Chemical equilibrium

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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 & Jones, 2001). Fundamentally, reactions do not go fully to completion, but reach an equilibrium, because of the entropy of mixing associated with reaction.

1 Equilibrium constant
2 Thermodynamics of equilibrium
3 Examples of chemical equilibrium
4 References
5 External links
6 See also

[edit] Equilibrium constant

Main article: Equilibrium constant

One example of a chemical equilibrium 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

<math>

mA + nB \leftrightarrow pC + qD </math>

The equilibrium constant <math>K_{eq}</math> is defined as

<math>

K_{eq} \ \stackrel{\mathrm{def}}{=}\ \frac{\left[C\right]^{p} \left[D\right]^{q}} {\left[A\right]^{m} \left[B\right]^{n}} </math>

<math>[A], [B]</math>, etc. represent the chemical activities of the reactants and products, which can sometimes be approximated by molar concentrations, or for gas phase reactions, by partial pressures giving us the approximate but simpler equilibrium constants <math>K_c</math> and <math>K_p</math> respectively.

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 <math>K_{eq}</math>. In such a solution, the concentrations would not be at equilibrium; they would start changing until the ratio of concentrations did equal <math>K_{eq}</math>. Thus, the concentrations in this system are at equilibrium (i.e., don't change with time) only if the reaction quotient equals <math>K_{eq}</math>, and vice versa.

Suddenly adding more reactant (say, [A]) to a system in equilibrium drives the equilibrium to the right (i.e., towards higher [C] and [D] concentrations and lower [B]). The sudden addition of [A] increases the instantaneous forward rate without changing the backward rate. Thus, the addition of [A] 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 point where the ratio of concentrations exactly equals <math>K_{eq}</math>.

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.

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

<math>

\Delta G^\circ = -RT \ln K_{eq} </math>

where ΔG° is the standard free energy difference between the products and reactants (e.g., in kcal/mol), <math>T</math> is the absolute temperature in kelvins and <math>R</math> is the universal gas constant. Thus, the equilibrium constant depends on the temperature <math>T</math> and also on variables that affect ΔG°, such as temperature, pH, other co-solvents, etc.

[edit] Thermodynamics of equilibrium

At the beginning of the reaction (when the system contains only reactant molecules), the entropy of the system is greater than at a later point when reactant and product molecules are randomly mixed. If the reaction were to go fully to completion (when the system would contain only product molecules), the system would again have greater entropy than earlier in the reaction when product and reactant molecules were randomly mixed.

Thermodynamic potentials are thermodynamic functions which may be used to characterize chemical equilibrium. Each potential corresponds to a particular set of conditions under which the chemical reaction takes place, and, for a closed system at equilibrium, that potential is minimized. For example, if we have a closed container containing some unreacted chemicals, and it is held at a fixed temperature, then after the chemicals have reacted and equilibrium is reached, the Helmholtz free energy will have dropped to a minimum value.

The Gibbs free energy is minimized for constant temperature and pressure, and is the simplest and most commonly used potential in chemical equilibrium calculations. For a system composed of m different possible molecules, the Gibbs free energy is defined as:

where U is internal energy, P is pressure, V is volume, T is temperature, and S is entropy, <math>\mu_i</math> is the chemical potential of the i-th molecule and <math>N_i</math> is the number of i molecules. At equilibrium, G is at a minimum:

For a closed system, no particles may enter or leave, although they may combine in various ways. The total number of atoms of each element will remain constant. This means that the minimization above must be subjected to the constraints:

where <math>a_{ij}</math> is the number of atoms of element i in molecule j and b_i⁰ is the total number of atoms of element i, which is a constant, since the system is closed. If there are a total of k types of atoms in the system, then there will be k such equations.

The condition of equilibrium, subject to these mass constraints can be written using Lagrange multipliers. Define:

<math>\mathcal{G}= G + \sum_{i=1}^k\lambda_i\left(\sum_{j-1}^m a_{ij}N_j-b_i^0\right)=0</math>

where the <math>\lambda_i</math> are the Lagrange multipliers, one for each element. This allows each of the <math>N_j</math> to be treated independently, and the equilibrium condition is given by

<math>\frac{\partial \mathcal{G}}{\partial N_j}=0</math> and <math>\frac{\partial \mathcal{G}}{\partial \lambda_i}=0</math>

This is a set of (m+k) equations in (m+k) unknowns (the <math>N_j</math> and the <math>\lambda_i</math>) and may therefore be solved for the equilibrium concentrations <math>N_j</math> as long as the chemical potentials are known as functions of the concentrations at the given temperature and pressure. (See Thermodynamic databases for pure substances).

This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of k atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations. (Gordon and McBride, 1994)

[edit] 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 brown nitrogen dioxide and the colourless dinitrogen tetroxide and also 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. A good example of this is the Belousov-Zhabotinsky reaction.

[edit] References

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, Andrew Thompson 2006. Leventhorpe publications