GENERAL CHEMISTRY TOPICS

Equilibrium - introduction and general principles

The equilibrium state and its underlying dynamic nature. The equilibrium composition of reactants and products in a chemical reaction is the result of a balance between rates of opposing processes, the forward and reverse reactions.

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The concept of equilibrium and the definition of an equilibrium state is of great importance in physics and chemistry. In order to gain an understanding of the principles that govern all equilibria, we'll take the approach of examining in detail a series of examples of different types of equilibria. We'll develop a general description of these from macroscale observation of physical or chemical processes that lead to and establish an equilibrium state, then consider in turn the corresponding molecular scale viewpoint. Ultimately, a theory that treats properties and behavior of molecules can be used to explain and predict macroscale observations, and we'll outline how this concordance emerges for the tendency of systems to evolve toward attainment of equilibrium.

Types of equilibria

On the macroscale we can draw from some familiar examples of equilibria such as the phase equilibria involving water. The balance of the physical process of a phase transition for any pure substance is temperature dependent, which we know to be true for water from common experience. A mixture of ice and liquid water will convert fully to ice at temperatures below 0 °C (at 1 atm pressure), and convert completely to liquid above 0 °C. However, if this mixture is maintained in a 1-atm surroundings at 0 °C, the mixture persists indefintely with no net conversion of ice to liquid water or vice-versa. This constitutes an equilibrium system, in that the composition of the system remains unchanged with time.

1. A liquid-vapor equilibrium. Consider the system of a closed container with a small amount of water

Chemical equilibrium

Although many of the examples of chemical reactions we consider are treated as if they start out with 100% reactants and end up as 100% products, this is by no means appropriate in general. We can just as easily cite a huge number of examples of reactions in which, starting with 100% reactants, only partial conversion to products is attained. The final composition of the reacting system is a mixture of products and reactants, a composition that then remains unchanged with time. We say that a reacting system that reaches its final composition, which undergoes no further observable changes in reactant and product concentrations with time, has reached a state of chemical equilibrium. We can restate the observations about the varying degrees of completion among chemical reactions by saying that while some reactions show a highly product-favored state of equilibrium, others show more intermediate equilibria in which neither products or reactants are highly favored. Still others display equilibria in which very little net conversion to products has occurred. Such reactions can justifiably be called reactant-favored. A deeper understanding of this state of affairs requires that we recognize the dynamic nature of chemical equilibrium, and the relation between reaction rates and equilibria. Any chemical reaction is in principle reversible, and chemical equilibrium is the result of the balance between the rates of the forward reaction (reactants → products) and the reverse reaction (reactants ← products). When these rates are equal, no change in the chemical composition of the reacting system is observed on the macroscopic level, yet on the nanoscale the forward and reverse reactions continue to interconvert reactants and products. This dynamic nature of chemical equilibrium is shared with physical processes, such as vapor-liquid equilibrium attained by a liquid with its vapor in an enclosed container.

In a closed system of reactants and products that are freely interconvertible at a chosen fixed temperature, a state of equilibrium is readily attained via a spontaneous process from any initial nonequilibrium state of the system. It follows from this that if such a system at equilibrium is perturbed in some fashion to give rise to a nonequilibrium state, the system will spontaneously change to restore the equilibrium state. A qualitative analysis of the response of systems perturbed from an equilibrium state can be based upon Le Châtelier's Principle, which predicts changes that directly counter the specific perturbation imposed.

To represent reactions in general, and to specifically call attention to the fact that all chemical reactions are dynamic processes, with forward and reverse directions, chemists use a double-arrow notation. For the generalized chemical reaction, with reactant species A, B, C, ... , and their corresponding stoichiometric coefficients a, b, c, ... , along with product species X, Y, Z, ... , and their corresponding stoichiometric coefficients x, y, z, ... , we write

which represents the balanced equation for the reaction between reactants and products, constituting a reacting system that is either at equilibrium or always tending toward equilibrium, whether the direction of approach to equilibrium is the net conversion of more reactants to products (forward arrow) or the net conversion of products back to reactants (reverse arrow).

Why do some reactions proceed to completion, attaining nearly 100% conversion of reactants to products, while others fall far short of such product-favored final compositions? While giving a satisfactory answer to this question requires a thorough study of chemical thermodynamics, what we can say here is that the balance between reactants and products at equilibrium represents a minimum of chemical potential energy, and for some reactions this minimum occurs at a high fraction of products over reactants, and for others it may occur at a high fraction of reactants over products, and still others have a minimum of chemical potential energy when a significant fraction both reactants and products are present. In other words, chemical reactions attain equilibrium when the reacting system has reached a minimum of chemical potential energy, a condition that is met for a given reaction at a specific concentrations of products and reactants. Depending on the reaction, this balance may be highly favorable to products, highly favorable to reactants, or anywhere in between. In a quantitative treatment of equilibrium, a quantity called the equilibrium constant (symbolized as K_eq) is characteristic of the degree to which a given reaction proceeds toward products. In cases where the reaction is neither strongly product- or reactant-favored ( 0.01 ≈< K_eq ≈< 100 ), the quantitative treatment is of particular importance. Such cases are well represented by the weak acid equilibrium example.

General principles of equilibria

Some general principles of equilibria are stated below

and discussed