Thermodynamic Properties of LiCl+ MgSO4+ H2O at Temperatures

Article pubs.acs.org/jced

Thermodynamic Properties of LiCl + MgSO4 + H2O at Temperatures from 273.15 K to 373.15 K and Representation with Pitzer IonInteraction Model Jie Zhang,†,‡ Dongdong Li,†,∥ Yan Yao,*,† Bai Sun,† Dewen Zeng,†,§ and Peng-Sheng Song† †

Key Laboratory of Salt Lake Resources and Chemistry, Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, 18 Xinning Road, Xining 810008, P. R. China ‡ School of Chemistry and Chemical Engineering, Henan Normal University, Xinxiang, Henan 453007, P. R. China ∥ University of Chinese Academy of Sciences, Beijing 100049, P. R. China § College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, P. R. China ABSTRACT: Osmotic coefficients, water activities, and vapor pressures for the systems of LiCl + H2O, MgSO4 + H2O, and LiCl + MgSO4 + H2O over the ionic strength ranges from I = (0.5552 to 7.0004, 4.1028 to 22.6048, and 1.1982 to 20.5863) mol·kg−1 respectively at T = (273.15, 298.15, 323.15, 348.15, and 373.15) K were determined by the isopiestic method with an improved simple apparatus. Aqueous CaCl2 solution was chosen as a reference standard. The measured osmotic coefficients for the binary solutions of LiCl + H2O and MgSO4 + H2O were in agreement with those from the literature. The experimental data of osmotic coefficients for the ternary mixtures were represented by using the Pitzer ion-interaction model; the expressions for the temperature dependencies of the model parameters were given. The standard deviations of all the measured osmotic coefficient data from those calculated by using the model over the temperature range were estimated. A set of model equations of apparent molar enthalpy and excess heat capacity for the mixtures as functions of molality and temperature were obtained by differentiating the model equations of excess Gibbs free energy. The mean activity coefficients, relative apparent molar enthalpies, and excess heat capacities were calculated by using the corresponding equations. The effects of composition and temperature on these thermodynamic properties were discussed.

1. INTRODUCTION LiCl + MgSO4 + H2O is a subsystem of the quaternary reciprocal system of Li+ + Mg2+ + Cl− + SO42− + H2O, which occurs in many salt lake brines and ground brines of oil field and is important to the utilization of brine resources. The thermodynamic properties of the binary subsystems of LiCl + H2O, MgCl2 + H2O, Li2SO4 + H2O, and MgSO4 + H2O have been extensively studied, and their models are available over a wide range of molality and temperature.1−9 The ternary subsystems with a common ion like LiCl + MgCl2 + H2O, Li2SO4 + MgSO4 + H2O, LiCl + Li2SO4 + H2O, and MgCl2 + MgSO4 + H2O at T = 298.15 K have been measured.10−13 Experimental redetermination and model simulation of the solubility phase diagram for the quaternary system of Li+, Mg2+//Cl−, SO42−−H2O at 298.15 K14 and 323.15 K15 and the solubility phase diagram of the ternary system of MgCl2− MgSO4−H2O at (323.15 and 348.15) K16 have been reported. The thermodynamic properties and phase diagrams predicted by using the Pitzer ion interaction model for some seawater systems at various temperatures,9,17 as well as for salt lake brine systems containing lithium at 298.15 K, have also been reported.18−20 However, the studies for the salt lake brine system and its ternary subsystems containing lithium at a wide © XXXX American Chemical Society

range of temperatures are lacking. For example, the data of the thermodynamic properties of LiCl + MgSO4 + H2O system in the temperature range from 273.15 to 373.15 K have not been found. As a result, it is difficult to determine the parameters of the ion-interaction model for Li+ + Mg2+ + Cl− + SO42− + H2O and some salt lake brine systems in a wide temperature range. In the present report osmotic coefficients of the binary systems of LiCl + H2O and MgSO4 + H2O, and the ternary system of LiCl + MgSO4 + H2O at T = (273.15, 298.15, 323.15, 348.15 and 373.15) K were measured. The coefficients of the equations for the temperature dependencies of the mixing parameters of Pitzer ion-interaction model were calculated simultaneously from the present experimental data and by using single salt parameters from literature. The standard deviations of the measured values in this work for the binary and ternary systems from the calculated values for the binary in literature and for the ternary system were estimated, respectively. The mean activity coefficients were calculated by using the parametrized ion-interaction model. The relative apparent Received: November 20, 2015 Accepted: June 1, 2016

A

DOI: 10.1021/acs.jced.5b00987 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

molar enthalpies and excess heat capacities for the ternary system in the temperature range of (273.15 to 373.15) K were calculated by using the equations derived from the equations of excess Gibbs free energy for mixtures1 and the temperature dependences of the parameters obtained in this work. The calculated values of the thermal properties for the binary system in the present work were compared with those from the literature.3,7 The effects of composition and temperature on these thermodynamic properties were discussed.

Table 1. Information of Chemicals in This Work final massa

initial mass

2. EXPERIMENT 2.1. Apparatus. In this work the isopiestic apparatus, experimental procedure and method are similar to our previous isopiestic studies.21,22 The isopiestic chamber was improved based on those described in the literature.23,24 The chamber was designed for precise measurements from very low to higher molalities and at elevated temperatures. An internal capping device was mounted at the top of the chamber for dropping and pressing the caps down onto the sample cups to seal the cups under equilibrium conditions before the chamber was removed from the constant temperature bath. This design reduced the experimental error effectively caused by evaporation of sample solution or condensation of water vapor, and avoided equilibrium water vapor getting out of the isopiestic chamber or laboratory air getting into the chamber in the process of dropping or raising the capping device. The chamber was made of stainless steel. A thick pure copper block with eight cylindrical holes was used for holding isopiestic cups, and the surface of the eight cylindrical holes was plated with gold metal. Of the eight sample cups with a volume of about 16 cm3 used in the experiment, six were made of titanium alloy and used for test solutions, and two were made of pure platinum and used for reference standard solutions. Teflon caps tightly fitting the cups with O-rubber rings were used. For the experiment at 273.15 K, the isopiestic apparatus was modified from a glass vacuum desiccator in which there was a thick pure copper block with 14 cylindrical holes for holding the cups, and the surface of the holes was also plated with gold. Gold-plated silver equilibration cups were used at low temperature. The experiments were performed in constant temperature baths at T = (273.15, 298.15, 323.15, 348.15 and 373.15) K with the standard uncertainties of 0.01 K for (273.15, 298.15, and 323.15) K, and less than 0.03 K for other temperatures. Two stirrers were used in the baths to minimize temperature gradients. The temperatures were measured by means of mercury standard thermometers that were calibrated by a standard platinum resistance thermometer. A Sartorius analytical electronic balance with the standard uncertainty of 0.0001 g was used for all weighing in this experiment. Atomic absorption spectroscopy technique was used for determining impurity contents in the purified chemicals. 2.2. Materials. Water was purified by deionization followed by distillation times two (once from KMnO4). The purified water with a conductivity of 1 × 10−4 S·m−1 was used for all of the experiment. The detailed information on chemicals used in this work is listed in Table 1. The stock solutions were prepared by dissolving the purified solids into the purified water, followed by filtration to remove any insoluble materials. The molalities of the stock solutions of CaCl2 and LiCl were determined by gravimetric chloride analysis from five samples. The molalities of stock solution of MgSO4 were determined by gravimetric sulfate analysis from four samples. The relative

chemical name

source

lithium chloride monohydrate calcium chloride dihydrate magnesium sulfate heptahydrate

Beijing Reagent Co. Ltd.,China Xi’an Reagent Co. Ltd., Chena Kaiyuan Reagent Co. Ltd., China

fraction purity

purification method

fraction purity

>0.970

recrystallization

>0.9980

>0.980

recrystallization

>0.9990

>0.990

recrystallization

>0.9995

a Confirmed by detecting impurity contents using atomic absorption spectroscopy.

standard uncertainty for the molalities of the stock solutions is 0.0004. The three mixed stock solutions of LiCl (A) and MgSO4 (B) were prepared by weighing the stock solutions of LiCl, MgSO4, and the purified H2O in appropriate proportions according to the desired concentrations using mass burets. The molality fractions of MgSO4 (YB, defined as eqs 1 and 2) for the mixed stock solutions were 0.2, 0.5, and 0.8, respectively. m T = mA + mB (1)

YB = mB /m T

(2)

where mA and mB are the molalities of LiCl and MgSO4 in the mixed solution, respectively, and mT is total molality of the mixed solution of LiCl and MgSO4. 2.3. Procedures. Aqueous CaCl2 solution was used as the isopiestic reference standard. The pressure and temperature of the laboratory air were measured using a standard atmospheric pressure gauge with an accurate thermometer, and humidity was obtained using a physical hygrometer. After the volume and the mass of each empty cup covered with a cap were measured, a total amount of about 2.5 g of sample solution was weighed into every sample cup using mass burets, and then the mass was checked by method of addition to make sure the weight was reproducible to avoid initial weighing random error. The sample cups were then placed in the isopiestic chamber and the air was then slowly evacuated to near vacuum using a vacuum apparatus with a pressure gauge. Finally the chamber was placed into the constant-temperature bath and was rocked back and forth for 30 min per hour with a frequency of 50 cycles per minute to make the system reach equilibration fast. Generally the experiments were performed for (3 to 4) days for temperatures higher than 298.15 K and for (6 to 7) days for a temperature of 273.15 K. When equilibrium was reached the sample cups were closed with the caps fixed previously in the capping device inside the isopiestic chamber, and then the chamber was removed from the thermostat bath. Clean dry air was introduced into the chamber, and all of the sealed cups were moved into a desiccator and kept there until the temperature reached room temperature. The closed cups were then weighed. The cups were weighed again after the air was slowly introduced into the cups by carefully lifting the caps. Meanwhile the pressure, temperature, and humidity of the laboratory air were measured again. Duplicate CaCl2 standard solutions were used in allexperimental runs. Duplicate samples taken from one mixing solution of YB = 0.5, and four single samples for other two mixing solutions with YB of 0.2 and 0.8 and two pure salt solutions of LiCl and MgSO4 were used in the each B



Article

Table 2. Fitted Coefficients ai of eq 9 for Calculating the Osmotic Coefficients of CaCl2(aq) Reference Standard as Functions of Molality m* at Various Temperatures and Standard uncertainties u(ϕ*)a T/K a0 a1 a2 a3 a4 a5 a6 a7 a8 u(ϕ*)

273.15

298.15

323.15

348.15b

0.94610 −0.70247 2.09483 −3.32776 3.82548 −2.72522 1.20397 −0.29406 0.02960 2.32·10−4

0.89956 −0.30476 0.54462 −0.15771 0.02981 0.04931 −0.01686

0.94782 −0.79847 2.29471 −3.50288 3.75496 −2.45351 0.97630 −0.21501 0.01961 2.27·10−4

0.93597 −0.72664 1.78818 −2.03066 1.39725 −0.36831

2.42·10−4

2.9·10−5

348.15c −74.770 332.67 −605.35 583.40 −313.86 89.473 −10.563

2.69·10−4

348.15d

373.15e

373.15f

18.8082 −44.5403 41.6696 −15.4140 −0.96527 2.69390 −0.81843 0.08168

0.90119 −0.50858 1.01157 −0.83433 0.50998 −0.11637

0.93725 −0.47454 0.71251 −0.37600 0.21526 −0.04626

1.88·10−4

1.82·10−4

1.74·10−4

u(ϕ*) is the fitting standard deviations of the osmotic coefficient data in the literature from the values calculated using eq 9 for aqueous CaCl2 solutions. Molality range of CaCl2 (aq) reference solutions: bm* ≤ 1; c1 < m* < 3; dm* ≥ 3; em* ≤ 2; fm* > 2. a

27

the ionic strength fraction weighting and the results are accurate enough for making buoyancy,23 the densities of the mixtures at 348.15 and 373.15 K were calculated by using eq 6,

experimental run. The duplicate samples for the mixing solution was allowed to be replaced with different mixing solutions in the next run because not enough cups could be used in the chamber.

ρmix ≈ Waq /(Waq(1)/ρ(1) + Waq(2)/ρ(2))

3. RESULTS AND DISCUSSION 3.1. Experimental Results. The empty cup was filled with laboratory air containing water vapor before the experiment. The total mass of the cup containing sample solution for final weighing included water vapor trapped inside the cup when the cup was capped in the chamber at the equilibrium temperature and laboratory air which was introduced after the sample cup reached room temperature. So corrections for the laboratory air and the water vapor trapped are necessary especially at higher temperatures to obtain accurate isopiestic equilibrium molalities. Correction for the laboratory air: calculating the mass of the air by using ideal gas state (eq 3),

where Waq(1) and Waq(2) are weightings of the binary solutions of LiCl and MgSO4, respectively, calculated by using formula, Waq(i) = YI(i) × Waq, ρ(i) is density of solution at the same ionic strength, YI(i) is ionic strength fraction of the corresponding component in mixed solution. To gain an accurate result, the mass of the air trapped in the isopiestic cup should be calculated by using the state equation of a real gas. However, the present experiment was carried out under relatively mild conditions in which no very high pressure or very low temperature was involved; the calculation result by using the state equation of an ideal gas is accurate enough. It was proven that the error caused by using the state equation of an ideal gas is less than the weighting error. The corrections for the water vapor trapped inside the cups as a solvent-vapor-saturated vapor head at elevated temperatures of (323.15, 348.15 and 373.15) K were performed according to the following six steps: (1) The initial molality of the reference solution was determined from the uncorrected final weight, and the molality of the stock solution and the amount added into cup. (2) The initial water activity aW was calculated by using eq 7,

W = MpV /(RT ) = (M1·(pair − p2 ) + M 2p2 )V /(RT ) (3)

where M1 and M2 are average molecular mass of dry air (no water molecule) and molecular mass of water respectively; pair is total air pressure measured and p2 is water partial pressure from measurement of humidity; R is the gas constant and T is temperature in kelvins; V is space volume inside the cup. The space volume of the cup containing sample solution was calculated by using eq 4, V = Vcup − Vaq

ln a w = −ν*m*M w ϕ*/1000

(4)

(7)

where the corresponding quantities for isopiestic reference standards are denoted with asterisks, v* denotes the number of ions formed by the complete dissociation of one molecule, v* = 3 for CaCl2, m* is the isopiestic equilibrium molality, ϕ* is the osmotic coefficient, Mw is molecular mass. (3) The initial water vapor pressure was calculated by using eq 8,23

where Vcup is the volume of the empty cup, Vaq is the volume of the liquid phase inside the cup, the simplified calculation for Vaq is given in eq 5,

Vaq = Waq /ρ

(6)

(5)

where Waq = (W2 − Wcup), W2 is total weight of the final weighing of isopiestic equilibrium cup, Wcup is the weight of the empty cup, ρ is the density of sample solution. For single salt solutions the densities were calculated by using reported density equations.25 For mixed salt solutions the densities at (273.15, 298.15, and 323.15) K were calculated by using the reported density equations.26 On the basis of the remark by Rard that densities for mixtures can be estimated from the densities of binary solutions at the same ionic strength by using

ln aw = ln(p /p0 ) + B2 (T )(p − p0 )/(RT )

(8)

where p is the equilibrium water vapor pressure of solution, p0 is the saturated vapor pressure of pure water at the experimental temperature, B2(T) is the second virial coefficient. (4) The amount of water trapped in the cups as vapor phase was calculated by using the gas state equation and then this amount of water was subtracted from the final weight which C



Article

Table 3. Ionic Strength, I, Isopiestic Equilibrium Molalities of LiCl and MgSO4 in the Aqueous Mixtures, mA and mB, Corresponding Osmotic Coefficients, ϕ, Water Activities, aw, and Water Vapor Pressures, p, for LiCl(A) + MgSO4(B) + H2O System at Different Temperatures, T, (m0 = 1 mol·kg−1)a I/m0

mA/m0

mB/m0

0.5552 1.1982 1.7584 4.1028 1.0093 2.1422 3.1058 6.7576 1.2908 2.7126 3.9056 8.0752 1.7426 3.6040 5.1011 9.8460 1.9893 4.0728 5.7154 10.6972 2.6859 5.3609 7.3753 3.5148 6.8463 4.0922 7.8407

0.5552 0.4434 0.3512 0.0000 1.0093 0.7926 0.6202 0.0000 1.2908 1.0038 0.7800 0.0000 1.7426 1.3336 1.0187 0.0000 1.9893 1.5072 1.1414 0.0000 2.6859 1.9837 1.4729 3.5148 2.5335 4.0922 2.9015

0.0000 0.1887 0.3518 1.0257 0.0000 0.3374 0.6214 1.6894 0.0000 0.4272 0.7814 2.0188 0.0000 0.5676 1.0206 2.4615 0.0000 0.6414 1.1435 2.6743 0.0000 0.8443 1.4756 0.0000 1.0782 0.0000 1.2348

0.6186 0.7179 1.0721 1.9462 3.2040 4.4596 1.1137 1.3022 1.9079 3.3888 5.4452 7.2760 1.7949 2.0912 3.0299 8.0057 10.1648 2.3119 2.6867 3.8619 6.5669 9.6691 11.9504 2.8446 3.2964 4.7037 7.7877 11.2254 7.9359 3.0552

0.6186 0.5931 0.5362 0.3886 0.1892 0.0000 1.1137 1.0758 0.9543 0.6768 0.3216 0.0000 1.7949 1.7272 1.5155 0.4729 0.0000 2.3119 2.2191 1.9315 1.3113 0.5711 0.0000 2.8446 2.7228 2.3525 1.5553 0.6630 1.5847 3.0552

0.0000 0.0312 0.1340 0.3894 0.7537 1.1149 0.0000 0.0566 0.2384 0.6780 1.2809 1.8190 0.0000 0.0910 0.3786 1.8832 2.5412 0.0000 0.1169 0.4826 1.3139 2.2745 2.9876 0.0000 0.1434 0.5878 1.5581 2.6406 1.5878 0.0000

ϕ

m*/m0

T = 273.15 K 0.9743 0.4006 0.8557 0.7695 0.5274 1.0258 0.7106 0.9163 0.8339 0.6129 1.0626 0.8958 0.9584 0.8784 0.6794 1.1220 1.1800 1.0284 0.9587 0.7943 1.1559 1.3299 1.0702 1.0064 0.8598 1.2601 1.7412 1.1968 1.1478 1.4000 2.2155 1.3624 1.5012 2.5351 1.4852 T = 298.15 K 0.9692 0.4430 0.9603 0.8946 0.7706 0.6358 0.5378 1.0276 0.7767 1.0106 0.9595 0.8447 0.7141 0.6291 1.1117 1.2041 1.0975 1.0534 0.8469 0.7852 1.1812 1.5124 1.1690 1.1312 1.0402 0.9596 0.9141 1.2593 1.8221 1.2498 1.2183 1.1505 1.0843 1.1619 1.8572 1.2887 1.9399 D

ϕ*

aw

0.9002

0.9807

598.8

0.9714

0.9634

588.2

1.0208

0.9518

581.1

1.1047

0.932

569.0

1.1526

0.9205

562.0

1.2958

0.8852

540.4

1.4807

0.8375

511.4

1.6155

0.8014

489.3

0.9023

0.9786

3100.8

0.9823

0.9596

3040.6

1.1048

0.9306

2948.7

1.2037

0.9063

2871.6

1.3106

0.8789

2784.9

1.3232 1.3530

0.8756 0.8677

2774.4 2749.4

Pb/Pa



Article

Table 3. continued I/m0

mA/m0

mB/m0

5.0478 8.3486 3.3732 4.4401 9.0384 3.8664 10.1220 4.5071 11.5124 5.7476 6.6038

2.5246 1.667 3.3732 3.0705 1.8048 3.8664 2.0212 4.5071 2.2988 5.7476 5.4548

0.6308 1.6704 0.0000 0.3424 1.8084 0.0000 2.0252 0.0000 2.3034 0.0000 0.2873

0.5787 0.9973 1.8458 3.0893 4.3732 1.0498 1.8111 3.2693 5.3131 7.2384 1.2409 2.1349 3.8231 6.1242 8.2120 2.0529 3.4786 6.0392 9.1556 11.6120 2.6112 4.3807 7.4342 10.9194 13.4796 3.4499 5.7123 9.4185 13.3515 16.0228 3.6858 6.0834 9.9599 13.9501 4.7233 7.7335 12.2820 4.8662 6.3742 7.1809 7.9370 5.4467 7.1150 5.7900 6.6897 6.7613 7.0115

0.5787 0.4989 0.3686 0.1825 0.0000 1.0498 0.9059 0.6529 0.3139 0.0000 1.2409 1.0677 0.7635 0.3618 0.0000 2.0529 1.7398 1.2060 0.5408 0.0000 2.6112 2.1911 1.4846 0.6450 0.0000 3.4499 2.8571 1.8809 0.7887 0.0000 3.6858 3.0426 1.9891 0.8241 4.7233 3.8679 2.4528 4.8662 4.4098 4.1905 3.9698 5.4467 4.9206 5.7900 5.5257 6.7613 6.6959

0.0000 0.1246 0.3693 0.7267 1.0933 0.0000 0.2263 0.6541 1.2498 1.8096 0.0000 0.2668 0.7649 1.4406 2.0530 0.0000 0.4347 1.2083 2.1537 2.9030 0.0000 0.5474 1.4874 2.5686 3.3699 0.0000 0.7138 1.8844 3.1407 4.0057 0.0000 0.7602 1.9927 3.2815 0.0000 0.9664 2.4573 0.0000 0.4911 0.7476 0.9918 0.0000 0.5486 0.0000 0.2910 0.0000 0.0789

ϕ

m*/m0

T = 298.15 K 1.2477 1.1797 1.3460 2.1278 1.3304 1.2566 1.4241 2.4026 1.3608 1.5276 2.7531 1.4960 1.7451 3.4334 1.7446 T = 323.15 K 0.9500 0.4145 0.8816 0.7450 0.6046 0.5028 1.0065 0.7372 0.9333 0.8084 0.6758 0.5839 1.0280 0.8617 0.9559 0.8346 0.7077 0.6213 1.1261 1.3654 1.0631 0.9575 0.8579 0.7963 1.2000 1.6956 1.1442 1.0543 0.9750 0.9298 1.3149 2.1725 1.2703 1.2047 1.1544 1.1324 1.3514 2.3074 1.3098 1.2509 1.2132 1.5069 2.8821 1.4723 1.4495 1.5271 2.9587 1.5178 1.5049 1.4977 1.6190 3.2790 1.6124 1.6729 3.4669 1.6652 1.8279 4.0029 1.8243

E

ϕ*

aw

Pb/Pa

1.4226

0.8491

2690.3

1.5278

0.8200

2598.3

1.6672

0.7803

2472.4

1.9476

0.6967

2207.4

0.8841

0.9804

12098.2

0.9555

0.9626

11885.4

0.9868

0.9551

11794.2

1.1287

0.9201

11358.5

1.2320

0.8932

11024.2

1.3920

0.8492

10487.1

1.4391

0.8357

10314.9

1.6463

0.7738

9550.9

1.6744

0.7651

9443.5

1.7929

0.7278

8983.5

1.8625

0.7054

8706.9

2.0584

0.6406

7907.4



Article


mA/m0

mB/m0

0.3556 0.6314 1.1761 1.9993 2.9056 0.9653 1.6791 3.0913 5.1668 7.2320 1.5002 2.5866 4.6758 7.5058 10.0132 1.9036 3.2649 5.7909 9.0421 11.6164 2.4268 4.1259 7.0644 13.5332 2.7073 4.5800 7.8801 11.7327 14.6252 3.2095 5.3882 9.1172 13.2537 16.2288 3.8706 6.4388 10.6861 15.1387 18.2208 12.0351 16.7388 18.5910 8.1740 6.2063 7.2043 6.7188 6.9899 7.3327 8.0439

0.3556 0.3158 0.2349 0.1181 0.0000 0.9653 0.8399 0.6173 0.3052 0.0000 1.5002 1.2938 0.9338 0.4434 0.0000 1.9036 1.6329 1.1565 0.5341 0.0000 2.4268 2.0635 1.4108 0.0000 2.7073 2.2908 1.5737 0.6931 0.0000 3.2095 2.6950 1.8208 0.7829 0.0000 3.8706 3.2204 2.1341 0.8943 0.0000 2.4035 0.9888 1.0982 4.7700 6.2063 5.9507 6.7188 6.6751 7.3327 7.1539

0.0000 0.0789 0.2353 0.4703 0.7264 0.0000 0.2098 0.6185 1.2154 1.8080 0.0000 0.3232 0.9355 1.7656 2.5033 0.0000 0.4080 1.1586 2.1270 2.9041 0.0000 0.5156 1.4134 3.3833 0.0000 0.5723 1.5766 2.7599 3.6563 0.0000 0.6733 1.8241 3.1177 4.0572 0.0000 0.8046 2.1380 3.5611 4.5552 2.4079 3.9375 4.3732 0.8510 0.0000 0.3134 0.0000 0.0787 0.0000 0.2225

1.0510 3.4308 8.4368 1.5866 2.7722 5.0801 11.1488 2.5210 4.3374 7.6862

1.0510 0.6852 0.0000 1.5866 1.3866 1.0145 0.0000 2.5210 2.1694 1.5350

0.0000 0.6864 2.1092 0.0000 0.3464 1.0164 2.7872 0.0000 0.5420 1.5378

ϕ

m*/m0

T = 348.15 K 0.9469 0.2661 0.8531 0.7161 0.5723 0.4636 0.9955 0.6942 0.9154 0.7775 0.6319 0.5315 1.0504 1.0407 0.9744 0.8429 0.7133 0.6295 1.0895 1.2864 1.0162 0.8959 0.7794 0.7142 1.1361 1.5885 1.0690 0.9763 0.8149 1.1842 1.7660 1.1197 1.0176 0.9284 0.8768 1.2495 2.0565 1.1906 1.1002 1.0281 0.9884 1.3441 2.4408 1.2926 1.2178 1.1677 1.1421 1.3276 2.7806 1.2966 1.4399 3.1679 1.5431 3.3600 1.6579 3.7277 1.6427 1.7332 4.0184 1.7242 1.8235 4.3720 1.8127 T = 373.15 K 0.9777 0.7540 0.7492 0.4872 1.0298 1.1025 0.9428 0.8045 0.5862 1.1379 1.6801 1.0580 0.9336 F

ϕ*

aw

Pb/Pa

0.8437

0.9879

38098.8

0.9228

0.9660

37250.8

1.0094

0.9448

36434.2

1.0748

0.9280

35785.4

1.1571

0.9054

34914.7

1.2102

0.8909

34354.3

1.3000

0.8655

33372.4

1.4210

0.8291

31967.9

1.5314

0.7944

30631.1

1.6580 1.7210 1.8402

0.7529 0.7316 0.6902

29028.1 28207.6 26611.2

1.9320

0.6573

25342.4

2.0389

0.6177

23813.5

0.9085

0.9637

97637.8

0.9880

0.9428

95525.1

1.1383

0.9018

91362.1



Article


mA/m0

mB/m0

ϕ

11.8606 15.0404 2.5905 4.4510 7.8501 12.1024 15.2880 3.5359 6.0098 10.2857 15.1101 18.4516 3.9625 6.6741 11.3423 16.4785 19.9184 4.8185 8.1047 13.4446 18.9833 22.6048 5.1677 8.6067 14.3043 5.2992 8.9364 20.5863 5.9644 6.5701 6.9692 6.3912 7.0258 7.0004 7.7538

0.7006 0.0000 2.5905 2.2262 1.5677 0.7148 0.0000 3.5359 3.0058 2.0541 0.8925 0.0000 3.9625 3.3381 2.2651 0.9733 0.0000 4.8185 4.0535 2.6850 1.1213 0.0000 5.1677 4.3047 2.8567 5.2992 4.4696 1.2159 5.9644 5.8429 5.7564 6.3912 6.2482 7.0004 6.8958

2.7900 3.7601 0.0000 0.5562 1.5706 2.8469 3.8220 0.0000 0.7510 2.0579 3.5544 4.6129 0.0000 0.8340 2.2693 3.8763 4.9796 0.0000 1.0128 2.6899 4.4655 5.6512 0.0000 1.0755 2.8619 0.0000 1.1167 4.8426 0.0000 0.1818 0.3032 0.0000 0.1944 0.0000 0.2145

0.8219 0.7629 1.1430 1.0642 0.9435 0.8314 0.7747 1.2589 1.1848 1.0825 1.0010 0.9650 1.3088 1.2430 1.1437 1.0694 1.0415 1.4154 1.3462 1.2689 1.2208 1.2069 1.4557 1.3982 1.3155 1.4882 1.4117 1.3017 1.5624 1.5468 1.5379 1.6235 1.6106 1.6994 1.6731

ϕ*

aw

Pb/Pa

1.7183

1.1488

0.8988

91058.9

2.2741

1.3049

0.8518

86292.4

2.5153

1.3745

0.8296

84034.7

3.0005

1.5154

0.7821

79224.2

3.1928

1.5708

0.7626

77242.1

3.2894

1.5984

0.7527

76235.2

3.6533

1.7005

0.7148

72396.0

3.9087

1.7697

0.6881

69687.1

4.2615

1.8610

0.6514

65969.4

m*/m0 T = 373.15 K

m* and ϕ* are the corresponding quantities for isopiestic reference solutions of CaCl2. The molality is expressed in moles per kilogram of solvent water. Standard uncertainties: u1(T) = 0.01 K for (273.15 to 323.15) K, u2(T) = 0.03 K for (348.15 and 373.15) K. Relative standard uncertainties: ur(m) = 0.0012 for isopiestic molalities, corresponding to u1(ϕ) = 0.002, combining ur(ϕ*) = 0.010 for the aqueous CaCl2 reference solutions,27 ur(ϕ) = 0.012 for the reported osmotic coefficients in this work, corresponding to ur(aw) = 0.003, ur(p) = 0.004. bThe saturated vapor pressure of pure water, p0, used for estimating p taken from the references.23,28 a

had already been corrected for the laboratory air, obtaining an improved molality of the reference solution. (5) The improved molality was used as a new input value, the corrected molality, and the water vapor pressure of the reference solution were obtained by using an iterative procedure through the calculation cycle consisting of the above steps 2−5 until the required accuracy of 0.00001 was achieved. (6) The amount of water in the vapor space of the other sample cups was calculated by using the final vapor pressure obtained from the reference solutions. The osmotic coefficients of the CaCl2 (aq) reference standard, ϕ*, were calculated by using the equations fitted by least-squares to the smoothed data taken from literature27 in which the estimated relative standard uncertainty of osmotic coefficients in the temperature range from (273.15 to 373.15) K and up to 9 mol·kg−1 was about 0.0096. The fitted equation in this work is as follow:

ϕ* = a 0 + a1m*1/2 + a 2m* + a3m*3/2 + a4m*2 + a5m*5/2 + a6m*3 + a 7m*7/2 + a8m*4

(9)

The coefficients in eq 9 and the fitting standard uncertainties, u(ϕ*), at various temperatures are listed in Table 2. The average values of the molalities at isopiestic equilibrium from replicate samples were taken as isopiestic equilibrium molalities. The molality based osmotic coefficients ϕ were calculated by using the fundamental equation (eq 10), ϕ = ν*m*ϕ*/∑ mi i

(10)

where mi is isopiestic equilibrium molality of ionic species in the studied solutions, ∑i mi is the sum of mi,∑i mi = 2(mA + mB) for LiCl + MgSO4 + H2O ternary system. The corresponding quantities for isopiestic reference standards are denoted with asterisks. The water activities αw and the vapor pressures p were calculated by using eq 7 and eq 8 respectively. G



Article

MgSO4 solutions at 273.15 K,29 and Rard’s data for aqueous MgSO4 solutions at 298.15 K.30 3.2. Representation of the Experimental Thermodynamic Properties for LiCl + MgSO4 + H2O in the Temperature Range (273.15 to 373.15) K with Pitzer Ion-Interaction Model. The experimental results of osmotic coefficients for LiCl + MgSO4 + H2O system were analyzed and represented by using osmotic coefficient equations of Pitzer ion-interaction model including higher-order electrostatic effects for mixed electrolyte solutions.1,17 The temperature dependence of Debye−Hückel limiting law slope for osmotic coefficient, Aφ, was obtained by a least-squares fit to the data taken from the literature1 with a standard deviation of 0.0003, given as follow:

The experimental results of isopiestic equilibrium molalities m, corresponding stoichiometric osmotic coefficients ϕ, water activities aw, and vapor pressures p at T = (273.15, 298.15, 323.15, 348.15 and 373.15) K for the system of LiCl + MgSO4 + H2O are listed in Table 3. The relationships between experimental equilibrium water vapor partial pressures and ionic strengths and between experimental osmotic coefficients and ionic strengths at different ionic strength fractions of MgSO4, YIB, at various temperatures for the aqueous mixtures of LiCl + MgSO4 are shown in Figures 1 and 2, respectively. Ionic strength I is defined in eq 11, I = (1/2) ∑ mizi2 = mA + 4mB i

(11)

where zi is the charge number on ion i, for this system, YIB = 4mB /(mA + 4mB)

Aφ = 0.377 + 4.5488·10−4t + 4.45593·10−6t 2 (12)

− 1.11693·10−8t 3 + 4.41862·10−11t 4

(13)

where t = T − 273.15 K. The single salt parameters of β(0)i,j, β(1)i,j, β(2)i,j, and CΦi,j for the four pure salts were from the literature.3,5,7,9 The single salt parameters and their temperature dependence were determined by a simultaneous least-squares fit of the model to various types of thermodynamic results in a wide temperature range. For LiCl, the parameters from thermodynamic data of isopiestic, vapor pressure measurement, electrochemical cell potential, freezing temperature determination, enthalpy of solution and dilution and heat capacity, were reported by Holmes.3 For Li2SO4, the excess free energies which had been studied as a function of temperature, calorimetric results at 298.15 K, and a good set of freezing temperature measurements were used in temperature dependencies of the single parameters due to lack of other thermodynamic property data, and were reported by Holmes.5 For MgCl2, the temperature equations of the parameters were obtained from Lima and Pitzer for β(0)i,j, β(1)i,j and from Pabalan and Pitzer9 for CΦi,j whose values were modified to fit the solubility data;9 the temperature range was (298.15 to 473.15) K. For MgSO4, the parameters and their temperature dependence were taken from a comprehensive regression of osmotic coefficient, capacity, and enthalpy data in the temperature range from (298.15 to 473.15) K by Phutela and Pitzer,7 and also were reported by Pabalan.9 On the basis of the standard deviations of fitting, all of the excess free energy data as functions of temperature and molality could be adequately described. As mentioned previously in the literature, various forms have been used to describe the temperature dependences of the ion interaction parameters. In this study a singular form (eq 14) was used to describe these dependences. The expressions of other different forms for these single salt parameters were transformed to the same form as eq 14 in order to make the calculations convenient by using the ion-interaction model for various thermodynamic properties and solubilities,

Figure 1. Experimental water vapor pressures, p, plotted against ionic strengths, I, for LiCl + MgSO4 + H2O system at different ionic strength fractions of MgSO4, YIB, at various temperatures. Symbols: ●, experimental results in this work; 1, YIB = 1.0; 2, YIB = 0.8; 3, YIB = 0.5; 4, YIB = 0.2; 5, YIB = 0.0.; 6, YIB = 0.3.

Figures 1 and 2 show that water vapor pressures increase with the increase of temperature T and ionic strength fraction of MgSO4, the osmotic coefficients increase with the decrease of temperature and ionic strength fraction of MgSO4. Obviously the effects of LiCl and MgSO4 on these properties are different in the temperature range of (273.15 to 373.15) K in the mixed ternary system, this is because LiCl has greater hydrophilicity compared with MgSO4, which is consistent with the great solubility difference between LiCl and MgSO4. Comparisons of osmotic coefficients for binary aqueous LiCl and MgSO4 solutions obtained in this work with the literature data are listed in Table 4. From standard deviations listed in this table, it can be seen that the data obtained in this work are in good agreement with Gibbard’s data for aqueous LiCl solutions at various temperatures,2 Platford’s data for aqueous

f (T ) = q0 + q1(T − TR ) + q2(T 2 − TR2) + q3(T 3 − TR3 ) + q4 ln(T /TR ) + q5(1/T − 1/TR )

(14)

where TR and T refer to the reference temperature of 298.15 K and the temperature of interest, respectively. The coefficients of eq 14 for single salt parameters are listed in Table 5. The calculated values of osmotic coefficients using the Pitzer model with the single parameters from eq 14 were compared with the measured values over the whole temperature range in H



Article

Figure 2. Experimental osmotic coefficients, ϕ, plotted against ionic strengths, I, for the LiCl + MgSO4 + H2O system at different ionic strength fractions of MgSO4, YIB, at various temperatures of (a) 273.15 K, (b) 298.15 K, (c) 323.15 K, and (d) 373.15 K. Symbols: experimental results in this work. Lines: calculated values by using the fitted Pitzer model (with higher order term and mixing parameters) in this work.

The osmotic coefficients for the aqueous mixed solutions of LiCl and MgSO4 at various temperatures were calculated by using the present fitted Pitzer model equations in three different forms: (1) the model with high order terms, with single salt parameters and mixing parameters; (2) the model with high order terms, with single salt parameters, but without mixing parameters; (3) the model with single salt and mixing parameters but without a high order term. Standard uncertainties of the calculated values obtained by using the three types of model equations from the present experimental data, u1, u2, and u3 for the models (1), (2), and (3), respectively, were estimated and are listed in Table 7. It can be seen that the standard uncertainties increase following the order: u1 < u2 < u3. This indicates that high order terms have a great effect on the standard uncertainty for the fitting of the experimental data, and the mixing parameters are also necessary for the calculations of the thermodynamic properties for the present ternary system. The deviations of all the osmotic coefficients measured in the present work at various temperatures for the ternary system from those calculated using the Pitzer model(1) are shown in Figure 4. Comparisons of the osmotic coefficients ϕ measured in this work with the calculated values by using the single salt model with parameters from eq 14 and from Table 5 at YB = 0.0 (aq LiCl) and YB = 1.0 (aq MgSO4) plotted against the total molalities, mT, at various temperatures are shown in Figure 5a,b, respectively; the comparison of these with the values calculated by using the present mixing model with parameters from eq 14 and from Tables 5 and 6 at YB = 0.5 plotted against the total molalities mT at various temperatures are shown in Figure 6. The results indicated that the osmotic coefficients

this work with standard deviations of 0.0078 and 0.0100 for LiCl + H2O and MgSO4 + H2O, respectively. The comparison results show that the models with single salt parameters from the literature are able to represent the measured data of LiCl (aq) and MgSO4 (aq) over the temperature range in the present work, and the experimental data from these measurements are reliable. The mixing ion interaction parameters containing Li and the coefficients of eq 14 for the temperature dependences of these parameters were estimated simultaneously by a least-squares fitting of Pitzer model equations of osmotic coefficient to the present experimental data in Table 3 in the temperature range of (273.15 to 373.15) K for LiCl + MgSO4 + H2O system, and the single salt parameters from eq 14 with the coefficients in Table 5 were used. The form of temperature dependence of these mixing parameters is the same as in eq 14, and the equation coefficients for mixing parameters of θLi,Mg, ΨLi,Mg,SO4, and ΨLMCS at various temperatures are listed in Table 6, where ΨLMCS = ΨLi,Mg,Cl + ΨLi,Cl,SO4, because the coefficient values of the two terms of ΨLi,Mg,Cl and ΨLi,Cl,SO4 in the model are equal. This means that the least-squares solution of addition of the two triple ion parameters of ΨLi,Mg,Cl and ΨLi,Cl,SO4 could be obtained for the ternary system without a common ion. If any one of the common ion-ternary subsystem in the quaternary reciprocal system Li+ + Mg2+ + Cl− + SO42− + H2O can be combined to estimate ion-interaction parameters, all the singular triple ion interaction parameters can be obtained. The mixing parameter of θCl,SO4 = 0.03 was set for all the temperatures in this work. The temperature dependence form for ΨMg,Cl,SO4 from literature9 was transformed to the same form as in eq 14 (see Table 6). The relationships between mixing parameters and temperatures are shown in Figure 3. I



Article

Table 4. Comparisons of Experimental Data of Osmotic Coefficients ϕ1 in This Work with ϕ2 in Literatures for Single Salt Solutions of LiCl and MgSO4 at different temperatures T/K 273.15

298.15

323.15

348.15

m/kg·mol−1 0.5552 1.0093 1.2908 1.7426 1.9893 2.6859 3.5148 4.0922 0.6186 1.1137 1.7949 2.3119 2.8446 3.0552 3.3734 3.8664 4.5071 5.7476 0.5787 1.0498 1.2409 2.0529 2.6112 3.4499 3.6858 4.7233 4.8662 5.4467 5.79 6.7613 0.3556 0.9653 1.5002 1.9036 2.4268

ϕ1a LiCl 0.9743 1.0258 1.0626 1.122 1.1559 1.2601 1.4 1.5012 0.9692 1.0276 1.1117 1.1812 1.2593 1.2887 1.3461 1.4241 1.5276 1.7451 0.95 1.0065 1.028 1.1261 1.2 1.3149 1.3514 1.5069 1.5271 1.619 1.6729 1.8279 0.9496 0.9955 1.0504 1.0895 1.1361

ϕ2b

devc

u(ϕ)d

T/K

m/kg·mol−1

2

ϕ1a

ϕ2b

devc

u(ϕ)d

2

0.9724 1.0238 1.0596 1.1214 1.1567 1.2629 1.4004 1.49 0.9733 1.0282 1.114 1.1847 1.2619 1.2936 1.3427 1.4211 1.5271 1.7428 0.9615 1.0092 1.0304 1.1282 1.2011 1.318 1.3522 1.5086 1.5339 1.6218 1.6763 1.8309 0.9359 0.9886 1.0438 1.0882 1.1458

0.0019 0.002 0.003 0.0006 −0.0008 −0.0028 −0.0004 0.0112 −0.0041 −0.0006 −0.0023 −0.0035 −0.0026 −0.0049 0.0034 0.003 0.0005 0.0023 −0.0115 −0.0027 −0.0024 −0.0021 −0.0011 −0.0031 −0.0008 −0.0017 −0.0068 −0.0028 −0.0034 −0.003 0.011 0.0069 0.0066 0.0013 0.0097

0.0046

373.15

0.0032

273.15

0.0045 298.15

2.7073 3.2095 3.8706 6.2063 6.7188 7.3327 1.051 1.5866 2.521 2.5905 3.5359 3.9625 4.8185 5.1677 5.2992 5.9644 6.3912 7.0004 1.0257 1.6894 2.0188 2.4615 2.6743 1.1149 1.819 2.5412 2.9876

LiCl 1.1842 1.1842 1.2495 1.2478 1.3441 1.3392 1.6579 1.6629 1.7332 1.7356 1.8235 1.8214 0.9777 0.9813 1.0298 1.0333 1.1379 1.1334 1.143 1.1413 1.2589 1.252 1.3088 1.3041 1.4154 1.4112 1.4557 1.4556 1.4882 1.4723 1.5624 1.5569 1.6235 1.6107 1.6994 1.6864 MgSO429,30 0.5274 0.5313 0.6129 0.6100 0.6794 0.6741 0.7943 0.7883 0.8598 0.8551 0.5378 0.5379 0.6291 0.6277 0.7852 0.7853 0.9141 0.9160

0 0.0017 0.0049 −0.005 −0.0024 0.0021 −0.0036 −0.0035 0.0045 0.0017 0.0069 0.0047 0.0042 0.0001 0.0159 0.0055 0.0128 0.013 −0.0039 0.0029 0.0053 0.0060 0.0047 −0.0001 0.0014 −0.0001 −0.0019

0.0083

0.0047

0.0012

a The osmotic coefficients measured in this work. bThe osmotic coefficient data taken from the references.2,29,30 cDeviations between ϕ1 and ϕ2. dStandard uncertainties for the osmotic coefficients at different temperatures (equal to standard deviations of the osmotic coefficients measured in this work from those in the references, ⎛ ∑i (ϕ − ϕ )2 ⎞1/2 σ = ⎜ n 1N 2 ⎟ ). ⎝ ⎠

0.0061

the aqueous mixed solutions of LiCl and MgSO4 to the mean activity coefficients of LiCl and MgSO4 in their aqueous pure solutions respectively at the corresponding same molalities (γi(in mixture)/γ0i (in pure)) change with the changing of molalities and temperatures, which indicated that there exist the largest values of the ratios at each temperature, implying that there exist the largest effect points of coexistent solutes on activity coefficients. Figure 10 shows that the effects of coexistent solute of LiCl on the mean activity coefficients of MgSO4, γMgSO4, are far more significant than the effects of MgSO4 in Figure 9. The effect of MgSO4 on activity coefficients of LiCl, γLiCl, and the effects of LiCl on mean activity coefficients of MgSO4, γMgSO4, both increase with the decrease of temperature. 3.3.2. Relative Apparent Molar Enthalpy. The relative apparent molar enthalpies for the ternary mixtures in the temperature range from (273.15 to 373.15) K were calculated by using eqs 15 to 20) derived from the excess Gibbs free energy equation for mixtures.1,31

increase with the increase of molalities and decrease with the increase of temperature and MgSO4 molality fraction; the experimental osmotic coefficients can be represented well by using the present parametrized ion-interaction model for the LiCl + MgSO4 + H2O system over the temperature range from (273.15 to 373.15) K in this work. 3.3. Calculations of Thermodynamic Properties for LiCl + MgSO4 + H2O at Various Temperatures with the Ion-Interaction Model. 3.3.1. Mean Activity Coefficients. The mean activity coefficients of LiCl and MgSO4 were calculated for the ternary mixed solutions at various temperatures by using the Pitzer ion-interaction model for the activity coefficient including higher-order electrostatic effects1,17 with the parameters from eq 14 of the temperature dependence and from Tables 5 and 6, and the relationships between the mean activity coefficients and the molalities at various temperatures are shown in Figures 7 and 8, which indicated that the mean activity coefficients of LiCl and MgSO4 in the ternary system decrease with the increasing of temperatures. The effects of coexistent solutes of MgSO4 and LiCl on activity coefficients at constant ionic strength of 8 mol·kg−1 in the ternary system are shown in Figures 9 and 10. The ratios of the calculated mean activity coefficients of LiCl and MgSO4 in

⎡ ⎛ Gex ⎞ ⎤ ⎟ /∂T ⎥ L = H − H ° = −T 2⎢∂⎜ ⎣ ⎝ T ⎠ ⎦ J

p,m

(15)



Article

Table 5. Coefficients of eq 14 for Calculating Ion-Interaction Parameters of Single Salts as a Function of Temperature at (273.15 to 473.15) Ka β(0)

β(1)

CΦ

β(2) b

q0 q1 q2 q3 q4 q5

1.484700·10−1 −1.546000·10−4 0.000000 0.000000 0.000000 0.000000

q0 q1 q2 q3 q4 q5

9.151910·10−2 −1.591550·10−3 0.000000 0.000000 5.084090·10−1 −1.478510·10

q0 q1 q2 q3 q4 q5

3.510884·10−1 −9.316540·10−4 5.939150·10−7 0.000000 0.000000 0.000000

q0 q1 q2 q3 q4 q5

2.149900·10−1 9.034180·10−1 −8.051210·10−4 3.615480·10−7 −2.259170·102 −2.121620·104

LiCl(aq) 3.070000·10−1 6.360000·10−4 0.000000 0.000000 0.000000 0.000000 Li2SO4(aq)c 8.367340·10−1 5.001170·10−2 0.000000 0.000000 −3.452300·10 −6.011390·103 MgCl2(aq)d 1.651187 −1.094380·10−2 2.601690·10−5 0.000000 0.000000 0.000000 MgSO4(aq)e 3.364600 −1.479800·10−1 1.576070·10−4 0.000000 0.000000 −5.780490·103

3.710000·10−3 0.000000 −3.710000·10−9 0.000000 0.000000 4.115000 4.742600·10−3 2.579510 −2.598330·10−3 1.306720·10−6 −5.681400·102 −4.682600·104 6.506891·10−3 −2.499490·10−4 2.418310·10−7 0.000000 0.000000 0.000000 2.797200·10−2 −4.050960·10−1 3.684120·10−4 −1.665020·10−7 9.816150·10 8.869120·103

−3.27430·10 −6.882000 2.020170·10−2 −2.303500·10−5 3.702980·10−6 −6.787690·104

a (0) (1) (2) β , β , β and CΦ are ion-interaction parameters of Pitzer osmotic coefficient equations1 for single salts, qi is coefficients of eq 14 at T = (273.15 to 473.15) K. Constant values, αi/(kg1/2·mol−1/2), in the equations: bα1 = 2.0, α2 = 0.0; cα1 = 1.4, α2 = 0.0; dα1 = 2.0, α2 = 0.0; eα1 = 1.4, α2 = 12.0.

Table 6. Coefficients of eq 14 for Calculating Mixing IonInteraction Parameters as a Function of Temperature at T = (273.15 to 373.15) K for LiCl + MgSO4 + H2O Systema q0 q1 q2 q3 q4 q5

θLi,Mg

θCl,SO4b

ΨLMCS

ΨLi,Mg,SO4

ΨMg,Cl,SO4

0.008016 0.000644 0 0 0 0

0.03 0 0 0 0 0

−0.003741 0 0 0 0 19.112547

0.004672 0 0 0 0 −19.018727

−0.008000 0 0 0 0 32.634700

Figure 3. Relationship between mixing parameters calculated from eq 14 and Table 6 and temperatures for LiCl + MgSO4 + H2O. Symbols: −, θLi,Mg; −•−, ψLi,Mg,SO4; ---, ψLMCS.

θLi,Mg is mixing ion-interaction parameter between ions of Li+ and Mg2+. bθCl,SO4 = 0.03 was set for all the temperatures in this work, ΨLMCS = ΨLi,Mg,,Cl + ΨLi,Cl,SO4, ΨLi,Mg,SO4 and ΨMg,Cl,SO4 represent triple ion interaction parameters, qi is the coefficients of eq 14 for calculating mixing ion-interaction parameters as the functions of temperature at (273.15 to 373.15) K. a

Gex /RT = f (I ) + 2 ∑ ∑ mc ma[Bca + (∑ mc zc)Cca] c

+ +

ϕ

L = L /n2

where n2 is the number of moles of solute. The operational

c′

a

∑ ∑ mama ′[2Φaa ′ + ∑ mcψaa ′ c] a

(16)

c

∑ ∑ mcmc′[2Φcc′ + ∑ maψcc′ a] c

The relative apparent molar enthalpy, ϕL, defined as eq 16,

a

a′

c

(17)

f (I ) = −(4IAϕ /b) ln(1 + bI1/2)

(18)

Bca = βca(0) + βca(1)g (α1I1/2) + βca(2)g (α2I1/2)

(19)

g (x) = 2[1 − (1 − x) exp(−x)]/x 2

(20)

expression of L for a mixed electrolyte was derived as indicated in eq 15, and is given in eq 21. K



Article

Table 7. Mixing Ion-Interaction Parameters and Standard Uncertainties, u, at Various Temperatures, T, for LiCl + MgSO4 + H2O Systema I/mol·kg−1

T/K

273 0.5−10.7 298 0.6−12.0 323 0.6−16.0 348 0.4−18.6 373 1.0−22.6 Average standard uncertainties u

θLi,Mg

ΨLMCS

ΨLi,Mg,SO4

u1

u2

u3

−0.008084 0.008016 0.024116 0.040216 0.056316

0.002126 −0.003741 −0.008700 −0.012947 −0.016625

−0.001166 0.004672 0.009607 0.013833 0.017493

0.0033 0.0044 0.0069 0.0142 0.0099 0.0077

0.0103 0.0100 0.0126 0.0206 0.0166 0.0140

0.0212 0.0234 0.0281 0.0264 0.0344 0.0251

I is ionic strength, θLi,Mg is mixing ion-interaction parameter between Li+ and Mg2+, ΨLMCS = ΨLi,Mg,Cl + ΨLi,Cl,SO4, ΨLi,Mg,SO4 and ΨMg,Cl,SO4 represent triple mixing ion-interaction parameters. The above parameters were determined from eq 14 and Table 6, u1 and u2 are the standard uncertainties of the osmotic coefficients measured from those calculated by using the present fitted Pitzer model equations with high order term, with and without the mixing parameters (θ = ψ = 0) respectively; u3 is the standard uncertainties of the osmotic coefficients measured from those calculated for the aqueous mixed solutions using the present fitted Pitzer model equations without high order term and with the mixing parameters. a

Figure 4. Deviations of the osmotic coefficients, ϕexpt, measured in this work from these, ϕcalc, calculated by using the Pitzer ion-interaction model1 with the parameters determined from eq 14 and from Tables 5 and 6 for LiCl + MgSO4 + H2O system at various temperatures. Symbols: □, 273.15 K; ○, 298.15 K; △, 323.15 K; ☆, 348.15 K; ◇, 373.15 K.

Figure 6. Comparisons of the osmotic coefficients, ϕ, measured with those calculated by using Pitzer model equations1 for aqueous mixing solutions with the parameters from eq 14 and Tables 5 and 6 at YB = 0.5 at various temperatures plotted against the total molalities, mT, for LiCl + MgSO4 + H2O. Symbols: lines − , calculated values from this work; points, measured values from this work; ■, 273.15 K; ●, 298.15 K; ▲, 323.15 K; ◆, 348.15 K; ★, 373.15 K.

Figure 5. Comparisons of the osmotic coefficients, ϕ, measured with those calculated by using the Pitzer ion-interaction model1 for aqueous single salt solutions with parameters from eq 14 and Table 5 at (a) YB = 0.0 and (b) YB = 1.0 at various temperatures plotted against the total molalities, mT, for LiCl + MgSO4 + H2O. Symbols: lines ―, calculated values from the literature;3,7 points, measured values from this work; ■, 273.15 K; ●, 298.15 K; ▲, 323.15 K; ◆, 348.15 K; ★, 373.15 K.

Figure 7. Calculated mean activity coefficients of LiCl, γLiCl, for LiCl + MgSO4 + H2O by using Pitzer model equations1 with parameters from eq 14 and Tables 5 and 6 at different molality fractions of MgSO4, YB, at various temperatures, plotted against ionic strengths I. Symbols: lines − , calculated values; 1, YB = 0.0; 2, YB = 0.2; 3, YB = 0.5; 4, YB = 0.8.

L = f L − RT 2{2 ∑ ∑ mc ma[BcaL + (∑ mc zc)CcaL] c

+

Equation 22 is the long-range electrostatic contribution and AL is the Debye−Hückel limiting law slope for enthalpy. The temperature dependence of the Debye−Hückel limiting law slope AL was determined by a least-squares fit to the data taken from ref 1, with a standard deviation of 0.011, and is given as follow:

c

∑ ∑ mcmc′[2ΦccL′ + ∑ maψccL′ a] c

+

a

c′

∑∑ a

a L mama ′[2Φaa ′

+

a′

∑ mcψaaL ′ c]} c

(21)

AL /RT = 0.53928 + 0.01093t − 1.13945· 10−5t 2

f L = (AL I /b) ln(1 + bI1/2)

+ 2.35592· 10−7t 3

(22) L

(23) DOI: 10.1021/acs.jced.5b00987 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

The calculated results of relative apparent molar enthalpies at molality fractions of MgSO4, YB = (0.0, 0.5 and 1.0), at total molalities, mT, of (1.0 and 2.0) mol·kg−1 for the ternary system from eq 16 and eqs 21 to 24, and the relationships between the apparent molar enthalpies and temperatures are shown in Figure 11a,b, respectively.

Figure 8. Calculated mean activity coefficients of MgSO4, γMgSO4, for LiCl + MgSO4 + H2O system by using Pitzer model equations1 with parameters from eq 14 and Tables 5 and 6 at different molality fractions of MgSO4, YB, at various temperatures, plotted against ionic strengths, I. Symbols: lines − , calculated values; 1, YB = 0.2; 2, YB = 0.5; 3, YB = 0.8; 4, YB = 1.0.

Figure 11. Relative apparent molar enthalpies, ϕL, at YB = (0.0, 0.5 and 1.0) and at total molalities, mT, of (a) 1.0 mol·kg−1 and (b) 2.0 mol· kg−1 for LiCl + MgSO4 + H2O system as a function of temperature calculated from the Pitzer model eqs 21 to 24 and from Tables 5 and 6. Symbols: lines − , calculated values from this work; ●, Holmes and Mesmer;3 ■, Phutela and Pitzer.7

It can be seen from Figure 11 that the calculated values of the relative apparent molar enthalpies of LiCl and MgSO4 (YB = 0.0 and YB = 1.0) from this work are in good agreement with the values of the enthalpies reported by Holmes and Mesmer3 and Phutela and Pitzer,7 respectively; the relative apparent molar enthalpies increase with the increase of molality fractions of MgSO4, YB, temperatures, T, and total molalities, mT, for LiCl + MgSO4 + H2O system. 3.3.3. Excess Heat Capacity. The pertinent thermodynamic equations for the heat capacity are defined in eqs 25 and 26,

Figure 9. Ratios of the calculated mean activity coefficients of LiCl in the mixing solutions of LiCl and MgSO4 to those in aqueous LiCl pure solutions (γLiCl/γ0LiCl) plotted against the corresponding molalities of LiCl, mLiCl, at constant ionic strength (8.0 mol·kg−1) for the aqueous mixed solutions of LiCl and MgSO4 at the various temperatures. Symbols: lines ―, calculated values; □, 273.15 K; ○, 298.15 K; △, 323.15 K; ☆, 348.15 K; ◇, 373.15 K.

Cp = (∂H /∂T )p , m = C p0 + (∂L /∂T )p , m

(25)

C pex = Cp − C p0 = (∂L /∂T )p , m

(26)

Cex p

C0p

where is excess heat capacity, is heat capacity at infinite dilution. Excess heat capacity per mole of solute is given in eq 27, CPex /m = CP , ϕ − CP0, ϕ

(27) 0 CP,ϕ

where CP,ϕ is apparent molar heat capacity, is apparent molar heat capacity at infinite dilution, and m is molality of solute. For an aqueous multicomponent solution m is the sum of molality of each solute. The operational expression of the excess heat capacity for a mixed electrolyte system was derived from eqs 21 and 22 based on refs 27 and 31 and is given as follow:

Figure 10. Ratios of the calculated mean activity coefficients of MgSO4 in the aqueous mixed solutions of LiCl and MgSO4 to those in aqueous MgSO4 pure solutions (γMgSO4/γ0MgSO4) plotted against the corresponding molalities of MgSO4, mMgSO4, at constant ionic strength (8.0 mol·kg−1) for the aqueous mixed solutions of LiCl and MgSO4 at the various temperatures. Symbols: lines ―, calculated values; □, 273.15 K; ○. 298.15 K; △, 323.15 K; ☆, 348.15 K; ◇, 373.15 K.

C pex = f J − RT 2{2 ∑ ∑ mc ma[BcaJ + (∑ mc zc)CcaJ] c

where t = T − 273.15 K. The parameters of the ion-interaction model for the relative enthalpy as a function of temperature is given in the following equation:

+

c

+

f L (T ) = ∂f (T )/∂T = q1 + 2q2T + 3q3T 2 + q4 /T − q5/T 2

∑∑

mc mc ′[2ΦccJ ′

M

+

∑

maψccJ ′ a]

a J mama ′[2Φaa ′

a′

f J = (AJ I /b) ln(1 + bI1/2)

(24)

c

c′

∑∑ a

a

+

∑ mcψaaJ ′ c]} c

(28) (29)



Article

Equation 29 is the long-range electrostatic contribution and AJ is the Debye−Hückel limiting law slope for heat capacity. The temperature dependence of the Debye−Hückel limiting law slope for heat capacity was determined by a least-squares fit to the data taken from reference1 with a standard deviation of 0.12 (eq 30),

experimental results of the osmotic coefficient are represented well by the Pitzer ion-interaction model with the expressions for the temperature dependencies of the model parameters. A set of model equations of apparent molar enthalpy and excess heat capacity for the mixtures as functions of composition and temperature have been obtained. The mean activity coefficients, relative apparent molar enthalpies, and excess heat capacities have been calculated by using the corresponding equations in the wider temperature range from (273.15 to 373.15) K. The present calculated results of the thermal properties for single salt solutions agree with the literature experimental data reasonably well. The water vapor pressures and water activities increase with the increase of temperature and ionic strength fractions of MgSO4; the osmotic and mean activity coefficients increase with the decrease of temperature and ionic strength fractions of MgSO4. The effects of LiCl and MgSO4 on these properties are different in the temperature range of (273.15 to 373.15) K in the mixed ternary system, indicating that LiCl has greater hydrophilicity than MgSO4. There exist the largest effect points of composition and temperature on activity coefficients. The effects of coexistent solute of LiCl on the mean activity coefficients of MgSO4 are far more significant than the effects of MgSO4. The relative apparent molar enthalpies and the excess heat capacities increase with the increase of molality fractions of MgSO4, total molalities, and temperature. However, the effect of temperature on the excess heat capacities is relatively less in the temperature range from (273.15 to 373.15) K for the LiCl + MgSO4 + H2O system.

AJ /R = 2.80894 + 0.05555t − 3.6947210−4t 2 + 2.8680910−6t 3

(30)

where t = T − 273.15 K. The parameters of the ion-interaction model for the heat capacity as a function of temperature is given as follow: f J (T ) = (2/T )∂f (T )/∂T + ∂ 2f (T )/∂T 2 = 2q1/T + 6q2 + 12q3T + q4 /T 2

(31)

The excess molar heat capacities calculated from eq 27 to 31 at molality fractions of MgSO4, YB = (0.0, 0.5 and 1.0), at total molalities, mT = (1.0 and 2.0) mol·kg−1, for the ternary system at various temperatures and the relationship between heat capacity and temperature is presented in Figure 12, which

■

AUTHOR INFORMATION

Corresponding Author

Figure 12. Excess heat capacities per mole of solute, Cex p /mT, at YB = (0.0, 0.5 and 1.0) and at total molalities of solutes, mT, of (a) 1.0 mol· kg−1 and (b) 2.0 mol·kg−1 for LiCl + MgSO4 + H2O system as a function of temperature, T, calculated from Pitzer model eqs 28 to 31 and from Tables 5 and 6. Symbols: lines ―, calculated values from this work; ●, Holmes and Mesmer;3 ■, Phutela and Pitzer.7

*E-mail: [email protected]. Tel.: +86 13683550677. Funding

This project was financially supported by the National Nature Science Foundation of P. R. China (Nos. 29471031, 20373084, 21571052), the Key Basic Research Foundation of the Chinese Academy of Sciences (No. KJ 952-J1−502), the 100 Top Talents Project of the Chinese Academy of Sciences and the Key Science and Technology Project of Henan Province (No. 152102210085).

indicates that the calculated values of the excess heat capacities (per mole of solute) of LiCl and MgSO4 (YB = 0.0 and YB = 1.0) from the present work are in agreement with the values of the heat capacity reported by Holmes and Mesmer,3 and Phutela and Pitzer,7 respectively. The excess heat capacities increase with the increase of molalities, mT, and increase more significantly with the increase of the molality fractions of MgSO4. However, the effect of temperature in the range from (273.15 to 373.15) K on the excess heat capacity for the studied system is relatively less.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors appreciate senior engineer H. L. Sheng for design of the experimental apparatus, Professor G. M. Long and Ms. J. Liu for helping in the experiment, Prof. W. Voigt for his suggestions for the preparation of the manuscript, and editors and reviewers for their valuable comments on this manuscript.

4. CONCLUSIONS In the present work the osmotic coefficients, water activities, and vapor pressures for the systems of LiCl + H2O, MgSO4 + H2O, and LiCl + MgSO4 + H2O at T = (273.15, 298.15, 323.15, 348.15 and 373.15) K have been determined by using an improved simple isopiestic apparatus and method. The measured osmotic coefficients of LiCl + H2O and MgSO4 + H2O are in good agreement with those from the literature, indicating that the experimental method and the data measured are reliable. This work provides accurate systemic experimental data of osmotic coefficient for the aqueous ternary mixed solutions which have not been reported previously. The

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REFERENCES

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Thermodynamic Properties of LiCl+ MgSO4+ H2O at Temperatures

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