Conductivity of Some Molten Chlorides at Elevated Temperatures I

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Conductivity of Some Molten Chlorides at Elevated Temperatures I. Experimental and Calculation Techniques for BeCl2, ZnCl2, and PbCl2 Alexander B. Salyulev and Alexei M. Potapov* Institute of High Temperature Electrochemistry, Ural Branch of Russian Academy of Sciences, Akademicheskaya st., 20, Ekaterinburg 620990, Russian Federation ABSTRACT: A cell for the electrical conductivity measurements of molten salts at the elevated temperatures and vapor pressures of several tens of atmospheres was constructed. The electrical conductivities of molten BeCl2, ZnCl2, and PbCl2 were measured up to temperatures of (823, 1421, and 1320) K, respectively. The melts density was estimated, and molar conductivities at the same temperatures were calculated.

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INTRODUCTION Until the present time, large amounts of data related to the electrical conductivity of molten salts have been accumulated.1−6 However, most of this information was obtained in a narrow temperature range close to the salts melting points, which is due to the great experimental difficulties, when the vapor pressure of salts reaches several atmospheres. Only a few studies7−10 in wide temperature ranges under conditions of essentially high vapor pressures have been performed. Such studies provide a better understanding the liquids nature, reveal changes in their structure, trace the change in the mechanism of electrical conductivity, and demonstrate the transition from the dielectric (molecular melt) to practically completely ionized fluid. Knowledge of these properties allows the behavior of such melts to be predicted in extreme conditions, as for example accidents, as well as new application areas to be gained. The aim of this work is to study the electrical conductivity of a number of molten salts in a much wider temperature range. To achieve this goal, a special high temperature, high pressure conductometric cell has been developed, the electrical conductivities of the molten BeCl2, ZnCl2, and PbCl2 were measured, and their molar conductivities were calculated. The density required for the calculation of the molar conductivities was estimated according to the proposed method. BeCl2 and ZnCl2 as representatives of strongly associated liquids and PbCl2 from ionic melts have been chosen for our first publication. The saturated vapor pressure of the salts reached (0.34, ∼ 3.0, and 0.24) MPa at maximum temperatures. However, it should be noted that the effect of pressure on electrical conductivity was not studied in the present work. No external pressure was applied; the increased pressure is their own saturated vapor pressure of the salts at elevated temperatures. © XXXX American Chemical Society

EXPERIMENTAL SECTION Chemicals. Reagents used in the present work are listed in Table 1. BeCl2 was synthesized by the direct chlorination of the Table 1. Sample Description Table chemical name

source

BeCl2 ZnCl2 PbCl2

synthesis KKa DRb

initial mole fraction purity

purification method

final mole fraction purity

analysis method

0.99 0.995

distillation distillation distillation

0.999 0.999 0.999

AESc AESc AESc

a Leningrad plant “Krasniy Khimik” bDonetsk Plant of chemicals ″Donetsk-reaktiv″ cAtomic emission spectrometry with an Optima 4300 DV spectrometer (Perkin-Elmer, USA).

high purity metal (mass fraction: ≥ 0.9995) with a dry gaseous hydrogen chloride. Analytical grade ZnCl2 and reagent grade PbCl2 were carefully dehydrated by the long-term (about 20 h) gradual heating up to (570 or 670) K, respectively, under reduced pressure (∼ 1 Pa). The crude salts (BeCl2, ZnCl2, and PbCl2) were distilled in the stream of Cl2 and then additionally purified by repeated (three and more times) sublimation or distillation in vacuum in sealed quartz tubes. After each step of purification, only the middle part of the salt was taken for the subsequent distillation. The final purity of the products exceeds 0.999 (mass fraction) according to the inductively coupled plasma atomic emission spectroscopy analysis. Received: May 16, 2014 Accepted: January 13, 2015

A

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distilled off the cell after calibration. A cell constant ranged from (4 to 70) cm−1. The loaded and sealed cell was heated in the electric furnace equipped with a metallic block. A bottom part of the quartz cell with a length of (70 to 100) mm was disposed outside of the furnace. During experiments the salt vapors penetrated into the small gaps, which remained after the cell fabrication, condensed there and filled the gaps, and as a result a highly hermetic quartz− tungsten junction was formed. The melt temperature was registered with accuracy of ± 1 K by Pt−PtRh (10 % Rh) thermocouple. The melt resistance was measured by the ACbridge at the input frequency of 10 kHz. Measuring procedure was described more detailed elsewhere.9 The electrical conductivity measurement error is composed of calibration error, temperature measurement error, and conductivity meter error. The combined expanded uncertainty of the measured electrical conductivity does not exceed Uc(κ) = 0.02·κ with a 0.95 level of confidence (k = 2).

Being highly sensitive to moisture, the investigated chlorides were carefully distilled directly in the measuring cell or in some cases they were loaded into the cell in a dry glovebox with a dry nitrogen atmosphere. Apparatus. The electrical conductivity measurements at high temperatures and pressures were performed in special hermetically sealed cells, entirely made of quartz glass; see Figure 1.

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RESULTS AND DISCUSSION Electrical Conductivity. BeCl2. The melting (Tm) and boiling temperatures (Tb) of BeCl2, according to different authors, lie in the range of (665 to 713) K and (747 to 828) K, respectively, and data on the critical point are unknown. Here according to ref 12, we assume that Tm = 688 and Tb = 760 K. The electrical conductivity of molten BeCl2 was measured in the range of (693 to 823) K. The results are listed in Table 2 and compared with the literature data in Figure 2. The conductivity rises about 20 times at heating and the vapor pressure in the cell changes from 0.018 MPa to about 0.34 MPa in this temperature range.17 The obtained results are in a good agreement with the Markov16 experimental data: at 690 K the difference is 3.7 % and at 740 K it is 1.4 %, respectively. The difference between our results and results provided by other authors13−15 is considerably greater. The obtained points lie below the points of data13 and15 by 72 and 49 %, respectively, and above the points of data14 by 51 % at 720 K. In comparison with the known “highesttemperature” conductivity measurements of molten BeCl2 by Delimarskii et al.,14 Tmax = 761 K the upper limit of measurements was extended by 62 K up to 823 K. Any further measurements at even higher temperatures were not performed because of the rapidly intensified interaction between the melt and the quartz walls of the conductometric cell. The conductivity polytherm of liquid BeCl2 obtained in the present work was approximated by a third power polynomial:

Figure 1. Quartz cell for the electrical conductivity measurements under elevated temperatures and saturated vapor pressures. 1, cutoff; 2, quartz tube; 3, molten salt; 4, quartz capillary; 5, carbon electrodes; 6, W current leads; 7, seal (rubber hose).

log(κ /S· cm−1) = − 99.4851 + 2.22426·105/T − 1.65245·108/T 2 + 3.97647·1010 /T 3

Electrodes were made of a “spectral purity” graphite, and a Wwire was used as current leads. One electrode was located inside the quartz capillary, and the second one semiencompassed the capillary. The inner diameter and the length of the measuring quartz capillary ranged within (1.0 to 2.5) mm and (1 to 20) mm, respectively, in dependence on the melt conductivity. A bottom part of the quartz capillary from (100 to 170) mm long, contained electrodes (5) and current leads (6) was sealed in order to obtain almost leak-tight junction. The cell was calibrated against the electrical conductivity κ of the molten ZnCl2, using the data11 (obtained by Bloom et al) as a standard. Their accuracy ur(κ) is ± 0.003. The molten NaCl, KCl, or their aqueous solutions could not be used because it was almost impossible to completely remove them from the cell. As the opposite of alkali chlorides, ZnCl2 is quite easily entirely

(1)

with the coefficient of determination R > 0.999, where κ is the electrical conductivity and T is the temperature, K. ZnCl2. According to ref 12, Tm(ZnCl2) = 591 K, Tb = 1004 K, the experimental data on the critical point are absent. The electrical conductivity of molten ZnCl2 is well studied at the temperatures below boiling point1,9,11,16−22 and remains almost unexplored at higher temperatures. In the present work for the first time the electrical conductivity of molten ZnCl2 was determined to the temperature as high as 1421 K when the vapor pressure above the melt reaches the value of about 3 MPa.17 The results are given in Table 3 and in Figure 3 along with some literature data. The points at the lowest temperatures correspond to the supercooled ZnCl2 melt. Having compared obtained 2

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Table 2. Electrical Conductivity of Molten BeCl2a T/K

κ·103/S·cm−1

T/K

κ·103/S·cm−1

T/K

κ·103/S·cm−1

T/K

κ·103/S·cm−1

693.15 695.15 698.65 701.65 705.65 711.65 714.65 719.65 721.65 724.65 726.15 728.15

0.7468 0.8045 0.8766 0.9611 1.073 1.321 1.430 1.646 1.743 1.864 1.932 2.016

735.65 738.15 739.65 741.65 744.65 746.15 747.15 750.15 752.15 755.15 759.65 761.15

2.526 2.703 2.876 2.974 3.266 3.352 3.484 3.755 3.981 4.367 4.545 4.875

763.15 765.15 766.35 767.35 770.15 772.85 775.15 777.65 781.65 783.65 786.15 787.15

5.050 5.311 5.446 5.720 6.095 6.355 6.700 7.069 7.305 7.626 8.243 8.360

788.15 790.15 793.15 795.15 795.65 797.15 801.65 807.65 809.65 822.65

8.512 8.866 9.348 9.542 9.660 10.06 10.86 11.64 11.85 13.92

Initial data. Uncertainties are u(t) = 1 K; ur(κ) = 0.01. The saturated vapor pressure of the salt varied from 5.0·10−3 to 0.34 MPa in the temperature range studied.17,31 a

Figure 3. Electrical conductivity polytherms of molten ZnCl2. The data represented in papers16,19,20 are not graphically shown because they merge with the demonstrated results. ●, experimental data of this work; ○, Bockris et al.;18 ▲, Grantham et al.;22 ■, Bloom et al.11

Figure 2. Electrical conductivity polytherms of molten BeCl2. ●, experimental data of this work; ■, Voigt et al.;13 ⧫, Delimarsky et al.;14 *, Ohmae et al.;15 ▲, Markov et al.16

results with those of Grantham and Yosim22 (Tmax = 1136 K), we extended the upper border of the measurements by 280 K. The electrical conductivity of ZnCl2 over the whole studied temperature range [(558 to 1421) K], including our earlier data9 related to lower temperatures, are well described by the general equation:

log(κ /S· cm−1) = 0.26654 + 381.67/T − 3.4064· 105/T 2 − 5.7406·108/T 3 ,

R2 > 0.9999.

(2)

Table 3. Electrical Conductivity of Molten ZnCl2a T/K

κ/S·cm−1

T/K

κ/S·cm−1

T/K

κ/S·cm−1

T/K

κ/S·cm−1

558.15 568.15 578.15 588.15 598.15 618.15 638.15 681.15 756.65 814.95 858.65 893.15 936.15 974.65 981.15

0.000363 0.000568 0.000874 0.001312 0.00179 0.0036 0.00646 0.01863 0.07134 0.1438 0.2190 0.2875 0.3881 0.4810 0.4977

1005.15 1030.15 1062.15 1078.15 1110.15 1128.15 1143.15 1163.15 1078.15 970.15 879.15 814.65 756.65 717.15 1092.15

0.5540 0.6142 0.6922 0.7348 0.8123 0.8569 0.8901 0.9355 0.7424 0.4696 0.2628 0.1445 0.0713 0.0393 0.7684

1100.15 1114.15 1131.15 1144.65 1167.15 1183.65 1195.65 1214.15 1225.15 1236.15 1245.65 1259.65 1279.65 1297.15 1306.15

0.7917 0.8277 0.8708 0.9033 0.9593 1.0000 1.0302 1.0739 1.1000 1.1259 1.1476 1.1783 1.2213 1.2571 1.2744

1316.65 1324.15 1341.65 1350.15 1359.65 1376.65 1386.65 1399.15 1406.15 1414.15 1421.15 739.15

1.2941 1.3083 1.3387 1.3522 1.3671 1.3933 1.4086 1.4230 1.4340 1.4439 1.4526 0.05573

Initial data. Uncertainties are u(t) = 1 K; ur(κ) = 0.01. The saturated vapor pressure of the salt varied from 4.2·10−7 to ∼ 3.0 MPa in the temperature range studied.17,31

a

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The electrical conductivity of molten ZnCl2 rises by almost 4 orders of magnitude as the temperature increases from (558 to 1421) K with a gradual slowdown of the rate of rise. PbCl2. The melting and boiling points of the lead chloride are reliably determined. According to ref 12, Tm(PbCl2) = 774 K, Tb = 1223 K, but no experimental data is provided for its critical point. Earlier, the electrical conductivity of molten PbCl2 was studied at the temperature as high as 1013 K.23 We extended the range to 1320 K (i.e., by 307 K). The vapor pressure at the maximum temperature is ∼ 0.24 MPa.17 Our results are presented in Table 4 and compared with the literature data in Figure 4.

d = AB−(1 − T / Tcr)

where d is the density of molten salt, A and B are constants, T is the temperature, K, and Tcr is the critical temperature, K. The constants A and B can be calculated using two known values of densities. The authors of refs 30 and 31 performed a comparative analysis of the accuracy of various equations for density calculations and found that eq 5 is the most precise; the uncertainty, ur(d), does not exceed 0.005, which is almost equal to the error of the experimental determination of density. The analysis was carried out using the density data on 150 inorganic compounds. Additional verification of eq 5 was performed using the data related to the density of molten BiCl3;32,33 see Figure 5. The

Table 4. Electrical Conductivity of Molten PbCl2a T/K

κ/S·cm−1

T/K

κ/S·cm−1

T/K

κ/S·cm−1

913.15 883.15 854.15 824.15 800.15 783.15 943.15

2.096 1.974 1.847 1.702 1.588 1.505 2.212

972.15 1001.15 1030.15 1058.15 1090.15 1118.15 1149.15

2.326 2.437 2.538 2.628 2.722 2.790 2.857

1177.15 1210.15 1230.15 1254.15 1279.15 1297.15 1320.15

2.917 2.982 3.023 3.086 3.147 3.184 3.211

(5)

a Initial data. Uncertainties are u(t) = 1 K; ur(κ) = 0.01. The saturated vapor pressure of the salt varied from 1.0·10−4 to 0.24 MPa in the temperature range studied.17,31

Figure 5. Density of molten BiCl3. The line is the extrapolation of the low temperature data on the BiCl3 density to high temperatures, up to the critical point. ■, Keneshea et al.;32 ▲, Johnson et al.;33 , extrapolation.

coefficients A and B in eq 5 were calculated using only the lowtemperature data,32 and then the extrapolation to the critical temperature was carried out. According to:32 d(BiCl3)/g· cm−3 = 5.0179 − 2.2· 10−3·T , ΔT = (523 to 723) K,

Figure 4. Electrical conductivity of molten PbCl2. The data given in works26−28 are not graphically identified as they merge with the presented results. ●, experimental data of this work; ■, Lantratov et al.;24 ⧫, Bell et al.;23 ▲, Easteal et al.25

log(κ /S· cm−1) = 0.55072 + 243.46/T − 3.6929· 105/T 2 R2 > 0.999.

(3)

Density Estimation. It is known that the density of the most molten salts is well described by the following linear equation:1 d = a + bT

(6)

The A and B constants (see eq 5) were calculated using the end points of the linear equation (d = 3.867 g·cm−3 at 523 K and d = 3.427 g·cm−3 at 723 K). The critical temperature Tcr(BiCl3) = 1178 K.33 The line in Figure 5 demonstrates the obtained results for BiCl3 in the full range of liquid state. The maximum difference from the experimental data reaches ± 3 % (in the vicinity of the critical temperature). At T < 1070 K the discrepancy is less than 1 %; that is, the uncertainty of calculated values does not exceed the experimental error. BeCl2. According to:1

The experimental points were approximated according to the following equation: − 3.9627·107 /T 3 ,

u(d) = 0.001 g· cm−3.

d(BeCl 2)/g· cm−3 = 2.26158 − 0.00108·T ,

(4)

ΔT = (706 to 746) K,

where d is the density of molten salt, a and b are constants, and T is the temperature, K. Such equations are convenient for small extrapolations. However, at temperatures near the boiling point and higher, the density of melts markedly deviates from the linear relationship to smaller values. The more precise Rackett’s equation was used to estimate the density of melts over a wide range of temperatures:29−31

ur(d) = 0.02

(7)

To calculate the molar conductivity these data should be extrapolated by 77 K, to the temperature of 823 K. Unfortunately, Tcr(BeCl2) is still unknown until now and should be evaluated in order to use eq 5. Virtually all methods for the critical temperature evaluation are based on its correlation with boiling temperature.31 Tcr = Tb/θ D

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where Tcr is the critical temperature, Tb is the boiling temperature, and θ is the reduced temperature at the boiling point 0.5 < θ < 0.7. To a first approximation, the critical temperature can be estimated by the Guldberg rule: Tcr = 1.5Tb. However, in many cases, it is an excessively rough approximation.31 The most precise estimation of Tcr is possible when at least three reliable values are available: the boiling temperature (Tb), the enthalpy of vaporization, and the molar volume of liquid at boiling temperature. The review on the methods for the Tcr evaluation is given in ref 31. All listed properties for BeCl2 are unreliable. That is why the following formula, which does not include unreliable parameters, was used to estimate BeCl2 reduced temperature:31,34 θ = 2 − exp(0.547 log M /M 0.265)

Figure 6 juxtaposes the results of density extrapolation using eqs 12 and 14. Lines derived using eq 5 deviate substantially from

(9)

where M/g·mol−1 is the molar mass of BeCl2. Substituting the values we get Tcr =

760 2 − exp

0.547 log(79.9182)

Figure 6. Density of molten ZnCl2. Black squares denote experimental data.1 Black line demonstrates the extrapolation of the experimental data1 using linear equation 12. Red line is the extrapolation of the experimental data1 by eq 5 taking Tcr(ZnCl2) = 1690 K (our estimation). Green line is the extrapolation of the experimental data by eq 5 taking Tcr(ZnCl2) = 1637 K.17 Blue line is the computed density of molten ZnCl2.35

= 1219 K (10)

0.265

79.9182

This value is in a good agreement with the calculated value of Tcr(BeCl2) = 1238 K, listed in the handbook.35 The A and B constants calculated by eq 5 using the end points of eq 7 resulted in eq 11, which is suitable for the evaluation of the molten BeCl2 density up to the critical temperature:

the straight-line extrapolation. At maximum temperature, the difference reaches about 7 %. At the same time, the difference between results extrapolated according to eq 5 using Tcr = 1690 (our data) and Tcr = 1637 K17 is small. The maximum difference is less than 1 %. Calculations for other salts also proved little effect of Tcr choice on the values of density. A large deviation of the data35 on the density of molten ZnCl2 from data1 is probably the result of an inadvertent error in the calculations. PbCl2. According to ref 1, the molten PbCl2 density

2/7

d(BeCl 2)/g· cm−3 = 0.41880· 0.19535−(1 − T /1219)

(11)

The maximum difference between the density estimations by eqs 7 and 11 does not exceed 0.36 % (at 823 K). The difference is considerably small because there is approximately 400 K to Tcr. Some uncertainty in the evaluation of the critical temperature [(1219 or 1238) K] has little effect on the result of density calculation, ur(d) ≈ 0.0003 at 823 K. Thus, eq 5 is, in the mathematical sense, highly stable relative to the choice of the value Tcr. The accuracy of eq 5 is specified by the accuracy of eq 7. According to ref 1, ur(d) = 0.02. ZnCl2. The handbook1 provides the equation for the molten ZnCl2 density calculation: d /g·cm

−3

d /g·cm−3 = 6.112 − 0.0015T , ur(d) = 0.005

= 2.8375 − 5.293· 10 T , ur(d) = 0.005.

(12)

To calculate the molar conductivity, eq 12 should be extrapolated to 1421 K, i.e., by 591 K. Since a fairly reliable ZnCl2 boiling temperature value (Tb(ZnCl2) = 1004 K12) is available, eq 13 was used to estimate the critical temperature, because according to ref 31, eq 13 is one of the most precise: Tcr = Tb + 0.89Tb0.2ψ + 0.92

2/7

d(PbCl 2)/g ·cm−3 = 1.3234 ·0.22102−(1 − T /2058) , ur(d) = 0.01

(13)

where ψ is the complexity factor of intermolecular interaction. For ZnCl2, ψ = 0.209.31 Substituting the values into equation, we get Tcr = 1690 K, which is 3 % higher than the value given by Yaws17 (1637 K). Using the end points of eq 12 (at T1 = 590 K, d1 = 2.525 g· cm−3; at T2 = 830 K, d2 = 2.398 g·cm−3) the parameters A and B in eq 5 were calculated. As a result, the eq 14 suitable for long extrapolations was obtained. d(ZnCl 2)/g·cm

−3

ur(d) = 0.015

= 1.1809·0.42346

(15)

The critical temperature and the density of molten PbCl2 to the temperature of 1320 K are estimated by the analogy to the ZnCl2 calculations. The critical temperature was estimated from eq 13, taking Tb(PbCl2) = 1223 K12 and ψ(PbCl2) = 0.214.31 We got Tcr = 2058 K, which is 3 % higher than the value calculated in ref 17 (1998 K). Using the end values of temperature in eq 15 to calculate the A and B coefficients (eq 5), the following expression was obtained:

−4

ΔT = (590 to 830) K,

ΔT = (789 to 983) K,

(16)

The difference between the density values obtained by extrapolation of linear eq 15 and eq 16 is 1.3 %, at 1320 K, see Figure 7. Uncertainty of the critical temperature (1998 or 2058) K, leads to a small error in the density calculation, maximum 0.16 % at 1320 K. Molar Conductivity. The molar conductivity (Λ) was calculated according to the common equation:

Λ = κMd −1

2/7

(17)

BeCl2. The results of the molten BeCl2 molar conductivity calculation are illustrated in Figure 8. The molar conductivity increases more than 20 times, from (0.0395 to 0.812) S·cm2·

−(1 − T /1690)

(14) E

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Figure 9. Molar conductivity of molten ZnCl2. Red line and circles, our data; blue line, Janz et al.;36 green line, Bloom et al.21

Figure 7. Density of molten PbCl2. Black squares denote experimental data.1 Black dashed line demonstrates the extrapolation of the experimental data1 using linear eq 15. Red line is the extrapolation of the experimental data1 with eq 5 taking Tcr(PbCl2) = 2058 K (our estimation). Blue line is the computed density of molten PbCl2.35

The combined expanded uncertainty Uc(Λ) = 0.05·Λ with the level of confidence 0.95 (k = 2). The obtained polytherm has no rectilinear sections (see Figure 9). In the temperature range studied, Λ increases by more than 5000 times, from 0.01946 (558 K) to 101.8 S·cm2·mol−1 (1421 K). PbCl2. The results of the molten PbCl2 molar conductivity calculation are illustrated in Figure 10. In the temperature range

Figure 8. Molar conductivity of molten BeCl2.

mol−1 in the temperature range studied. Numerical data are approximated by eq 18 2

Figure 10. Molar conductivity of molten PbCl2. , our data; ■, Janz et al.;36 ▲, Lantratov et al.24

−1

ln(Λ /S ·cm ·mol ) = −221.994 + +

4213569 2.60819·1010 − RT (RT )2

5.22406· 1013 (RT )3

studied, the PbCl2 molar conductivity increases only 1.78 times, from (123 to 219) S·cm2·mol−1. The numerical data are approximated by eq 20: ln(Λ /S ·cm 2·mol−1)

(18)

where R is the gas constant (8.31441 J·K−1·mol−1) and T is the temperature, K. The combined expanded uncertainty Uc(Λ) = 0.05·Λ with level of confidence 0.95 (k = 2). At T < Tb the dependence is close to linear. At higher temperatures, there are marked negative deviations from the Arrhenius equation. ZnCl2. Using our data on the electrical conductivity of molten ZnCl2 (see Table 3) and eq 14 for density the molar conductivity was calculated. The results are illustrated in Figure 9 and approximated by eq 19.

= 6.9163 −

24111 1.2163·108 4.5382·1011 + − 2 RT (RT ) (RT )3 (20)

The combined expanded uncertainty Uc(Λ) = 0.05·Λ with the level of confidence 0.95 (k = 2). For this melt our experimental data and literature data related to the molar conductivity almost coincide. The maximum difference does not exceed ± 0.4 %. In spite of the wide temperature range (537 K), the polytherm only slightly deviates from the Arrhenius equation. The line seems to be straight within the range of (100 to 200) K.

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ln(Λ /S ·cm 2·mol−1)

ACTIVATION ENERGY The activation energy it is the minimal energy which a particle should have to go from one equilibrium state to another state. Cations, anoins, and more complex particles take part in the

16274 7.8809·107 1.0155·1012 = 6.0508 − + − 2 RT (RT ) (RT )3 (19) F

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electricity transfer to different extents. That is why the activation energy calculated according to experimental data is the average effective value consisting of activation energies of all mechanisms of electrical conductivity. Mathematically, the activation energy is calculated as a slope ratio of electrical conductivity polytherm built in the coordinates ln(Λ) vs 1/RT.

EA = −

d ln(Λ) d

( RT1 )

. (21)

Obviously such a calculation is a slightly ambiguous procedure. The results depend on the calculation technique, particularly on the type of function that approximates the experimental points in the ln(Λ) vs. 1/T coordinates. For the estimation of the result stability, the calculations are performed with the use of several functions, for example, polynomials of different powers. The calculation procedure is demonstrated on the ZnCl2 example. ZnCl2. The expression for activation energy was derived by differentiation eq 19 with respect to (1/RT): EA /kJ·mol−1 = − 24111 + 2·1.2163·108 − 3·4.5382·1011

(1) RT

Figure 11. Activation energy of molar conductivity of molten BeCl2, ZnCl2, and PbCl2. Vertical bars indicate the melting and boiling points of these salts. Blue continuous line with squares and blue dashed lines demonstrate different estimations of molten BeCl2 activation energy at heating according to our data. Pink dashed line with open squares denotes molten BeCl2 activation energy at heating according to ref 16. Green line and triangles, ZnCl2; red line and circles, PbCl2.

1 RT

the approximation is performed using polynomials of second, third, and fourth powers, almost identical bell-shaped curves are formed. One of them is demonstrated by a blue dashed line in Figure 11. Then the activation energy near the melting point is equal to 119 kJ·mol−1 (693 K). EA increases up to 127 kJ·mol−1 as the temperature increases up to 725 K and then rapidly decreases to 63 kJ·mol−1 at 823 K. There is only one paper16 on the molten BeCl2 electric conductivity, which provides data that may be used to calculate the BeCl2 activation energy. The results of the EA calculations according to the data in ref 16 are presented in Figure 11 (pink dashed line with open squares). The curve also is bell-shaped, even though the EA values differ from our data. It should be noted that the numerical data were digitalized from a figure in ref 16 and therefore are not accurate. Thus, the form of the BeCl2 EA vs T curve has not been established. It remains unstudied whether the cupola is reproducible at cooling. Due to rapid quartz corrosion the temperature cycling was not carried out. PbCl2. The activation energy of this salt weakly depends on the temperature. When heated from (783 to 1320) K, EA decreases from (18.9 to 13.3) kJ·mol−1.

2

(22)

The same data on the ZnCl2 molar electrical conductivity were also approximated by polynomials of fourth and fifth power: ln(Λ /S ·cm 2·mol−1) = 7.9400 − +

73742 7.1248·108 4.0161·1012 + − RT (RT )2 (RT )3

5.1551·1015 (RT )4

(23)

ln(Λ /S ·cm 2·mol−1) = 5.1285 + −

31837 8.3152·108 6.9773·1012 − + RT (RT )2 (RT )3

3.2987·1016 5.1663·1019 + 4 (RT ) (RT )5

(24)

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Two more expressions for the activation energy were obtained by differentiation of these equations. Comparison of all three EA estimates showed that the maximal difference between them is not more than 0.05 %. Thus, in a mathematical sense, the result of EA calculations is very stable. Graphically, this result is shown as the green line in Figure 11. The activation energy decreases smoothly over the entire temperature range from 118 kJ·mol−1 at 558 K (supercooled liquid) to 25.5 kJ·mol−1 at 1433 K. BeCl2. The molar conductivity activation energy of molten BeCl2 was obtained by differentiation of eq 18 with respect to (1/ RT) in accordance with (21). In contrast to ZnCl2, two probable EA estimates were obtained here in dependence on the type of function chosen for approximation of initial data. If the points in the ln(Λ) vs 1/RT coordinates are approximated by a straight line, then nearly straight a little downward convex line is formed in the EA vs T coordinates; see Figure 11 (continuous line with squares). In this case, the activation energy smoothly decreases from (141 to 88) kJ·mol−1 in the studied temperature interval. If

DISCUSSION BeCl2. Molten beryllium dichloride is known37,38 to be strongly associated liquid. The BeCl2 melting is followed by a ∼ 25 % molar volume increase, and a rather viscous liquid37 with a low electrical conductivity less than 0.01 S·cm−1 is formed.37 High viscosity and low conductivity of the melt imply that the “chain” and “cluster” structures are neutral and have high molecular weight. To ensure neutrality it is necessary to terminate these structures with BeCl3 end units. The ending of the cluster structure could also be attained with BeCl3 units having one terminal chlorine and two others vertex linked to different BeCl4 tetrahedra of the same or different clusters.37,38 A smooth reduction of the activation energy signifies the cluster structure destruction with the formation of charged particles and separate ions. The clusters make the ion motion more difficult, however with increasing temperature the clusters are destructed and the electric conductivity activation energy decreases. G

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no big and stable complexes) and varies slightly with temperature (structure changes are minor).

According to ref 37, beryllium chloride has been known to display unusual structural properties making it distinct from many other MX2 salts such as MgX2, ZnX2, HgX2 (X is a halide anion), and others. Particularly with increasing temperature the “cluster” structures of the melt unfold to form “chains”. In addition, a part of ions becomes free, which leads to increasing electrical conductivity. The chain structure is assumed to offer greater resistance to the ion motion than the cluster structure and in the particular temperature range the activation energy increases despite temperature growth. The further temperature growth destroys all structure elements and electric conductivity activation energy rapidly decreases. The data presented in ref 16 qualitatively testify to the assumption that the molten BeCl2 conductivity activation energy curve has the maximum. Unfortunately, the BeCl2 conductivity is represented only as a figure and the calculations were performed using the points, obtained by the figure digitalization. The difference between the EA values obtained in the present work and the EA values computed according to data in ref 16 may be caused by the digitalization error. ZnCl2. Near the melting point liquid ZnCl2 has high viscosity (∼ 3.7 Pa·s;1 cf. water 10−3 Pa·s), low electrical conductivity (∼ 0.001 S·cm−1), and ionic diffusivity (∼ 1.2·10−7 cm2·s−1 39). Its network structure consists of ZnCl4/2 tetrahedra bound to each other by apex- and edge-bridged halides.40 The substructure of the melt is formed by mixing a variety of tetrahedra participating in “open”, “cluster”, and “chain” network structures, which are bound to each other by bridged halides. The boundaries of the substructure involve neutral or charged terminal halide bonds with zinc of the average 3-fold coordination. The temperature rise breaks up the substructure to smaller fragments, increases the number of terminal bonds, and rearranges the apex- and edgebridging network structures.40 This results in the growth of both the number of electricity carriers and their mobility. The electrical conductivity rapidly increases and activation energy decreases see Figures 3 and 11. The transition from strongly associated molecular liquid to completely ionic liquid is observed in the studied temperature range. The liquid ZnCl2 electrical conductivity increases from 0.019 S·cm2·mol−1 at 558 K to 102 S· cm2·mol−1 at 1421 K, i.e., to the values, which are typical for ionic melts. For comparison Λ(RbCl) = 93.9 and Λ(CsCl) = 94.1 S· cm2·mol−1 at 1073 K.41 At the highest temperatures the ions mobility continuously increases, but the electrical conductivity growth rate decreases (Figure 9). This indicates the increasing process of ions association into neutral molecules. The melt becomes more “gas-like”. The zinc vapors are known42 to be composed of linear Cl−Zn−Cl monomers. PbCl2. According to ref 43, the structural studies of molten PbCl2 are inconsistent. Even the results of the latest studies are contradictory. For instance, the XAFS analysis made in ref 43 resulted in the 4-fold coordination as the nearest interaction around Pb2+ ion. The nearest Pb2+−Cl− interaction consists of the 4-fold coordination and the additional loose 2 or 3 Cl− ions coordination in molten PbCl2. However, refs 44 and 45 describe 6-fold coordinated PbCl64‑ complexes. We assume that the discrepancy occurs because molten PbCl2 is a poorly associated liquid that is difficult for identification. The structure is so simple that no significant changes may occur at heating. This is proved by the nearly linear ln(Λ) vs 1/T dependence; see Figure 10. The temperature dependence of activation energy visually demonstrates the peculiarities of the structure; see Figure 11. The activation energy is small (there are

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CONCLUSIONS The cell for measuring an electrical conductivity of molten salts at temperatures as high as 1500 K and vapor pressures of salts up to several tens of atmospheres was designed. The electrical conductivity of the molten BeCl2, ZnCl2, and PbCl2 was measured at temperatures as high as 823, 1421, and 1320 K, respectively, which is by 62, 280, and 307 K higher than the temperature values previously achieved. The technique for the long density data extrapolation, which considered the nonlinear decrease in density at high temperatures (near and beyond boiling point), was proposed. The collection of data achieved in this work and literature data allows us to make some conclusions regarding the structural changes in the melts being studied with temperature. The structure of the molten PbCl2 was found to vary a little throughout the investigated temperature range. It is an entirely ionic melt. The ZnCl2 is a strongly associated liquid at temperatures close to Tm. When heated the associates are disintegrated, and the liquid becomes more and more ionic. However, at the maximal studied temperatures the increase of the electrical conductivity slows due to the rising of the inverse association of ions into molecules (ZnCl2). When heating, the structure of the molten BeCl2 changes in a complicated manner. This process requires further study.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/je500433d J. Chem. Eng. Data XXXX, XXX, XXX−XXX