Table of Contents
Overview
Chemical equilibrium and the law of mass action together form one of the central frameworks of chemistry. They tell us:
- Under which conditions chemical reactions can reach a stable “balance”.
- How far a reaction proceeds before reactants and products coexist in constant proportions.
- How to predict and quantify these proportions using the equilibrium constant.
This chapter introduces the general ideas. Detailed aspects such as temperature effects, pressure changes, or specific equilibria (ammonia synthesis, solubility equilibria) are treated in later chapters of this section.
Macroscopic View: Reactions That Seem to “Stop”
In everyday experience, many reactions appear to stop before all reactants are used up. For example:
- When dissolving a slightly soluble salt in water, some solid remains undissolved even after long stirring.
- In industrial synthesis of ammonia from nitrogen and hydrogen, not all nitrogen and hydrogen become ammonia, even with long reaction times.
Empirically, one observes:
- Concentrations of reactants and products approach constant values.
- No further macroscopic changes (no visible gas evolution, no more solid dissolving, constant composition) occur after some time.
- These final states are reproducible under the same external conditions (temperature, pressure, concentrations).
This empirical behavior motivates the concept of chemical equilibrium.
Dynamic Nature of Chemical Equilibrium
Although nothing seems to change macroscopically at equilibrium, the underlying molecular processes usually continue.
For a generic reversible reaction
$$
\ce{A <=> B}
$$
we can distinguish:
- Forward reaction: $\ce{A -> B}$
- Reverse reaction: $\ce{B -> A}$
On a microscopic level at equilibrium:
- Molecules of A continue to convert to B.
- Molecules of B continue to convert back to A.
- The rates of the forward and reverse reactions are equal.
Thus, the net change in concentrations is zero:
- $[\ce{A}]$ and $[\ce{B}]$ remain constant with time.
- The system is in a dynamic equilibrium, not a static one.
Key characteristics of chemical equilibrium:
- Dynamical: Microscopic processes continue.
- Time-independent on the macroscopic level: Observable properties (color, pressure, concentration) are constant.
- Condition-dependent: Changes in temperature, pressure, or composition can disturb equilibrium and lead to new equilibrium states (treated in “Shifting Chemical Equilibria”).
Reversible Reactions and the Concept of Extent
Many chemical reactions are reversible, at least in principle. Instead of thinking only in terms of “going to completion,” we describe their extent:
- At low extent, mostly reactants are present.
- At high extent, mostly products are present.
- At intermediate extent, appreciable amounts of both reactants and products coexist.
The equilibrium state is the particular extent at which:
- The free tendency of the reaction to proceed in either direction is balanced.
- The forward and reverse reaction rates match.
- For given conditions (temperature, pressure, total composition), the system has a characteristic equilibrium composition.
Irreversible reactions in practice:
- Some reactions proceed so far in one direction and so completely (e.g. heavy gas evolution, precipitation of an insoluble solid) that the reverse reaction is negligible under normal conditions.
- Even then, thermodynamically, a reverse process exists; it is just extremely unfavorable.
This chapter focuses on systems where both directions are appreciable and equilibrium is readily observable and controllable.
The Law of Mass Action: Qualitative Idea
The law of mass action provides a quantitative relationship between the equilibrium composition and the chemical equation.
For many reactions, the rate of a reaction step depends on the concentrations (or, more generally, activities) of the reacting species:
- The more particles of a species are present in a given volume, the more frequently they collide and react.
- This dependence can often be approximated by a product of concentration terms.
Although rigorous rate laws belong to kinetics, the equilibrium situation can be obtained by setting the forward rate equal to the reverse rate. This leads to a simple relationship that only involves the concentrations at equilibrium.
The law of mass action in its equilibrium form links this relationship to a characteristic constant, the equilibrium constant.
Equilibrium Constant Expression
Consider a general reaction written with stoichiometric coefficients:
$$
\ce{aA + bB <=> cC + dD}
$$
Lowercase letters ($a, b, c, d$) are the stoichiometric coefficients; uppercase letters ($\ce{A, B, C, D}$) denote chemical species.
The law of mass action states that at equilibrium (under given $T$ and $p$), the following ratio is constant:
$$
K = \frac{[\ce{C}]^c[\ce{D}]^d}{[\ce{A}]^a[\ce{B}]^b}
$$
Here:
- $[\ce{A}]$, $[\ce{B}]$, $[\ce{C}]$, $[\ce{D}]$ denote equilibrium concentrations (e.g., in $\mathrm{mol\,L^{-1}}$).
- $K$ is the equilibrium constant at that temperature (often denoted $K_c$ if concentration-based).
Important features:
- Each concentration term is raised to the power of its coefficient in the balanced chemical equation.
- $K$ depends only on temperature (and, in more general formulations, on the chosen standard state and activities).
- For a given $T$, no matter how you start (different initial concentrations), the system will adjust until the ratio equals $K$.
In more advanced treatments:
- Concentrations are replaced by activities to account for non-ideal behavior.
- For gas-phase equilibria, partial pressures can be used, leading to $K_p$.
These refinements are treated in later sections when specific equilibria (gas reactions, solubility, acid–base, redox) are discussed.
Interpreting the Magnitude of the Equilibrium Constant
The numerical value of $K$ gives a direct, though approximate, sense of how far a reaction lies to one side at equilibrium.
For a reaction written as:
$$
\ce{Reactants <=> Products}
$$
- $K \gg 1$:
- Numerator dominates: Equilibrium mixture contains mostly products.
- Reaction is said to be “product-favored”.
- $K \approx 1$:
- Significant amounts of both reactants and products at equilibrium.
- Neither side is strongly favored.
- $K \ll 1$:
- Denominator dominates: Equilibrium mixture contains mostly reactants.
- Reaction is “reactant-favored”.
The value of $K$ must always be interpreted relative to how the reaction is written. If you write the chemical equation in the reverse direction, the new equilibrium constant is the reciprocal:
- For $\ce{aA + bB <=> cC + dD}$ with $K$,
- The reversed reaction $\ce{cC + dD <=> aA + bB}$ has equilibrium constant $K' = 1/K$.
This sensitivity to equation direction and stoichiometry is crucial when comparing equilibrium data.
Reaction Quotient and Direction of Spontaneous Change
To predict how a given mixture will evolve, the reaction quotient $Q$ is introduced. It has the same mathematical form as the equilibrium constant expression, but uses current (possibly non-equilibrium) concentrations:
For
$$
\ce{aA + bB <=> cC + dD}
$$
define
$$
Q = \frac{[\ce{C}]^c[\ce{D}]^d}{[\ce{A}]^a[\ce{B}]^b}
$$
Interpretation:
- At equilibrium: $Q = K$.
- If $Q < K$:
- The numerator is “too small” relative to denominator.
- System contains “too few” products or “too many” reactants compared to equilibrium.
- The reaction will proceed in the forward direction (towards products) to increase $Q$ until $Q = K$.
- If $Q > K$:
- The numerator is “too large”.
- System contains “too many” products or “too few” reactants.
- The reaction will proceed in the reverse direction (towards reactants) to decrease $Q$ until $Q = K$.
Thus, comparing $Q$ to $K$ provides a clear criterion for predicting the direction of the spontaneous approach to equilibrium for a given starting mixture.
Phase and Concentration Conventions in Equilibrium Expressions
In practice, not all species that appear in the chemical equation show up explicitly in the equilibrium constant expression.
Pure Solids and Pure Liquids
For heterogeneous equilibria involving more than one phase, pure solids and pure liquids typically have activity ≈ 1, so their concentration terms are absorbed into $K$ and omitted from the expression.
Example:
$$
\ce{CaCO3(s) <=> CaO(s) + CO2(g)}
$$
The equilibrium expression depends only on the gas:
$$
K_p = p_{\ce{CO2}}
$$
Because $\ce{CaCO3(s)}$ and $\ce{CaO(s)}$ are pure solids with constant activity (as long as some of each phase is present), they do not appear in the expression.
Consequences:
- Changing the amount (mass) of a pure solid at equilibrium does not change $K$ or the equilibrium gas composition, as long as some of the solid phase remains.
- This is important in solubility equilibria (treated later): the solubility of a sparingly soluble salt does not depend on the mass of undissolved solid.
Solvents in Dilute Solutions
For dilute solutions, the solvent (often water) also usually has activity close to 1 and is not explicitly included.
Example:
$$
\ce{HA(aq) <=> H+(aq) + A-(aq)}
$$
For a weak acid in water, the equilibrium expression is typically written:
$$
K_a = \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}
$$
Water, though present in large excess, does not appear explicitly.
These conventions make equilibrium expressions simpler and more practically useful, but they rely on assumptions about phase purity and dilution.
Multiple Equilibria and Overall Constants
Many systems involve several equilibria that can interconnect.
Sequential Equilibria
Consider a stepwise process:
- $\ce{A <=> B}$ with $K_1$
- $\ce{B <=> C}$ with $K_2$
The overall reaction is:
$$
\ce{A <=> C}
$$
Its equilibrium constant is the product:
$$
K_\text{overall} = K_1 K_2
$$
More generally:
- Adding chemical equations corresponds to multiplying their equilibrium constants.
- Reversing a sub-reaction inverts the corresponding $K$ for that step.
This rule is often used to construct equilibrium constants for complex reactions from tabulated data for simpler steps.
Competing Equilibria
Sometimes, different equilibrium reactions share components. For instance, a metal ion might form several different complexes with a ligand, or an acid may participate in both acid–base and complexation equilibria. The resulting system is governed by all of the relevant equilibrium constants simultaneously.
The concept of multiple equilibria is essential later in:
- Complex formation equilibria in coordination chemistry.
- Polyprotic acid–base systems.
- Competing precipitation and complexation in analytical chemistry.
At this stage, the key idea is: each independent reaction has its own $K$, and the overall composition of a system is determined by satisfying all equilibrium conditions together, subject to mass balance and charge balance constraints.
Equilibrium and Thermodynamic Tendency
Chemical equilibrium is not just a balance of rates; it is also the state of minimal thermodynamic driving force under the given conditions.
Thermodynamically:
- For a closed system at constant $T$ and $p$, the equilibrium state corresponds to a minimum in the Gibbs free energy.
- Away from equilibrium, there is a driving force pushing the reaction in the direction that lowers free energy.
- At equilibrium, this driving force is zero; the system has no net tendency to change in composition.
The quantitative relationship between the equilibrium constant and standard Gibbs free energy change is treated in the later subsection “Relationship Between the Equilibrium Constant and Standard Gibbs Free Energy Change.” Here it suffices to connect equilibrium qualitatively with:
- A balance of driving forces in both directions.
- A state function minimum under the imposed constraints.
Practical Use of Equilibrium Concepts
The framework developed in this chapter underlies many applications:
- Predicting the composition of a gas mixture formed by a reversible reaction at given $T$ and $p$.
- Estimating how far a reaction goes (to what extent reactants are consumed).
- Designing conditions that favor desired products by manipulating initial concentrations, temperature, or pressure (shift of equilibrium).
- Understanding buffer solutions, solubility limits, redox equilibria, and complex formation.
Later chapters in this section will:
- Analyze how equilibrium is approached in time (from the kinetic perspective).
- Show how equilibrium shifts when external conditions change (Le Chatelier-type considerations).
- Apply the law of mass action to specific important systems such as the ammonia equilibrium and solubility equilibria.
In all these contexts, the central ideas remain:
- Equilibrium is a dynamic, condition-dependent balance.
- The law of mass action allows us to describe this balance with an equilibrium constant.
- The reaction quotient $Q$ compared to $K$ reveals how any mixture will spontaneously evolve toward equilibrium.