Page 188 - Physical Chemistry

lev38627_ch05.qxd 3/3/08 9:33 AM Page 169

169
The lowest temperature reached in bulk matter by using adiabatic demagnetization is Further Reading
1.2 10 5 K [K. Gloos et al., J. Low. Temp. Phys., 73, 101 (1988); Discover, June
1989, p. 16]. Using a combination of laser light, an applied inhomogeneous magnetic
field, and applied radiofrequency radiation, physicists cooled a sample of 2000 low-
87
pressure Rb gas-phase atoms to 2 10 8 K [M. H. Anderson et al., Science, 269,
198 (1995); jilawww.colorado.edu/bec/). Silver nuclei have been cooled to a nuclear-
spin temperature of 2 10 9 K by adiabatic demagnetization (O. V. Lounasmaa,
Physics Today, October 1989, p. 26).

5.12 SUMMARY
The standard state (symbolized by the ° superscript) of a pure liquid or solid at tem-
perature T is defined as the state with P 1 bar; for a pure gas, the standard state has
P 1 bar and the gas behaving ideally.
The standard changes in enthalpy, entropy, and Gibbs energy for the chemical re-
action 0 → n A are defined as H° n H° m,T,i , S° n S° , and G°
T
T
i m,T,i
i
i
i
i
i
i
T
n G° m,T,i and are related by G° H° T S°. H° and G° of a reaction can
i
i
T
T
T
be calculated from tabulated H° and G°values of the species involved by using
f
f
H° n H° and G° n G° , where the standard enthalpy and Gibbs
i
i
f
i
T,i
T
i
f
T,i
T
energy of formation H°and G°correspond to formation of one mole of substance
i
f
f
i
i from its elements in their reference forms.
The convention that S° 0 for all elements and the third law of thermodynamics
0
( S 0 for changes involving only substances in internal equilibrium) lead to a con-
0
ventional S° value of zero for every substance. The conventional S° m,T value of a sub-
0
stance can then be found by integration of C° /T from absolute zero with inclusion of
P,m
S of any phase transitions.
Using H° (or S°) at one temperature and C° data, one can calculate H° (or
P
S°) at another temperature.
To avoid confusion, it is essential to pay close attention to thermodynamic sym-
bols, including the subscripts and superscripts. The quantities H, H, H°, and H°
f
generally have different meanings.
Important kinds of calculations discussed in this chapter include:
• Determination of H° of a reaction by combining H°values of other reactions
(Hess’s law).
• Calculation of U from adiabatic bomb calorimetry data.
r
• Calculation of H° from U°, and vice versa.
• Calculation of S° of a pure substance from C° P,m data, enthalpies of phase
m
3
changes, and the Debye T law.
• Calculation of H°, S°, and G° of chemical reactions from tabulated H°, S° ,
f
m
and G° data.
f
• Determination of H° (or S°) at one temperature from H° (or S°) at another
temperature and C° (T ) data.
P,m
• Estimation of H° using bond energies.
• Use of a spreadsheet to fit equations to data.
FURTHER READING
Heats of reaction and calorimetry: McGlashan, pp. 17–25, 48–71; Rossiter, Hamilton,
and Baetzold, vol. VI, chap. 7; S. Sunner and M. Mansson (eds.), Combustion
Calorimetry, Pergamon, 1979. The third law: Eyring, Henderson, and Jost, vol. I,
pp. 86–96, 436–486.
For data sources, see Sec. 5.9.