Recall the definition of the equilibrium constant, i.e., for the reaction:

The equilibrium constant (in terms of concentrations) is:

Understanding the definition of the equilibrium constant allows the numerical combination of equilibrium constants from manipulation of the reaction equation

Consider the Decomposition of NO₂

Consider the Oxidation of SO₂

Reaction 1 is really an oxidation in reverse, i.e. we can also write the same reaction as the oxidation of NO:

The reaction of NO₂ with SO₂ can be considered as the sum of reactions (1) and (2)

Clearly this reaction equation is not formally balanced, but half of this reaction is.

Each of the above reaction five reaction equations has an associated equilibrium constant, labeled K₁ through K₅. A clear mathematical relationship exists between the between the above equilibrium constants. For instance, equation (3) is the reverse of equation (1). Therefore:

Reaction (5) is the simple sum of reactions (1) and (2) where the redundant O₂ is removed from both sides of the reaction equation. The equilibrium constant for this combined reaction is:

The equilibrium constant is sensitive to an overall scaling of the reaction equation stoichiometry. The halving of all the stoichiometric coefficients, , has the result:

Other Important Features of the Equilibrium Constant

• The Equilibrium Constant is a function of temperature only
• All pure phases are ignored in the Equilibrium expression
• 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)
• The values of the equilibrium constant can vary greatly, i.e.

or on the other hand

and very importantly for Acid Base Equilibria

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 expression for K_C:

The proper quotient of equilibrium partial pressures, assuming the ideal gas equation of state (pV=nRT) is

Therefore the relationship relating the equilibrium constants K_p and K_C is temperature dependent