# Equilibrium

A state of equilibrium exists in a process when the rate of the forward process equals the rate of the reverse process. The equilibrium condition exists in relation to thermal, mechanical, and chemical changes. For example, within a closed flask, liquid water evaporates to form vapor, and at the same time the vapor condenses to form liquid. When the rate of evaporation equals the rate of condensation, the system is said to be in a state of equilibrium:

A state of thermal equilibrium exists when the heat loss of a system is equal to the heat gain. Chemical equilibrium exists when a reversible chemical reaction occurs within a closed system, such as a sealed flask, and the rate of the reaction in the forward direction equals the rate of the reaction in the reverse direction. For example: N 2 + 3H 2 ⇄ 2NH 3 .

In this reaction, nitrogen and hydrogen gases react to form gaseous ammonia, NH 3 . When nitrogen and hydrogen are first introduced into the reaction chamber, they begin to form ammonia molecules. As the concentration of ammonia increases, ammonia molecules start to decompose, forming nitrogen and hydrogen. When the rate at which ammonia is formed equals the rate at which it decomposes, the system is at equilibrium. A reaction at equilibrium never goes completely to completion; molecules of reactants continue to collide to form product molecules, and product molecules constantly decompose to form reactant molecules.

A state of mechanical equilibrium is a special physical state in which the external forces and moments on an object are zero. All forces are balanced, and the object is at rest. Examples of systems in mechanical equilibrium include a ball hanging motionless on a string and a mass suspended motionless from a spring.

Every equilibrium system follows predictable mathematical rules. The law of mass action states that the product of the concentrations of a reaction's products, each raised to the power of the coefficient of the species, divided by the product of the concentrations of the reactants, each raised to the power of the coefficient of the species, is a constant at constant temperature. Thus for the ammonia reaction:

N 2 + 3 H 2 ⇄ 2 NH 3

The equation describing the equilibrium reaction is called an equilibrium expression, and K eq , the equilibrium constant, is a definite numerical value for each equilibrium reaction. The equilibrium constant for a particular reaction is specific for that reaction and changes only with variations in temperature. The presence of a catalyst does not alter K eq but does cause the reaction to reach equilibrium more rapidly.

The size of K eq can be used to predict whether the reaction goes further toward completion (results in the formation of large quantities of products) or favors reactants (results in higher concentrations of reactants present at equilibrium). For example, hydrogen and iodine react at 200°C (392°F) to form hydrogen iodide in the following equilibrium reaction: H 2 + I 2 ⇄ 2HI. The value of K eq for the reaction has been determined to be 50, experimentally. At equilibrium, if the concentrations of hydrogen and iodine were 1.0 moles per liter, the concentration of hydrogen iodide would be or 7.1 moles per liter.

Le Châtelier's principle states that if a stress is brought to bear upon a system at equilibrium, the equilibrium reaction shifts in a direction that relieves the stress. Put more simply, if the concentration of one of the reactants or products is increased at equilibrium, the reaction moves in the direction that consumes the added material. Adding hydrogen and iodine to the reaction mixture above would result in the formation of more hydrogen iodide.

Similarly, adding hydrogen and nitrogen to the reaction mixture that forms ammonia would result in the formation of more ammonia, and removing ammonia would shift the equilibrium to the right, forming even more ammonia. Ammonia, hydrogen, and nitrogen are all gases, and one mole of each gas occupies a volume of about 22.4 liters at STP . In the reaction N 2 + 3H 2 ⇄ 2NH 3 , 22.4 liters of nitrogen react with 3 times 22.4 liters of hydrogen to form 44.8 liters of ammonia. This means that 4 times 22.4 liters of reactants form 2 times 22.4 liters of products. Le Châtelier's principle predicts that increasing pressure on the system at equilibrium causes the equilibrium to shift to the right. Therefore, ammonia is manufactured in a continuous loop by pumping in N 2 and H 2 and removing NH 3 by liquefaction as it is formed, causing the unreacted N 2 and H 2 to form more ammonia. The presence of a catalyst helps the hydrogen and nitrogen molecules interact to form ammonia more rapidly.

Equilibrium constants are dependent upon the temperature of the system. Formation of ammonia is exothermic—heat is released as the reaction occurs: N 2 + 3H 2 ⇄ 2NH 3 + 93.7 kilojoules of energy. Therefore, cooling the reaction mixture favors the formation of even more ammonia.

Systems may be in chemical or mechanical equilibrium, and they may also exhibit thermal equilibrium. If a hot object is placed in contact with a colder mass of the same material inside an insulated container, heat flows from the hot object into the colder object until the temperatures of the two are equal. Heat lost by the warm object is equal to the amount gained by the cold object. The amount of heat needed to raise the temperature of an object a certain amount is equal to the amount which that object would lose in cooling by the same amount. The amount of heat needed to warm or the amount lost when cooling equals the product of the specific heat (or heat capacity) of the substance, the mass, and the change in temperature. For example, if a 50-gram (1.8-ounce) piece of silver at 70°C (158°F) is placed in 50 grams (1.8 ounces) of water at 15°C (59°F), the principle of thermal equilibrium can be used to calculate the final temperature of the water and silver:

At equilibrium, if the concentrations of hydrogen and iodine were 1.0 mole/Liter, the concentration of hydrogen iodide would be or 7.1 moles/Liter.

As a result of heat flowing from the silver into the water to establish a thermal equilibrium between the two, the final temperature of the silver and water is 18.1°C (64.6°F).

Dan M. Sullivan

## Bibliography

Brown, Theodore L.; Lemay, H. Eugene; Bursten, Bruce E.; and Burdge, Julia R. (2002). Chemistry, 9th edition. Upper Saddle River, NJ: Prentice-Hall.

McMurry, John, and Fay, Robert C. (2004). Chemistry, 4th edition. Upper Saddle River, NJ: Pearson Education Inc.

McQuarrie, Donald A., and Rock, Peter A. (1984). General Chemistry. New York: Freeman Publications.

Silberberg, Martin S. (2000). Chemistry, 2nd edition. Boston: McGraw-Hill.