Modern Engineering Thermodynamics

628 CHAPTER 15: Chemical Thermodynamics
Equation (15.31) can be written on a per unit mole basis for chemical species i with partial pressure p i and
negligible entropy production as
dg i = v i dp i − s i dT
When the system has a constant temperature T and a constant total pressure p m and the substances involved can
be treated as ideal gases, this equation reduces to
d g i = v i dp i = RTðdp i /p i Þ
which can be easily integrated from the standard reference state pressure p° to any other state at partial pressure
p i and temperature T as
g i ðp, TÞ = g • i
ðp°, TÞ+ RT ln ðp i /p° Þ (15.33)
where p° is the standard reference state pressure of 0.100 MPa, and g • i
is known as the molar specific Gibbs
function at (unfortunately) a new reference state of 0.100 MPa and temperature T.
The new reference temperature is normally chosen to be the mixture temperature T m rather than the traditional
standard reference state temperature of 25.0°C. Consequently, there are new fourth reference states for thermodynamic
properties discussed in this chapter. They are 4
1. The arbitrarily chosen reference state (e.g., the triple point, as in the steam tables).
2. The standard reference state at 0.1 MPa and 25°C.
3. The absolute value reference state at 0.1 MPa and 0 K.
4. The mixture temperature reference state at 0.1 MPa and T m .
Although the introduction of an additional reference state at this point whose temperature is not given a fixed
value (like 25.0°C) tends to complicate the logic somewhat, it does simplify the notation and the resulting calculations.
Using the definition of the Gibbs function and some simple algebraic manipulation, we can arrive at
a working formula for calculating accurate values of g i ðp, TÞ by using property values listed in Table C.16c in
Thermodynamic Tables to accompany Modern Engineering Thermodynamics and Table 15.7. The required algebraic
manipulations are
or
g • i ðat p°, TÞ = ðg f °Þ i + ½g• i ðat p°, TÞ − ðg f °Þ i Š
= ðg f °Þ i
+ f½ðhðat TÞ − T sðat p°, TÞŠ i
− ½ðh°ðat T°Þ − T°s°ðat p°, T°ÞŠ i
g
g • i ðat p°, TÞ = ðg f °Þ i + ½hðat TÞ − h°ðat T°ÞŠ i − T½sðat p°, TÞŠ i + T°½s°ðat p°, T°ÞŠ i (15.34)
where T° is the standard reference state temperature of 298 K or 537 R. The superscript ∘ on a quantity implies
that it is at the standard reference state, whereas the superscript • impliesthatitisatthenewreferencestateof
T = T m and 0.100 Mpa. Values for ðg f °Þ i
and ½s°ðat p°,T°ÞŠ i
can be found in Table 15.7, and values for
½h ðat TÞ − h°ðat T°ÞŠ i and ½s ðat p°,TÞŠ i (and also ½s°ðat p°,T°ÞŠ i ) can be found in Table C.16c for various common
substances.
Substituting Eq. (15.33) into Eq. (15.32) gives
∑
R′
v i g • i −∑ v i g • i
P′
= RT ∑
P′
v i lnðp i /p°
Þ−∑
R′
v i lnðp i /p° Þ
= RT ln ∏ ðp i /p° Þ v i
− ln ∏ ðp i /p° Þ v
i
P′
2
∏ ðp i /p°
6 P′
= RT ln4
ðp i /p°
∏
R′
Þ vi
Þ v i
R′
3
7
5 = RT ln
K e
4 Confusing, isn’t it?