Chemical equilibrium

Chemical equilibrium is the state in which the concentrations of the reactants and products have no net change over time. Usually, this state results when the forward chemical reactions proceed at the same rate as their reverse reactions. The rates of the forward and reverse reactions are generally not zero but, being equal, there are no net changes in any of the reactant or product concentrations. This process is known as dynamic equilibrium Atkins, Peter; Jones, Loretta. Princípios de química : Questionando a vida moderna e o meio ambiente. Tradução por Ignez Caracelli et alii. Porto Alegre : Bookman, 2001. (Translated from Atkins, Peter; Jones, Loretta. Chemistry: the quest for insight). Vaibhav Patel 2005, Christian Hart 2006, Glen Paxman 2006. Leventhorpe publications.

Chemical equilibrium in solution/gas phase reactions

One example of a chemical equilibrum reaction is with ferric nitrate and potassium thiocynate. The Fe3+ and SCN- ions form the ion, FeSCN2+, which is red in color. This is called a red complex ion.

For illustration, consider the generic reversible reaction in solution (or in the gas phase)

mA + nB \leftrightarrow pC + qD

By the law of mass action, the forward rate should equal $k_{AB} [B^{n}$ , whereas the backward rate should equal $k_{CD} [D^{q}$ , where $k_{AB}$ and $k_{CD}$ are the forward and backward reaction rate constants, respectively, and $[B$ , etc. represent the concentrations (or, more correctly, the chemical activities) of the reactants and products. Setting the forward and backward rate constants equal and cross-dividing, we arrive at the equilibrium constant $K_{eq}$

K_{eq} \equiv \frac{k_{AB}}{k_{CD}} = \frac{\left\left ^*^{m}" target="_blank" >\left[B\right^{n}}

Of course, anyone could prepare a solution in which the ratio of concentrations on the right-hand side of the equation (called the reaction quotient) did not equal $K_{eq}$ . In such a solution, the concentrations would not be at equilibrium; they would start changing until the ratio of concentrations did equal $K_{eq}$ . Thus, the concentrations in this system are at equilibrium (i.e., don't change with time) only if the reaction quotient equals $K_{eq}$ , and vice versa.

Suddenly adding more reactant (say, ^*) to a system in equilibrium drives the equilibrium to the right (i.e., towards higher and ^*)." target="_blank" > The sudden addition of [A increases the instantaneous forward rate without changing the backward rate. Thus, the addition of ^* will cause C and D to be made faster and B to be lost faster than the reverse reactions. Eventually, the system will reach a new equilibrium where the ratio of concentrations exactly equals $K_{eq}$ .

The equilibrium position of a reaction is said to lie far to the right if, at equilibrium, nearly all the reactants are used up and far to the left if hardly any product is formed from the reactants. Changing the conditions of a reaction can shift the equilibrium to the right or left.

The kinetics of a reaction can be changed without altering its equilibrium concentrations. Specifically, the forward and backward rate constants can be both multiplied by the same factor without affecting their ratio (the equilibrium constant). This situation occurs quite commonly when a catalyst (such as an enzyme) is added to a reaction. Thus, the same equilibrium constant can be found in very fast and very slow reactions, and a fast forward reaction (by itself) does not imply that the reaction equilibrium lies far to the right.

In solids or other situations, the forward and backward rates may be described by different equations, but one can usually define an equivalent equilibrium constant by equating the forward and backward rates and factoring out the constants (such as $k_{AB}$ and $k_{CD}$ ) from the variables (such as and [B).

Chemical equilibrium and thermodynamics

Although chemical equilibrium is defined kinetically (forward and backward rates are equal), its properties can be studied thermodynamically, i.e., from the free energies of the reactants and products. The main equation is

\Delta G^\circ = -RT \ln K_{eq}

where ΔG° is the standard free energy difference between the products and reactants (e.g., in kcal/mol), $T$ is the absolute temperature in kelvins and $R$ is the universal gas constant. This equation can be written equivalently as

K_{eq} = e^{-\frac{\Delta G^{\circ}}{RT}}

Thus, the equilibrium constant depends on the temperature $T$ and also on variables that affect ΔG°, such as temperature, pH, other co-solvents, etc.

Examples of chemical equilibrium

A common example given is the Haber-Bosch process, in which hydrogen and nitrogen combine to form ammonia. Equilibrium is reached when the rate of production of ammonia equals its rate of decomposition. Le Chatelier's principle describes qualitative predictions that can be made about a chemical equilibrium.

Classical equilibria are that between the colorless nitrogen dioxide and the brown dinitrogen tetroxide and the Schlenk equilibrium.

In practice, most sets of reversible reactions have a stable equilibrium. In rare cases, the concentrations may not settle to fixed equilibrium values, but rather oscillate indefinitely.

References

2. P W Atkins Physical Chemsitry, Oxford University Press.

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Chemical equilibrium in solution/gas phase reactions

Chemical equilibrium and thermodynamics

Examples of chemical equilibrium

References

See also