Ways of Expressing Equilibrium Constants

In my previous post, I posted how to express the Equilibrium Constant Expressions for a given reaction, the standard format using molarity as unit for the concentration of reactants and products.  But we can't avoid the fact that we have different types of reactions, there are reactions which involve the same reacting species and involve all gases, and there are some the same reacting species but involve aqueous solutions. There are also reactions that the reacting species are of different phases.  This post will introduce to you the different ways of expressing equilibrium constant expression.

Homogeneous Equilibria

Homogeneous equilibrium applies to the reaction where the reacting species are in the same phase. Let us have an example: 

In the above reaction, it shows the dissociation of N2O4; the reactant is a gas and the product is a also a gas. We can express two equilibrium constant expressions in this type of reaction:

Kc denotes that the reacting species is expressed in molarity or mole per liter.  Since the reactant and the product in the above reaction are all gases the concentration can also be expressed in terms of their partial pressures.  In gases, at constant temperature the pressure P of a gas is directly related to the concentration in moles per liter; that is P=(n/V)RT.  Thus the above equation, the equilibrium constant can also be expressed using the partial pressures of gases.

PNO2 and PN2O4 are the equilibrium partial pressures (in atmospheres) of NO2 and N2O4 respectively.  On the other hand, the subscript in Kp tells us the equilibrium is expressed in terms of pressures.

Kc is not equal to Kp because the concentration of the reactants and the products are not the same with the partial pressures of the reactants and products.  The relationship between Kc and Kp can be derived using the ideal gas equation PV=nRT.  Since : 

and so Kc and Kp are related 

where 

               0.0821 L.atm/K.mol.  is the universal gas constant (R).  To use the above equation, the pressures in Kp must be in atm.  

In general Kc and Kp are not equal but in special case that the change in n is equal to zero therefore Kc = Kp.

And with regards to the unit of Kc and Kp, since the units are canceled out. there is no unit for K.

Let us have an example.  Write the Kc or Kp expressions of the following reactions if applicable:

We need to keep in mind the following:

     a.  Kp expression applies only to gaseous reaction.

     b.  The concentration of the solvent (particularly water) does not appear in the equilibrium constant expression.

Solution:

a.  

b.  

c.   

Heterogeneous Equilibria

Heterogeneous equilibrium is a reversible reaction involving reactants and products that are in different phases.  Example is the decomposition of calcium carbonate when heated, below is the equilibrium reaction:

There are three separate phases in the above reaction, two solid phases and one gas phase.  In writing equilibrium constant, not only pure liquid which is not included in the equilibrium constant but also pure solids.  Therefore the equilibrium constant expression of the above reaction is:

This was taken from

Since CaO and CaCO3 are solids, the concentration can be converted to 1, and so the final equilibrium constant expression is 

Kp can also be used since CO2 is a gas, therefore  Kp = PCO2.

Sample Problem:

Calculate the Kp and Kc of the reaction below at 800 degree Celsius. The pressure of CO2 is 0.236 atm.

                                       

Solution:

                  Kp = PCO2

                        =  0.236

so,

                  

            

In this case T = 800 + 273 = 1073 K, 🔺n =1. Substituting values,