# B. Equilibrium Constants

Without a lot of experience in chemistry, it is difficult to just look at the reactants and products and determine whether the reaction is irreversible, or reversible, favoring either reactants or products (with the exception of obvious irreversible reactions described above). However this data can be found in tables of equilibrium constants. The equilibrium constant, as its name implies, is constant, independent of the concentration of the reactants and products. A Keq > 1 implies that the products are favored. A Keq < 1 implies that reactants are favored. When Keq = 1, both reactants and products are equally favored. For the more general reaction,

$\mathrm{aA + bB \rightleftharpoons pP + qQ,}$

where a, b, c, and d are the stoichiometric coefficients,

$K_{eq} = \dfrac{[P]^p[Q]^q}{[A]^a[B]^b}$

where all the concentrations are those at equilibrium. For a simple reaction where a, b, p, and q are all 1, then

$K_{eq} = \dfrac{([P]_{eq}[Q]_{eq})}{ [A]_{eq}[B]_{eq}}$

(Note: Equilibrium constants are truly constant only at a given temperature, pressure, and solvent condition. Likewise, they depend on concentration to the extent that their activities change with concentration.)

For a irreversible reaction, such as the reaction of a 0.1 M HCl(aq) in water, [HCl]eq = 0, so you can't easily measure a Keq. However, if we assume the reaction goes in reverse to an almost imperceptible degree, [HCl]eq might equal 10-10 M. Hence Keq >> 1.

In summary, the extent of reactions can vary from completely irreversible (favoring only the products) to reactions that favor the reactants . Our next goal is to understand what controls the extent of a reaction. That is, of course, the change in the Gibbs free energy. Two different pairs of factors influence the ΔG. One pair is concentration and inherent reactivity of reactants compared to products (as reflected in the Keq). The other pair is enthalpy/entropy changes. We will now consider the first pair .

Contributions of Molecule Stability (Keq) and concentration to ΔG

Consider the reactions of hydrochloric acid and acetic acid with water.

• $$\mathrm{HCl(aq) + H_2O(l) \rightarrow H_3O^+(aq) + Cl^-(aq)}$$
• $$\mathrm{CH_3CO_2H(aq) + H_2O(l) \rightarrow H_3O^+(aq) + \sideset{}{_{2}^{-}}{CH_3CO}(aq)}$$

Assume that at t = 0, each acid is placed into water at a concentration of 0.1 M. When equilibrium is reached, there is essentially no HCl left in solution, while 99% of the acetic acid remains. Why are they so different? We rationalized that HCl(aq) is a much stronger acid than H3O+(aq) which itself is a much stronger acid than CH3CO2H(aq). Why? All we can say is there is something about the structure of these acids (and the bases) that makes HCl much more intrinsically unstable, much higher in energy, and hence much more reactive than the acid it forms, H3O+(aq). Likewise, H3O+(aq) is much more intrinsically unstable, much higher in energy, and hence more reactive than CH3CO2H(aq). This has nothing to do with concentration, since the initial concentration of both HCl(aq) and CH3CO2H(aq) were identical. This observation is reflected in the Keq for these acids (>>1 for HCl and <<1 for acetic acid). This difference in intrinsic stability of reactants compared to products (which is independent of concentration) is one factor that contributes to ΔG.

The other factor is concentration. A 0.25 M (0.25 mol/L or 0.25 mmol/ml) solution of acetic acid does not conduct electricity, implying that very few ions of H3O+(aq) + CH3CO2-(aq) exist in solution. However, if more concentrated acetic acid is added, a dim light becomes evident. Adding more reactant seemed to drive the reaction to form more products, even though the reverse reaction is favored if one considers only the intrinsic stability of reactants and products. Before the concentrated acid was added, the system was at equilibrium. Adding concentrated acid perturbed the equilibrium, which drove the reaction to form additional products. This is an example of Le Chatelier's Principle, which states that if a reaction at equilibrium is perturbed, the reaction will be driven in the direction that will relieve the perturbation. Hence:

• if more reactant is added, the rx. shifts to form more products
• if more product is added, the rx. shifts to form more reactants
• if products are selectively removed (by distillation, crystallization, or further reaction to produce another species), the rx. shifts to form more product.
• if reactants are removed (as above), the rx. shifts to form more reactants.
• if heat is added to an exothermic reaction, the rx. shifts to get rid of the excess heat by shifting to form more reactants. (opposite for an endothermic rx).