The equilibrium expression symbolized by Keq or Kc has the reactants and products written in brackets [ ] to represent molar concentration. The reaction N2O4 2NO2(g) according to the law of mass action would be written as:
However since both species of the reaction are gases, it is possible to write an equilibrium expression based upon the partial pressure of each gas
The two expression, Kp and Kc, are not numerically the same. To convert from one equilibrium constant to the other requires a correction factor where n =( moles of gaseous products - moles of gaseous reactants). To convert Kc to Kp use the equation
.
The equation is derived from the Kp for a general reaction, aA(g) bB(g) where a and b are stoichiometric coefficients. The equilibrium expression for the above reaction in terms of concentration units (mols/L) is written as
The same equation using partial pressures of both A and B is formulated as
Both of these are legitimate ways to express the equilibrium of the equation aA(g) <=> bB(g) since A and B are gases.
To derive the equation begin with the equilibrium expression for and substitute the values of PA and PB shown here as
into the equilibrium expression to obtain the following formula
Since moles/volume are concentration terms then the equation is reduced to
Where (b-a) is the change in moles of gaseous components written as Dn which renders the equation for converting Kp to Kc as
. Note that R can be expressed as 0.082 L atm/mol K, so the equation can be amended to be .