Page 130 - Essentials of physical chemistry

92 Essentials of Physical Chemistry

reasons, it turns out to be impossible to reach absolute 08K. Another problem is an isotope effect in
molecular structure. Suppose, we somehow freeze DCH 3 to a very low temperature near 18K. The
basic structure of methane is tetrahedral, but the orientation of the deuterium atom in the molecule
could be in any of four positions. Thus, even if we purify the substance and use something like
adiabatic nozzle expansion of He followed by the adiabatic demagnetization trick, we will still have
a matrix in which there is a randomness of the orientation of the C–D bond that leads to an
approximate entropy using Boltzmann’s equation of S k B ln (4) per molecular unit or on a molar
basis S R ln (4). Similar statistics are easy to see for molecules such as monodeuterobenzene,
where we would have something like S(1 K) R ln (6), S(1 K) R ln (3) for NDH 2 , and so forth

just to show the possibilities with deuterium (D) substitution for hydrogen.
The problem of behavior of the heat capacity of solids near 18K has been treated by Einstein
and by Debye to include the effects of vibration. For undergraduate treatment, it is sufficient to say
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that near 18K heat capacities of lattices vary roughly as T [2] so the heat capacity curve increases
after 18K. Other texts and monographs should be consulted for studies of materials at very low
temperatures, but here the ‘‘essential’’ facts are that S ¼ R ln (W) gives an approximate value for
3
low-temperature entropy due to isotope impurities and that the heat capacity varies as roughly T in
3
the 18K range. There would be a constant ‘‘A’’ characteristic of the material and then C P AT .As
usual there are alternate verbal descriptions of the third law of thermodynamics but our summary
would be

The entropy of a pure crystalline substance should be zero at 08K, but you really cannot get to 08K.

We will see in later chapters of this text that there are some strange quantum phenomena, which
occur at very low temperatures. In this chapter for what is known as ‘‘classical thermodynamics,’’ it
is sufficient to say that S ¼ R ln (W) is a valid formula that predicts an idealized value of zero for the
entropy of a substance at 08, but there are several reasons why you will not be able to reach absolute
zero in a practical way.

ENTROPY OF REACTIONS
Since entropy is a state variable, we can compute the change in entropy in a reaction just as we did
for enthalpy:

prod react
X X
0 0 0
i
rxn
j
DS (298 K) ¼ n i S n j S :
i j
Example
Hg (liq) þ 1=2O 2(gas) ! HgO (red) ,
0
DS (298 K) ¼ 70:25 75:90 (205:152=2) ¼ 108:226 J= K mol:

rxn
The entropy change is negative and quite large mainly due to the fact that the random O 2 gas
becomes localized in the red solid HgO, which is a drastic reduction in spatial randomness. We note
that if DS 0 is negative, the process is going toward a more ordered state. That is quite against the
rxn
natural tendency of entropy to increase, but if we compute the heat of the reaction, we see that the
reaction is also very exothermic, so we could say in this case the energy released in the reaction
makes it possible for the reaction to proceed to a more ordered state (Table 5.1):
0
DH (298) ¼ 90:79 0 (0=2) ¼ 90:79 kJ=mol:
rxn