Page 181 - Physical Chemistry

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Chapter 5 The standard entropy of formation S° is calculated from tabulated entropy values
T,i
f
Standard Thermodynamic S° for substance i and its elements. Knowing H° and S° , we can calculate and
Functions of Reaction m,T f T,i f T,i
then tabulate G° .
f T,i
EXAMPLE 5.9 Calculation of G°
f 298
Use Appendix H° and S° data to calculate G° for H O(l) and com-
f 298 m,298 f 298 2
pare with the listed value.
1
The formation reaction is H (g) O (g) → H O(l), so
° 2 2 2 2
∆ f G 298 1
¢ S° 298,H 2 O1l2 S° m,298,H 2 O1l2 S° m,298,H 2 1g2 2 m,298,O 2 1g2
S°
f
¢ S° 369.91 130.684 1 2 1205.13824 J>1mol K2 163.34 J>1mol K2
f
3
298
H° is 285.830 kJ/mol, and (5.40) gives
f 298
¢ G° 285.830 kJ>mol 1298.15 K21 0.16334 kJ>mol-K2
298
f
3
237.129 kJ>mol
which agrees with the value listed in the Appendix.
Exercise
Use Appendix H°and S° data to calculate G° for MgO(c) and compare
f m f 298
with the listed value. (Answer: 569.41 kJ/mol.)
Figure 5.12 plots some G° values, and the Appendix lists G° for many
f 298 f 298
substances. From tabulated G° values, we can find G° for a reaction using
f T T
(5.39).

EXAMPLE 5.10 G°for a reaction

Find G° for 4NH (g) 3O (g) → 2N (g) 6H O(l) from Appendix data.
298 3 2 2 2
Substitution of Appendix G° values into (5.39) gives G° as
f 298 298
32102 61 237.1292 3102 41 16.4524 kJ>mol 1356.97 kJ>mol
Exercise
Use Appendix data to find G° for C H (g) 5O (g) → 3CO (g) 4H O(l).
298 3 8 2 2 2
(Answer: 2108.22 kJ/mol.)
Figure 5.12
G° values. The scale is
f 298 Suppose we want G° for a reaction at a temperature other than 298.15 K. We
logarithmic.
previously showed how to find S°and H° at temperatures other than 298.15 K. The
use of G° H° T S° then gives G° at any temperature T.
T T T
We have discussed calculation of thermodynamic properties from calorimetric
data. We shall see in Chapter 21 that statistical mechanics allows thermodynamic
properties of an ideal gas to be calculated from molecular data (molecular structure,
vibrational frequencies, etc.).

An alternative to tabulating G°values is to tabulate conventional standard-state Gibbs
f
energies G° , defined by G° H° TS° , where H° and S° are conventional
m,T m,T m,T m,T m,T m,T
enthalpy and entropy values (Secs. 5.4 and 5.7). For an element in its reference form, the
conventional H° is zero [Eq. (5.17)], but S° is not zero. (S° is zero.) Therefore the
m,298 m,298 m,0
conventional G° of an element is not zero.
m,298