La3+) determined from V̅ 0(LaCl3)2 = 14.30 cm3 mol−1.

2. CALCULATIONS The densities of rare earths have been determined by a number of workers.13−20 The earlier studies by Jones et al.19 and Dunn20 are limited to LaCl3. In this study the volume properties of the rare earth chlorides, nitrates, and perchlorates at 25 °C and approximately (0.02 to 4) molal were examined using the density data of Spedding and co-workers.13−16 These studies provide the most extensive densities for the rare earths at 25 °C. Additional studies by Spedding et al.17,18 include density measurements for some rare earth chlorides from (5 to 80) °C and (0.1 to 3.5) molal. The original density measurements (ρ) of Spedding et al.13−18 were made as specific gravities © XXXX American Chemical Society

ion

(ρ/ρ0) or relative densities (ρ − ρ0), where ρ0 is the density of pure water in g mL−1. To be consistent with the direct Received: March 11, 2013 Accepted: May 7, 2013

A

dx.doi.org/10.1021/je4002398 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. The Pitzer Volume Coefficients for the Rare Earth Chlorides at 25 °Ca salt LaCl3 PrCl3 NdCl3 SmCl3 EuCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3 YCl3 a

β(0)V

V̅ 0

β(1)V −05

14.30 11.31 10.74 11.71 12.33 13.09 13.18 12.68 12.05 11.29 9.63 9.19 7.96 13.54

−04

−1.79780·10 −2.49057·10−04 −2.95156·10−04 −2.73800·10−04 −2.04450·10−04 −2.10010·10−04 −2.25830·10−04 −2.31144·10−04 −2.70145·10−04 −2.70050·10−04 −2.15910·10−04 −2.57650·10−04 −2.27540·10−04 −3.21290·10−04

2.13570·10 2.15903·10−05 2.15741·10−05 1.60430·10−05 1.31699·10−05 1.40774·10−05 1.74534·10−05 1.81482·10−05 1.97106·10−05 2.01166·10−05 1.79974·10−05 2.00816·10−05 1.95515·10−05 2.06170·10−05

CV

σ

−1.57850·10−06 −1.16247·10−06 −1.01690·10−06 −1.27500·10−07 1.52610·10−07 −1.74400·10−07 −8.88070·10−07 −8.76600·10−07 −1.02530·10−06 −1.116008·10−06 −5.46000·10−07 −9.56470·10−07 −7.82730·10−07 −1.34870·10−06

0.05 0.03 0.03 0.02 0.04 0.04 0.04 0.04 0.05 0.05 0.05 0.04 0.05 0.06

Units: V̅ 0 in cm3 mol−1; β(0)V and β(1)V in kg mol−1 bar−1; CV in kg2 mol−2 bar−1.

Table 3. The Pitzer Volume Coefficients for the Rare Earth Nitrates at 25 °Ca V̅ 0

salt La(NO3)3 Pr(NO3)3 Nd(NO3)3 Sm(NO3)3 Eu(NO3)3 Gd(NO3)3 Tb(NO3)3 Dy(NO3)3 Ho(NO3)3 Er((NO3)3 Tm(NO3)3 Yb(NO3)3 Lu(NO3)3 a

48.28 45.29 44.72 45.69 46.31 47.07 47.16 46.66 46.03 45.27 43.61 43.17 41.94

β(0)V

β(1)V −04

−04

−3.20450·10 −2.08950·10−04 −3.28975·10−04 −6.49890·10−04 −4.12500·10−04 1.64580·10−04 −2.45930·10−04 −1.82500·10−04 1.02930·10−03 2.41200·10−05 −1.11840·10−04 −8.78000·10−05 −2.58340·10−04

8.86300·10 6.74230·10−04 1.14478·10−03 1.45018·10−03 9.79070·10−04 −2.66700·10−04 3.22160·10−04 2.24100·10−04 −1.96595·10−03 −2.24400·10−04 1.13100·10−04 5.80670·10−05 3.87600·10−04

CV

σ

6.4130·10−04 4.7570·10−04 5.8517·10−04 1.9067·10−03 9.4790·10−04 −7.6170·10−04 8.6070·10−04 4.9890·10−04 −3.8815·10−03 −2.9110·10−05 2.2990·10−04 1.9190·10−04 6.8399·10−04

0.08 0.06 0.09 0.05 0.05 0.02 0.03 0.04 0.04 0.04 0.06 0.02 0.05


Table 4. The Pitzer Volume Coefficients for the Rare Earth Perchlorates at 25 °Ca V̅ 0

salt La(ClO4)3 Pr(ClO4)3 Nd(ClO4)3 Sm(ClO4)3 Eu(ClO4)3 Gd(ClO4)3 Tb(ClO4)3 Dy(ClO4)3 Ho(ClO4)3 Er(ClO4)3 Tm(ClO4)3 Yb(ClO4)3 Lu(ClO4)3 a

93.68 90.69 90.12 91.09 91.71 92.47 92.56 92.06 91.43 90.67 89.01 88.57 87.34

β(0)V

β(1)V −05

−04

−4.0350·10 −4.8790·10−04 −4.9730·10−04 −5.1140·10−04 −4.3520·10−04 −4.5470·10−04 −3.9109·10−04 −3.7910·10−04 −4.4800·10−04 −4.7570·10−04 −4.4100·10−04 −4.8270·10−04 −4.5915·10−04

2.6510·10 2.5440·10−05 2.6574·10−05 1.7730·10−05 1.4054·10−05 1.3144·10−05 1.3785·10−05 1.6180·10−05 1.7220·10−05 1.7977·10−05 1.8810·10−05 1.9730·10−05 2.0390·10−05

CV

σ

−1.9780·10−06 −1.5440·10−06 −1.8876·10−06 −7.3220·10−07 −4.1480·10−07 −5.0389·10−07 −8.5010·10−07 −1.3918·10−06 −1.2295·10−06 −1.2814·10−06 −1.4018·10−06 −1.5160·10−06 −1.6690·10−06

0.07 0.06 0.07 0.03 0.06 0.07 0.03 0.09 0.05 0.05 0.03 0.06 0.03


The value of ρ0 = 0.9970751 g mL−1 for water at 25 °C used by Spedding et al.13−16 is the same as the value determined from the equations of Kell.22 The apparent molal volumes (Vϕ) of the salts were calculated from the densities13−18 using the equation

measurements, the revised density of water equation of Gildseth et al.21 was used to calculate ρ0 as a function of temperature (t, °C) (t − 3.9863)2 (t + 288.9414) 508929.2(t + 68.12963) ⎛ 377.145 ⎞⎟ + 0.0119893 exp⎜ − ⎝ ⎠ t

ρ0 /( ml mol−1) = 1 −

Vϕ = 1000(ρ0 − ρ)/(mρ0 ρ) + M 2 /ρ

(1) B

(2)



Article

Figure 4. A comparison of our values of CV for the rare earth chlorides at 25 °C with those determined by May et al.2

Figure 1. A comparison of our values of V0 for the rare earth chlorides at 25 °C with those determined by May et al.,2 Spedding et al.13−15 and Dunn.20

Figure 2. A comparison of our values of β(0)V for the rare earth chlorides at 25 °C with those determined by May et al.2

Figure 5. The values Vϕ − DH for EuCl3 as a function of molality determined in this study. The extrapolated value of May et al.2 is indicated by the arrow.

This conversion has a very minor effect on the values of Vϕ (± 0.001 cm3 mol−1 at 25 °C to ± 0.004 cm3 mol−1 at higher temperatures and molalities). Spedding and co-workers13−18 evaluated the values of Vϕ by fitting them to a function of m0.5. We have fit the values of Vϕ to the Pitzer equations1 Vϕ = V̅ 0 + DH + 2RTνMνXm[β (0)V + β (1)V g (y) + mCV ] (4)

where V̅ is the partial molal volume at infinite dilution, ν = νM + νX are the number of ions of cation M or anion X with charge ZM and ZX. The ionic strength I = 6m and g(y) = (2/y2)[1 − (1 + y) exp(−y)] where y = 2(I0.5). The Pitzer volume parameters, β(0)V, β(1)V, and CV, are functions of temperature. The Debye−Hückel term (DH) is given by 0

Figure 3. A comparison of our values of β(1)V for the rare earth chlorides at 25 °C with those determined by May et al.2

where M2 is the molecular weight of the salt and m is the molality. Traditionally,2−7 values of Vϕ are given in units of cm3 mol−1. The values determined from eq 2 in units of mL mol−1 were converted to cm3 mol−1. At 25 °C the ratio ρ0/(g cm−3): ρ0/(g mL−1) is 0.999972 mL cm−3 and was determined using the equation of Kell22 corrected to the 1990 Temperature Scale (t90 °C) by Spieweck and Bettin23 as shown below:

DH = (ν /2)(Z MZ X)(AV /1.2) ln(1 + 1.2I 0.5) = (6/1.2)AV ln(1 + 1.2I 0.5)

The values of AV, the Debye−Hückel limiting slopes for volume, as a function of temperature (t, °C) have been determined from24

ρ0 /( g cm−3) = (0.99983952 + 0.016940805t

AV /( cm 3 kg1/2 mol−3/2)

−6 2

− 7.9829204· 10 t − 4.6134743 −8 3

= 1.50619 + 0.0130073t + 4.8307·10−5t 2

−10 4

·10 t + 1.0545415· 10

t

+ 8.95087·10−7t 3 − 3.7279·10−9t 4

−13 5

− 2.8018091· 10

t )

/(1 + 0.016875495t )

(5)

+ 2.3942·10−11t 5

(6)

At 25 °C, one obtains a value of Av = 1.8743 cm kg

(3)

3

C

1/2

−3/2

mol

.



Article

function of molality. Initially, the values of Vϕ were fit to the Pitzer equations (eq 4) by the float method as described by Connaughton et al.25 This method generates empirical values for V̅ 0(RCl3), V̅ 0(R(NO3)3) and V̅ 0(R(ClO4)3) at 25 °C, where R = rare earth metal. The value found for lanthanum chloride was V̅ 0 (LaCl3) = 14.88 cm3 mol−1. This was much higher than the value found by Dunn20 and May et al.2 where V̅ 0(LaCl3) = 14.3 cm3 mol−1 at 25 °C. Since the Dunn20 measurements were made in dilute solutions, we have used his value for V̅ 0(LaCl3) = 14.3 cm3 mol−1. Ionic values of the partial molal volumes for the rare earths can be estimated through additivity from these results for the chloride, nitrate, and perchlorate salts. This was performed using the ionic values of V̅ i0(Cl−), V̅ i0(NO3−), and V̅ i0(ClO4−) derived from the Pitzer extrapolated partial molal volumes of Krumgalz et al.5 The V̅ i0(H+) is assumed to be zero, giving V̅ i0(Cl−) = 17.824 cm3 mol−1 from V̅ 0(HCl)5 = 17.824 cm3 mol−1. The value of V̅ i0(Na+) = −1.144 cm3 mol−1 is determined from V̅ 0(NaCl)24 = 16.681 cm3 mol−1 and the value of V̅ i0(ClO4−) = 44.284 cm3 mol−1 is determined from V̅ 0(NaClO4)5 = 43.14 cm3 mol−1. The values of the V̅ i0(R) for the rare earths obtained from the chloride and nitrate salts are in good agreement (values within ± 0.2 cm3 mol−1); however, the values determined from the perchlorate salts differ significantly (± 0.8 cm3 mol−1). We have thus used the average values of V̅ i0(R) for the rare earths determined from the chloride and nitrate salts. These ionic values are tabulated in Table 1. The calculations of Vϕ for the chloride, nitrate, and perchlorate salts were then forced into the pure water values determined by additivity and the results were fit to the Pitzer equations.

Figure 6. The effect of temperature on the values of V0 and β(0)V for some rare earth chlorides.

Vϕ − V̅ 0 − DH = 2RTνMνXm[β (0)V + β (1)V g (y) + mCV ] (7)

The Pitzer volume parameters V̅ , β , β and C determined at 25 °C are given in Tables 2 to 4. It should be noted that some of the dilute experimental data was discarded to preserve the assumed infinite dilution values at 25 °C. This generally included data for which m < 0.02 mol kg−1 for the nitrate salts, and for m < 0.1 mol kg−1 for the chloride and perchlorate salts. A comparison of the results of this study with the results of May et al.,2 Spedding et al.,13−15 and Dunn19 for some rare earth chlorides are shown in Figures 1 to 4. Our Pitzer results are in reasonable agreement with the results of May et al.2 except for EuCl3. As shown in Figure 5 the extrapolated value of V̅ 0 from May et al.2 does not agree with our extrapolation of the Spedding et al.13−15 studies. We are not sure what causes these differences. Our values of V̅ 0 for the rare earth chlorides are in good agreement with the extrapolations of Spedding et al.13−15 Previous studies2,16,26 have also examined the relative difference between the values of V̅ 0 for chloride and nitrate salts at 25 °C. In this study the average difference across the rare earth series was found to be: V̅ 0(RCl3) − V̅ 0(R(NO3)3) = −34.2 ± 0.5 cm3 mol−1. This agrees reasonably well with the previous studies (−33.9 ± 0.4 cm3 mol−1).2,16,26 2.2. Treatment of the Rare Earth Chloride Data from (0 to 80) °C. The densities of rare earth chlorides have been measured from approximately (0.1 to 3.5) molal, at temperatures between (5 and 80) °C by Spedding and co-workers.17,18 The values of Vϕ calculated from this data were examined using the Pitzer equations. The Pitzer parameters (X = V̅ 0, β(0)V, β(1)V and CV) expressed as a function of temperature have been fitted relative to the 25 °C equations (Table 2) using the equations 0

Figure 7. The effect of temperature on the values of β(1)V and CV for some rare earth chlorides.

2.1. Treatment of the 25 °C Data. The 25 °C dilute density data of Spedding et al.13−16 for rare earth chloride, nitrate, and perchlorate solutions were used to calculate values of Vϕ as a

(0)V

(1)V

V

X = X(25°C) + a1(T − TR ) + a 2(T − TR )2 + a3(T − TR )3 + ... D

(9)



Article

Table A-I. Temperate Dependence of the V̅ 0 Pitzer values for the Rare Earth Chlorides from (5 to 80) °C Fit Relative to the Reference Temperature (TR = 298.15 K): V̅ 0 = V̅ TR0 + a1(T − TR) + a2(T − TR)2 + a3(T − TR)3 + a4(T − TR)4a

a

salt

V̅ TR0

a1

a2

a3

a4

σ (Vϕ)

LaCl3 PrCl3 NdCl3 SmCl3 EuCl3 GdCl3 TbCl3 DyCl3 HoCl3 ErCl3 TmCl3 YbCl3 LuCl3 YCl3

14.30 11.31 10.74 11.71 12.33 13.09 13.18 12.68 12.05 11.29 9.63 9.19 7.96 13.54

1.15360·10−01 8.03000·10−02 7.45150·10−02 6.49780·10−02

−4.15830·10−03 −4.66224·10−03 −4.51337·10−03 −4.49005·10−03

3.50985·10−06 1.51290·10−05 1.37480·10−05 1.65360·10−05

−3.58640·10−08 −9.01570·10−08 −8.91000·10−08 −1.07390·10−07

5.79750·10−02

−4.00370·10−03

1.14760·10−05

−6.68564·10−08

5.24300·10−02

−4.27690·10−03

1.14200·10−05

−6.00280·10−08

5.33480·10−02

−4.49490·10−03

1.36890·10−05

−9.78200·10−08

5.18470·10−02

−4.67510·10−03

1.93495·10−05

−1.34470·10−07

0.02 0.03 0.03 0.03 0.04 0.03 0.04 0.04 0.05 0.04 0.05 0.04 0.05 0.06

LaCl3 density data is only available from (20 to 80) °C. NdCl3 density data taken from Series II.17

Table A-II. Temperate Dependence of the β(0)V Pitzer Values for the Rare Earth Chlorides from (5 to 80) °C Fit Relative to TR = 298.15 K: β(0)V = βTR(0)V + b1 (T − TR) + b2 (T − TR)2 + b3 (T − TR)3 salt

BTR(0)V

b1

b2

b3


2.13570·10−05 2.15903·10−05 2.15741·10−05 1.60430·10−05 1.31699·10−05 1.40774·10−05 1.74534·10−05 1.81482·10−05 1.97106·10−05 2.01166·10−05 1.79974·10−05 2.00816·10−05 1.95515·10−05 2.06170·10−05

−2.50960·10−07 −4.25500·10−07 −4.19390·10−07 −3.31166·10−07

3.05206·10−09 6.84410·10−09 6.76150·10−09 6.01800·10−09

−1.94397·10−11 −3.84860·10−11 −3.25065·10−11 −3.80990·10−11

−2.56238·10−07

5.18290·10−09

−2.93390·10−11

−3.18670·10−07

5.64290·10−09

−3.35050·10−11

−3.58120·10−07

5.85320·10−09

−3.08182·10−11

−4.03740·10−07

6.38350·10−09

−4.22500·10−11

Table A-III. Temperate Dependence of the β(1)V Pitzer Values for the Rare Earth Chlorides from (5 to 80) °C Fit Relative to the Reference Temperature (TR = 298.15 K): β(1)V = βTR(1)V + c1 (T − TR) + c2 (T − TR)2 salt

BTR(1)V

c1

c2


−1.79780·10−04 −2.49057·10−04 −2.95156·10−04 −2.73800·10−04 −2.04450·10−04 −2.10010·10−04 −2.25830·10−04 −2.31144·10−04 −2.70145·10−04 −2.70050·10−04 −2.15910·10−04 −2.57650·10−04 −2.27540·10−04 −3.21290·10−04

−1.17930·10−05 −5.65570·10−06 −4.88790·10−06 −5.28220·10−06

1.04550·10−07 5.94340·10−08 4.73500·10−08 5.21410·10−08

−06

−08

−7.39730·10

4.01610·10

−6.49580·10−06

5.08500·10−08

−06

−08

−5.63530·10

5.77170·10

−4.81010·10−06

5.64540·10−08

Table A-IV. Temperate dependence of the CV Pitzer Values for the Rare Earth Chlorides from (5 to 80) °C fit relative to TR = 298.15 K: CV = CTRV + d1 (T − TR) + d2 (T − TR)2 salt

CTRV

d1

d2


−1.57850·10−06 −1.16247·10−06 −1.01690·10−06 −1.27500·10−07 1.52610·10−07 −1.74400·10−07 −8.88070·10−07 −8.76600·10−07 −1.02530·10−06 −1.11601·10−06 −5.46000·10−07 −9.56470·10−07 −7.82730·10−07 −1.34870·10−06

1.79015·10−08 5.31230·10−08 5.22790·10−08 4.11870·10−08

−5.34670·10−10 −5.80040·10−10 −4.70645·10−10

2.93060·10−08

−4.46160·10−10

3.30340·10−08

−4.21200·10−10

3.77840·10−08

−4.81720·10−10

4.89600·10−08

−4.71100·10−10

values of V̅ 0, β(0)V, β(1)V and CV for LaCl3, PrCl3, DyCl3 and YbCl3 are shown as a function of temperature in Figures 6 and 7. Across the rare earth series, these parameters are similar orders of magnitude, and appear to behave in a similar manner with respect to temperature. However, the parameters for LaCl3 deviate

where T is absolute temperature and TR is the reference temperature of 298.15 K. The coefficients for the Pitzer parameters (a1, a2, etc.) along with the standard errors of the fits are tabulated in the tables in the Appendix. The resulting E



Article

(12) Criss, C. M.; Millero, F. J. Modeling heat capacities of high valence-type electrolyte solutions with Pitzer’s equations. J. Sol. Chem. 1999, 28, 849−863. (13) Spedding, F. H.; Pikal, M. J.; Ayers, B. O. Apparent molal volumes of some aqueous rare earth chloride and nitrate solutions at 25 °C. J. Phys. Chem. 1966, 79, 2440−2449. (14) Spedding, F. H.; Cullen, P. F.; Habenschuss, A. Apparent molal volumes of some dilute aqueous rare earth salt solutions at 25 °C. J. Phys. Chem. 1974, 78, 1105−1110. (15) Spedding, F. H.; Saeger, V. W.; Gray, K. A.; Boneau, P. K.; Brown, M. A.; DeKock, C. W.; Baker, J. L.; Shiers, L. E.; Weber, H. O.; Habenschuss, A. Densities and apparent molal volumes of some aqueous rare earth solutions at 25 °C. I. Rare earth chlorides. J. Chem. Eng. Data 1975, 20, 72−81. (16) Spedding, F. H.; Shiers, L. E.; Brown, M. A.; Derer, J. L.; Swanson, D. L.; Habedschuss, A. Densities and apparent molal volumes of some aqueous rare earth solutions at 25 °C. II. Rare earth perchlorates. J. Chem. Eng. Data 1975, 20, 81−88. (17) Gildseth, W. M.; Habenschuss, A.; Spedding, F. H. Densities and thermal expansion of some aqueous rare earth chloride solutions between 5 and 80 °C. I. LaCl3, PrCl3, and NdCl3. J. Chem. Eng. Data 1975, 20, 292−308. (18) Habenschuss, A.; Spedding, F. H. Densities and thermal expansion of some aqueous rare earth chloride solutions between 5 and 80 °C. II. SmCl3, GdCl3, DyCl3, ErCl3 and YbCl3. J. Chem. Eng. Data 1976, 21, 95−113. (19) Jones, G.; Stauffer, R. E. The viscosity of solutions of electrolytes as a function of the concentration. VI. Potassium bromide and lanthanum chloride. J. Am. Chem. Soc. 1940, 62, 335−337. (20) Dunn, L. A. Apparent molar volumes of electrolytes. Trans. Faraday Soc. 1966, 62, 2348−2354. (21) Gildseth, W. M.; Habenschuss, A.; Spedding, F. H. Precision measurements of densities and thermal dilation of water between 5 and 80 °C. J. Chem. Eng. Data 1972, 17, 402−409. (22) Kell, G. S. The density, thermal expansivity and compressibility of liquid water from 0 to 150 °C: correlations and tables for atmospheric pressure and saturation reviewed and expressed on the 1968 temperature scale. J. Chem. Eng. Data 1975, 20, 97−105. (23) Spieweck, F.; Bettin, H. Review: Solid and liquid density determination. Tech. Messen 1992, 59, 285−292. (24) Pierrot, D.; Millero, F. J. The apparent molal volume and compressibility of seawater fit to the Pitzer equations. J. Solution Chem. 2000, 29, 719−742. (25) Connaughton, L. M.; Hershey, J. P.; Millero, F. H. PVT properties of concentrated aqueous electrolytes: V. Densities and apparent molal volumes of the four major sea salts from dilute solution to saturation and from 0 to 100 °C. J. Sol. Chem. 1986, 15, 989−1002. (26) Millero, F. J. In Water and Aqueous Solutions; Horne, R. A., Ed.; Wiley-Interscience: NY, 1972; Chapters 13, 14.

slightly from these trends. In future studies, sound speed measurements on the rare earths will be made to derive partial molal compressibilities of the rare earths. These results will be useful in estimating of effect of pressure on the reactions of the rare earths in seawater at high pressures.

■

APPENDIX The coefficients for the Pitzer parameters (a1, a2, etc.) along with the standard errors of the fits are tabulated in Tables A-I to A-IV.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We wish to acknowledge the support of the oceanographic section of the National Science Foundation, for supporting our Marine Physical Chemical Studies over the years. We also wish to acknowledge the pioneering molal volume work of Dr. Boris Krumgalz who was the first to extensively use the Pitzer equation to examine the volume properties of a number of electrolytes in water.

■

REFERENCES

(1) Pitzer, K. S. Activity Coefficient in Electrolyte Solutions; CRC Press: Boca Raton, FL, 1991. (2) May, P. M.; Rowland, D.; Hefter, G.; Königsberger, E. A generic and updatable pitzer characterization of aqueous binary electrolyte solutions at 1 bar and 25 °C. J. Chem. Eng. Data 2011, 56, 5066−6077. (3) Krumgalz, B. S.; Pogorelsky, R.; Losilevskii, Ya. A.; Weiser, A.; Pitzer, K. S. Ion interaction approach for volumetric calculations for solutions of single electrolytes at 25 °C. J. Solution Chem. 1994, 23, 849− 875. (4) Krumgalz, B. S.; Pogorelsky, R.; Pitzer, K. S. Ion interactions approach to calculations of volumetric properties of aqueous multiplesolute electrolyte solutions. J. Solution Chem. 1995, 24, 1025−1038. (5) Krumgalz, B. S.; Pogorelsky, R.; Pitzer, K. S. Volumetric properties of single aqueous electrolytes from zero to saturation concentration 298.15 K represented by Pitzer’s ion interaction equations. J. Phys. Chem., Ref. Data 1996, 25, 663−689. (6) Krumgalz, B. S.; Starinsky, A.; Pitzer, K. S. Ion-interactions approach: Pressure effect on the solubility of some minerals in submarine brines. J. Solution Chem. 1999, 28, 667−292. (7) Krumgalz, B. S.; Pogorelsky, R.; Sokolov, A.; Pitzer, K. S. Volumetric Ion interaction parameters for single-solute aqueous electrolyte solutions at various temperatures. J. Phys. Chem. 2000, 29, 1123−1140. (8) Monnin, C. The influence of pressure on the activity coefficients of the solutes and on the solubility of minerals in the system Na−Ca−Cl− SO4−H2O to 200 °C and 1 kbar and to high NaCl concentration. Geochim. Cosmochim. Acta 1990, 54, 3265−3282. (9) Monnin, C. An ion interaction model for the volumetric properties of natural waters: Density of the solution and partial molal volumes of electrolytes to high concentrations at 25 °C. Geochim. Cosmochim. Acta 1989, 53, 1177−1188. (10) Rodriguez, C.; Millero, F. J. Estimating the density and compressibility of seawater to high temperatures using the pitzer equations. Aquat. Geochem. 2013, 19, 115−133. (11) Oakes, C. S.; Rard, J. A.; Archer, D. G. Enthalpies of dilution of NdCl3(aq) at temperatures from 297.89 to 372.08 K and an extended pitzer ion-interaction model for the NdCl3 + H2O System. J. Chem. Eng. Data 2004, 49, 313−325. F


Apparent Molal Volumes of Aqueous Rare Earth ... - ACS Publications

Recommend Documents