Lesson Explainer: Dynamic Equilibrium

In this explainer, we will learn how to define a dynamic equilibrium and examine how one can be established.

Let us consider the following reversible chemical reaction:

At the very start of the reaction, the concentration of nitrogen and hydrogen gas is high, while the concentration of ammonia is zero as it has not yet been produced.

As the reaction proceeds, nitrogen and hydrogen react to form ammonia. If we monitored the concentration of each species just after the reaction began, we would see the concentration of nitrogen and hydrogen decrease while the concentration of ammonia increases.

If the reaction was irreversible and assuming that neither the nitrogen nor hydrogen were in excess, all of the reactants would be converted into ammonia.

However, this reaction is reversible. Eventually, the reaction reaches a point where the concentration of nitrogen, hydrogen, and ammonia no longer changes regardless of how long we monitor the reaction. When this point is reached, the reaction is said to be in equilibrium.

It is important to recognize what is occurring at equilibrium. The graph at equilibrium for this reaction shows that the concentration of nitrogen is 3 M, the concentration of hydrogen is 9 M, and the concentration of ammonia is 4 M. It may seem like the reaction has simply stopped because the concentration of products and reactants no longer changes. In actuality, both, the forward reaction and the reverse reaction continue to occur simultaneously at the same constant rate. This means that as one mole of nitrogen and three moles of hydrogen react to form two moles of ammonia, two moles of ammonia react to form one mole of nitrogen and three moles of hydrogen. The result is that there is no net change in the amount of nitrogen, hydrogen, or ammonia. This is demonstrated in the figure below.

This equilibrium is said to be dynamic as the reactions are continuing to occur. For a chemical reaction to be in dynamic equilibrium, the rate of the forward reaction and the rate of the reverse reaction must be the same and must remain constant. When the forward and reverse reaction rates are the same, the concentration of the reactants and products remain constant even though both reactions continue to occur.

Definition: Dynamic Equilibrium

Dynamic equilibrium is an equilibrium between forward and reverse reactions where both reactions are occurring at the same nonzero rate.

Example 1: Determining Which Dynamic Equilibrium Statement Is Incorrect

Five students are asked to write the definition of dynamic equilibrium. Which student has not fully understood the concept?

A dynamic equilibrium is a reversible reaction that stops when the amount of each substance is stable.
A dynamic equilibrium is a reversible reaction where the concentration of each substance does not change.
A dynamic equilibrium is a reaction where the speed of the forward reaction equals the speed of the backward reaction.
A dynamic equilibrium is a reaction that goes in both directions, where the amount of each substance does not change.
A dynamic equilibrium is a forward and backward reaction that occurs at the same time with the same rate.

Answer

A dynamic equilibrium is established when the forward and reverse reactions of a reversible reaction occur at the same constant rate. At dynamic equilibrium, the concentration of the reactants and products remain constant even though both the forward and reverse reactions continue to occur.

All of the students recognized that a reversible reaction, a reaction that proceeds both forward and backward, is necessary for dynamic equilibrium. All of the students either recognized that the rate of the forward and backward reactions is the same or that the concentration of all substances involved remains constant at equilibrium. However, student A states that the reaction stops when the amount of each substance remains stable. This is not the case. Both the forward and reverse reactions proceed at equilibrium. The student that has not fully understood the concept is student A.

Let us return to this reaction:

All of the species involved in the reaction are gases. If the reaction was performed in an open container, the gases could escape and equilibrium would not be established.

A dynamic equilibrium can only be established when all of the matter initially present in the reaction vessel remains. For this to be true, the reaction must occur in a closed system. A closed system allows for the transfer of energy but not matter, while an open system allows for the transfer of matter and energy.

Definition: Closed System

Closed system is a system that does not exchange matter but can exchange energy with its surroundings.

Definition: Open System

Open system is a system that can exchange matter and energy with its surroundings.

An example of an open system in chemistry is a test tube. If a reaction was performed in a test tube, matter could easily be lost out of the top. We can turn a test tube into a closed system by adding a stopper. This prevents matter from being lost.

Example 2: Recognizing Why a Reaction Does Not Reach Equilibrium

Calcium oxide can be made on a large scale by heating calcium carbonate in a furnace. The furnace uses a lot of energy when heating up to the required temperature and additional calcium carbonate is frequently added to keep the reaction running, as shown:

Why does this reaction not reach equilibrium?

The reaction is irreversible.
The amount of reactants and products remains constant.
The furnace is too hot.
The furnace is not a closed system.
The rate of reaction is too slow.

Answer

Dynamic equilibrium is established when the rate of the forward and reverse reactions is the same. The rate of the reactions in a dynamic equilibrium may be fast or slow, so long as the forward and reverse reaction rates are equal. Thus, we can eliminate answer choice E.

By definition, a reaction at equilibrium must be able to proceed in both directions. In other words, the reaction must be reversible. Reversible reaction equations use an equilibrium arrow (). The reaction shown is reversible. Thus, we can eliminate answer choice A.

As the process proceeds, more calcium carbonate is added to the furnace to keep the reaction running. Therefore, the amount of reactant is changing. Thus, we can eliminate answer choice B.

The temperature of a reaction may affect the overall equilibrium, but equilibrium can be established whether the reaction is hot or cold. Thus, we can eliminate answer choice C.

This leaves us with answer choice D. The furnace is not a closed system. This means that the carbon dioxide gas can escape from the furnace. If the carbon dioxide is no longer present, then the furnace no longer has the compounds necessary for the reverse reaction to proceed. Without the reverse reaction, equilibrium cannot be established. So, the correct answer is answer choice D.

Let us consider the following equilibrium:

Dinitrogen tetroxide () is a colorless gas, while nitrogen dioxide () has a dark brown color. When dinitrogen tetroxide is added to a closed system, the initial concentration becomes high, while the concentration of nitrogen dioxide becomes zero as it has yet to be produced.

At first, the initial rate of reaction from to is large as there is no product to compete with the forward reaction. As nitrogen dioxide begins to be made, the rate of the forward reaction begins to slow as there are fewer reactant molecules. Simultaneously, the rate of the reverse reaction begins to increase as there are more product molecules. The reaction vessel during this process will begin to appear an orangish brown as the concentration of nitrogen dioxide increases.

Eventually, the reaction vessel no longer changes color. At this point, the rate of the forward and reverse reactions is the same and the concentration of the product and reactant remains constant. The reaction is in dynamic equilibrium. Although the concentration of the product and reactant remains constant, the reactions are still occurring, with being converted into and being converted into simultaneously.

It is important to know that dynamic equilibrium is reached when the forward and reverse rates of reaction are the same, not when the concentration of reactants and products are the same. It is also important to recognize that the concentration of the products may or may not exceed the concentration of the reactants at equilibrium. The graphs below show the concentration of dinitrogen tetroxide and nitrogen dioxide over time.

Notice that, in the rightmost graph, neither nor have an initial concentration of zero. Yet, in all three examples, we can determine when dynamic equilibrium is established by finding the time at which the concentrations no longer change (i.e., the time at which the slope of both graphs becomes zero, indicated by the dashed line).

Example 3: Identifying the Graph of a Dynamic Equilibrium Using the Initial and Equilibrium Concentrations

A dynamic equilibrium is established between two reactants A and B according to the equation shown:

Compound A has an initial concentration of 0.8 mol/dm³ that drops to 0.4 mol/dm³ once equilibrium is established.

Which graph for this equilibrium is correct?

Answer

The initial concentration of compound A is 0.8 mol/dm³. This means that at a time of zero, the graph of compound A should be at 0.8 mol/dm³. Looking at the graphs, we can eliminate graphs C and D as the initial concentration of compound A in each graph is 0 mol/dm³.

Once equilibrium has been established, the concentration of compound A should be 0.4 mol/dm³. Equilibrium is established when the concentration of each compound no longer changes or when the graph has a slope of zero. Both graphs A and B show compound A at a concentration of 0.4 mol/dm³ at equilibrium.

Compound B is the product. At the start of the reaction, no product should be present. Thus, at a time of zero, the concentration of compound B should be 0 mol/dm³. This is the case for graphs A and B.

Looking at the stoichiometric coefficients in the chemical equation, we can see that one mole of A produces two moles of B. This means that as the concentration of compound A decreases, the concentration of compound B should increase by twice the amount.

The concentration of compound A decreased from 0.8 mol/dm³ to 0.4 mol/dm³. Thus, the concentration of compound A decreased by 0.4 mol/dm³. The concentration of compound B should increase by twice this amount, or 0.8 mol/dm³. If the concentration of compound B is initially zero, then the concentration of compound B at equilibrium should be 0.8 mol/dm³. When the graph of compound B has a slope of zero, the concentration of compound B is given as 0.4 mol/dm³ in graph A and 0.8 mol/dm³ in graph B. The graph that correctly represents the equilibrium reaction is graph B.

Example 4: Identifying Which Statement Is Always True at Equilibrium

Which of the following statements concerning concentrations is always true at equilibrium?

The concentrations of the products are greater than the reactants.
The concentrations of reacting substances do not change.
The concentrations of the reactants and products are constantly changing.
The concentrations of reacting substances are equal.
The concentrations of the reactants are decreasing.

Answer

When an equilibrium reaction occurs, there is initially a change in the rate of the forward and reverse reactions. This results in a change in the concentration of the products and the reactants. Eventually, the rate of the forward and reverse reactions will be the same. This is the point at which equilibrium is established. The forward and reverse reactions continue to occur, but as they occur at the same rate, the concentration of the reactants and products remain constant. Equilibrium may be established when the concentration of the reactants is greater than the concentration of the products, less than the concentration of the products, or equal to the concentration of the products. Thus, at equilibrium, the concentration of the reactants and products may be any value, but that value must not fluctuate. The statement that is always true at equilibrium is answer choice B: the concentrations of reacting substances do not change at equilibrium.

A dynamic equilibrium can be described by the equilibrium position, which is given by dividing the concentration of the reactants by the concentration of the products after equilibrium has been established:

When the equilibrium position is greater than one, there is a greater concentration of reactants than that of products at equilibrium.

When the equilibrium position is less than one, there is a greater concentration of products than that of reactants at equilibrium.

When the equilibrium position is equal to one, the concentration of reactants and products is the same at equilibrium.

The equilibrium position of a dynamic equilibrium can be affected by changing the concentration of the reactants or products, changing the temperature, or changing the pressure of reactions involving gases. For example, the dynamic equilibrium for the conversion of to at room temperature can be represented by the following graph.

This graph indicates that the concentration of is greater than at equilibrium and that the equilibrium position is greater than one. However, if the temperature is increased, more can be produced and the equilibrium position will change accordingly.

The addition of a catalyst to a dynamic equilibrium has no effect on the equilibrium position. This is because a catalyst has the effect of speeding up both the forward and reverse reactions to the same degree. However, as a catalyst increases the rate of the reactions, equilibrium is established more quickly.

Example 5: Recognizing Factors That Affect the Equilibrium Position

Which of the following will never affect the position of an equilibrium?

The temperature
A catalyst
The concentration of reactants
The pressure
The concentration of products

Answer

The position of an equilibrium can be represented by dividing the concentration of the reactants by the concentration of the products:

The equilibrium position can be changed by changing the concentration of the reactants or products, the temperature of the reaction, or the pressure of the reaction when gases are involved. The addition of a catalyst speeds up the rate of the forward and reverse reactions to the same extent. As such, the equilibrium will be established more quickly, but the equilibrium position will be unaffected. The factor that never affects the position of an equilibrium is a catalyst, answer choice B.

Let us summarize what we have learned in this explainer.

Key Points

Dynamic equilibrium is established when the rate of the forward and reverse reactions is the same.
At dynamic equilibrium, the concentrations of all species involved in the reaction remain constant.
Dynamic equilibrium can only be established in a closed system.
Concentration, temperature, and pressure can affect the equilibrium position.
The addition of a catalyst will allow the reaction to reach equilibrium more quickly but will not affect the equilibrium position.