Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 6
SEC TION 14.3 ? Entropy Changes in a System
575
Practice Problem A t t e m p t ? Determine the change in entropy (?Ssys ), for the expansion of 0.10
mole of an ideal gas from 2.0 L to 3.0 L at constant temperature.
Practice Problem b u i l d? To what fraction of its original volume must a 0.50-mole sample of
ideal gas be compressed at constant temperature for ?Ssys to be –6.7 J/K?
Practice Problem c o n c e p t ua l i z e ? Which equation is correct for calculating DSsys for a
gaseous reaction that occurs at constant volume?
P
P
nR
DSsys 5 nR????DSsys 5 nRT ln _____?
?? initial
??????DSsys 5 nR ln _____?
?? initial
??????DSsys 5 ___?ln
?? ??
Pfinal
Pfinal
T
(i)
(ii)
(iii)
P
_____?
?? final???
Pinitial
(iv)
Standard Entropy, S°
Although Equation 14.1 provides a quantitative definition of entropy, we seldom use it or Equation
14.3 to calculate the entropy change for a real process because of the difficulty involved in determining W, the number of different possible arrangements (Equation 14.2) in a macroscopic system.
Instead, for processes other than isothermal expansion or compression of an ideal gas (for which we
can use Equation 14.4), we routinely determine entropy changes using tabulated values.
Using calorimetry [9 Section 10.4], it is possible to determine the absolute value of the
entropy of a substance, S; something we cannot do with either energy or enthalpy. (Recall that
while we can determine ?U and ?H for a process that a system undergoes, we cannot determine
the absolute values of either U or H for a system [9 Sections 10.2 and 10.3].) Standard entropy
is the absolute entropy of a substance at 1 atm. (Tables of standard entropy values typically are
the values at 25°C because so many processes are carried out at room temperature—although
temperature is not part of the standard state definition and therefore must be specified.) Table 14.2
lists standard entropies of a few elements and compounds. Appendix 2 provides a more extensive
listing. The units of entropy are J/K ? mol. We use joules rather than kilojoules because entropy
values typically are quite small. The entropies of substances (elements and compounds) are always
positive (i.e., S > 0), even for elements in their standard states. (Recall that the standard enthalpy
of formation, ?H°, for elements in their standard states is arbitrarily defined as zero, and for comf
pounds it may be either positive or negative [9 Section 10.6].)
Referring to Table 14.2, we can identify several important trends:
• For a given substance, the standard entropy is greater in the liquid phase than in the solid
phase. [Compare the standard entropies of Na(s) and Na(l).] This results from there being
greater molecular motion in a liquid, resulting in many possible arrangements of atoms in
the liquid phase; whereas the positions of atoms in the solid are fixed.
• For a given substance, the standard entropy is greater in the gas phase than in the liquid
phase. [Compare the standard entropies of Na(l) and Na(g) and those of H2O(l) and H2O(g).]
This results from there being much greater molecular motion in a gas, resulting in many
more possible arrangements of atoms in the gas phase than in the liquid phase—in part
because the gas phase occupies a much greater volume than either of the condensed phases.
• For two monatomic species, the one with the larger molar mass has the greater standard
entropy. [Compare the standard entropies of He(g) and Ne(g).]
• For two substances in the same phase, and with similar molar masses, the substance with
the more complex molecular structure has the greater standard entropy. [Compare the
Ta b le 1 4 .2
Student Annotation: You will find that
tables, including Appendix 2, contain ????????????????????????????????????)?????U????????????????????????????????)????????????????????????????Q????????????????????????????????????????)???????????????????????????????)????????????????????????????????)????????????????????????????????e?)?????????????????????????????????)????????????????????????????????)???????????????()M????????????Y?????O
??????M????M???????????
? ()M??????()O
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