8.4 Types of Equilibrium

Based on the physical states of the reactants and products involved in a reversible reaction, chemical equilibria can be classified into two main types.

i. Homogeneous Equilibria

A homogeneous equilibrium is an equilibrium system in which all reactants and products are in the same phase (e.g., all gaseous or all aqueous).

Example Reactions (Gaseous Phase):

• Haber process for ammonia synthesis: ${\mathrm{N}}_{2(\mathrm{g})}+3{\mathrm{H}}_{2(\mathrm{g})}\rightleftharpoons 2N{\mathrm{H}}_{3(\mathrm{g})}$

• Contact process for sulfuric acid production: $2S{\mathrm{O}}_{2(\mathrm{g})}+{\mathrm{O}}_{2(\mathrm{g})}\rightleftharpoons 2S{\mathrm{O}}_{3(\mathrm{g})}$

• Formation of nitrosyl chloride: $2N{\mathrm{O}}_{(\mathrm{g})}+\mathrm{C}{\mathrm{l}}_{2(\mathrm{g})}\rightleftharpoons 2NOC{\mathrm{l}}_{(\mathrm{g})}$

Example Reaction (Liquid Phase):

• Esterification of acetic acid with ethanol: $\mathrm{C}{\mathrm{H}}_3\mathrm{COO}{\mathrm{H}}_{(\mathrm{l})}+{\mathrm{C}}_2{\mathrm{H}}_5\mathrm{O}{\mathrm{H}}_{(\mathrm{l})}\rightleftharpoons \mathrm{C}{\mathrm{H}}_3\mathrm{COO}{\mathrm{C}}_2{\mathrm{H}}_{5(\mathrm{l})}+{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{l})}$

ii. Heterogeneous Equilibria

A heterogeneous equilibrium is an equilibrium system in which the reactants and products are present in more than one phase (e.g., a mix of solids, liquids, and gases).

Example Reactions:

• Thermal decomposition of calcium carbonate: $\mathrm{CaC}{\mathrm{O}}_{3(\mathrm{s})}\rightleftharpoons \mathrm{Ca}{\mathrm{O}}_{(\mathrm{s})}+\mathrm{C}{\mathrm{O}}_{2(\mathrm{g})}$

• Reaction of carbon with steam (water gas production): ${\mathrm{C}}_{(\mathrm{s})}+{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{g})}\rightleftharpoons \mathrm{C}{\mathrm{O}}_{(\mathrm{g})}+{\mathrm{H}}_{2(\mathrm{g})}$

• Reaction of iron with steam: $3F{\mathrm{e}}_{(\mathrm{s})}+4{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{g})}\rightleftharpoons \mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_{4(\mathrm{s})}+4{\mathrm{H}}_{2(\mathrm{g})}$

Equilibrium Constants for Heterogeneous Equilibria

A key rule for writing equilibrium constant expressions ($K_c$ or $K_p$) is that the concentrations (or partial pressures) of pure solids and pure liquids are considered constant and are not included in the expression. This is because their concentration (density) does not change significantly during the reaction.

Example 1: Decomposition of Water

• Reaction: $2{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{l})}\rightleftharpoons 2{\mathrm{H}}_{2(\mathrm{g})}+{\mathrm{O}}_{2(\mathrm{g})}$

• Since ${\mathrm{H}}_2\mathrm{O}$ is a pure liquid, it is omitted from the expression.

• Equilibrium Constant ($K_c$): $K_c=[{\mathrm{H}}_2{]}^2[{\mathrm{O}}_2]$

• Equilibrium Constant ($K_p$): $K_p=(P_{{\mathrm{H}}_2}{)}^2(P_{{\mathrm{O}}_2})$

Example 2: Decomposition of Calcium Carbonate

• Reaction: $\mathrm{CaC}{\mathrm{O}}_{3(\mathrm{s})}\rightleftharpoons \mathrm{Ca}{\mathrm{O}}_{(\mathrm{s})}+\mathrm{C}{\mathrm{O}}_{2(\mathrm{g})}$

• The pure solids $\mathrm{CaC}{\mathrm{O}}_3$ and $\mathrm{CaO}$ are omitted.

• Equilibrium Constant ($K_c$): $K_c=[\mathrm{C}{\mathrm{O}}_2]$

• Equilibrium Constant ($K_p$): $K_p=P_{\mathrm{C}{\mathrm{O}}_2}$

Example 3: Reaction of Iron with Steam

• Reaction: $3F{\mathrm{e}}_{(\mathrm{s})}+4{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{g})}\rightleftharpoons \mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_{4(\mathrm{s})}+4{\mathrm{H}}_{2(\mathrm{g})}$

• The pure solids, $\mathrm{F}{\mathrm{e}}_{(\mathrm{s})}$ and $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_{4(\mathrm{s})}$, are omitted.

• Equilibrium Constant ($K_c$): $K_c=\frac{[{\mathrm{H}}_2{]}^4}{[{\mathrm{H}}_2\mathrm{O}{]}^4}$

• Equilibrium Constant ($K_p$): $K_p=\frac{(P_{{\mathrm{H}}_2}{)}^4}{(P_{{\mathrm{H}}_2\mathrm{O}}{)}^4}$

Concept Assessment Exercise 8.3

Write the $K_c$ and $K_p$ expressions for each of the following reactions.

i. $\mathrm{Fe}{\mathrm{O}}_{(\mathrm{s})}+\mathrm{C}{\mathrm{O}}_{(\mathrm{g})}\rightleftharpoons \mathrm{F}{\mathrm{e}}_{(\mathrm{s})}+\mathrm{C}{\mathrm{O}}_{2(\mathrm{g})}$

1. Identify phases: $\mathrm{FeO}$ and $\mathrm{Fe}$ are solids. $\mathrm{CO}$ and $\mathrm{C}{\mathrm{O}}_2$ are gases.
2. Write expression: Exclude the solids from the equilibrium constant expressions.
3. Answer:
   • $K_c=\frac{[\mathrm{C}{\mathrm{O}}_2]}{[\mathrm{CO}]}$
   • $K_p=\frac{P_{\mathrm{C}{\mathrm{O}}_2}}{P_{\mathrm{CO}}}$

ii. ${\mathrm{P}}_{4(\mathrm{s})}+5{\mathrm{O}}_{2(\mathrm{g})}\rightleftharpoons {\mathrm{P}}_4{\mathrm{O}}_{10(\mathrm{s})}$

1. Identify phases: ${\mathrm{P}}_4$ and ${\mathrm{P}}_4{\mathrm{O}}_{10}$ are solids. ${\mathrm{O}}_2$ is a gas.
2. Write expression: Exclude the solids. The products side only contains a solid, so it is represented by 1 in the numerator.
3. Answer:
   • $K_c=\frac{1}{[{\mathrm{O}}_2{]}^5}$
   • $K_p=\frac{1}{(P_{{\mathrm{O}}_2}{)}^5}$

iii. $\mathrm{C}{\mathrm{H}}_{4(\mathrm{g})}+4C{\mathrm{l}}_{2(\mathrm{g})}\rightleftharpoons \mathrm{CC}{\mathrm{l}}_{4(\mathrm{l})}+4HC{\mathrm{l}}_{(\mathrm{g})}$

1. Identify phases: $\mathrm{C}{\mathrm{H}}_4$, $\mathrm{C}{\mathrm{l}}_2$, and $\mathrm{HCl}$ are gases. $\mathrm{CC}{\mathrm{l}}_4$ is a pure liquid.
2. Write expression: Exclude the pure liquid ($\mathrm{CC}{\mathrm{l}}_4$).
3. Answer:
   • $K_c=\frac{[\mathrm{HCl}{]}^4}{[\mathrm{C}{\mathrm{H}}_4][\mathrm{C}{\mathrm{l}}_2{]}^4}$
   • $K_p=\frac{(P_{\mathrm{HCl}}{)}^4}{(P_{\mathrm{C}{\mathrm{H}}_4})(P_{\mathrm{C}{\mathrm{l}}_2}{)}^4}$