# Slide 1

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Free Energy of a Gas
‘Define’ the molar Gibbs free
Energy, μ:

G
G                  Pseudo-definition
n

We will call μ the Chemical Potential
Right now we will think of it as the molar free energy, but
we will refine this definition later…
Note: this is a little sloppy:
Really:
μ(T,p) = μ0(T) + RT ln (p/p0)
(argument of ln dimensionless)

I (and many others) will continue to be sloppy in
this regard, so remember p is in the units
defined by the Standard State !!!

The above holds for an Ideal Gas, Only!!!
Standard
state

We can now use any relation that we derive for
an ideal gas mixture for real gases --- just
replace p with f everywhere.
f (the ‘effective pressure’) cannot be read on a
gauge but must be evaluated from an EOS!
Chemical Reactions and Free Energy
Holds for any ideal mixture, not just gases
For an IDEAL MIXTURE (even liquids/solids):
Gmix is solely the result of the increase in Entropy!
Hmix = 0
Vmix = 0

Danger!
This is not always the case: (Ethanol/Water for example)
Important Features of the Equilibrium Constant

•The Equilibrium Constant is a function of temperature only

•All pure phases are ignored in the Equilibrium expression (exact)

•The concentration of the solvent is ignored in solution equilibrium
(approximation)

•The Equilibrium Constant is taken as a dimensionless number with all
concentration values referenced to a standard state
(Standard state arbitrary but its choice has numerical consequence)
Consider any reaction (even solution phase) whose constituents can be
considered an ideal mixture
aA + bB ↔ cC + dD

The free energy change will be:

where

At equilibrium, G=0 and K≡Q

Which defines the ‘equilibrium expression’

or
In analogy to what we did for real gases, we can define an
‘effective concentration’ for real solutions called the activity, and
replace the concentration with it everywhere
A note on KC and Kp: The equilibrium constant is taken as a dimensionless
number that is a function of temperature only. Since there are no units, we
must be careful to reference the proper definition of concentration (molecular
number density). For gases, the concentration may be quoted as pressure
(atm) or molarity (mol/l). If the standard of concentration is 1 mol/L, we say
the equilibrium constant is KC, if the standard is 1 atm pressure, the
equilibrium constant is labeled Kp
Recall the definition of KC:

The proper quotient of equilibrium partial pressures, assuming the
ideal gas equation of state (pV=nRT) (only choice, really) is:
Therefore, the numerical value of the equi8librium constant depends
on the choice of standard state and the temperature through a
difference in the number of gas phase moles between products and
reactants:
Recall The temperature Dependence of G??
Fin

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