What allows us to incorporate the concentrations of pure solids and liquids into \(K_{\text {eq }}\) instead of writing these concentrations explicitly in the equilibrium constant expression?

The equilibrium constant (K_eq) is a value that expresses the relationship between the concentrations of reactants and products at equilibrium for a given chemical reaction. It is typically written in terms of the concentrations of the species involved in the reaction raised to the power of their respective stoichiometric coefficients. For a generic reaction: aA + bB ⇌ cC + dD The equilibrium constant expression (K_eq) would be given as: \(K_{eq} = \frac{[C]^c [D]^d}{[A]^a [B]^b}\) Now let's analyze the incorporation of concentrations of pure solids and liquids in K_eq.

In the context of equilibrium expressions, concentrations of substances are only meaningful for species that are in solution, i.e., their particles are freely moving and interacting with each other. For pure solids and liquids, the particles are not free to move and interact in the same way as they do in solutions. This is due to the fact that solids and liquids have virtually constant concentrations that are not dependent on the number of moles or the volume of the system. In other words, adding or removing a portion of a pure solid or liquid will not affect the concentration of the particles within it. Therefore, the concentrations of pure solids and liquids are considered constant in reactions and do not impact the equilibrium constant expression.

As we now understand that the concentrations of pure solids and liquids are considered constant in equilibrium reactions, we can incorporate them into the K_eq by simply incorporating their constant values. Since constants do not affect the overall equilibrium expression, it is easier to omit them from the expression entirely. This means, if a reaction involves pure solids or liquids, their concentrations will not be included in the K_eq expression. Only the concentrations of the reactants and products in the aqueous or gaseous phase are considered in the equilibrium constant expression. This simplifies the expression and makes it easier to interpret the relationship between the concentrations of species at equilibrium. For example, consider the reaction: A(s) + B(aq) ⇌ C(aq) + D(l) The K_eq expression for this reaction would be: \(K_{eq} = \frac{[C]}{[B]}\) Here, the concentrations of A (solid) and D (liquid) are not included in the K_eq expression, as they are considered constant and do not influence the equilibrium state.