The word equilibrium is usually interpreted to mean balance or stability. In chemistry, equilibrium refers to physical or chemical changes that proceed in both directions at the same rate. Let’s look at an insulated container containing a “mixture” of ice and water at 0 C. Because no energy is getting into or out of the system, the amount of ice and water in the system stay the same. The reason for this is that the rate of melting of ice is equal to the rate of freezing of the water.

H₂O _(s)  <-->   H₂O _(l)

We see no change because for every solid molecule that enters the liquid state, there is a liquid molecule that enters the solid state. Since the forward and reverse reactions are still taking place, we refer to this as a dynamic equilibrium. In the previous unit, we used DG to determine whether or not a reaction was spontaneous. A negative DG indicates the reaction is spontaneous whereas a positive DG indicates the reaction is not spontaneous. At equilibrium, the DG of the system is zero, indicating equal likelihood of forward and reverse reactions taking place.

Most chemical reactions do not go to completion, but reach a state of equilibrium. For example, the reaction H₂ + I₂ <-->  2 HI. The double arrow indicates the reaction can proceed both directions. If we were to place some H₂ and I₂ into a container and follow the amount of reactants and products, we would see a decrease in concentration of reactants and an increase in the product concentration. At some point the concentrations of reactants and products would level off. We notice at some point the concentrations of reactant and product no longer change. Does the reaction stop or does it continue?

A graph of the concentration of reactants and products over time is shown below. As we can see, the reactants start out at an initial concentration which declines over a period of time until it levels off. The products are not present initially, but increase over time until level off at a certain concentration.

If we examine a graph of the rates of the forward and reverse reactions, the rate for both reactions changes over time. Initially, the forward reaction is at a maximum. Over time, it slowly decreases until it reaches a steady state at equilibrium. The reverse reaction initially has a rate of zero because at the very beginning, there is no product that can react. Over time the amount of product increases and the rate of the reverse reaction increases until it reaches a steady state at equilibrium.

When equilibrium is reached, both the forward and reverse reactions continue, but at the same rate. This results in no change in the concentration of reactants or products at equilibrium. This type of equilibrium is referred to as a dynamic equilibrium.

Notice that in the concentration graph, the reactants and products level off at different concentrations. In nearly all situations, the products and reactants have different concentrations at equilibrium.

Examining the rate graph shows us that even though the reactants and products end up at a different concentration, the rates of forward and reverse reactions are the same at equilibrium.

Why does the rate of the forward reaction start out fast and slow down whereas the rate of the reverse reaction start slow and speed up? The answer lies in the graphs of the concentrations. Initially the concentration of the reactants is high, which increases the probability of them colliding with each other and reacting. As the concentration of reactants decreases, the probability that they will collide and react with each other decreases. This decreases the rate. The rate at equilibrium doesn’t change because the concentration of the reactants does not change. Why does the rate of the reverse reaction increase?

What would happen if we started with products rather than reactants?

Equilibrium Constant (K_eq)

The K_eq is written as the concentration of products/ reactants (at equilibrium), each raised to an exponent that corresponds to the coefficient.

K_eq = [HI]_eq²  

The magnitude of the K_eq tells us how far the reaction proceeds until equilibrium is established. A large K_eq would tell us that the reaction proceeds nearly to completion before equilibrium is established. If this was the case, we would expect to see many more products than reactants at equilibrium. A smaller K_eq tells us that there are more reactants at equilibrium than reactants. The K_eq of the above reaction is less than 1. Compare the amount of reactants and products at equilibrium.

Heterogeneous Systems

Another example would be the dissolving of the slightly soluble salt AgCl. When it is added to water, AgCl dissociates only slightly before an equilibrium is established     

The concentration of the solid, AgCl is a constant so the equilibrium constant for dissociation of this sparingly soluble salt, K_eq is

Irreversible Reactions

Some reactions that take place are irreversible. Reactions that take place in aqueous systems that form a precipitate are irreversible because the insoluble precipitate is removed from the aqueous system and "doesn't have a chance" to reach an equilibrium concentration. It is essentially removed from the system.

LeChatelier's principle

An equilibrium can be perturbed by removing or adding reactant or product to a system at equilibrium. When this occurs, the system is "knocked out" of equilibrium. When a reaction in equilibrium is perturbed, it will always try to reestablish equilibrium. This is referred to as LeChatelier's Principle.

If we look at the equilibrium involving the reaction H₂ + I₂ à 2 HI, if we remove HI from the equilibrium mixture, the reaction will produce more products until equilibrium is reestablished. Likewise, it H₂ and I₂ are removed from a system in equilibrium, the reaction will produce more reactants until equilibrium is reestablished.

While this might be easy to see qualitatively, another, more quantitative way to look at it is by using the reaction quotient, Q. The reaction quotient expression is identical to the K_eq expression except the concentrations are not at equilibrium. For example, the reaction quotient with the preceeding reaction would be

We can see that "too much" product gives a reaction quotient that is larger than K_eq. This causes the reaction to shift back towards the reactants.

                                                                  Q = [HI] ²            Q > K_eq
                                                                         [H₂][I₂]
 

whereas too much reactant results in a Q that is smaller than K_eq. This causes the reaction to shift towards the products.