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… Free Energy of a Gas Define the molar Gibbs free Energy, μ: Pseudo-definition
Note: this is a little sloppy: Really: μ(T,p) = μ 0 (T) + RT ln (p/p 0 ) (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!!!
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! Standard state
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 KQ 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 K C and K p : 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 K C, if the standard is 1 atm pressure, the equilibrium constant is labeled K p Recall the definition of K C: 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: