Standard free energy of formation of calcium chromate

Materials Science and Engineering A 437 (2006) 334–339

Standard free energy of formation of calcium chromate Yong M. Lee ∗ , Claudia. L. Nassaralla Vesuvius Research, 4604 Campbells Run Road, Pittsburgh, PA 15205, United States Received 9 May 2006; received in revised form 21 July 2006; accepted 3 August 2006

Abstract The standard free energy of CaCrO4 was determined by solid/gas equilibrium and assessed. The thermodynamic properties of CaCrO4 are determined as ◦ HfCaCrO (298 K) = 1402 ± 10 kJ/mol; 4

◦ SCaCrO (298 K) = 130.9 ± 1.9 J/mol K. 4

© 2006 Elsevier B.V. All rights reserved. Keywords: Calcium chromate; Chromite; Standard free energy; Thermodynamics

1. Introduction Calcium chromate, CaCrO4 , is the stable Cr(VI) containing compound formed from ␤-CaCr2 O4 below 1073 ◦ C in air. The phase diagrams of the Ca–Cr–O system under oxidizing conditions available in the literature have several discrepancies below ∼1200 ◦ C [1–6]. The equilibrium temperatures for the reactions of Cr(VI) containing compounds are not consistent because they are affected by oxygen partial pressures. The stability limits for CaCrO4 are also different in the literature [3–6]. Because of the inconsistencies apparent in the CaO–Cr2 O3 system in air, it is important to obtain reliable thermodynamic data which will allow for the prediction of formation of CaCrO4 at given temperatures and oxygen pressures. CaCrO4 is a major Cr(VI) compound present in spent magnesite-chrome refractory and chromium oxide containing steelmaking slags [7,8]. The knowledge of more accurate formation temperature and the stability limit of CaCrO4 would allow refractory producers and steelmakers to design their operations to minimize or avoid the formation of Cr(VI) during the cooling steps of their processes. Several attempts have been made to measure the standard free energy of CaCrO4 at temperatures ranging from 700 to 1300 K [9–13]. Typical experimental method has been the solid-tate electrochemical galvanic cell: Pt, O2 ∗

Corresponding author. Fax: +1 412 787 5718. E-mail address: [email protected] (Y.M. Lee).

0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.08.010

|CaO + CaF2 ||CaF2 ||CaF2 + Cr2 O3 + CaCrO4 | O2 , Pt under oxygen partial pressures varying from 0.1 to 1 atm. The overallchemical reaction taking place is CaO(s) + 1/2Cr2 O3 (s) + 3/4O2 (g) = CaCrO4 (s)

(1)

In a separate experiment, Havlica used the solid–gas equilibrium technique to measure the equilibrium oxygen pressures in CaCrO4 , Cr2 O3 , and ␤-CaCr2 O4 at 700–1300 K and determine the standard free energy for the reaction 4/3CaCrO4 + 2/3Cr2 O3 = 4/3␤-CaCr2 O4 + O2 . A summary of these investigations is shown in Table 1. Havlica’s experimental results are converted to the corresponding standard free energies of reaction (1) for the purpose of comparison. The G◦ values for CaCrO4 are rather scattered from one set of measurements to another. The values of G◦ obtained by Azad et al. are about 38% greater than those obtained by Havlica et al. The discrepancies may result from several experimental complications in high temperature equilibriums with the varied oxygen pressures. Among the most critical of these are maintaining the stability and the reversibility of an EMF. The goal of this work is to determine the standard free energy of CaCrO4 using the gas–solid equilibrium technique with thermogravimetric analysis and to assess the existing thermodynamic data for CaCrO4 . The experiments were designed to determine the stable phase(s) present in the final product when pure CaCrO4 , CaO and ␤-CaCr2 O4 are equilibrated under a fixed oxygen partial pressure at a given temperature.

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Table 1 Summary of the standard free energy data from previous investigations: CaO(s) + 1/2Cr2 O3 (s) + 3/4O2 (g) = CaCrO4 (s) Method

Temperature range (K)

G◦ (J/mol)

References

EMF Solid/gas EMF EMF EMF

873–1073 700–1300 1000–1200 870–1100 788–1070

−176340 + 86T −230711 + 122.75T −177100 + 93.1T −219250 + 121.76T −166440 + 88.21T

[9] [10] [11] [12] [13]

2. Experimental procedures 2.1. Preparation of CaCrO4 and β-CaCr2 O4 + CaO The CaO was obtained from calcination of CaCO3 at 950 ◦ C for 6 h. A 2:1 mole ratio of CaO and Cr2 O3 were homogenized by a mixer and heated in an MgO crucible at 850 ◦ C under air for 30 days to prepare CaCrO4 . CaCrO4 was characterized by XRD. Mixtures of ␤-CaCr2 O4 + CaO were prepared from CaCrO4 by the reducing CaCrO4 to ␤-CaCr2 O4 + CaO at 850 ◦ C for 12 h with a mixture of Ar and CO, then heated at 1400 ◦ C under Ar for 24 h, and finally quenched using liquid nitrogen to avoid the formation of Cr(VI) during cooling. The final product was identified as a mixture of ␤-CaCr2 O4 + CaO by XRD. The mixture of ␤-CaCr2 O4 + CaO was used as a starting material for thermogravimetric analysis. 2.2. Thermogravimetric analysis The experimental setup for thermogravimetric analysis is shown in Fig. 1. A quartz tube (outer diameter 5 cm, length 120 cm) was used as a reaction tube. A magnesia crucible containing the specimen was suspended by Pt wire and attached to an analytical balance interfaced with a computer to

Fig. 2. Formation of CaCrO4 as a function of time.

continuously monitor the weight change of the specimen. The analytical balance (Mettler AT20) was used and its specification is 22 g weighing capacity with 2 ␮g readability. The specimen containing the mixtures of ␤-CaCr2 O4 + CaO was rapidly heated to the desired temperature under low partial oxygen pressures. Upon reaching the desired temperature, a gas mixture (O2 /Ar) was introduced into the reaction tube to maintain the predetermined partial oxygen pressure. The major difference from the previous work was the use of a gas mixture of O2 /Ar instead of CO2 /CO [10]. The partial oxygen pressure was varied by changing the ratio of the precertified gas mixture (50 or 900 ppm O2 in Ar) to Ar (99.999%). The error from one mass flow controller was within 1% of full flow. The error of K type thermocouple was within 1%. The total error range in thermogravimetric analysis is estimated as 3%. The partial oxygen pressure was increased incrementally and the samples were equilibrated at given oxygen pressures for 4–24 h. Once the partial oxygen pressure exceeded beyond the equilibrium partial oxygen pressure at a given temperature, the mixture of ␤-CaCr2 O4 + CaO began to oxidize to CaCrO4 and the weight of the specimen increased. When the weight of the specimen stabilized, the furnace was lowered, and the specimen in the reaction tube was cooled rapidly using an electrical fan. The specimen was then taken and analyzed by XRD to identify the phases present. Typical formation of CaCrO4 is shown in Fig. 2. No multiple steps were observed, showing no metastable phases during formation of CaCrO4 . 3. Results The standard free energy change for reaction (2) is expressed in Eq. (3): 1/2CaO(s) + 1/2␤-CaCr2 O4 (s) + 3/4O2 (g) = CaCrO4 (s)

Fig. 1. Experimental set-up for thermal gravimetric analysis.

(2)

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Table 2 Stable phases at different temperatures and oxygen partial pressures Temperature (◦ C)

log PO2

Stable phases

764 784 785 807 810 836

−5.240 −5.003 −4.960 −4.770 −4.810 −4.365

CaO + ␤CaCr2 O4

764 784 785 807 810 836

−5.220 −4.870 −4.900 −4.700 −4.770 −4.318

CaCrO4

G◦ = −RT ln

aCaCrO4 1/2 1/2 3/4 aCaO aCaCr2 O4 PO2

(3)

where ai is activity for compound i and PO2 is oxygen partial pressure of the system. When using pure CaO, ␤-CaCr2 O4 , and CaCrO4 , their activities in Eq. (3) are equal to one. The standard free energy change is expressed only as a function of temperature and oxygen pressure, as shown in Eq. (4): G◦ =

3 RT ln(PO2 ) 4

(4) is valid over a temperature range of 1037–1109 K:

The results of equilibrium experiments in controlled oxygen pressures at a given temperature are shown in Table 2. Typical XRD patterns for a final product containing CaCrO4 and a final product containing CaO + ␤-CaCr2 O4 are shown in Fig. 3. Using the results in Table 2, oxygen partial pressure is plotted as a function of temperature as shown in Fig. 4. Equilibrium oxygen partial pressure as a function of temperature is obtained by linear regression and expressed in Eq. (5): log PO2 (atm) = 7.6 −

Fig. 4. Effect of temperature and oxygen partial pressure on the stability of CaO, ␤-CaCr2 O4 , and CaCrO4 (top x-axis is temperature (K) and bottom x-axis is inverse temperature).

13, 317 T

(5)

The standard free energy change of reaction (2) can be expressed as a function of temperature using Eqs. (4) and (5), and is shown as Eq. (6). This experimentally obtained expression for the standard free energy change (G◦ ) for reaction (2)

Fig. 3. XRD patterns showing the different phases in the final product after experimental run: (a) CaCrO4 and (b) CaO + ␤-CaCr2 O4 , where the phases are H (CaCrO4 ), L (CaO), and ␤ (␤-CaCr2 O4 ).

1/2CaO(s) + 1/2β-CaCr2 O4 (s) + 3/4O2 (g) = CaCrO4 (s) G◦ = −191, 250 + 109T (J/mol)

(6)

4. Discussions 4.1. Thermodynamic properties related to the formation of CaCrO4 To assess the reliability of the expression for the standard free energy change obtained in this work, it is necessary to obtain the reliable thermodynamic properties related to the formation of CaCrO4 . The thermodynamic properties of CaO, O2 , and Cr2 O3 are relatively well known [18,19]. The thermodynamic data of ␤-CaCr2 O4 in the literature are summarized in Table 3. The third law evaluation was performed to evaluate the thermodynamic data of ␤-CaCr2 O4 available in the literature. The third law evaluation provides more reliable temperature coefficient values of free energy. Once the reliable temperature coefficient is determined, the corresponding heat of reaction can be also obtained. The evaluation procedure is well introduced [19]. The entropy values at 298 K from Jacob, Kovba, and Havlica were within the range of 6.3%. Havlica’s entropy value was very close to Richter’s calculated value. In general, the calculated entropies of oxide compounds at 298 K are in good agreement with the spectroscopic or calorimetric measurements [19]. Therefore, Havlica’s data for ␤-CaCr2 O4 is used to evaluate the thermodynamic data of CaCrO4 in Sections 4.2 and 4.3.

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Table 3 Standard free energy change data: CaO(s) + Cr2 O3 (s) = ␤-CaCr2 O4 (s) T (K)

T (K)

G◦ (J/mol)

◦ S␤-CaCr (298 K) (J/mol K) 2 O4

References

1260 1828 1400 1723 –

1050–1475 1743–1913 1250–1550 1473–1973 –

−60970 − 11.29T (±350) −218330 + 89.69T (±750) −61700 − 13.5T (±280) −55439 − 5.40T (±800) –

131.1 30.5 133.3 125.4 124.2

[12] [14] [15] [17] [16]

Table 4 Thermodynamic properties related to the formation of CaCrO4 ◦ H298 K (kJ/mol)

CaO ␤-CaCr2 O4 Cr2 O3 O2 CaCrO4

−634.9 ± 0.8 −1829.663 ± 8.3 −1134.7 ± 7.5 0 −1396.3 ± 17.2

S298 K (J/mol K)

38.1 125.2 81.2 205.1 130.9

± ± ± ± ±

0.3 0.4 1.3 0.5 1.9

Cp = a + b(10−3 )T + c(106 )/T2 + d(10−6 )T2 (J/mol K) a

b

c

d

50.42 169.66 109.65 29.15 127.92

4.18 13.26 15.46 6.48 35.73

−0.85 −2.40 – −0.18 −2.26

– – – −1.02 –

All thermodynamic properties related to CaCrO4 are shown in Table 4. The specific heat of CaCrO4 from 54.6 to 301.3 K was measured by the vacuum adiabatic calorimeter to yield valuable information for entropy and specific heat at 298 K [24]. The differential scanning calorimeter was used to measure and assess the specific heats of CaCrO4 as a function of temperature [25]. The standard enthalpies of CaCrO4 at 298 K available in the literature are estimated values and their values will be assessed in Sections 4.2 and 4.3 [20–22]. In order to compare the current work with results in the literature, the standard free energy for reaction (2) needs to be converted to reaction (1). The conversion of reaction (2) into reaction (1) can be obtained by using Hess’s law, i.e., by adding reaction (2) and its standard free energy change expression to Eq. (7):

References

[18,19] [17–19] [18,19] [18,19] [20–25]

of entropies instead of obtaining the entropies from the temperature coefficient. The goal of this section is to assess the entropy and enthalpy of reaction (1). The calorimetric measured entropy of CaCrO4 , 130.9 ± 1.9 J/mol K at 298 K, was used to calculate the value of entropy at the average temperature for each measurement. This type of assessment is called the third law evaluation. The third law evaluation shows that Kovba’s temperature coefficient is in good agreement with the calculated value of entropy at the average temperature. The assessment of the enthalpy values was performed in the following. By combining ST with the experimental value of GT at the same temperature, the values for the enthalpy change (HT ) can be calculated. Using HT and heat capacity, the stan◦ dard enthalpy change for reaction (1) at 298 K (H298 K ) can be

1/2CaO(s) + 1/2Cr 2 O3 (s) = 1/2␤-CaCr 2 O4 (s) G = −27, 720 − 2.70T (J/mol)

(7)

The comparison among the standard free energy changes of CaCrO4 for reaction (1) is shown in Fig. 5. The results are rather scattered, which is mainly due to the complexity of equilibrium experiments affected by temperatures and oxygen partial pressures. The variation in data requires the further study to obtain the accurate thermodynamic standard values. Assessment will be discussed in Sections 4.2 and 4.3. 4.2. Second/third law evaluation of standard free energy of calcium chromate The entropy values of free energy measurements depend on temperature coefficients. However, temperature coefficients obtained from free energy measurements are scattered within about 40% error range from one measurement to another, as shown in Table 5. Therefore, it is safer to combine the measured free energy values with the calorimetric or spectroscopic values

Fig. 5. Comparison among standard free energy changes for CaO(s) + 1/2Cr2 O3 (s) + 3/4O2 (g) = CaCrO4 (s) obtained in this work and previous values available in the literature.

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Table 5 The standard enthalpy changes at 298 K for the reaction: CaO(s) + 1/2Cr2 O3 (s) + 3/4O2 (g) = CaCrO4 (s) ◦ c H298 K (kJ/mol)

GT (J/mol)

T (K)

ST a (J/mol K)

GT (kJ/mol)

HT b (kJ/mol)

Prasad Havlica Kovba Jacob Azad This work

−176340 + 86T −230711 + 122.75T −177100 + 93.1T −219,250 + 121.76T −166440 + 88.21T −218970 + 106.3T

973 1000 1100 1000 929 1073

−94.04 −93.52 −91.58 −93.52 −94.88 −92.11

−92.66 −107.96 −74.69 −97.49 −84.49 −104.80

−184.17 −201.49 −175.43 −191.01 −172.64 −203.64

−190.11 −209.94 −183.92 −197.47 −177.78 −211.56

Average

–

–

–

–

−198.20

a b c

ST = S298 K +

–

T 298 K

Cp T

dT.

HT = GT + TST . T H298 K = HT − 298 K Cp dT.

obtained and its average value is −198.20 kJ/mol, disregarding Azad’s. Even though the temperature coefficient from Kovba et al. is in good agreement with the calculated entropy value (ST ), their enthalpy value at 298 K is in high end comparing to those from other measurements. Further assessment will be made in Section 4.3 to determine better reliable enthalpy value at 298 K. 4.3. Assessment of standard enthalpy changes of calcium chromate using phase diagram The phase diagram provides information on the stability of phases at given temperatures, oxygen pressures, and compositions. At the equilibrium, the temperature, oxygen pressure, and composition of element are fixed and these values can be used to obtain the standard free energy. Several phase diagrams of CaO–Cr2 O3 binary system are available in literature [1–6]. The most recently revised phase diagram of CaO–Cr2 O3 is shown in Fig. 6 [5]. The reliability of the free energy of CaCrO4 can be further assessed by using this revised CaO–Cr2 O3 phase diagram. From

the phase diagram, the eutectoid reaction of ␤-CaCr2 O4 into CaCrO4 and Cr2 O3 occurs at 1022 ◦ C that can be written as shown in reaction (8): ␤-CaCr2 O4 + 3/4O2 = CaCrO4 + 1/2Cr2 O3

(8)

The free energy change of reaction (8) can be easily estimated from this phase diagram knowing that it was obtained under air (PO2 = 0.21 atm) and all the compounds involved in this reaction are pure, i.e., their activities are equal to one: 1/2

G◦1295 K = −RT ln

aCaCrO4 aCr2 O3 3/4

aCaCr2 O4 PO2

= RT ln(PO2 )3/4

= −12, 603 J/mol

(9)

The G◦ value at 1022 ◦ C obtained using Eq. (9) can be used to calculate the free energy change of CaCrO4 for the following reaction at 1022 ◦ C by combining Eq. (7) with Eq. (9): CaO + 1/2Cr 2 O3 + 3/4O2 = CaCrO4 G◦1295 K = −75, 035 J/mol CaO + Cr2 O3 = β-CaCr 2 O4 G◦1295 K = −62, 432 J/mol The standard enthalpy change at 298 K for the reaction CaO + 1/2Cr2 O3 + 3/4O2 = CaCrO4 can be obtained as follow:  1295 K ◦ = H − Cp dT = −201, 752 J/mol H298 1295 K K 298 K

where H 1295 K = ΔG1295 K + (1295 K) ΔS 1295 K = −188, 632 J/mol : ◦ S1295 K = S298 K+

Fig. 6. CaO–Cr2 O3 phase diagram in air revised by Kaiser, where A is Ca5 (CrO4 )3 O, W is Ca3 (CrO4 )2 (i.e., 9CaO·4CrO3 ·Cr2 O3 ), and C is Ca5 Cr3 O12 .



1295 K

298 K

Cp dT = −87.72 J/mol K T

The standard enthalpy change of CaCrO4 from the revised phase diagram is compared with those from the literature and the current work, as shown in Table 6. Disregarding Azad’s value, the average value of standard enthalpy at 298 K is in good agreement with the value estimated from the revised CaO–Cr2 O3

Y.M. Lee, Claudia.L. Nassaralla / Materials Science and Engineering A 437 (2006) 334–339 Table 6 Comparison of standard enthalpy changes at 298 K: CaO + 1/2Cr2 O3 + 3/4O2 = CaCrO4 ◦ H298 K (kJ/mol)

Prasad Havlica Kovba Jacob Azad This work Average value disregarding Azad’s Estimate from phase diagram

−190.11 −209.94 −183.92 −197.47 −177.78 −211.56 −198.20 −201.75

phase diagram. Azad’s value is discounted because it leads to high standard deviation. The enthalpy change for reaction (1) is determined as −200 ± 10 kJ/mol. Following the assessments in the current investigation, the more reliable thermodynamic properties of CaCrO4 are: ◦ HfCaCrO (298 K) = 1402 ± 10 kJ/mol; 4

Acknowledgement The authors wish to thank Professor Douglas J. Swenson, Michigan Technological University, for his keen interest and helpful discussions during the progress of this work. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

◦ SCaCrO (298 K) = 130.9 ± 1.9 J/mol K 4

where

[12]

1 3 ◦ ◦ ◦ ◦ ◦ HfCaCrO = H298 K + HfCaO + HfCr2 O3 + HfO2 ; 4 2 4 1 ◦ 3 ◦ ◦ ◦ ◦ = S298 SCaCrO K + SCaO + SCr2 O3 + SO2 4 2 4

[13]

5. Conclusions This work determined the standard free energy of formation of CaCrO4 using gas/solid equilibrium. The standard free energy change for the following reaction is expressed as 1/2CaO(s) + 1/2␤-CaCr2 O4 (s) + 3/4O2 (g) = CaCrO4 (s)

[14] [15]

[16] [17] [18]

[19] [20] [21]

◦

G = −191, 250 + 109T (J/mol) The thermodynamic properties of CaCrO4 were assessed because their values are scattered in literature. The assessment used the second/third law evaluation and the phase diagram of CaO–Cr2 O3 . The accurate thermodynamic properties of CaCrO4 are determined through assessment:

[22]

[23] [24]

◦ (298 K) = 1402 ± 10 kJ/mol; HfCaCrO 4 ◦ SCaCrO (298 K) = 130.9 ± 1.9 J/mol K 4

339

[25]

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