Definition of Equilibrium Constant

A reaction's equilibrium constant, K_eq, measures the extent to which reactants are converted to products by the reaction. Equilibrium constants are found by multiplying the concentrations of the reaction's products raised to the power of their stoichiometric coefficients divided by the multiplication product of the concentrations of its reactants raised to the power of their stoichiometric coefficients.

On first reading, that might seem complicated, but it gets a bit easier with some discussion.

Discussion and Examples

Chemical reactions often do not convert all reactants to products. In practice, many reactions reach a state of balance or dynamic equilibrium in which both reactants and products are present.

K_eq measures the extent to which reactants are converted to products in a reaction. K_eq is a number that, under specified conditions, is always the same for a given reaction. If the temperature changes, the equilibrium constant will change. This means that when you quote an equilibrium constant, you must also quote the temperature it was obtained at.

Example of an equilibrium constant for a very simple reaction

Let's consider a simple case of a reaction in which substances A and B have reached equilibrium with one another - shown by the reverse arrow.

A B

Equilibrium does not necessarily mean that the substances are present in equal amounts. It means that the reaction has reached a point where the concentrations of the reactant and product are unchanging with time, because the forward and backward reactions have the same rate.

For the reaction, as it is written above, the equilibrium constant, K_eq, is equal to:

K_eq = [B]/[A]

The square [ ] brackets indicate the concentration of the chemical species. i.e., for example, K_eq[A] is the concentration of subtance A.

We can deduce the following:

Useful rules of thumb are:

Example of an equilibrium constant for a reaction where there are two reactants and two products

For the balanced reaction:

aA + bB cC + dD

the equilibrium constant, Keq is:

           [C]c [D]d
Keq = -------------
           [A]a [B]b 

Again, the square [ ] brackets indicate the concentration of the chemical species.

Rules for Writing K_eq Expressions

Example of an equilibrium constant for a reaction involving gases and solutes in solution

Zn_(s) + 2H⁺_(aq) Zn²⁺_(aq) + H_{2 (g)}

	 
       [Zn2+] . PH2 
K  =  ----------------
            [H+]2 
		

P is the partial pressure of H₂.

Do equilibrium constants have units?

The correct answer is usually they do. The units are decided by the calculation for K_eq. Every time you calculate an equilibrium constant, you need to calculate the units for the equilibrium constant too.

For example, let's look at the gas phase reaction that produces ammonia from hydrogen and nitrogen. The reaction equilibrium is:

N_{2 (gas)} + 3H_{2 (gas)} 2NH_{3 (gas)}

The equilibrium constant is:

	 
              (PNH3)2
Keq =  ----------------
              PN2 (PH2)3
		

If the partial pressures of each gas are measured in atmospheres, the units of the equilibrium constant for this reaction will be:

	 
                atm2
Units =  ----------------
             atm . atm3
		

Which simplifies by algebraic cancellation to atm ^-2

Sometimes the algebraic cancellation will result in the equilibrium constant having no units.

Equilibrium constants in specific types of reaction

In many instances, rather than seeing the equilibrium constant written in its general way K_eq, you will see it written otherwise - in a specific way. For example in gas phase reactions where partial pressures rather than concentrations are used, the equilibrium constant will be written as K_p.

Here are more examples of equilibrium constants with specific names for different classes of reactions:

• Gas-phase reactions that use units of partial pressure: K_p
• Dissociation of water: dissociation constant of water, K_w
• Dissociation of acids: acid dissociation constant, K_a
• Reaction of bases with water: base hydrolysis constant, K_b
• Solubility of precipitates: solubility product, K_sp
• Formation of complexes: formation constant, K_f






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