Research: Science and Education
Use of Tabulated Thermochemical Data for Pure Compounds Nathan Jacobson NASA John Glenn Research Center, 21000 Brookpark Rd., Cleveland, OH 44135;
[email protected] Overview Determining the entropy, enthalpy, and free energy changes associated with a chemical reaction is important in many areas of chemistry. When faced with such a problem the student and even the practicing scientist may have several questions. The first question is simply, Where do I obtain such data? Once the data are located, the question is how to use them effectively. Different tabulations list data in different formats. This paper discusses the common sources for thermodynamic data and derives equations for converting from one format to another. These are illustrated with practical examples. Table 1 lists the major sources for thermochemical data. These sources are available in most technical libraries, and in some cases on the World Wide Web (14). The focus here is on inorganic compounds; however, these tabulations list many organic compounds as well. The focus is also on calculations at constant temperature and pressure, as used by most chemists. Thermodynamic data are presented either in tabular form with entries every 100 K or as polynomial expressions. Three types of fundamental data are needed to calculate the entropy, enthalpy, and free energy changes associated with a given reaction (15). These are the heat capacity (Cp°), the heat of formation at 298.15 K (∆ f H °(298)), and any heats of transition (∆ tr H(Ttr)). The databases listed in Table 1 give these
fundamental quantities and, for convenience, additional derived quantities, including entropy, enthalpy, and free energy in various formats. First, it is essential to clarify the issue of standard state and reference states. Enthalpy and Gibbs free energy are only meaningful as a difference between the conditions of interest and a specified standard state. The standard state is generally chosen as the most stable form of aggregation of a pure element or compound at 1 bar (105 Pa), designated by “°” as in H ° (16 ). Temperature must also be specified. In some compendia the standard-state temperature is taken as the temperature of interest; in others the standard-state temperature is taken as 298.15 K. The latter convention puts all data on a common basis and avoids problems where the temperature of interest leads to an ill-defined state (17 ). The SGTE database (6 ), used in computational thermodynamics codes is based on this standard state. It should be noted that reference state has a somewhat different meaning from standard state. Standard states always refer to 1 bar, as indicated by the “°”. Reference states can refer to different pressures. The term reference state is used in regard to chemical potentials and activities. For condensed phases these quantities show little pressure dependence and hence reference states and standard states become equivalent. For gases, the reference state pressure can be fixed at one bar, which also makes these terms equivalent.
Table1. Sources of Thermochemical Data Source and Reference
Format
Quantities
Chase et al. JANAF Thermochemical Tables , 1998 (1)
Tabular, electronic
Cp°(T ), S°(T ), FEF(298), H °(T ) – H °(Tr ), ∆ f H °(T ), ∆ f G°(T ), log Kf , ∆ tr H
Gurvich et al. Thermochemical Properties of Indivual Substances , 1989 (2)
Tabular, electronic
Cp°(T ), FEF(0), H °(T ) – H °(0), S °(T ), log Kf , ∆ f H °(0), ∆ f H °(298), ∆ tr H °
Barin. Thermochemical Data of the Indivual Substances, 1995 (3)
Tabular
Cp°(T ), S°(T ), FEF(298), H °(T ), H °(T ) – H °(298), G °(T ), ∆ f H °(T ), ∆ f G°(T ), log Kf , ∆ tr H
Pankratz. Thermodynamic Properties of Elements and Oxides ; Thermodynamic Properties of Halides; Thermodynamic Properties of Carbides, Nitrides, and Other Selected Substances (4) Pankratz et al. Thermodynamic Properties of Sulfides ; Thermodynamic Data for Mineral Technology (4)
Tabular, analytic functions
Cp°(T ), S°(T ), FEF(298), H °(T ) – H °(298), ∆ f H °, ∆ f G°(T ), log Kf , ∆ tr H
Tabular
Cp°(T ), S°(T ), H °(T ) – H °(298), ∆ f H °(T ), ∆ f G °(T )
Dinsdale. SGTE Data for Pure Elements (5)
Analytic functions
G – H SER
SGTE Database (6)
Electronic
G – H SER; or Cp°, ∆ f H °(298), S °(298) for some compounds
Database for HSC (7)
Electronic, analytic functions ∆ f H °(298), S °(298), Cp°(T )
Cox et al. CODATA Key Values for Thermodynamics (8)
Tabular
Cp°(T ), FEF(0), H °(T ) – H °(0)
Hultgren et al. Selected Values of the Thermodynamic Properties of the Elements (9)
Tabular
Cp°, H °(T ) – H °(298), S°(T ) – S°(298), FEF(298), ∆ vapG°, ∆ vapH °, ∆ tr H, log P (vapor)
Robie and Hemingway. Thermodyanamic Properties of Minerals and Related Substances at 298.15 K and 1 Bar Pressure and Higher Temperatures (10)
Tabular
S °(298), ∆ f H °(298), ∆ f G °(298) for many minerals; Cp°(T ), ST°(T ), H °(T ) – H °(298), FEF(298), ∆ f H °(T ), ∆ f G°(T ), log Kf , ∆ tr H (T ) for selected minerals
Kubachewski. The Thermodynamic Properties of Double Oxides (11) Analytic functions
∆f G°
Kubachewski et al. Materials Thermochemistry (12)
Tabular, analytic functions
Cp°(T ), S °(298), ∆ f H °(298), ∆ tr H
Mills. Thermodynamic Data for Inorganic Sulfides, Selenides, and Tellurides (13)
Tabular
Cp°(T ), S°(T ), FIF(298), H °(T ) – H °(298), ∆ f H °(T ), ∆ f G°(T ), log Kp
814
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
Research: Science and Education
Entropies of Reaction By the third law, entropy at 0 K (S °(0)) is zero for a perfect crystal (15). This provides a natural reference point for entropy and all compendia list entropy in the same way. The entropy at 298.15 K, S °(298), is determined from lowtemperature calorimetric data: 298
S°(298) – S°(0) = S°(298) =
C po(T ) T
0
dT + Σ
∆trH m Ttr, m Ttr, m
m
(1)
The second term sums all the phase transformation entropies between 0 and 298.15 K. The entropy at higher temperatures is determined by an analogous equation: T
S°(T ) = S°(298) + 298
C po(T) T
dT + Σ
∆tr H n Ttr,n
n
Ttr,n
(2)
For the general chemical reaction η1R1 + η2R2 + … + η i R i = ν1P1 + ν2P2 + … + νj Pj (3)
the associated entropy change is
∆rxnS°(T ) = Σ ν( j)S °(T, j) – Σ η(i)S °(T, i) j
i
The important point for the student is that whereas entropies have a natural reference point of 0 K, there is no natural reference point for enthalpy. Hence enthalpies are best expressed as a difference:
298
Cpo(T )dT
(5)
This quantity, H °(T ) – H °(298), is referred to as the sensible heat (18). The JANAF tables (1) list H °(T ) – H °(Tr) for every element and compound for Tr equal to 298.15 K. This means that H °(T ) – H °(Tr) is zero at 298.15 K, negative when Tr < 298.15 K, and positive when Tr > 298.15 K. The JANAF tables (1) also list the heat of formation, ∆ f H °(298), for each substance. For the elements in their standard state, defined as the stable aggregation at the temperature of interest, this is zero. However for the compounds, it is defined as follows. The first term in the sensible heat, H °(T ), is termed the enthalpy function (3). Following the notation of Barin (3), consider the formation of a compound B from the elements Ei : η1E1 + η2E2 + … + ηi Ei = B
(6)
First consider the determination of ∆ f H °(298) from enthalpy functions at 298.15 K : ∆ f H °(298,B) = H °(298,B) – Σi η(i )H °(298,Ei )
Equation 9 is thus used to determine the enthalpy of formation of B at a temperature T from the sensible heats. The TPIS compendium (2) lists ∆ fH °(0) and ∆ f H °(298) as well as H °(T ) – H °(0). The enthalpy of formation at any temperature, ∆ f H °(T ), can be calculated in a manner analogous to that described above. Now, instead of 298.15 K, the reference point becomes 0 K in eq 9. Barin (3) lists H °(T ) – H °(298), which is the same as the JANAF H °(T ) – H °(Tr) (1). In addition, Barin (3) lists the enthalpy function H °(T ). In order to do this, H °(298) must be defined. He defines H °(298) as zero for the elements in their most stable aggregation state at 298.15 K. The relationship of the enthalpy function to sensible heats and heats of formation can be easily derived from eq 7. The summation term is zero for the elements at 298.15 K, so (10) ∆ f H °(298,B) = H °(298,B) Adding H °(T,B) – H °(298,B) to both sides leads to (19) H °(T,B) = ∆ f H °(298,B) + [H °(T,B) – H °(298,B)] (11) Thus eq 11 relates JANAF data to the enthalpy function, H °(T ).
Enthalpies of Reaction
T
∆ fH °(T,B) = ∆ f H °(298,B) + [H °(T,B) – H °(298,B)] – Σi η(i )[H °(T,Ei ) – H °(298,Ei )] (9)
(4)
Here ν( j ) and η (i ) are the stoichiometric coefficients of the products and the reactants, respectively.
H °(T ) – H °(298) =
Next consider the determination of ∆ f H °(T ) from enthalpy functions: (8) ∆ f H °(T,B) = H °(T,B) – Σi η(i)H °(T,Ei ) Equation 7 can be subtracted from eq 8 to give
(7)
Example 1 Consider the oxidation of SiCl4(g) to produce SiO2(s), which is one of the principal methods of producing highly pure silica for optical fibers: SiCl4(g) + O2(g) = SiO2(s) + 2Cl2(g) Calculate the enthalpy change for the reaction at 1000 K, using the data in Table 2. There are four equivalent ways to do this simple calculation. They illustrate the equivalence of the various formats for enthalpy. The first way is from the heats of formation at 1000 K in column 2: ∆rxnH °(1000) = Σj ν( j)∆fH °(1000,j) – Σi η(i)∆ f H °(1000,i) = 905.144 – ( 659.413) = 245.731 kJ/mol The second way is from the enthalpy functions at 1000 K in column 3: ∆rxnH °(1000) = Σj ν( j)H °(1000,j) – Σi η(i)H °(1000,i) =
( 865.498 + 2 × 25.585) – (591.300 + 22.700) = 245.728 kJ/mol Table 2. Enthalpy Data from Barin (3)
Compound SiCl4(g) O2(g) SiO2(quartz) Cl2(g)
∆f H °(1000)/ (kJ mol1)
∆f H °(298)/ H °(1000)/ [H °(1000) – (kJ mol1) H °(298)] /(kJ mol1) (kJ mol1)
659.413
591.300
71.446
0.000
22.703
22.703
0.000
905.144
865.498
45.359
910.857
0.000
25.585
25.585
0.000
JChemEd.chem.wisc.edu • Vol. 78 No. 6 June 2001 • Journal of Chemical Education
662.746
815
Research: Science and Education
The third way is from the sensible heats in column 4 and enthalpy functions in column 3: ∆rxnH °(1000) = Σj ν( j)[H °(1000,j) – H °(298,j)] –
Σi η(i)[H °(1000,i) – H °(298,i)] + Σj ν( j)∆fH °(298,j) – Σi η(i)∆ f H °(298,i)
The value of ∆ f H °(298,SiCl4) and ∆ fH °(298,SiO2) are first determined: Si(s) + 2Cl2(g) = SiCl4(g) This is simply an application of eq 11: ∆ f H °(298,SiCl4) = H °(1000,SiCl4) – [H °(1000,SiCl4) – H °(298,SiCl4)] = 591.300 – 71.446 = 662.746 kJ/mol Similarly, ∆ f H °(298,SiO2) can be calculated to be 910.857. Note that ∆ f H °(298,O2) and ∆ f H °(298,Cl2) are zero. Thus: ∆ rxn H °(1000) = (45.359 + 2 × 25.585) – (71.446 + 22.703) + (910.857) – ( 662.746) = 245.731 kJ/mol The fourth way is from the sensible heats in column 4 and the enthalpies of formation at 298.15 K in column 5. This the same as in the previous part, but the ∆ f H °(298) are given. Gibbs Free Energy Calculations The most useful calculation at constant temperature and pressure is the Gibbs free energy change associated with a reaction. As noted, free energies may be given as free energies of formation from the elements referenced to the temperature of interest, Gibbs energies referenced to 298.15 K, or free energy functions based on 0 or 298.15 K. Each of these is discussed and formulas for converting from one form to the other are given.
Free Energy of Formation According to convention, the free energy of formation of the elements in their pure form, at the temperature of interest, is taken as zero. Thus ∆ f G °(T ) is zero for all pure elements. Of course, it is not zero for compounds. The free energy change for the general reaction in eq 3 is given by the familiar expression ∆ rxnG °(T ) = Σ ν( j)G °(T, j) – Σ η(i)G°(T, i) j
i
(12)
Gibbs Energy Another expression for the Gibbs free energy is G °(T ), termed the Gibbs energy (3, 17, 20). It is analogous to the enthalpy function, H °(T ). Although the Gibbs energy is not commonly covered in textbooks, it is the principal method of utilizing free energy in computer data banks. It is defined by G °(T ) = H °(T ) – T S °(T )
(13)
Combining this with eq 11 gives: G °(T ) = 再∆ f H °(298) + [H °(T ) – H °(298)]冎 – T S °(T ) (14) Equation 14 can be used for the conversion of JANAF (1) data to Gibbs energies. 816
The Gibbs energy is referenced to the elements in their most stable form at 298.15 K. This is the standard element reference or SER. Dinsdale (5) has taken data from a range of sources and converted it to the Gibbs energies for the elements. Gibbs energies are often written as G – H SER
or
G – H298
(15)
Here H SER or H298 is the weighted average of the enthalpies for the elements in the particular compound at 298.15 K (17 ), which is zero. Thus the H SER in the above quantities is always zero and simply a mnemonic to specify the Gibbs energy referenced to 298.15 K. Typically, G – H SER is presented in the following functional form: G – H SER = A + BT + CT ln(T ) + DT 2 + ET 3 + F /T
(16)
This expression may be differentiated to obtain the entropy, enthalpy, and heat capacity according to standard equations (5). In analogy with the enthalpy function, consider eq 6. The free energy of formation of compound B can be calculated from the Gibbs energies as follows: ∆ f G °(T,B) = G °(T,B) – Σi η(i )G °(T,Ei )
(17)
Also, if the free energy of formation of a compound is known from the JANAF tables and the Gibbs energies for its constituent elements are known, the compound’s Gibbs energy, G °(T,B), can be determined from the above equation.
Free Energy Functions The major advantage of free energy functions is that they vary slowly with temperature and hence are much more amenable to interpolation than free energies of formation. Free energy functions may be based on either 298.15 K or 0 K. The free energy function (FEF) based on 298.15 K is defined as FEF298(T ) =
G °(T ) – H °(298) T
(18)
Similarly, free energy functions based on 0 K are defined as FEF0(T ) =
G °(T ) – H °(0) T
(19)
Note that in some cases the free energy functions are defined with a negative sign (2), whereas in others they are defined as above (21). It is important to be cognizant of this. The major advantage of the free energy function based on 0 K for gases is that it is readily calculated from spectroscopic data (21). However, H °(0) data are needed to obtain a free energy of formation and these may not be available. The free energy function based on 0 K can be converted to the free energy function based on 298.15 K, as follows: FEF298(T ) =
G ° – H °(0) H °(298) – H °(0) – = T T H °(298) – H °(0) FEF0(T ) – T
(20)
The second term is calculated from the low-temperature heat capacities. As pointed out by Lewis and Randall (21), reasonable estimates can be made for this second term which
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
Research: Science and Education Table 3. Data for Calculating the Free Energy of Reaction for the Oxidation of SiCl4(g) at 1000 K Data from Barin (3) Compound SiCl4(g)
∆f G°(1000)/ (kJ mol1) 530.806
380.935
662.746
∆f H °(0)/ (kJ mol1)
1043.681
362.034
660.076
220.875
0.000
220.875
212.197
0.000
70.664
910.857
981.521
63.760
905.719
0.000
241.242
0.000
241.242
232.022
0.000
introduce minimal error. The free energy function based on 298.15 K is given in the JANAF tables (1) and the compendium of Barin (3). The free energy of formation and the Gibbs energy can be readily calculated from the free energy function. The free energy of formation of compound B in reaction 6 can be determined according to the following definition (21): T
FEF0(1000)/ (J K1 mol1)
G°(1000)/ (kJ mol1)
0.000
Cl2(g)
∆ f G°(TB)
Data from TPIS (2)
∆f H °(298)/ (kJ mol1)
730.256
O2(g) SiO2(quartz)
FEF298(1000)/ (J K1 mol1)
= FEF298(T,B)– Σ η(i) FEF298 T,Ei +
∆ f H(298,B) T
i
(22)
For a compound, H °(298) does not equal zero, and one can use FEF298(T ) to calculate G °(T ) as follows: G °(T ) = ∆ fH °(298) + T × FEF298(T )
∆ rxn G °(1000)
= 70.664 + 2(241.242) – 1000 380.935 + (220.879) + (910.857) – (662.746) = 199.449 J/(mol K) ∆rxnG (1000) = 199.449 kJ/mol
(21)
The Gibbs energy can also be readily obtained from the free energy function. Consider eq 18. For pure elements, where H °(298) is equal to zero, G °(T ) = FEF298(T ) × T
The ∆ rxn H °(298) term can be determined from the data in Table 3, column 4.
(23)
The fourth way is from the free energy functions based on 0 K, in Table 3, columns 6 and 7. This is the same type of calculation as was the second calculation, from the Gibbs energies. One can either use the form of eq 21 for FEF0(T ) or one can convert the FEF0(T ) to FEF298(T ) using eq 20 and use eq 21 directly. Applying the first method:
∆ rxn G °(1000) 1000
∆ rxn G °(1000) = 730.256 – (530.806) = 199.450 kJ/mol The second way is from the Gibbs energies in Table 3, column 5: ∆ rxn G °(1000) = Σj ν( j)G °(1000,j) – Σi η(i)G °(1000,i) = [ 981.521 + 2(241.242)] – [1043.681 + (220.875)] = 199.449 kJ/mol The third way is from the free energy functions based on 298.15 K, Table 3, column 3. This is a modification of eq 21.
∆ rxn G°(1000) 1000
= Σ ν( j)FEF298 1000, j – j
Σi η(i)FEF298 1000,i
+
∆rxn H°(298) 1000
j
Σi η(i)FEF0(1000,i) +
Note that Gibbs energies are only simply related to free energy functions for the elements.
Example 2 Calculate the free energy of reaction for the oxidation of SiCl4(g) at 1000 K in Example 1. The necessary data are given in Table 3. This calculation can be done four equivalent ways. The first way is from the free energies of formation, Table 3, column 2. This is an application of eq 12.
= Σ ν( j)FEF0(1000, j) – ∆ rxn H °(0) 1000
=
[63.760 + 2(232.022)] – [362.034 + (212.197)] + [905.719 – (660.076)] = 199.22 J/(mol K) ∆rxnG °(T ) = 199.22 kJ/mol This example illustrates four common formats for free energies and their use to calculate the free energy change in a chemical reaction.
Example 3 This example is for the reaction SiO2(s) + 2H2O(g) = Si(OH)4(g) A recent transpiration study on Si(OH)4(g) (22) reports the equilibrium constant for the above reaction from ∼1400– 1800 K as
log K =
0.2963 ± 0.0087 × 104 + 3.4563 ± 0.0545 T
This reaction is important when silica is used in hightemperature industrial environments that contain steam. From these data, obtain the polynomial form of the Gibbs energy, G °(T,Si(OH)4), and the free energy of formation, ∆ - f G °(T,Si(OH)4), from the elements.
JChemEd.chem.wisc.edu • Vol. 78 No. 6 June 2001 • Journal of Chemical Education
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Research: Science and Education Table 4a. SGTE Data (6): Cp = a + bT + cT 2 + d/T 2 ∆f H °(298)/ (J mol1)
Compound
S °(298)/ (J K1 mol1)
∆tr H/ Upper Tem(J mol1) perature/K
a
b
c
0.55179899 × 10
2
d
0.44783401 × 10
5
113165
H2(g)
0.0
130.67999
—
1000
31.3571
O2(g)
0.0
205.147
— —
900 3700
22.2586 33.557301
0.20477301 × 101 0.24697999 × 102
0.80396803 × 106 0.100166 × 106
188.832
—
1100
28.409201
0.124748 × 101
0.360916 × 106
128327
— — 410 —
540 770 848 1800
61.132301 452.13699 1404.54 58.429199
0.378407 0.857768 2.56809 0.103199 × 101
0.29705901 × 103 0.54550602 × 103 0.141029 × 102 0.1484 × 108
1708800 24953400 0.112805 × 109 190226
H2O(g)
241826.00
SiO2(quartz)
910700
41.459999
153499 1079770
Table 4b. Polynomial Forms for G o(T ) and Values for G o(1000) Derived from Table 4a G (T ) = A + BT + CT ln T + DT 2 + ET 3 + F/T UpperTemperature/ K
Compound
A
B
C
D
E
F
G (1000)
H2(g)
1000
9.51865866 ×103
78.51308805
31.3571
2.75899495 ×103
7.4639001 ×107
5.65825 ×104
145533
O2(g)
900 3700
6.96068535 ×103 1.31360792 ×104
51.18329164 24.74366333
22.2586 33.557301
0.01023865 1.23489995 ×103
1.33994672 ×106 1.66943333 ×108
7.97495 ×104 5.374885 ×106
— 220876
Si(s)
1687
8.16378192 ×103
137.2445098
22.831699
1.926905 ×103
3.5517835 ×109
1.76667 ×105
30388
H2O(g)
1100
2.50423445 ×10
4.4549719
28.409201
8
6.41635 ×104
448574
SiO2(quartz)
540 770 848 1800
9.0093633 ×105 1.09146673 ×106 1.56348589 ×106 9.29142543 ×105
360.8922571 2.88267483 ×103 9.17862379 ×103 356.70139918
61.132301 452.13699 1.40454 ×103 58.429199
8.544 ×105 1.24767 ×107 5.64025 ×107 9.5113 ×104
— — — 981311
5
The needed data, directly from the SGTE database (6 ), are listed in Table 4a. The first step is to determine the Gibbs energies for each of these elements and compounds. This is a simple but cumbersome application of eqs 2, 5, and 13 and is best done with a mathematics “scratch-pad”-type program such as MathCad (23). The results are listed in Table 4b. Calculation of G °(1000) from the resultant polynomial and comparison to the tabulated values provides a check of the polynomial. This is shown in last column of Table 4b. Now one needs to convert the equilibrium constant expression to the ∆rxnG °(T ) for the reaction of quartz and water vapor (multiply the equilibrium constant expression by 2.303RT, where R is the gas constant): ∆rxnG °(T ) = (56,733 + 66.178T ) J/mol From the generalized form of eq 17, ∆ rxn G °(T ) = Σj ν( j)G °(T,j ) – Σi η(i)G °(T,i) = G °(T,Si(OH) 4) – G °(T,SiO 2) – 2G °(T,H 2O) Thus G °(T,Si(OH)4) = ∆rxnG °(T ) + G °(T,SiO2) + 2G °(T,H2O) = 1.373259 × 106 + 431.893T – 1.152476 × 102T ln T – 1.763475 × 102T 2 – 1.205527 × 107T 3 – (2.2344 × 104/T ) To obtain ∆ fG °(T,Si(OH)4) one also applies eq 17: Si(s) + 2O2(g) + 2H2(g) = Si(OH)4(g) ∆fG °(T ) = G°(T,Si(OH)4) – G°(T,Si) – 2G°(T,O2) – 2G°(T,H2) = 1.319786 × 106 + 8.803133 × 10T + 3.741290 × 10T ln T – 1.875604 × 102T 2 + 1.342390 × 106T 3 – (1.1126304 × 107/T ) 818
3
6.2374 ×10
-0.1892035 0.428884 1.284045 5.15995 ×103
6.0152667 ×10
4.9509835 ×105 9.091767 ×105 2.35048333 ×104 2.47333333 ×1010
This example illustrates the manipulation of data in the SGTE database, which is the most widely used computer database of thermochemical data. It also shows the necessity for computers in manipulating this type of data! In fact, the availability of powerful desktop computers has created a renaissance of thermochemistry. Summary and Conclusions There are numerous sources of thermochemical data for inorganic compounds. The major ones are listed and discussed. The data in these compendia are in different forms. The goal is to effectively use them to calculate entropy, enthalpy, and free energy changes at constant pressure and temperature. To this end, equations are provided for use of the data and conversion between the different data formats. These points are illustrated with practical examples. Such topics would be a useful part of the curriculum for chemistry students about to enter the work force or begin their research. The most recent computer databases utilize thermodynamic data in the form of the Gibbs energy, which is not commonly covered in textbooks. This is referenced to 298.15 K. This quantity and its relation to Gibbs energy of formation and to free energy functions are discussed. This format is likely to become the dominant format for presenting thermochemical data in the future. Literature Cited 1. Stull, D. R.; Prophet, H. JANAF Thermochemical Tables, 2nd ed.; NSRDS–NBS 37; National Bureau of Standards: Washington, DC, 1971. Chase, M. W. Jr.; Davies, C. A.;
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
Research: Science and Education Downey, J. R. Jr.; Frurip, D. J.; McDonald, R. A.; Syerud, A. N. JANAF Thermochemical Tables, 3rd ed.; J. Phys. Chem. Ref. Data 1985, 14; American Chemical Society and American Physical Society for National Bureau of Standards: New York, 1986. Chase, M. W. Jr. NIST-JANAF Thermochemical Tables, 4th ed.; J. Phys. Chem. Ref. Data; Monograph 9; American Chemical Society and American Physical Society for National Bureau of Standards: New York, 1998. The JANAF tables and a good deal of useful information are available on the NIST Chemistry Web Page: http://webbook.nist.gov/chemistry/ (accessed Jan 2001). The JANAF are perhaps the most widely used thermochemical tables. These data have been carefully assessed. A detailed description is given for the source of each data set. It is now in its fourth edition, although the second and third editions are still in common use. 2. Glusko, V. P.; Gurvich, L. V.; Bergman, G. A.; Veitz, I. V.; Medvedev, V. A.; Khachkuruzov, G. A.; Jungman, V. S. Thermodynamic Properties of Pure Substances, Vols. I–IV, 3rd ed.; Nauka: Moscow, 1982; in Russian. Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of Individual Substances, Vols. I and II, 4th ed.; Hemisphere: New York, 1989. Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of Individual Substances, Vol. III, 4th ed.; Begell House: New York, 1989. Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of Individual Substances, Vol. IV, 4th ed.; Begell House: New York, in press. Gurvich, L. V.; Iorish, V. S.; Chekhovskoi, D. V.; Yungman, V. S. IVTANTHERMO—A Thermodynamic Database and Software System for the Personal Computer; NIST Special Database 5; National Institutes of Standards and Technology: Gaithersburg, MD, 1993. These tables are also carefully assessed data. A detailed text describes the sources of the data and a level of accuracy is given to each substance. Listed above are the Russian version, the English translation of Vols. I–III (Vol. IV is expected out soon), and the electronic version, which has the option of selecting the format of the output: JANAF form, TPIS form, or functional form of Cp°, FEF(0), FEF(298), H°(T ) – H°(0), H°(T ) – H°(298), and S°(T ). 3. Barin, I.; Knacke, O. Thermochemical Properties of Inorganic Substances; Springer: Berlin, 1973. Barin, I.; Knacke, O.; Kubachewski, O. Thermochemical Properties of Inorganic Substances; Springer: Berlin, 1977. Barin, I. Thermochemical Data of Pure Substances, Vols. 1 and 2, 3rd ed.; VCH: Weinheim, Germany, 1995. These are the only major tables to contain data in the form of the Gibbs energies. The older version gives the heat capacity in both tabular and functional form; the newer version gives the heat capacity only in tabular form. 4. Pankratz, L. B. Thermodynamic Data of Elements and Oxides; Bureau of Mines Bulletin 672, 1982. Pankratz, L. B. Thermodynamic Properties of Halides; Bureau of Mines Bulletin 674, 1984. Pankratz, L. B.; Mah, A. D.; Watson, S. W. Thermodynamic Properties of the Sulfides; Bureau of Mines Bulletin 388, 1987. Pankratz, L. B. Thermodynamic Properties of Carbides, Nitrides, and Other Selected Substances, Parts 1 and 2; Bureau of Mines Bulletin 696, 1994. Pankratz, L. B.; Stuve, J. M.; Gokcen, N. A. Thermodynamic Data for Mineral Technology; Bureau of Mines Bulletin 677, 1984. These bulletins were published by the U.S.
Department of the Interior: Washington, DC. 5. Dinsdale, A. T. Calphad 1991, 15, 317–425. 6. Erikson, G.; Hack, K. Metall. Mater. Trans. B 1990, 21, 1013– 1023. Sundman, B.; Jansson, B.; Anderson, J.-O. Calphad 1985, 9, 153. SGTE Home Page; http://www.sgte.org/ (accessed Jan 2001). The Scientific Group Thermodynamic Europe (SGTE) Pure Substance Database is used in several computational thermochemical codes. References for two commonly used codes are given here. 7. Roine, A. Outokumpu HSC Chemistry® for Windows, version 3.0; Outokumpu Research Oy, Finland, 1997; the database for this computational thermochemical code for pure substances is extensive (although it has not been assessed) and the manual contains numerous references to additional data sources. 8. Cox, J. D.; Wagman, D. D.; Medvedev, V. A. CODATA Key Values for Thermodynamics; Hemisphere: New York, 1989. 9. Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.; Kelley, K. K.; Wagman, D. D. Selected Values of the Thermodynamic Properties of the Elements; American Society for Metals: Metals Park, OH, 1973. 10. Robie, R. A.; Hemingway, B. S. Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 Bar Pressure and Higher Temperatures; U.S. Geological Survey Bulletin 1452; U.S. Government Printing Office: Washington, 1978. This deals primarily with mineral compositions. Data at 298.15 K are available on the World Wide Web at http://www.science.ubc. ca/%7Egeol323/thermo/robtable.htm (accessed Jan 2001). 11. Kubachewski, O. High Temp. High Pressures 1972, 4, 1–12. 12. Kubachewski, O.; Alcock, C. B.; Spencer, P. J. Materials Thermochemistry, 6th ed.; Pergamon: New York, 1993. This textbook is a classic; it contains a wealth of information on experimental thermochemistry as well as extensive tables. 13. Mills, K. C. Thermodynamic Data for Inorganic Sulphides, Selenides, and Tellurides; Plenum: New York, 1974; this extensive compendium contains assessed data on the sulfides, selenides, and tellurides. 14. A useful Web site that lists inorganic thermochemical information is Web Sites in Inorganic Chemical Thermodynamics, maintained by Ecole Polytechnique of Montreal, Canada; http://www.crct.polymtl.ca/FACT/websites.htm (accessed Jan 2001). 15. Gokcen, N. A.; Reddy, R. G. Thermodynamics, 2nd ed.; Plenum: New York, 1996. 16. IUPAC Commission I.2. J. Chem. Thermodyn. 1982, 14, 805. 17. Hack, K. The SGTE Casebook Thermodynamics at Work; Institute of Materials: London, 1996. 18. Lupis, C. H. P. Chemical Thermodynamics of Materials; North Holland: New York, 1983. 19. Turkdogan, E. T. Physical Chemistry of High Temperature Technology; Academic: New York, 1980. 20. Barin, I.; Knacke, O. Metall. Trans. 1974, 5, 1769. 21. Lewis, G. N.; Randall, M. Thermodynamics; Revised by Pitzer, K. S.; Brewer, L.; McGraw Hill: New York, 1961. 22. Hashimoto, A. Geochim. Cosmochim. Acta 1992, 56, 511–532. 23. MathSoft Home Page; MathSoft: Cambridge, MA; http:// www.mathsoft.com/ (accessed Jan 2001).
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