Table of Contents
Overview
When a reversible reaction has reached chemical equilibrium, the forward and reverse reaction rates are equal and the macroscopic composition no longer changes. However, the position of this equilibrium (which side is favored) can still be influenced by changing external conditions.
The central idea for this chapter is:
- Equilibrium is dynamic and condition-dependent.
- Changing conditions (e.g. temperature, pressure, concentrations) can shift the equilibrium composition.
- The equilibrium constant $K$ is fixed only for a given temperature; it changes if the temperature changes.
The detailed mechanisms of how $K$ is defined and how equilibria are established are treated elsewhere; here, the focus is on what happens after an equilibrium is established and conditions are changed.
The qualitative tool for discussing shifts is often summarized as Le Châtelier’s principle:
If an external change (stress) is imposed on a system at equilibrium, the system responds in such a way as to counteract this change as far as possible.
Mathematically, these shifts can be described using the reaction quotient $Q$ and the equilibrium constant $K$ (already introduced in the parent chapter). Here, we apply these ideas to different kinds of changes.
Types of Disturbances to an Equilibrium
For a general reaction
$$
\alpha\,\mathrm{A} + \beta\,\mathrm{B} \rightleftharpoons \gamma\,\mathrm{C} + \delta\,\mathrm{D},
$$
an equilibrium can be disturbed by:
- Changing concentrations (or, for gases, partial pressures)
- Changing total pressure (for gas-phase reactions)
- Changing temperature
- In some cases, changing volume (for gas reactions, equivalent to changing pressure)
- Changing inert components (e.g. adding an inert gas)
A catalyst can change the rate at which equilibrium is reached, but not the position of equilibrium (i.e. not $K$). Therefore, catalysts are not a way of “shifting” equilibria in the thermodynamic sense.
In this chapter family, the specific influences are split into:
- Influence of temperature and pressure
- Influence of additional reaction conditions
Below is the conceptual framework that both subchapters build on and that is specific to “shifting” equilibria.
Reaction Quotient $Q$ versus Equilibrium Constant $K$
At any moment, the composition of a reacting mixture can be described with the reaction quotient $Q$:
- $Q$ has the same algebraic form as $K$ but uses current concentrations (or activities/partial pressures), not the equilibrium ones.
- For the example reaction above (using concentrations):
$$
Q_c = \frac{[\mathrm{C}]^{\gamma} [\mathrm{D}]^{\delta}}
{[\mathrm{A}]^{\alpha} [\mathrm{B}]^{\beta}}.
$$
At equilibrium, $Q = K$.
If a disturbance is applied, at the next instant $Q$ usually changes, but $K$ (at the same temperature) does not. The direction in which the system will move can be predicted by comparing $Q$ and $K$:
- If $Q < K$: too many reactants relative to products → reaction proceeds forward (toward products) until $Q = K$ again.
- If $Q > K$: too many products relative to reactants → reaction proceeds backward (toward reactants) until $Q = K$ again.
Thus, “shifts” of chemical equilibria are simply the system changing composition until $Q$ is brought back to the (temperature-dependent) constant $K$.
This $Q$ vs. $K$ framework underlies all of the specific cases described in the child chapters.
Qualitative Description of Equilibrium Shifts
Concentration changes
If at equilibrium you add or remove one of the reacting species (changing its concentration or partial pressure), you instantly change $Q$.
- Adding a reactant (e.g. increasing $[\mathrm{A}]$ or $[\mathrm{B}]$) generally makes $Q$ smaller (numerator unchanged, denominator larger), so $Q < K$. The system responds by producing more products until $Q = K$ again.
- Adding a product increases $Q$ so that $Q > K$, and the reaction shifts toward reactants.
- Removing a reactant or product has analogous effects (shifts equilibrium to make up for what was removed).
This is the most direct embodiment of Le Châtelier’s principle: the system “uses up” an added component or “replenishes” a removed one.
Volume changes for gas-phase equilibria
For gas-phase equilibria, changing the container volume changes partial pressures and thus $Q$.
For a reaction involving gases:
$$
\nu_1 \mathrm{A}(g) + \nu_2 \mathrm{B}(g) \rightleftharpoons \nu_3 \mathrm{C}(g) + \nu_4 \mathrm{D}(g),
$$
define the change in moles of gas:
$$
\Delta n_\mathrm{gas} = (\nu_3 + \nu_4) - (\nu_1 + \nu_2).
$$
- Decreasing volume (at constant amount of substance and temperature) increases total pressure and tends to favor the side with fewer moles of gas ($\Delta n_\mathrm{gas} < 0$).
- Increasing volume (thus decreasing pressure) tends to favor the side with more moles of gas ($\Delta n_\mathrm{gas} > 0$).
Chemically, this translates into a shift in composition so that the pressure change is opposed.
Adding inert gases
For gas-phase equilibria, the effect of adding an inert (nonreactive) gas depends on the conditions:
- At constant volume: adding an inert gas increases the total pressure but leaves the partial pressures of reacting species essentially unchanged (their mole amounts and the volume are unchanged). Thus $Q$ stays the same and there is no shift in equilibrium.
- At constant total pressure: adding an inert gas forces an expansion of volume, lowering partial pressures of all gases; this is similar in effect to increasing volume and can shift equilibrium if $\Delta n_\mathrm{gas} \ne 0$.
This is an example where “pressure change” only matters for equilibria if it affects the partial pressures of the reacting species.
Temperature changes: changing $K$
Unlike changes in concentration, volume, or pressure at fixed temperature, a temperature change actually changes the equilibrium constant $K$ itself. The direction of the shift depends on whether the reaction is:
- Exothermic ($\Delta_\mathrm{r} H < 0$): heat is released; “heat” can be treated qualitatively as a product.
- Endothermic ($\Delta_\mathrm{r} H > 0$): heat is absorbed; “heat” can be treated qualitatively as a reactant.
Raising the temperature “adds heat”:
- For an exothermic reaction, this favors the reactant side (consumes heat), so the equilibrium shifts toward reactants and $K$ decreases.
- For an endothermic reaction, this favors the product side, so the equilibrium shifts toward products and $K$ increases.
Lowering the temperature has the opposite effect. The quantitative link between $K$ and temperature is handled elsewhere (via the van ’t Hoff equation and Gibbs free energy); here, we use the qualitative picture for understanding shifts.
Distinguishing Kinetic and Thermodynamic Effects
When discussing “shifts,” it is important to distinguish:
- Thermodynamic position of equilibrium: determined solely by $K(T)$, i.e. by thermodynamic parameters such as $\Delta_\mathrm{r} G^\circ$, $\Delta_\mathrm{r} H^\circ$, $\Delta_\mathrm{r} S^\circ$ at a given temperature.
- Rate of approach to equilibrium: determined by kinetics (rate constants, activation energies, presence of catalysts).
Changes such as:
- adding a catalyst, or
- stirring more vigorously,
do not change $K$ and thus do not change the ultimate equilibrium composition. They merely affect how fast equilibrium is reached.
By contrast, changes such as:
- changing temperature,
- changing total pressure for gas reactions, or
- changing concentrations of reacting species,
alter either $K$ (temperature) or $Q$ (composition/pressure), and therefore change the position of equilibrium or induce a transient shift.
Graphical and Conceptual Representations
Shifts in equilibrium can be visualized in several ways:
- Concentration–time diagrams: after a disturbance, concentrations of species change smoothly from one plateau (old equilibrium) to a new plateau (new equilibrium).
- Energy diagrams: show that thermodynamic changes (e.g. temperature dependence of $K$) correspond to different relative depths of “product” and “reactant” energy wells.
- $Q$–$K$ comparison: a conceptual “scale” where $Q$ moves relative to a fixed (for a given $T$) $K$ after a disturbance; the system then reacts until $Q$ returns to $K$.
These tools are useful for systematically predicting how an equilibrium will respond to changes, beyond the simple verbal rule of Le Châtelier’s principle.
Practical Importance of Shifting Equilibria
Shifting equilibria is central in many chemical applications, for example:
- Industrial synthesis: conditions (temperature, pressure, removal of products) are chosen to maximize yields of desired products in processes such as ammonia or sulfuric acid production.
- Analytical chemistry: equilibria can be driven to completion (or to a particular side) by adjusting pH, adding complexing agents, or changing ionic strength.
- Biological systems: biochemical pathways are controlled through concentration changes (substrate/product, cofactors) and compartmentalization, effectively shifting numerous coupled equilibria.
- Environmental chemistry: speciation of pollutants or nutrients (e.g. between dissolved and gaseous forms, or between different oxidation states) is often governed by equilibria that depend on pH, temperature, and other conditions.
The detailed, quantitative treatment of temperature and pressure effects, and of more specific additional reaction conditions, is developed in the subsequent subchapters.