Vapor Pressure Measurements for Metal Chloride Systems

by the Knudsen Effusion Method

Yanling Zhang, Etsuro Shibata, Eiki Kasai and Takashi Nakamura

Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, Sendai 980-8577, Japan

Thermodynamic knowledge of metal chlorides, such as vapor pressure and activity in salt/slag, are of remarkable industrial interest,particularly in fields related to the recovery/recycle/reuse of metal materials. In this study, a new apparatus for measuring the vapor pressure ofmetal chlorides from molten salt/slag was designed and tested with reference compounds. The results are in a good agreement with the availableliterature data. Using the developed apparatus, vapor pressure measurements for a KCl–NaCl–CaCl2 system have been performed. Using themeasured data the activities of components were obtained. Simultaneously, the activities of components were calculated using a thermodynamiccode, Factsage 5.2 wherein the Modified Quasi-chemical Model was employed to obtain the necessary thermodynamic parameters. The bothdata agree reasonably well with each other. The results suggested that the KCl–NaCl system exhibits similar behavior with ideal solution; whilein the KCl–CaCl2 and NaCl–CaCl2 systems there are possible interactions between CaCl2 and KCl/NaCl. For the ternary system KCl–NaCl–CaCl2, in some concentration range (mole fraction of NaCl 0.25–0.50) NaCl behaves as in an ideal solution, suggesting a larger affinity betweenKCl and CaCl2 than that between NaCl and CaCl2.

(Received March 1, 2005; Accepted April 21, 2005; Published June 15, 2005)

Keywords: vapor pressure measurement, metal chlorides, Knudsen effusion method, Modified Quasi-chemical Model

1. Introduction

The thermodynamic behaviors of metal chlorides are ofconsiderable industrial interest, particularly in fields relatedto the recovery/recycle/reuse of metal materials. Forexample, some basic knowledge, such as vapor pressuresand activities of metal chlorides in salt/slag, are very usefuland urgently needed during the recovery/recycling of metalsfrom wastes by high temperature processes; and the recoveryprocess of metals from their ores by chlorination. However,such basic information, particularly experimental data, israther limited, primarily because of operational difficulties.

There are several methods of determining the vaporpressure, e.g., static, boiling point, and transpiration. TheKnudsen method is a direct way and is particularlyappropriate in the case of pressures lower than 100 Pa.1,2)

Although it has still not been used for metal chlorides, it haslong been employed for the vapor pressure measurements ofcompounds.3–7)

In the present study, an apparatus was designed for themeasurement of the vapor pressure of metal chlorides fromsalt/slag systems by the Knudsen effusion method; it wasthen tested with reference compounds. The vapor pressure ofa KCl–NaCl–CaCl2 system was measured, thus obtaining theactivities of its components. Simultaneously, the activities ofcomponents were calculated using FactSage 5.2,8) whereinthe Modified Quasi-chemical Model9–12) was employed toobtain the necessary thermodynamic parameters. The calcu-lated activities of components agree reasonably well with theexperimental data.

2. Principle of the Knudsen Effusion Method

The theoretical basis of the Knudsen effusion method is thekinetic theory of gas. In the experiment, the sample iscontained in an inert cell provided with a small, thin orificeon the center of the lib, as shown in Fig. 1. The cell is placedin a high vacuum system at a constant temperature. If the

orifice is sufficiently small, an equilibrium condition ismaintained inside the cell. Hence, the amount of vaporeffusing through the orifice in a certain period of will bedetermined by the vapor pressure, temperature, molecularweight of vapor species, and the dimensions of the orifice.Equation (1) describes this relationship, which was derivedby Knudsen:13)

PK ¼1

KcA0

��W

t�

ffiffiffiffiffiffiffiffiffiffiffiffi2�RT

M

rð1Þ

where PK (Pa) is the vapor pressure near the orifice, A0 (m2)

is the area of the orifice,M (kg/mol) is the molecular mass ofthe effusing vapor, t (s) is the experimental time, �W (kg) isthe mass loss of the sample, T (K) is the temperature, R(8.314 J/mol�K) is the gas constant, and Kc is a coefficientrelated with the geometrical condition of the orifice,determined by its thickness L (m) and diameter d (m).2)

Equation (1) holds when there are no collisions betweenthe molecules either in the cell or near the orifice and whenthe escaped molecules do not disturb the equilibrium betweenthe vapor and the condensed phases. These conditions areestablished when the mean free path of the molecular � ,which is determined by the vapor pressure and temperature,is considerably larger than the diameter of the orifice d; and

D

H

d

L

Molecular effusion

Fig. 1 Scheme of Knudsen effusion cell.

Materials Transactions, Vol. 46, No. 6 (2005) pp. 1348 to 1353#2005 The Japan Institute of Metals

when the surface area of the condensed phase As issufficiently larger than the orifice area A0. It was reported

1,2)

that eq. (1) is accurate when �=d > 10 and A0=As < 100.The saturated vapor pressure of the sample Peq would be

higher than PK since the Knudsen cell is not actually anequilibrium system. While both Whitman14) and Motzfeldt15)

arrived at the conclusion that in a Knudsen cell of typicaldimensions (cylindrical shape wherein height equals diam-eter), if A0=As < 100, the saturated vapor pressure of thesample is very close to that near the orifice: Peq � PK.Moreover some researches3) indicated that in such geometricshapes of the Knudsen cell the experimental error is greatenough to mask the difference between Peq and PK. There-fore, this study used eq. (1) to evaluate the vapor pressure ofthe sample.

3. Experimental Condition and Theoretical Basis ofCalculation

3.1 SamplesKCl (Wako Pure Chem. Ltd., mass fraction 99.5%), NaCl

(Wako Pure Chem. Ltd., mass fraction 99.5%) and CaCl2(Wako Pure Chem. Ltd., mass fraction 99.5%) were used asreference compounds to test the apparatus. Different mixturesof these were used to measure the vapor pressures of a KCl–NaCl–CaCl2 system. All samples were in powdered state.

3.2 Apparatus and procedureThe schematic diagram of the apparatus is shown in Fig. 2.

A cylindrical cell made of pure platinum with equal heightand diameter (D ¼ H ¼ 10mm) was used. The cell consistsof two parts, i.e., upper and lower pans. The upper pan has anorifice and its diameter d is 0.07, 0.13, 0.20, or 0.30mm. Thesample powder was charged and compressed in a thin layeron the bottom of the lower pan. Then, the lips of the two panswere press-sealed and the cell was hung with the hook of thebalance by a platinum wire, which was set at the center of thereaction tube. The balance gives an accuracy of 0.01mg. Ahigh vacuum condition (� 10�2 Pa) was maintained by a

turbo molecular pump and a rotary pump, and the temper-ature of the sample was controlled by an electric furnace.Weight loss of the sample was continuously recorded by thedata system.

3.3 Analysis methodThe vapor pressure of pure chlorides can be obtained

directly using eq. (1). In the case of KCl–NaCl system, it wasassumed that the mixed condensed and vapor phases exhibitthe same behavior with ideal solution and ideal gas,respectively, since they have similar molecule structuresand vapor pressure values. Therefore, the composition andmolecular weight of the vapor could be estimated by eqs. (2)and (3):

NvKCl

NvNaCl

¼NcKCl

NcNaCl

�P0KCl

P0NaCl

ð2Þ

Mv ¼MKCl � Nc

KCl � P0KCl þMNaCl � Nc

NaCl � P0NaCl

NcKCl � P0

KCl þ NcNaCl � P0

NaCl

ð3Þ

where NcKCl, N

cNaCl, N

vKCl, N

vNaCl are the mole fractions of KCl

and NaCl in condensed and vapor phases, respectively, andP0KCl, P

0NaCl are the vapor pressures of pure KCl and NaCl,

respectively. Mv is the molecular mass of the vapor; MKCl,MNaCl are the molecular mass of KCl and NaCl, respectively.After the experiment, the total vapor pressure of the samplewas obtained by using its weight loss at a controlledtemperature and combining eqs. (1) and (3).

For KCl–CaCl2, NaCl–CaCl2, and KCl–NaCl–CaCl2systems, after the experiment, the compositions of K andNa were analyzed by ICP (inductively coupled plasma),based on which the weight loss of KCl and NaCl werecalculated. Then, their partial vapor pressures and activitiesin the system could be obtained by using eq. (1). However inthe case of CaCl2, the weight loss of CaCl2 could not bedetected because of its extremely low vapor pressure (0.05–0.18 Pa) at the experimental temperature (1073–1103K) andthe ICP analysis error. Therefore, it is very difficult to obtainthe partial vapor pressure and activity of CaCl2 in the presentstudy.

3.4 Thermodynamic model for solutionsIn addition to experimental measurements, the activities of

components in the chloride systems of KCl–CaCl2, NaCl–CaCl2, and KCl–NaCl–CaCl2 were calculated using FactS-age 5.2,8) wherein the Modified Quasi-chemical Model wasemployed to obtain the necessary thermodynamic parame-ters. The theory of the Modified Quasi-chemical Model forsolution was proposed by Pelton et al. and described in detailin the literatures.9–12) In this paper, a brief introduction of themodel is presented as follows. The parameters of the modelare the Gibbs energy change �gAB/Cl of the pair change forthe following pair-exchange reactions:

(A-Cl-A)pair þ (B-Cl-B)pair ¼ 2(A-Cl-B)pair ð4Þ

As �gAB/Cl becomes more negative, reaction (4) is shiftedto the right, (A-Cl-B) pairs dominate, and the solutionbecomes progressively more ordered. The �gAB/Cl approx-imately corresponds to the excess free energy of the solution.

For example, XKCa is the mole fraction of the second-

11

1. Balance2. High vacuum room3. Water cooling4. Knudsen cell

5.Thermal couple6. Electric furnace7. Turbo molecular pump8. Rotary pump

9. Temperature controller10. Data system11. Reaction tube

21

87

3

3

4

6

910

5

Fig. 2 Apparatus schematic for Knudsen effusion method.

Vapor Pressure Measurements for Metal Chloride Systems by the Knudsen Effusion Method 1349

nearest-neighbor (K–Cl–Ca) pairs, and the model alsorequires definitions of the cation-cation coordination num-bers Zi

i j for all binary subsystems. The coordination numberschosen in this study based on the literature16) are listed inTable 1. For example, the choice of ZK

KCa ¼ 1=2ZCaKCa ensures

that the composition of the maximum short-range orderingwill approximate the K2CaCl4 composition, wherein themolar enthalpy and entropy of mixing for the system assumethe lowest values. The mole fractions of KCl and CaCl2 in thebinary solution can be derived using the coordinationnumbers XKCa, XKK, and XCaCa.

9–12) As described in detailin the literatures,9–12) it is necessary to geometrically defineall ternary systems as either ‘‘symmetric’’ or ‘‘asymmetric’’.In the present case, the systems with one alkali-earth and twoalkali chlorides are asymmetric, with the alkali-earth chlorideas the asymmetric component.

Through optimization with available experimental data,the parameters �gAB/Cl of reaction (4) are expanded for eachpair (K–Cl–Na, K–Cl–Ca and Na–Cl–Ca) as empiricalpolynomials in molar fractions Xij.

16) The equations of�gAB/Cl for each pair are shown in Table 2. Ternary excessparameters for the solution were not required for the ternarysystem of KCl–NaCl–CaCl2. Table 3 lists all thermodynamicdata (H�

298.15K, S�298.15K, and Cp) for the pure liquids of the

KCl–NaCl–CaCl2 system.17,18)

4. Results and Discussion

4.1 Reliability of the apparatusThe vapor pressures of the reference compounds KCl,

NaCl, and CaCl2 were measured at 873–1023K, 913–1023Kand 1273–1353K, respectively. This is because under suchtemperature conditions, their vapor pressure values fall in therange of 0.1–50 Pa, in which the Knuden effusion method ismore accurate. The experimental temperature range for the

further measurements of the KCl–NaCl–CaCl2 system wasselected in a similar manner.

The comparisons between the experimental and referencedata for the vapor pressures of KCl, NaCl, and CaCl2 areshown in Figs. 3, 4, and 5, respectively. There are reasonableagreements between the data for KCl and NaCl (shown inFigs. 3 and 4). Although most of the experimental data fallwithin the range of reference values, some deviation isobserved in the case of CaCl2. This might be due to the

Table 1 Cation-cation coordination numbers of the solution.

i j Zii j Z

ji j

Na K 6 6

Na Ca 4 6

K Ca 3 6

Table 2 Gibbs energy change of the pair change for the pair-exchange reactions.

Binary System (A-Cl-B) �gAB/Cl (J/mol)

NaCl–KCl �gNaK/Cl ¼ �695:5� 67:0XNaNa=ðXKK þ XNaK þ XKKÞ

NaCl–CaCl2�gNaCa/Cl ¼ �4710:2þ 0:7805T þ ð�1347:8þ 0:5726TÞXNaNaþ

ð�1580:0þ 0:1473TÞXCaCa

KCl–CaCl2 �gKCa/Cl ¼ �12281:0þ 3:9706T � 852:56XKK � 5930:6XCaCa

Table 3 Thermodynamic properties of pure liquids.16;17Þ

Temperature range

(T/K)

H�298.15K

(J/mol)

S�298.15K(J/molK)

Cp

(J/molK)

NaCl17Þ298.15 to 1500 �394956:0 76.0761 77:7638� 0:0075312T

1500 to 2000 �390090:1 84.5055 66.9440

KCl17Þ 298.15 to 2500 �421824:9 86.5225 73.5966

CaCl218Þ 660 to 2500 �606887:4 117.2971 92.0480

1000 (K/T)

-2

-1

0

1

2

3

4

5

6

7

0.8 0.9 1 1.1 1.2

this study

by Kubaschewski19)

ln (

p/Pa

)

Fig. 3 Vapor pressures of KCl.

-4

-3

-2

-1

0

1

2

3

4

5

0.9 1 1.1 1.2 1.3

this study

by I.Barin20)

ln (

p/Pa

)

1000 (K/T)

Fig. 4 Vapor pressures of NaCl.

1350 Y. Zhang, E. Shibata, E. Kasai and T. Nakamura

handling difficulty caused by the strong deliquescent prop-erty of CaCl2, despite its preparation in a glove box filledwith Ar. However, the results reveal that this apparatus issuitable for measuring the saturated vapor pressures ofsubstances at high temperatures.

4.2 Measurement for the KCl–NaCl–CaCl2 system4.2.1 KCl–NaCl

Samples of KCl:NaCl = 0.2:0.8, 0.5:0.5, and 0.8:0.2 (inmolar fractions) were prepared, and the measurements were

performed from 963 to 1003K. Figure 6 shows the measuredresults, wherein the line is the relation between the vaporpressures of pure KCl and NaCl. As evident, at lowertemperatures the points representing the total vapor pressureof the KCl–NaCl system mostly lie on the line, whichsuggests that the total vapor pressure could be estimated byeq. (5):

Pt ¼ P0KCl � N

cKCl þ P0

NaCl � NcNaCl ð5Þ

where Pt (Pa) is the total pressure of the KCl–NaCl system.Further, it proves that the condensed and vapor phases of theKCl–NaCl system exhibit same behavior with ideal solutionand ideal gas, respectively. The deviation from the lineincreases with increasing temperature. This could be ex-plained by the fact that the experiment was conducted fromlow to high temperatures, during which the composition ofthe sample changed continuously. The concentration of KCldecreased becauae its vapor pressure was slightly higher thanthat of NaCl. This led to a decrease in the total vapor pressureof the sample.4.2.2 KCl–CaCl2

The experimental situation and the measured results of thepartial vapor pressure and activity of KCl in the KCl–CaCl2system are shown in Table 4, along with the calculatedactivity of KCl obtained using Factsage 5.2, wherein thenecessary thermodynamic parameter was obtained from theabove mentioned Modified Quasi chemical Model. Figure 7shows the comparison at 1073K. As evident, the datameasured using this apparatus agree reasonably well with thecalculation result. The activities of KCl showed a negativedeviation from Raoult’s Law, which suggests a possibleinteraction between KCl and CaCl2.4.2.3 NaCl–CaCl2

Table 5 showes the experimental condition and themeasured results of the partial vapor pressure and activityof NaCl in the NaCl–CaCl2 system, along with the caculatedactivity of NaCl using Factsage 5.2, in a manner similar to theKCl–CaCl2 system. Figure 8 shows the comparison at1073K. There is a reasonable agreement between theexperimental and calculated results. The activities of NaClshowed a negative deviation from Raoult’s Law, which alsosuggests a possible interaction between NaCl and CaCl2.

0

1

2

3

4

0.7 0.75 0.8 0.85

this study

by Kubaschewski19)

ln(p

/Pa)

1000 (K/T)

Fig. 5 Vapor pressures of CaCl2.

0.2 0.4 0.6 0.8 1.00

5

10

15

20

25

30

0

963K

973K

983K

993K

1003K

Mole fraction of KCl in the KCl-NaCl system

Vap

or p

ress

ures

of

the

KC

l-N

aCl

syst

em (

p/Pa

)

Fig. 6 Vapor pressures of the KCl–NaCl system.

Table 4 The experimental and calculated data on partial vapor pressure and activity of KCl in the KCl–CaCl2 system.

Experimental resultsCaculation

dataSample compositon,

mole fraction

Temperature

(T/K) Partial vapor

pressure of

KCl (p/Pa)

Activity of

KCl

Activity of

KCl

1073 13.07 0.14 0.05

0.25KCl+0.75CaCl2 1103 16.98 0.11 —

1123 43.06 0.19 0.06

1073 25.45 0.27 0.23

0.50KCl+0.50CaCl2 1103 37.98 0.24 —

1123 83.61 0.37 0.24

1073 62.10 0.67 0.61

0.75KCl+0.25CaCl2 1103 113.71 0.71 —

1123 138.70 0.61 0.62

Vapor Pressure Measurements for Metal Chloride Systems by the Knudsen Effusion Method 1351

4.2.4 KCl–NaCl–CaCl2Table 6 shows the measured data of partial vapor pressures

and activities of KCl and NaCl in the KCl–NaCl–CaCl2system, along with the calculated results obtained usingFactsage 5.2. Figure 9 shows the comparison between theexperimental and calculated data on the activities of KCl andNaCl in a 0.25CaCl2–NaCl–KCl system at 1073K. As

evident, they agreed well with each other. As compared toNaCl, KCl shows a larger negative deviation from Raoult’sLaw, and in some concentration scopes (mole fraction 0.25–0.50), the activity coefficient of NaCl is approximately l.0,which suggests that NaCl behaves as in an ideal solution.This suggests that there is a stronger affinity between KCl andCaCl2 than that between NaCl and CaCl2.

0.2 0.4 0.6 0.8 1.000

0.1

0.2

0.3

0.4

0.5

0.7

0.8

0.9

1.0

Experimental data

Calculation result

0.6

Mole fraction of NaCl in the NaCl-CaCl2 system

Act

ivity

of

NaC

l

Fig. 8 Activity of NaCl in the NaCl–CaCl2 system at 1073K.

Table 6 The experimental and calculated data on partial vapor pressures and activities of KCl and NaCl in the KCl–NaCl–CaCl2 system.

Sample composition,

mole fraction

Temperature

(T/K)

Experimental resultCaculation

data

Partial vapor

pressure (p/Pa)Activity Activity

KCl NaCl KCl NaCl KCl NaCl

1073 12.92 13.12 0.14 0.19 0.10 0.20

0.50CaCl2+0.25NaCl+0.25KCl 1103 31.10 19.41 0.09 0.13 — —

1123 34.62 27.75 0.15 0.18 0.10 0.20

1073 41.44 18.57 0.44 0.27 0.35 0.25

0.50KCl+0.25CaCl2+0.25NaCl 1103 64.75 17.55 0.40 0.15 — —

1123 87.93 41.42 0.39 0.26 0.36 0.25

1073 9.35 33.47 0.10 0.49 0.16 0.47

0.50NaCl+0.25CaCl2+0.25KCl 1103 20.52 51.39 0.13 0.45 — —

1123 37.08 60.89 0.16 0.39 0.16 0.47

Table 5 The experimental and calculated data on partial vapor pressure and activity of NaCl in a NaCl–CaCl2 system.

Experimental resultsCaculation

dataSample compositon,

mole fraction

Temperature

(T/K) Partial vapor

pressure of

NaCl (p/Pa)

Activity of

NaCl

Activity of

NaCl

1073 7.32 0.11 0.12

0.25NaCl+0.75CaCl2 1103 20.01 0.18 —

1123 28.53 0.18 0.12

1073 24.45 0.36 0.34

0.50NaCl+0.50CaCl2 1103 55.24 0.48 —

1123 66.22 0.42 0.35

1073 45.01 0.66 0.67

0.75NaCl+0.25CaCl2 1103 81.15 0.71 —

1123 109.76 0.70 0.67

Mole fraction of KCl in KCl-CaCl2 system

0.2 0.4 0.6 0.8 1.0

0

0.1

0.2

0.4

0.5

0.6

0.7

0.9

1.0

Experimental data

Calculation result

0.8

0.3

0

Act

ivity

of

KC

l

Fig. 7 Activity of KCl in the KCl–CaCl2 system at 1073K.

1352 Y. Zhang, E. Shibata, E. Kasai and T. Nakamura

5. Conclusion

The testing results indicated that the present apparatusis suitable for detecting the vapor pressures of metalchlorides. The vapor pressures of the KCl–NaCl–CaCl2systems were measured, and the results agree reasonablywell with the calculation data obtained using Factsage 5.2.For the KCl–NaCl system, the results suggested that itscondensed and vapor phases exihibit similar behaviorswith ideal solution and ideal gas, respectively. In the KCl–CaCl2 and NaCl–CaCl2 systems, the activitis of KCl/NaClshowed negative deviations from Raoult’s Law, whichsuggested possible interactions between KCl and NaCl withCaCl2. In the ternary system, KCl–NaCl–CaCl2, the activityof KCl showed a larger negative deviation from Raoult’sLaw than that of NaCl, and in some concentration range(mole fraction 0.25–0.50), NaCl behaves as in an idealsolution (the activity coefficient is approximately 1.0), which

suggests a greater affinity between KCl and CaCl2 thanbetween NaCl and CaCl2.

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Act

ivity

Mole fraction

0.15 0.3 0.45 0.6 0.75

0.15

0

0.3

0.45

0.6

0.75

0

NaCl KCl

NaCl

KCl

Fig. 9 Activities of KCl and NaCl in the 0.25CaCl2–KCl–NaCl system at

1073K.

Vapor Pressure Measurements for Metal Chloride Systems by the Knudsen Effusion Method 1353