Heterogeneous Equilibrium

Introduction

Some equilibria include gases, solutions and pure solids or liquids in the same reaction. Their equilibrium expressions look unusual if every written formula is treated as a concentration factor. Pure solid and liquid activities are conventionally one, so their amounts are omitted while those phases remain present.

Core explanation

Consider CaCO₃(s) ⇌ CaO(s) + CO₂(g). The activity expression is K = a(CaO)a(CO₂)/a(CaCO₃). For pure CaO and CaCO₃ at the stated reference conditions, each solid activity is one, leaving K = a(CO₂), approximated by its relative gas pressure. The equation still needs the solids: they define the reaction and supply or receive matter. Omission from the expression does not mean they are chemically irrelevant.

The concentration of a pure solid, understood as amount per its own phase volume, is essentially fixed by its density at a given condition. Adding more of that same pure solid increases its total amount and surface area but does not change its thermodynamic activity as a pure phase. Thus adding extra CaCO₃ while both pure solids remain does not shift the equilibrium CO₂ pressure by a concentration-factor effect. It could change how quickly equilibrium is approached by changing available surface area.

If a pure phase disappears completely, the previous phase coexistence condition no longer applies in the same way. For example, a container with insufficient CaCO₃ may consume it all before reaching the CO₂ pressure that would coexist with both solids. One must check material inventory, not merely calculate K and assume every written phase remains present.

A pure liquid such as liquid water is likewise often omitted when it is the solvent or a separate pure phase with activity near one. Dissolved water in a nonideal mixture is a different situation; its activity may vary. The “omit liquids” shortcut applies to pure liquids, not every species with liquid-like behavior or every solvent concentration under all conditions.

Heterogeneous equilibria show why phase labels are essential. CO₂(g) appears in the gas pressure expression; CaCO₃(s) does not. If Ca²⁺(aq) or CO₃²⁻(aq) appeared in a dissolution reaction, their dissolved activities would enter Ksp. A formula alone is not enough; phase and standard-state treatment determine the factors.

Step-by-step reasoning

1. Balance the reaction and label all phases. 2. Write the full activity ratio conceptually. 3. Replace pure solid and pure liquid activities with one. 4. Retain gas and dissolved-species factors and verify pure phases remain present.

Visual explanation

Draw a sealed vessel containing two solid piles and CO₂ gas. Cross out the two pure-solid activity factors in a K fraction, leaving only the gas factor.

Real-world analogy

Adding more ice to a glass containing ice and water changes how long both phases coexist but does not by itself change their equilibrium melting temperature at fixed pressure.

Real-world example

Heating calcium carbonate in a sealed vessel can establish a CO₂ pressure associated with coexistence of CaCO₃ and CaO at a given temperature. The solid masses matter for whether both remain.

Why?

Why are pure solids omitted? Their standard-state activities remain one while the pure phases exist, so including them would multiply the expression by constant factors of one.

Common misconception

“If a solid is omitted from K, removing all of it cannot matter.” Complete removal changes the available phases and may make that equilibrium state impossible.

Worked example

Write K for NH₄HS(s) ⇌ NH₃(g) + H₂S(g). The pure solid activity is one; the gases contribute their activities. Under ideal relative-pressure treatment, Kp = (p NH3/p°)(p H2S/p°). If both gases begin absent and sufficient solid remains, their pressures rise until this product reaches K.

Quick check

1. Does CaCO₃(s) appear as a concentration factor in K for CaCO₃(s) ⇌ CaO(s) + CO₂(g)? Answer: No. Its pure-solid activity is one while that phase is present.

Exam focus

Always write phase labels. Omit pure solid and liquid factors, but keep dissolved ions and gases. Check whether the pure phases can coexist at the predicted equilibrium.

Advanced insight

Activities of solids in solid solutions or nonpure phases need not equal one. The pure-phase simplification is a standard-state statement, not a universal rule that all condensed-matter contributions vanish.

Summary

Heterogeneous equilibrium expressions include gas and dissolved activities while pure solid and liquid activities are one. Phase inventory still matters because an omitted pure phase must remain present for coexistence.

Practice questions

1. Write the variable part of K for CaCO₃(s) ⇌ CaO(s) + CO₂(g). Answer: The CO₂ gas activity, often approximated by p CO2/p°. 2. Does adding more pure CaO necessarily change K at fixed temperature? Answer: No. K is temperature-dependent and pure CaO activity remains one while present. 3. Can a dissolved Ca²⁺ concentration be omitted just because calcium is also in a solid? Answer: No. Aqueous ion activity is generally a variable factor in the relevant expression.