Table of Contents
Overview
In addition to temperature and pressure, various further conditions can influence the position of a chemical equilibrium. In this chapter, the focus is on how such “additional” factors change concentrations, activities, or effective reaction pathways, and how this leads to a shift of the equilibrium position according to the law of mass action and Le Châtelier’s principle.
We will consider:
- Change of concentrations by adding or removing reactants/products
- Use of inert gases (at constant volume vs. constant pressure)
- Influence of solvents and ionic strength
- Influence of pH
- Use of complexing agents, precipitating agents, and gas removal
- Role of catalysts with respect to equilibrium
Temperature- and pressure-effects on equilibrium are treated separately in their own chapter and are therefore not discussed in detail here.
Changes in Concentration of Reactants and Products
For a general reaction
$$
a\,\mathrm{A} + b\,\mathrm{B} \rightleftharpoons c\,\mathrm{C} + d\,\mathrm{D},
$$
the equilibrium constant (for activities or, in dilute solutions, concentrations) is
$$
K = \frac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{A}]^a[\mathrm{B}]^b}.
$$
At a given temperature, $K$ is constant. However, the actual ratio of concentrations may temporarily deviate from $K$ when conditions change. The reaction quotient
$$
Q = \frac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{A}]^a[\mathrm{B}]^b}
$$
describes the current state. If $Q \neq K$, the system will evolve until $Q = K$ again.
Addition of a Reactant
Adding more of a reactant (e.g. increasing $[\mathrm{A}]$) changes $Q$:
- Since $[\mathrm{A}]$ appears in the denominator, an increase in $[\mathrm{A}]$ makes $Q$ smaller.
- If $Q < K$, the reaction will proceed in the forward direction until $Q = K$ again.
Qualitatively: adding a reactant shifts the equilibrium towards products.
Example: For
$$
\mathrm{N_2(g)} + 3\,\mathrm{H_2(g)} \rightleftharpoons 2\,\mathrm{NH_3(g)},
$$
at constant $T$ and $P$, adding $\mathrm{N_2}$ or $\mathrm{H_2}$ increases the equilibrium amount of $\mathrm{NH_3}$.
Removal of a Reactant
Removing a reactant (e.g. decreasing $[\mathrm{A}]$) has the opposite effect:
- $[\mathrm{A}]$ in the denominator decreases, $Q$ increases.
- If $Q > K$, the reaction shifts towards the reactants until $Q = K$.
Qualitatively: removing a reactant shifts the equilibrium towards reactants.
Addition or Removal of a Product
Analogously:
- Adding a product (increasing $[\mathrm{C}]$ or $[\mathrm{D}]$) increases $Q$ and shifts the equilibrium toward the reactant side.
- Removing a product lowers $Q$ and shifts the equilibrium toward the product side.
Many industrial processes exploit this by continuously removing a product (e.g. by distillation, absorption, crystallization, or gas stripping) to “pull” the equilibrium toward product formation.
Influence of Inert Gases
Inert gases (e.g. $\mathrm{Ar}$, $\mathrm{N_2}$ in some contexts) do not participate chemically in the reaction. Nevertheless, they can change partial pressures and thereby affect equilibria involving gases. The effect depends critically on whether volume or pressure is held constant.
Addition of an Inert Gas at Constant Volume
If the volume $V$ is held constant and an inert gas is added, the total pressure increases, but the partial pressures (and thus the concentrations) of the reacting gases remain unchanged:
- Number of moles of reactants and products stay the same.
- Volume is fixed.
- For each reacting gas $i$, the concentration $c_i = n_i / V$ is unchanged.
Therefore:
- $Q$ does not change.
- No shift of the equilibrium occurs.
So: adding an inert gas at constant volume does not affect the equilibrium position.
Addition of an Inert Gas at Constant Pressure
If the total pressure is held constant and an inert gas is added, the system must expand (volume increases) to keep the total pressure unchanged.
- The partial pressures (and thus concentrations) of all gaseous species decrease.
- The new value of $Q$ will usually differ from $K$.
The direction of the subsequent equilibrium shift depends on the stoichiometric change in the number of gaseous moles, $\Delta n_{\text{gas}}$:
- For a reaction where the number of gas moles decreases (e.g. $2 \to 1$), the equilibrium is typically shifted toward the side with fewer gas moles when the overall concentration of gases is reduced.
- For a reaction where the number of gas moles increases (e.g. $1 \to 2$), lowering all partial pressures tends to favor the side with more gas moles.
Thus, at constant pressure, adding inert gas can indirectly influence the equilibrium of gas-phase reactions through changes in concentrations.
Solvent and Ionic Strength Effects
In solution, equilibrium constants are properly expressed in terms of activities $a_i$, not simple concentrations. For dilute systems, activities are often approximated by concentrations, but this approximation can fail as ionic strength or solvent composition changes.
Change of Solvent or Solvent Composition
Changing the solvent (or mixing solvents) alters:
- Solvation and stabilization of ions or molecules
- Dielectric constant $\varepsilon$
- Hydrogen bonding characteristics
- Polarity
These factors modify the relative stabilization of reactants and products and therefore the equilibrium constant $K$ itself.
Qualitative rules:
- Increasing solvent polarity often stabilizes charged species relative to neutral ones, favoring equilibria that produce ions.
- Less polar solvents can favor neutral molecules over ionic species.
Thus, simply dissolving the same reacting substances in a different solvent (e.g. water vs. ethanol) can result in a different equilibrium composition.
Ionic Strength and Activity Coefficients
For ionic equilibria (e.g. acid–base equilibria, solubility equilibria, complex formation), the ionic strength $I$ of the solution plays a central role. It influences the activity coefficients $\gamma_i$ of ions:
$$
a_i = \gamma_i \,[i].
$$
As ionic strength increases:
- Electrostatic interactions between ions are screened.
- Activity coefficients usually deviate more from 1.
- Even if concentrations stay the same, activities change.
Because equilibrium expressions are written in terms of activities, changing the ionic strength shifts the apparent equilibrium position when expressed in concentrations. This is important in:
- Salt effects on solubility equilibria
- Salt effects on acid–base equilibria (apparent $K_a$, $K_b$)
- Stability of complexes in solutions with high salt content
Influence of pH
For reactions involving species that can be protonated or deprotonated, the pH of the solution is a crucial additional condition. Many equilibria are coupled to acid–base equilibria.
General Principle
If a species in an equilibrium can be converted (by protonation or deprotonation) into a form that does not appear in the equilibrium expression, this removal or addition effectively shifts the equilibrium.
Example pattern:
- Original equilibrium: $\mathrm{HA} \rightleftharpoons \mathrm{H^+} + \mathrm{A^-}$
- If $\mathrm{A^-}$ takes part in a further equilibrium (e.g. complex formation) or precipitates, or if $\mathrm{H^+}$ is consumed in another reaction, the position of the acid–base equilibrium is displaced.
pH Control as a Tool
By setting and maintaining a specific pH (using buffers, acids, or bases), chemists can:
- Favor a particular protonation state of a molecule (e.g. $\mathrm{CO_2}$ vs. $\mathrm{HCO_3^-}$ vs. $\mathrm{CO_3^{2-}}$).
- Steer complex formation equilibria that depend on ligand protonation.
- Control solubility of sparingly soluble hydroxides or salts (which depends strongly on $[\mathrm{H^+}]$ or $[\mathrm{OH^-}]$).
For example, many metal hydroxides precipitate at higher pH due to
$$
\mathrm{M^{n+}} + n\,\mathrm{OH^-} \rightleftharpoons \mathrm{M(OH)_n(s)},
$$
so increasing $[\mathrm{OH^-}]$ (raising pH) pushes the equilibrium to the right, promoting precipitation.
Complex Formation and Precipitation as Driving Forces
Some reactions can be made to appear “irreversible” in practice when a product is removed from the equilibrium mixture through a secondary process—such as complexation, precipitation, or gas removal. These additional conditions change the effective equilibrium position of the original reaction.
Complexation
If a product of a reaction forms a stable complex with another species that is not part of the original equilibrium, the free (uncomplexed) concentration of that product decreases.
Consider:
$$
\mathrm{M^{2+}} + \mathrm{L} \rightleftharpoons \mathrm{ML^{2+}} \quad (K_1)
$$
If the complex $\mathrm{ML^{2+}}$ then binds further ligands:
$$
\mathrm{ML^{2+}} + 3\,\mathrm{L} \rightleftharpoons \mathrm{ML_4^{2+}} \quad (K_2),
$$
the equilibrium between $\mathrm{M^{2+}}$ and ligand $\mathrm{L}$ is effectively shifted towards complexed forms. For another equilibrium involving $\mathrm{M^{2+}}$, the free $\mathrm{M^{2+}}$ concentration becomes much lower than without complexation, which shifts that other equilibrium.
Practical implications:
- Complexing agents (e.g. EDTA) are used to “bind” metal ions and pull equilibria toward decomplexed partners (e.g. removing $\mathrm{Ca^{2+}}$ shifts solubility equilibria of calcium salts).
- In analytical chemistry, complexation can be used to mask certain ions, changing the outcome of precipitation reactions and separations.
Precipitation
For a solubility equilibrium
$$
\mathrm{AB(s)} \rightleftharpoons \mathrm{A^+ (aq)} + \mathrm{B^- (aq)},
$$
the solubility product is
$$
K_\text{sp} = [\mathrm{A^+}][\mathrm{B^-}].
$$
If any process reduces either $[\mathrm{A^+}]$ or $[\mathrm{B^-}]$ (e.g. by forming an insoluble salt or complex), the equilibrium shifts to produce more of that ion, often leading to more precipitation of the solid. Conversely, complex formation with one of the ions can increase solubility by lowering the free ion concentration and thereby allowing more solid to dissolve to maintain $K_\text{sp}$.
Thus, by introducing precipitating or complexing agents, one can control solubility equilibria and thereby indirectly force other coupled equilibria to shift.
Gas Removal or Supply
For equilibria involving gases dissolved in or in contact with a liquid, changing the partial pressure of the gas above the solution acts as an “additional condition.”
For example, for dissolution of a gas:
$$
\mathrm{CO_2(g)} \rightleftharpoons \mathrm{CO_2(aq)},
$$
and subsequent reaction:
$$
\mathrm{CO_2(aq)} + \mathrm{H_2O} \rightleftharpoons \mathrm{H_2CO_3(aq)},
$$
lowering the partial pressure of $\mathrm{CO_2}$ (e.g. by flushing with an inert gas, or lowering total pressure) reduces $[\mathrm{CO_2(aq)}]$, which shifts the carbonic acid–carbonate equilibria. Similarly, continuously removing a gaseous product from the reaction mixture (by sparging or vacuum) pulls the main equilibrium towards product formation.
Role of Catalysts: Kinetics vs. Equilibrium
Catalysts provide an important example of a condition that affects the rate at which equilibrium is reached but does not change the equilibrium position itself.
- A catalyst lowers the activation energy for both forward and reverse reactions.
- It accelerates both directions by the same factor (or in a way that leaves $K$ unchanged).
- Therefore, the value of $K$ at given temperature remains the same; only the time to reach equilibrium is reduced.
From the perspective of “shifting” equilibria:
- A catalyst does not shift the equilibrium.
- However, it can make a shifted equilibrium (due to some other change in conditions) be established faster.
This distinction—kinetic vs. thermodynamic control—is central when interpreting the influence of experimental conditions on observed compositions.
Summary
- At constant temperature, the equilibrium constant $K$ is fixed, but changing concentrations (by adding/removing reactants or products) changes $Q$ and thus shifts the equilibrium until $Q = K$ again.
- Adding inert gas at constant volume does not change the equilibrium composition, because partial pressures and concentrations of reacting species are unaltered. At constant pressure, adding inert gas changes concentrations and can shift gas-phase equilibria.
- Changing solvent or ionic strength alters activities and can modify the position of equilibrium even if concentrations appear unchanged.
- pH is a powerful control parameter for equilibria involving protonatable species; protonation–deprotonation coupling can shift equilibria dramatically.
- Complex formation, precipitation, and gas removal or supply can effectively remove species from an equilibrium expression, thereby driving the equilibrium in a desired direction.
- Catalysts speed up the approach to equilibrium but do not change the equilibrium position itself.