Equilibrium Constant

Biochemistry, Cell Biology

Equilibrium Constant Definition

An equilibrium constant is a variable that describes a chemical reaction’s tendency to proceed to completion, meaning all the reactants are converted to products. The equilibrium of a reaction is the point at which the conversion of reactants into products equals the conversion of products back into reactants. The equilibrium constant is often represented by the variable Keq, which is defined by the equilibrium constant expression seem below. A large equilibrium constant means that the reaction proceeds in the forward direction, from reactants to products, until almost all the reactants have been converted to products. A small equilibrium constant, or when Keq is less than one, means that the chemical reaction will favor the reactants and the reaction will proceed in the opposite direction.

Equilibrium Constant Expression

The equilibrium constant expression describes the concentration of products divided by the concentration of reactants, when the reaction reaches equilibrium. This expression can be seen below.

Equation 1

In the reaction:

aA + bB <=> cC + dD

Each term describes the concentration of a reactant or product in the reaction where chemicals A and B combine to produce products C and D. The lowercase letters indicate the number of moles of each chemical. The brackets around a letter, [A], indicate the concentration of each chemical, and the subscript denotes that the equilibrium constant is determined by the concentration of each molecule at equilibrium.

J. Willard Gibbs, a famous scientist who studied the energy present in reactions, showed that the equilibrium constant was directly related to the amount of free energy change that occurs during a reaction, denoted ∆G. Gibbs showed that every reaction has a standard free-energy change, or ∆G°. While total free energy change of each reaction is also governed by the initial concentrations of chemicals, the standard free energy is calculated with the equation below, using the equilibrium constant of the equation.

∆G° = -RTln(Keq)

This equation shows that the standard free energy change is simply another way of describing the driving forces of a reaction, and which way they will proceed. While the equilibrium constant tells us whether we will have more reactant or products at the end of a reaction, it does not hint at how fast this reaction would take place. This is known as the rate constant and is denoted by a lowercase k. The rate constant is related to a variety of other equations related to the speed at which reactions happen. The equilibrium constant is important to a number of biological reaction, as seen in the examples below.

Examples of Equilibrium Constant

Ionization of Water

Water is the basis for all life on Earth. One of the main reasons water is such a good solvent is its ability to form hydrogen bonds with both itself and non-water molecules. Not only does this ability allow water to dissolve and diffuse solutes, but also allows water to carry an electrical current. When water, H2O, forms hydrogen bonds, the hydrogen is pulled away from the oxygen and the molecule disassociates into a hydrogen ion (H+) and a hydroxide ion (OH). Individual hydrogen protons rarely exist freely in solution, and immediately forms a bond with water molecule it was hydrogen bonded to. This forms a hydronium ion, or H3O+. The equilibrium constant for this reaction is therefore the concentration of hydrogen ions and hydroxide ions, divided by the concentration of normal water molecules, as seen below.

Equation 2

The equilibrium constant of this reaction can be measured by the electrical conductivity of water, which is determined by the concentration of (H3O+). Hydronium ions pass an electrical signal in the form of the transfer of electrons, which can be measured by sensitive electrical equipment. Thus, the equilibrium constant of water has been measured by sensitive electrical equipment to be 1.8 x 10-16, meaning water has a much higher probability of being the reactant H2O than becoming the hydronium ion. The process can be seen in the image below.
H2O Auto Ionization

Cells, Free Energy, and the Equilibrium Constant

Although the equilibrium constant is measured when a reaction is at equilibrium, this does not mean that all reactions are allowed to proceed to equilibrium. In the cell, many reactions are constantly resupplied with various chemicals, which keeps the reactions of the cells far from equilibrium. The equilibrium constant, however, describes the tendency of these reactants to form products. Some reactions are exergonic, and release energy when they happen. These reactions have a high equilibrium constant, describing their tendency to become products. These reactions can also be said to have a positive change in free energy, meaning they give off energy to reactions around them. Other important reactions are endergonic, and require energy to take place. These reactions have a low equilibrium constant, describing their tendency to remain as reactants. Cells couple these reactions to allow the endergonic reactions to take place. This can be seen in many typical cellular reactions that use the high equilibrium constant of ATP converting to ADP to drive endergonic reactions, such as the formation of proteins or fatty acids.

Related Biology Terms

  • Equilibrium – When the forward reaction of reactants into products is the same as the backwards reaction of products into reactants.
  • Free Energy – Energy available in the environment and from reactions which can cause more molecules to react.
  • Enthalpy – The number and types of bonds in a system, which reflect the energy stored within.
  • Entropy – The amount of disorder in a system, which increases as molecules separate and become more random.

Quiz

1. In animals, the regulation of glucose is important. In some cases, excess glucose must be stored. To store glucose, glucose molecules must be chained together in large molecules called glycogen. To chain the glucose together, the energy from a molecule of ATP must be used. Which of the following statement about the equilibrium constant of the reaction of combining glucose molecules is true?
A. Keq = 1
B. Keq < 1
C. Keq > 1

Answer to Question #1

2. When an ATP molecule is converted to ADP, the molecule loses a phosphate group. This reaction has an extremely high equilibrium constant. In the cell, ATP is stored in high concentrations to fuel important reactions. Why doesn’t this ATP convert all at once to ADP, and then to AMP?
A. The rate of the reaction is not determined by the equilibrium constant
B. It does, but the cell replaces it at a faster rate
C. The equilibrium constant is not high enough to drive the reaction forward

Answer to Question #2

3. What is the difference between the equilibrium constant of a reaction and the free energy change present in a reaction?
A. There is no difference.
B. Free energy change only describes the energy, not the concentration
C. Free energy change in a reaction is determined by the standard free energy and the ratio of the initial concentrations, where the equilibrium constant is determined only by the ratio of concentrations at equilibrium.

Answer to Question #3
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