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```							Reaction Equilibrium and Chemical Potential
Criteria for chemical equilibrium are:

 
i
i   i   0
13.8
  (G T ) 
           0
   T , P
These criteria are not in a useable form.
 Recall our definition of fugacity which applies to any species
in any phase (vapour, liquid, solid)
ˆ
i  Gi (T )  RT ln fi

Recall that Gi(T) is a temperature-dependent constant.
Also recall that enthalpy, internal energy and Gibb’s energy are
always specified an tabulated using a reference state.

CHEE 311                                                    1
Standard States
For reaction equilibrium calculations, the Gibbs energy at standard
conditions is the usual reference state.
Gio  Gi (T )  RT ln fio
These standard conditions are:
 pure component i
 at the reaction temperature
 in a user-defined phase (gas, liquid or solid)
 at a user-defined pressure (often 1 bar)

A great deal of thermodynamic data are published as the standard
properties of formation at STP (Table C.4 of the text)
 DGfo is standard Gibbs energy of formation per mole of the
compound when formed from its elements in its standard
state at 25oC.
» Gases: pure, ideal gas at 1 bar
» Liquids: pure substance at 1 bar

CHEE 311                                                    2
Chemical Potential and Activity
Subtracting this expression for the standard Gibbs energy (Gio) gets
rid of Gi(T):
ˆ
fi
i    Gio    RT ln o                           13.9
fi

We define a new parameter, activity, to simplify this expression:
i  Gio  RT ln ai
ˆ
where,
a ˆ
ˆ i  fi fio
The activity of a component is the ratio of its mixture fugacity to its
pure component fugacity at the standard state.

CHEE 311                                                        3
Reaction Equilibrium and Activity
When a reactive system reaches an equilibrium state, we know that
the equilibrium criterion is satisfied:

  ii  0
i
where i is the stoichiometric coefficient of component i and i is
the chemical potential of component i at the given P,T, and
composition.

Substituting for i in terms of activity gives:

i

 ii   i Gi  RT ln ai  0
i
o
ˆ         
Or,

 iiGio
 i ln ai 
ˆ
i              RT
CHEE 311                                                      4
The Equilibrium Constant
Our equilibrium expression for reactive systems can be expressed
concisely in the form:
i      i iGio
ˆ
ln  ai                                      13.10
i               RT
How does the sum  turn in to a product P ?

The right hand side of equation 13.10 is a function of pure
component properties alone, and is therefore constant at a given
temperature.
 The equilibrium constant, K, for the reaction is defined as:
 i iGio
K  exp                ˆ
  ai i                     13.11
RT         i

K is calculated from the standard Gibbs energies of the pure
components and the stoichiometric coefficients of the reaction.
CHEE 311                                                    5
Standard Gibbs Energy Change of Reaction
The conventional means of writing the equilibrium constant uses DGo,
the standard Gibbs energy change the reaction.
DGo  ii Gio

Using this notation, our equilibrium constant assumes the usual form:
 DGo                        13.11
K  exp
RT
When calculating an equilibrium constant (or interpreting a literature
value), pay attention to standard state conditions.
 Each Gio must represent the pure component at the
temperature of interest and in the state of interest.

DGo
  ln K
RT
CHEE 311                                                     6
Temp. Dependence of Reaction Equilibrium

DGo
  ln K
RT
K depends on temperature because DG/RT depends on T
d (DG o / RT )  DH o
           Gibbs-Helmholtz eqn.
dT          RT 2
From which we can derive the temperature dependence of K:

d ln K DHo                              13.14

dT     RT2
If we assume that DHo is independent of temperature, we can integrate
13.14 directly to yield:
13.15
K    DHo  1 1 
ln         
K1    R  T T1 
CHEE 311                                                  7
K vs Temperature
Equation 12.15 predicts that ln K
versus 1/T is linear. This is based on
the assumption that DHo is only a
weak function of temperature over the
range of interest.
 This is true for the
reactions, in Figure13.2

 Why is DHo a function of T?

 What do we do if we are
computing K?

CHEE 311                               8
Equilibrium State of a Reactive System
Let’s use the equilibrium constant to determine concentrations at
eq’m.
 i iGio
exp                    ˆ
 K   ai i
RT             i

Consider the gas phase reaction:
CH4  H2O             CO  3H2
The equilibrium constant gives us:

ˆ ˆ3
aCOaH2
K
ˆ    ˆ
aCH4 aH2O
Or

ˆ       o    ˆ      o
( fCO / fCO )( fH2 / fH2 )3
K
ˆ         o     ˆ        o
( fCH / fCH )( fH O / fH O )
4      4     2     2
CHEE 311                                                   9

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