Heterogeneous equilibria Knowledge-Based Study

Study notes

1. What is a Heterogeneous Equilibrium?

   In chemical equilibrium, reactions are classified based on the physical states of the participating substances:

   • Homogeneous equilibrium: All reactants and products are in the same phase (for example, all gases or all aqueous species).
   • Heterogeneous equilibrium: Reactants and products exist in more than one distinct phase (such as a mixture of solids and gases, liquids and gases, or solids and aqueous solutions).

   A classic example is the thermal decomposition of solid calcium carbonate in a closed container:

   $$\text{CaCO}_3\text{(s)} \rightleftharpoons \text{CaO(s)} + \text{CO}_2\text{(g)}$$

   In this system, two separate solid phases ($\text{CaCO}_3$ and $\text{CaO}$) coexist with a gas phase ($\text{CO}_2$).

   Why Pure Solids and Liquids Are Omitted

   The equilibrium constant expression is formulated using the activities of the chemical species involved. For ideal gases or dilute solutions, activity is approximated by partial pressure or molar concentration. However, for pure solids and pure liquids:

   • The concentration of a pure solid or liquid depends solely on its density and molar mass: $$\text{Molar Concentration} = \frac{\text{density}}{\text{molar mass}}$$
   • Because density and molar mass are intrinsic, intensive properties that remain constant at a given temperature, the concentration of a pure solid or liquid does not change as the reaction proceeds.
   • By convention, the activity of any pure solid or pure liquid in its standard state is assigned a value of 1.

   Therefore, pure solids and pure liquids do not appear explicitly in the equilibrium constant expression ($K_c$ or $K_p$).

   Formulating $K_c$ and $K_p$

   When constructing equilibrium expressions for heterogeneous systems, include only gaseous species ($\text{g}$) and dissolved aqueous species ($\text{aq}$).

   Example 1: Decomposition of Calcium Carbonate

   $$\text{CaCO}_3\text{(s)} \rightleftharpoons \text{CaO(s)} + \text{CO}_2\text{(g)}$$

   The concentration equilibrium constant is:

   $$K_c = [\text{CO}_2]$$

   The pressure equilibrium constant is:

   $$K_p = P_{\text{CO}_2}$$

   Example 2: Reaction of Carbon with Carbon Dioxide

   $$\text{C(s)} + \text{CO}_2\text{(g)} \rightleftharpoons 2\text{CO(g)}$$

   Because solid carbon is omitted:

   $$K_c = \frac{[\text{CO}]^2}{[\text{CO}_2]} \quad \text{and} \quad K_p = \frac{(P_{\text{CO}})^2}{P_{\text{CO}_2}}$$

   Effects of Perturbations

   Applying Le Chatelier's principle to heterogeneous systems highlights several key characteristics:

   • Adding or removing pure solids or liquids: As long as some amount of each solid or liquid remains present to maintain equilibrium, changing the amount or surface area of a solid or liquid does not change its activity and therefore does not cause a shift in the position of equilibrium.
   • Changing gas volume or pressure: A change in container volume shifts the equilibrium toward the side with fewer moles of gas, completely ignoring stoichiometric coefficients of pure solids and liquids.
   • Temperature changes: Altering temperature changes the numerical value of $K$, which in turn alters the equilibrium partial pressures of the gases according to whether the forward process is endothermic or exothermic.