Appendix  A

Selected Thermodynamic and

Thermochemical Data

TABLE A.1: THE STANDARD GIBBS FREE ENERGY

CHANGES FOR SEVERAL REACTIONS

Table  A.1 lists the standard Gibbs free energy changes for selected reactions in
the form

∆GT = A + BT J

or

∆GT = A + BT ln T + CT J

and lists the range of temperature in which the expression is valid.

Example : For the oxidation of solid copper to form solid cuprous oxide accord-
ing to

1
2Cu( s ) + O2( g ) = Cu2O( s )
2
∆ G °  = –  162,200 +  69.24T  J

in the range 298– 1356 K. Thus, at the melting temperature of Cu, 1356 K,

∆G1356

K = −162, 200 + 69.24 × 1, 356
= −68, 311 J
For the oxidation of liquid copper to form solid cuprous oxide according to

1
2Cu(l ) + O2( g ) = Cu2O( s )
2
∆GT = −188, 300 + 88.48T J

in the range 1356– 1509 K. Thus, at 1356 K,

∆G1356

K = −188, 300 + 88.48 × 1, 356 J
= −68, 321 J

649
650 APPENDIX A

Table A.1  The Standard Gibbs Free Energy Changes for Several Reactions

Reaction  Δ  G°, J  Range, K 
2Ag( s )  + ½ O2( g )  = Ag2 O( s )  – 30,540 + 66.11 T  298– 463
Al( l )  = [Al](1 wt% in Fe)  – 43,100 –  32.26 T 
2Al( l )  + 1.5O2( g )  = Al2 O3( s )  – 1,687,200 + 326.8 T  993– 2327
C( s )  + ½ O2( g )  = CO( g )  – 111,700 –  87.65 T  298– 2000
C( s )  + O2( g )  = CO2( g )  – 394,100 –  0.84 T  298– 2000
C( s )  + ½ O2( g )  + ½ S2( g )  = COS( g )  – 202,800 –  9.96 T  773– 2000
C( gr )  + 2H2( g )  = CH4( g )  – 91,040 + 110.7 T  773– 2000
C( gr )  = [C](1 wt% in Fe)  22,600 –  42.26 T 
CaO( s )  + CO2( g )  = CaCO3( s )  – 168,400 + 144 T  449– 1150
2CaO( s )  + SiO2( s )  = 2CaO· SiO2( s )  – 118,800 –  11.30 T  298– 2400
CoO( s )  + SO3( g )  = CoSO4( s )  – 227,860 + 165.3 T  298– 1230
2Cr( s )  + 1.5O2( g )  = Cr2 O3( s )  – 1,110,100 + 247.3 T  298– 1793
2Cu( s )  + ½ O2( g )  = Cu2 O( s )  – 162,200 + 69.24 T  298– 1356
2Cu( l )  + ½ O2(g)  = Cu2 O( s )  – 188,300 + 88.48 T  1356– 1509
2Cu( s )  + ½ S2( g )  = Cu2 S( s )  – 131,800 + 30.79 T  708– 1356
3Fe(α )  + C( gr ) = Fe3 C( s )  29,040 –  28.03 T  298– 1000
3Fe(γ )  + C( gr ) = Fe3 C( s )  11,234 –  11.00 T  1000– 1137
Fe( s )  + ½ O2( g )  = FeO( s )  – 263,700 + 64.35 T  298– 1644
Fe( l )  + ½ O2( g )  = FeO( s )  – 256,000 + 53.68 T  1808– 2000
3Fe( s )  + 2O2( g ) = Fe3 O4( s )  – 1.102,200 + 307.4 T  298– 1808
Fe( s )  + ½ S2( g )  = FeS( s )  – 150,200 + 52.55 T  412– 1179
H2( g )  + Cl2( g )  = 2HCl( g )  – 188,200 –  12.80 T  298– 2000
H2( g )  + I2( g )  = 2HI( g )  – 8,370 –  17.65 T  298– 2000
H2( g )  + ½ O2( g )  = H2 O( g )  – 247,500 + 55.85 T  298– 2000
Hg( v )  + ½ O2( g )  = Hg0( s )  – 152,200 + 207.2 T 
Li( g )  + ½ Br2( g )  = LiBr( g )  – 333,900 + 42.09 T  1289– 2000
Mg( l )  + Cl2( g )  = MgCl2( l )  – 603,200 + 121.43 T  987– 1368
Mg( g )  + ½ O2( g )  = MgO( s )  – 729,600 + 204 T  1363– 2200
2MgO( s )  + SiO2( s )  = Mg2 SiO4( s )  – 67,200 + 4.31 T  298– 2171
MgO( s )  + CO2( g )  = MgCO3( s )  – 117,600 + 170 T  298– 1000
MgO( s )  + Al2 O3( s )  = MgO· Al2 O3( s )  – 35,560 –  2.09 T  298– 1698
Mn( s )  + ½ O2( g )  = MnO( s )  – 388,900 + 76.32 T  298– 1517
N2( g )  + 3H2( g )  = 2NH3( g )  – 87,030 + 25.8 T  ln T  + 31.7 T  298– 2000
2Ni( s )  + O2( g )  = 2NiO( s )  – 471,200 + 172 T  298– 1726
2Ni( l )  + O2(g)  = 2NiO( s )  – 506,180 + 192.2 T  1726– 2200
½ O2(g)  = [O](1 wt% in Fe)  – 111,070 –  5.87 T 
Pb( l )  + ½ O2( g )  = PbO( s )  – 208,700 + 91.75 T  600– 1158
Pb( l )  + ½ O2( g )  = PbO( l )  – 181,200 + 68.03 T  1158– 1808
Pb( l )  + ½ S2( g )  = PbS( s )  – 163,200 + 88.03 T  600– 1386
(Continued)
APPENDIX A 651

TableA.1 (Continued) The Standard Gibbs Free Energy Changes for Several Reactions
Reaction  Δ  G°, J  Range, K 
PbO( s )  + SO2( g )  + ½ O2( g )  = – 401,200 + 261.5 T  298– 1158
PbSO4( s ) 
PCl3( g ) + Cl2( g ) = PCl5( g )  – 95,600 –  7.94 T  ln T  + 235.2 T  298– 1000
½ S2( g )  + O2( g )  = SO2( g )  – 361,700 + 76.68 T  718– 2000
Si( s ) +  O2( g )  = SiO2( s )  – 907,100 + 175 T  298– 1685
3Si( s )  + 2N2( g )  = Si3 N4( s )  – 723,800 + 315.1 T  298– 1685
Sn(l ) + Cl2( g )  = SnCl2( l )  – 333,000 + 118.4 T  520– 925
SO2( g )  + ½ O2( g )  = SO3( g )  – 94,600 + 89.37 T  298– 2000
U( l )  + C( gr )  = UC( s )  – 102,900 + 5.02 T  1408– 2500
2U( l )  + 3C( gr )  = U2 C3( s )  – 236,800 + 25.1 T  1408– 2500
U( l )  + 2C( gr )  = UC2( s )  – 115,900 + 10.9 T  1408– 2500
V( s )  + ½ O2( g )  = VO( s )  – 424,700 + 80.04 T  298– 2000
Zn( v )  + ½ O2( g )  = ZnO( s )  – 460,200 + 198 T  1243– 1973
Note : Standard states are noted by subscript.

TABLE A.2: THE CONSTANT-PRESSURE MOLAR

HEAT CAPACITIES OF VARIOUS SUBSTANCES

The constant-pressure molar heat capacities are presented as

c p = a + bT + cT –2 J/K

or as

c p = a + bT + cT –2 + dT 2 J/K

and Table  A.2 includes the ranges of temperature in which the expressions are valid.
Example : For Ag in the range 298– 1234 K,

c p = 21.30 + 8.54 × 10 −3 T + 1.51 × 105 T −2 J/K

and for graphite in the range 298– 1100 K,

c p = 0.11 + 38.94 × 10 −3 T − 1.48 × 105 T −2 − 17.38 × 10 −6 T 2 J/K

652 APPENDIX A

Table A.2  The Constant-Pressure Molar Heat Capacities of Various Substances ( c  p =  a

+ bT + cT  – 2   J/mole· K) 
Substance  a   b  × 10 3   c  × 10 – 5   Range, K  Remarks 
Ag 21.30 8.54 1.51 298– 1234 (T m  )
Ag( l )  30.50 —  —  1234– 1600
Al( s )  20.67 12.38 —  298– 933(T m  )
Al( l )  31.76 —  —  933– 1600
Al2 O3  106.6 17.78 – 28.53 298– 2325(T m  )
Ba(α )  – 473.2 1587.0 128.2 298– 648
Ba(β )  – 5.69 80.33 —  648– 1003
BaO 53.30 4.35 – 8.30 298– 2286(T m  )
BaTiO3  121.46 8.54 – 19.16 298– 1800
C(graphite)  0.11 38.94 – 1.48 298– 1100 – 17.38 × 
10– 6 T 2 
C(graphite)  24.43 0.44 – 31.63 1100– 4000
C(diamond)  9.12 13.22 – 6.19 298– 1200
CO 28.41 4.10 – 0.46 298– 2500
CO2  44.14 9.04 – 8.54 298– 2500
Ca(α )  25.37 – 7.26 —  298– 716 23.72 × 
10– 6 T 2 
Ca(β )  – 0.36 41.25 —  716– 1115
CaO 49.62 4.51 – 6.95 298– 1177
CaTiO3  127.49 5.69 – 27.99 298– 1530
Cr( s )  24.43 9.87 – 3.68 298– 2130(T m  )
Cr2 O3  119.37 9.30 – 15.65 298– 1800
Cu( s )  22.64 6.28 —  298– 1356(T m  )
Fe(α /δ )  37.12 6.17 —  298– 1183/1664– 1809
Fe(γ )  24.47 8.45 —  1187– 1664
Fe( l )  41.8 —  —  1809– 1873
H2 O( g )  30.00 10.71 0.33 298– 2500
O2( g )  29.96 4.18 – 1.67 298– 3000
2MgO· 2Al2 O3 · 5SiO2  626.34 91.21 – 200.83 298– 1738(T m  )
N2  27.87 4.27 —  298– 2500
Si3 N4  70.54 98.74 —  298– 900
SiO2(α -quartz)  43.89 1.00 – 6.02 298– 847
Ti 22.09 10.46 —  298– 1155
TiO2(rutile)  75.19 1.17 – 18.20 298– 1800
Zr(α )  21.97 11.63 —  298– 1136
Zr(β )  23.22 4.64 —  1136– 2128
ZrO2(α )  69.62 7.53 – 14.06 298– 1478
ZrO2(β )  74.48 —  —  1478– 2950(T m  )
APPENDIX A 653

TABLE A.3: THE STANDARD MOLAR HEATS OF FORMATION

AND MOLAR ENTROPIES OF VARIOUS SUBSTANCES AT 298 K

Example : For the reaction

3
2Al( s ) + O2( g ) = Al 2O3( s )
2
∆H 298

K = −1, 675, 700 J

which is thus the standard molar heat of formation of Al2 O3  at 298 K. The molar
entropy of Al2 O3  at 298 K is 50.9 J/K. By convention, the standard molar enthalpies
of elements in their standard states at 298 K are assigned the value of zero.

Table A.3  The Standard Molar Heats of Formation

and Molar Entropies of Various
Substances at 298 K
o o
∆H 298 ,J S298 ,J K
Substance 
Al2 O3  – 1,675,700 50.9
Ba —  62.4
BaO – 548,100 72.1
BaTiO3  – 1,653,100 107.9
C(graphite)  —  5.73
C(diamond)  1,900 2.43
CH4  – 74,800 186.3
CO – 110,500 197.5
CO2  – 393,500 213.7
Ca —  41.6
CaO – 634,900 38.1
CaTiO3  – 1,660,600 93.7
3CaO· Al2 O3 · 3SiO2  – 6,646,300 241.4
CaO· Al2 O3 · SiO2  – 3,293,200 144.8
CaO· Al3 O3 · 2SiO2  – 4,223,700 202.5
2CaO· Al2 O3 · SiO2  – 3,989,400 198.3
Cr2 O3  – 1,134,700 81.2
H2 O( g )  – 241,800 232.9
N2  —  191.5
O 2  —  205.1
SiO2,(α -quartz)  – 910,900 41.5
Si3 N4  – 744,800 113.0
Ti —  30.7
TiO – 543,000 34.7
Ti2 O3  – 1,521,000 77.2
Ti3 O5  – 2,459,000 129.4
TiO2  – 944,000 50.6
Zr —  39.0
ZrO2  – 1,100,800 50.4
654 APPENDIX A

TABLE A.4: THE SATURATED VAPOR PRESSURES

OF VARIOUS SUBSTANCES

The saturated (equilibrium) vapor pressures of substances, in the stated ranges of

temperatures, are presented in the form

A
+ B ln T + C
ln p (atm ) = −
T
Example : The saturated vapor pressure exerted by liquid CaF2  in the range of tem-
perature 1691– 2783 K is given by

50, 200
ln p (atm ) = − − 4.525 ln T + 53.96
T
Thus, at its normal boiling temperature of 2783 K, the saturated vapor pressure of
liquid CaF2  is

50, 200
ln p (atm ) =− − 4.525 ln(2, 783) + 53.96
2, 783
=0
That is, at the normal boiling temperature, the saturated vapor pressure is 1 atm.

Table A.4  The Saturated Vapor Pressures of Various Substances 

ln p (atm) = − A / T + B ln T + C 
Substance  A   B   C   Range, K 
CaF2(α )  54,350 – 4.525 56.57 298– 1430
CaF2(β )  53,780 – 4.525 56.08 1430– 1691(T m  )
CaF2( l )  50,200 – 4.525 53.96 1691– 2783 (T b  )
Fe( l )  45,390 – 1.27 23.93 1809 (T m  )– 3330 (T b  )
Hg( l )  7,611 – 0.795 17.168 298– 630 (T b  )
Mn( l )  33,440 – 3.02 37.68 1517 (T m  )– 2348 (T b  )
SiCl4( l )  3,620 —  10.96 273– 333 (T b  )
Zn( l )  15,250 – 1.255 21.79 693 (T m  )– 1177 (T b  )
APPENDIX A 655

TABLE A.5: MOLAR HEATS OF MELTING AND TRANSFORMATION

Example : At the melting temperature of Ag (1234 K), the enthalpy change for

Ag( s ) → Ag(l )

is 11.090 J. Thus, at 1234 K, the molar heat of melting of Ag is 11,090 J. The change
in molar entropy due to melting at 1234 K is thus

∆H m 11, 090
= = 8.987 J/K
Tm 1234
At 1187 K, the enthalpy change for the transformation

Fe( α ) → Fe( γ )

is 670 J. The corresponding change in the molar entropy at 1187 K is thus

∆H trans 670
∆Strans = = = 0.56 J/K
Ttrans 1187

Table A.5   Molar Heats of Melting and Transformation

Substance  Trans.  ∆H trans , J T  trans , K 

Ag s  →  l  11,090 1,234
Al s  →  l  10,700 934
Al2 O3  s  →  l  107,500 2,324
Au s  →  l  12,600 1,338
Ba α  →  β  630 648
Ba β  →  l  7,650 1,003
Cu s  →  l  12,970 1,356
Ca α  →  β  900 716
CaF2  s  →  l  31,200 1,691
Fe α  →  γ  670 1,187
Fe γ  →  δ  840 1,664
Fe δ  →  l  13,770 1,809
H2 O s  →  l  6,008 273
K2 O· B2 O3  s  →  l  62,800 1,220
MgF3  s  →  l  58,160 1,563
Na2 O· B2 O3 s  →  l  67,000 1,240
Pb s  →  l  4,810 600
PbO s  →  l  27,480 1,158
Si s  →  l  50,200 1,685
V s  →  l  22,840 2,193
Zr α  →  β  3,900 1,136
ZrO2  α  →  β  5,900 1,478