8.5: Equilibrium

Learning Objectives

• Define chemical equilibrium and the equilibrium constant, K.
• Recognize chemical equilibrium as a dynamic process.

Consider the following reaction occurring in a closed container (so that no material can go in or out):

H₂ + I₂ → 2HI

This is the reaction between elemental hydrogen and elemental iodine to make hydrogen iodide. The way the equation is written, we are led to believe that the reaction goes to completion, that all the H₂ and the I₂ react to make HI.

However, this is not the case. The reverse chemical reaction is also taking place:

2HI → H₂ + I₂

It acts to undo what the first reaction does. Eventually, the reverse reaction proceeds so quickly that it matches the speed of the forward reaction. When that happens, the reaction has reached chemical equilibrium, the point at which the forward and reverse processes balance each other's progress.

Because two opposing processes are occurring at once, it is conventional to represent an equilibrium using a double arrow, like this:

\[H_{2}+I_{2}\rightleftharpoons 2HI\nonumber \]

The double arrow implies that the reaction is going in both directions. Note that the reaction must still be balanced.

Example \(\PageIndex{1}\)

Write the equilibrium equation that exists between calcium carbonate as a reactant and calcium oxide and carbon dioxide as products.

Solution

As this is an equilibrium situation, a double arrow is used. The equilibrium equation is written as follows:

\[CaCO_{3}\rightleftharpoons CaO+CO_{2}\nonumber \]

Exercise \(\PageIndex{1}\)

Write the equilibrium equation between elemental hydrogen and elemental oxygen as reactants and water as the product.

Answer

\[2H_{2}+O_{2}+\rightleftharpoons 2H_{2}O\nonumber \]

One thing to note about equilibrium is that the reactions do not stop; both the forward reaction and the reverse reaction continue to occur. They both occur at the same rate, so any overall change by one reaction is canceled by the reverse reaction. We say that chemical equilibrium is dynamic, rather than static.The concentration of reactants and products does not change over time.

Both reactions are occurring simultaneously, the equilibrium can be written backward. For example, representing an equilibrium as

\[H_{2}+I_{2}\rightleftharpoons 2HI\nonumber \]

is the same thing as representing the same equilibrium as

\[2HI\rightleftharpoons H_{2}+I_{2}\nonumber \]

The reaction must be at equilibrium for this to be the case.

The Equilibrium Constant

In the mid 1860s, Norwegian scientists C. M. Guldberg and P. Waage noted a peculiar relationship between the amounts of reactants and products in an equilibrium. No matter how many reactants they started with, a certain ratio of reactants and products was achieved at equilibrium. Today, we call this observation the law of mass action. It relates the amounts of reactants and products at equilibrium for a chemical reaction. For a general chemical reaction occurring in solution,

\[aA+bB\rightleftharpoons cC+dD\nonumber \]

the equilibrium constant, also known as K_eq, is defined by the following expression:

\[K_{eq}=\frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}\nonumber \]

where [A] is the molar concentration of species A at equilibrium, and so forth. The coefficients a, b, c, and d in the chemical equation become exponents in the expression for K_eq. The K_eq is a characteristic numerical value for a given reaction at a given temperature; that is, each chemical reaction has its own characteristic K_eq. The concentration of each reactant and product in a chemical reaction at equilibrium is related; the concentrations cannot be random values, but they depend on each other. The numerator of the expression for K_eq has the concentrations of every product (however many products there are), while the denominator of the expression for K_eq has the concentrations of every reactant, leading to the common products over reactants definition for the K_eq.

Example \(\PageIndex{2}\)

Balance the reaction equation and then write the corresponding equilibrium constant expression:

CO(g) + O₂(g) ⇌ CO₂(g)

Solution

The balanced chemical equation is:

2CO(g) + O₂(g) ⇌ 2CO₂(g)

The equilibrium constant expression is:

Many chemical reactions involve substances in the solid or liquid phases. For example, a particular chemical reaction is represented as follows:

\[\ce{2NaHCO3(s) <=> Na2CO3(s) + CO2(g) + H2O(l)} \]

This chemical equation includes all three phases of matter. This kind of equilibrium is called a heterogeneous equilibrium because there is more than one phase present.

The rule for heterogeneous equilibria is as follows: Do not include the concentrations of pure solids and pure liquids in K_eq expressions. See example 3 and 4 below.

Example \(\PageIndex{3}\)

Write the equilibrium constant expression for the following reaction:

C(s) + H₂O(g) ⇌ CO(g) + H₂(g)

Solution

The equilibrium constant expression is:

The concentration of the solid C(s) is the number of moles present in a given volume, a value that never changes at a given temperature, so the concentration of solid reactants or products are omitted in the equilibrium constant expression.

Example \(\PageIndex{4}\)

Write the equilibrium constant expression for the following reaction:

H₂SO₄(aq) + H₂O(l) ⇌ HSO₄^-(aq) + H₃O⁺(aq)

Solution

The equilibrium constant expression is:

The solvent (H₂O) is left out of the equilibrium constant expression because the concentration of the solvent is very high and does not change significantly during a reaction.