# Dynamic equilibrium

At dynamic equilibrium, the reaction rate of the forward reaction is equal to the reaction rate of the backward reaction.

### Introduction

A reaction rate determines how fast a reaction proceeds.  It is the change in concentration over the change in time.  For more information, please read Measuring Reaction Rates.   An example of a fast reaction would be fire burning (combustion of oxygen) and an example of a slow reaction is iron rusting (oxidation of a metal).  Reactions do not only proceed forward; reactions often occur in a mixture of forward and reverse, the more prevalent being the observed course of the reaction.

Instead of thinking about reactions as one substance completely changing into another, we should instead think of a reaction being composed of two components acting in opposite directions.  In this tug of war of sorts, there is a point where the two components are acting at equal rates.  We call this equilibrium.  At equilibrium, the reaction rates of the forward and reverse reactions are equal. However, there are two different types of equilibrium: dynamic equilibrium and static equilibrium.

### Dynamic Equilibrium

At dynamic equilibrium, reactants are converted to products and products are converted to reactants at an equal and constant rate.  An example of a reaction in dynamic equilibrium is the dissociation of acetic acid, e.g., CH3COOH ↔ H+ + CH3COO-

For the reaction, A--> B

Figure 1: Before the reaction of A--> B occurs

Figure 2: Reaction A--> B at dynamic equilibrium

NOTE: Although Figures 1 and 2 depict a reaction with an equilibirum both reactants A and B having the same moles, reactions do not necessarily and most often don't end up with equal concentrations.  Remember that equilibrium is the state of equal opposite rates, not equal concentrations!

### Static Equilibrium

Static equilibrium, also called mechanical equilibrium, occurs when all particles in the reaction are at rest and there is no motion between reactants and products.  Static equilibrium can also be seen as a steady-state system in a physics-based view.  Dynamic forces are not acting on the potential energies of the reverse and forward reactions.  An example of static equilibrium is graphite turning into diamond. This reaction is considered at static equilibrium after it occurs because there is no more forces enacting upon the reactants (graphite) and products (diamond).

Ex: C (graphite) --> C(diamond)

For reaction C--> D

Figure 3: Before the reaction of C--> D occurs

Figure 4: Reaction C--> D at static equilibrium under equilibrium conditions

Note: Static equilibrium does not neccessarily mean there will be no moles in the reactant side after the reaction has occured.  This is only an example of static equilibrium.

### Le Chatelier's Principle and Equilibrium

Equilibrium can be explained by Le Chatelier's principle.  The kinetics of a reaction change and position of equilibrium depends on the properties of the reactants and products.  Simply put, the equilibrium will shift towards one side or the other depending on concentration, temperature, pressure, and volume.  Le Chatelier's principle is not the same as dynamic equilibrium; they are similar but distinct concepts.  Le Chatelier's principle describes on how equilibrium can change.  Dynamic and static equilibrium describe on how equilibrium behaves.

### Comparison between Dynamic and Static Equilibrium

A reaction at dynamic equilibrium has the ability to be reversible while a reaction at static equilibrium is irreversible. A reversible reaction is a reaction that can proceed in the direction of products to reactants. Looking at the equilibrium constant will not determine whether a reaction is in static or dynamic equilibrium because the equilibrium constants are determined by the concentrations of products over reactants. A reaction is at dynamic equilibrium if the rate of the forward reaction is equal to the rate of the reverse reaction. It is at static equilibrium if the reaction has occurred and there is no forward or reverse reaction rate. The rate of reactions cannot be determined by the stoichiometric factors of a balanced equation. Reaction orders and reaction rates have to be determined experimentally.

### Relationship Between Equilibrium and Rate Constants

For a simple reaction:

A --> B where A is the reactants and B is the products

The equilibrium constant Keq is given by:

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where [A]eq represents the reactants at equilibrium conditions and [B]eq represents the products at equilibrium conditions.

The rate of reactions is given by:

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where kf is the rate constant for the forward reaction and kb is the rate constant for the backward reaction.

The equilibrium constant can also be determined by the rate constant of the forward reaction over the rate constant of the reverse reaction.

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when [A] and [B] are at equilibrium concentrations.

### References

1. Petrucci, Harwood, Herring, and Madura. General Chemistry: Principles and Modern Applications. 9th ed. Upper Saddle River, New Jersey: Pearson Education, 2007.
2. Zhumdal, Zhumdal. Chemistry. 7th ed. Boston, New Jersey: Massachusetts Houghton Miffle Company, 2007.

### Problems

1. What can the reaction rate determine?

2. What is the definition of a dynamic equilibrium?

3. What is the the definition of a static equilibrium?

4. Can the rate of reaction be determined by the stoichiometric factors of a balanced equation?

5. For a reaction:

à D at equilibrium, what is the equilibrium constant when the rate constant for the forward reaction is 2.5 x10-5 and the rate constant for the backward reaction is 5.0 x 10-5?

6. For a reaction:

à F at equilibrium, what is the rate constant for the backward reaction when the equilibrium constant is 20 and the rate constant for the forward reaction is 100?

### Solutions

1. The reaction rate determines the speed of the reaction.

2. A reaction in dynamic equilibrium has reactants converted to products and products converted to reactants at a constant rate.

3. A reaction in static equilibrium would be a reaction that has not net movement after equilibrium has been reached.

4. No, the rate of reaction cannot be determined by the stoichiometric factors of a balanced equation. In order to determine the rate of reaction, experiments must be conducted.

5. The equilibrium constant, Keq, is 0.5.

The rate constant for the forward reaction, kf, is 2.5 x10-5.

The rate constant for the backward reaction, kb, is 5.0 x 10-5.

Then substitute into the equation

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= 0.5

6.

The rate constant for the backward reaction, kb, is 5.

The equilibrium constant, Keq, is 20.

The rate constant for the forward reaction, kf, is 100.

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Rearrange the equation to solve for kb.

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= 5

### Contributors

• Esther Lee (UCD)
• Jiaxu Wang
• Jonathan Wang

09:25, 2 Oct 2013

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