Equilibrium as Rate Balance

Equilibrium as a Balance of Forward and Reverse Rates

Run a simulation of a reversible gas-phase reaction.
Consider a molecule that contains two identical parts that are weakly held together. We sometimes call this type of molecule a dimer for which many examples exist. If the molecule has sufficient internal energy (meaning if the temperature is high enough), the dimer may fall apart:

Once the dissociation takes place, however, the two parts, called monomers, may reassociate, in effect reversing the original reaction:

At a given temperature, it would be nice to know how much dimer (D) there is compared to monomer (A) at equilibrium.
The phrase equilibrium refers to the situation when the concentrations of species in the reactor no longer change with time, i.e. when the forward and reverse rates balance.
What is the time rate of change of the species in the reactor?

When this net rate equals zero the concentration of the species in the reactor is constant and equilibrium is achieved.

--- or ---

Note that this equation holds only at equilibrium, which is why the concentrations have subscript e's on them. The ratio of forward to reverse rate constants is defined as the equilibrium constant, K_eq. (Forward, in this case, is in the direction of the dimer dissociation or the direction of the first reaction on this page.)

The Definition of the Equilibrium Constant
In general, the equilibrium constant is equal to the "proper quotient of equilibrium concentrations", but it does that mean? For every reaction, the equilibrium expression is is different. (The equilibrium expression is the equation that relates the equilibrium constant to some function of the reactant and product concentrations.) Suppose we right a general (but fictitious) reaction between two products and two reactants, with some set of stoichiometric coefficients which we will leave as greek letters:

the proper quotient of concentrations, or reaction quotient is related to the concentrations of the reactants and products for this reaction in the following way:

If the reaction is in equilibrium, then all the concetrations are constant in time, and at their equilibrium value. The Equilibrium Constant is then equal to the proper quotient of equilibrium concentrations, or:

We have assumed that the concetrations of all species are given in moles per liter or molar. (That is what the square brackets mean). Sometimes for gases, it is nicer to express concentrations in terms of partial pressure. Then the reation quotient is equal to:

If the reaction is at equilibrium, all the partial pressures have their equilibrium values, and the reaction quotient (or proper quotient of partial pressures) is equal to the Equilibrium Constant, and:

Note that the equilibrium constant may be quoted in terms of molarity, in which case it is called K_C, or in terms of partial pressures, in which case it is called K_p. If we have a mixed set of standard states, or if we simply don't state what types of concentrations are used, we can call the equilibrium constant K_eq or simply K.

The choice of concentration units (or standard state) and all of its ramifications will be discussed in greater depth later. For now, we note how the equilibrium expression results from the balanced chemical reaction directly from the stoichiometric coefficients.

TOP