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5.9 THERMODYNAMICS TABLES Section 5.9
Thermodynamics Tables
Tabulations of thermodynamic data most commonly list H° , S° , G° , and
f 298 m,298 f 298
C° . Older tables usually use the thermochemical calorie ( 4.184 J) as the energy
P,m,298
unit. (Some physicists and engineers use the international-steam-table calorie, defined
as 4.1868 J.) Newer tables use the joule.
Prior to 1982, the recommended standard-state pressure P°was 1 atm, and values
in older tables are for P° 1 atm. In 1982, the International Union of Pure and
Applied Chemistry (IUPAC) changed the recommended standard-state pressure to 1
5
bar, since 1 bar ( 10 Pa) is more compatible with SI units than 1 atm. Most newer
tables use P° 1 bar. Thermodynamic properties of solids and liquids vary very
slowly with pressure (Sec. 4.4), and the change from 1 atm (760 torr) to 1 bar (750.062
torr) has a negligible effect on tabulated thermodynamic properties of solids and liq-
uids. For a gas, the standard state is an ideal gas. For an ideal gas, H and C depend
m P,m
on T only and are independent of pressure. Therefore H°and C° of gases are un-
f P,m
affected by the change to 1 bar. The effect of an isothermal pressure change on an
ideal-gas entropy is given by (3.30) and Boyle’s law as S S nR ln (P /P ), so
2 1 1 2
S S 18.314 J>mol-K2 ln 1760>750.0622 0.1094 J>1mol K2 (5.41)
m,T,1 bar m,T,1 atm
The change from 1 atm to 1 bar adds 0.109 J/(mol K) to S° of a gas. This change is
m
small but not negligible. Since S° is changed, so is G° if any species in the forma-
m f
tion reaction is a gas (see Prob. 5.49). For a full discussion of the effects of the 1-atm
to 1-bar change, see R. D. Freeman, J. Chem. Educ., 62, 681 (1985).
The tabulated values of G° and H° depend on the reference forms chosen for
f T f T
the elements at temperature T. There is a major exception to the rule that the reference
form is the most stable form at T and 1 bar. For elements that are gases at 25°C and 1
bar, most thermodynamics tables choose the reference form as a gas for all tempera-
tures below 25°C, even though the stable form might be the liquid or solid element. In
mixing G° and H° data from two tables, one must be sure the same reference
f f
forms are used in both tables. Otherwise, error can result.
H°, S°, and G° at temperatures other than 25°C can be calculated from tables
of H°, S° , and G° at various temperatures. Instead of tabulating H°and G°
f m f f f
versus T, some tables list H° H° (or H° H° ) versus T and (G° H° )/
m,T m,298 m,T m,0 m,T m,298
T [or (G° H° )/T] versus T. To find H° and G° from such tables, we use
m,T m,0 T T
¢H° ¢H° a n 1H° H° 2 (5.42)
T 298 i m,T m,298 i
i
¢G° ¢H° T a n 31G° H° 2>T4 (5.43)
T 298 i m,T m,298 i
i
Equation (5.42) follows from n (H° H° ) n H° n H°
i i m,T m,298 i i i m,T,i i i m,298,i
H° H° . Equation (5.43) is proved similarly.
T 298
EXAMPLE 5.11 G°
T
At T 1000 K, some values of (G° H° )/T (note the minus sign) in
m,T m,298
J/(mol K) are 220.877 for O (g), 212.844 for CO(g), and 235.919 for CO (g).
2 2
Find G° for 2CO(g) O (g) → 2CO (g).
1000 2 2
Using Appendix H° data, we find H° 565.968 kJ/mol (as in
f 298 298
Example 5.5 in Sec. 5.5). Substitution in (5.43) gives
¢G° 565.968 kJ>mol 11000 K2 321 235.9192 21 212.8442
1000
3
1 220.8772410 kJ>1mol K2
391.241 kJ>mol