Table of Contents
Temperature and Chemical Equilibria
In an earlier chapter, the general idea of chemical equilibrium and the equilibrium constant $K$ has been introduced. Here, the focus is on how changing the temperature affects equilibria that are already established or can be established.
The two key viewpoints you need are:
- the Le Châtelier viewpoint: “How does the system respond to a disturbance?”
- the thermodynamic viewpoint: “How is $K$ related to temperature and reaction enthalpy?”
Exothermic and Endothermic Reactions
Every chemical reaction has an associated standard reaction enthalpy $\Delta_\mathrm{r}H^\circ$ (at a chosen reference temperature, usually $298\,\mathrm{K}$):
- Exothermic reaction: $\Delta_\mathrm{r}H^\circ < 0$
Heat is released; we can treat “heat” as a product. - Endothermic reaction: $\Delta_\mathrm{r}H^\circ > 0$
Heat is absorbed; we can treat “heat” as a reactant.
For equilibrium considerations, it is often helpful to write, conceptually:
- exothermic:
$$\text{Reactants} \rightleftharpoons \text{Products} + \text{Heat}$$ - endothermic:
$$\text{Reactants} + \text{Heat} \rightleftharpoons \text{Products}$$
This is not a real new “species” in the reaction equation, but a mental aid to predict the direction of the shift when temperature changes.
Qualitative Effect of Temperature on the Position of Equilibrium
Le Châtelier’s principle says that when you disturb an equilibrium, the system will react in a way that partially counteracts the disturbance.
When you increase temperature, you are effectively adding heat:
- For an endothermic reaction ($\Delta_\mathrm{r}H^\circ > 0$):
Heat is a reactant. Adding heat drives the equilibrium toward the products. - For an exothermic reaction ($\Delta_\mathrm{r}H^\circ < 0$):
Heat is a product. Adding heat drives the equilibrium toward the reactants.
When you decrease temperature, you are effectively removing heat:
- Endothermic: removing a reactant (heat) shifts equilibrium toward reactants.
- Exothermic: removing a product (heat) shifts equilibrium toward products.
So, summarizing the direction of the shift with rising temperature:
- Endothermic forward reaction: equilibrium shifts to the products.
- Exothermic forward reaction: equilibrium shifts to the reactants.
Temperature Dependence of the Equilibrium Constant
The thermodynamic link between the equilibrium constant $K$ and temperature involves the reaction enthalpy. A key relation is the van ’t Hoff equation (here in a simplified integrated form):
$$
\ln \frac{K_2}{K_1}
= -\,\frac{\Delta_\mathrm{r}H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)
$$
where
- $K_1$ and $K_2$ are equilibrium constants at temperatures $T_1$ and $T_2$,
- $\Delta_\mathrm{r}H^\circ$ is (approximately) constant in the temperature range considered,
- $R$ is the gas constant.
From this equation:
- If $\Delta_\mathrm{r}H^\circ > 0$ (endothermic), then an increase in temperature ($T_2 > T_1$) makes $\ln(K_2/K_1)$ positive, so $K_2 > K_1$.
- If $\Delta_\mathrm{r}H^\circ < 0$ (exothermic), then an increase in temperature makes $\ln(K_2/K_1)$ negative, so $K_2 < K_1$.
This is the quantitative expression of what was argued qualitatively using Le Châtelier’s principle.
A larger $K$ at a given temperature corresponds to a stronger tendency for products to be present at equilibrium; a smaller $K$ corresponds to a stronger tendency for reactants to predominate.
Pressure and Chemical Equilibria (Gas-Phase Reactions)
Pressure effects are important when gases are involved. For reactions involving only solids and/or liquids (in condensed phases), pressure effects on equilibrium position are usually minor at ordinary pressures and are often neglected.
For gas-phase equilibria, it is often convenient to work with partial pressures and an equilibrium constant $K_p$ instead of $K_c$ (in terms of concentrations). The basic ideas, however, are the same.
Changing the Total Pressure by Changing Volume
For a gas mixture at constant temperature, decreasing the volume increases the total pressure and all partial pressures. Le Châtelier’s principle can be applied using the total amount of gas (in moles) as the internal variable that can adjust.
Consider a general gas-phase reaction:
$$
a\,\mathrm{A(g)} + b\,\mathrm{B(g)} \rightleftharpoons c\,\mathrm{C(g)} + d\,\mathrm{D(g)}
$$
Define the change in moles of gas:
$$
\Delta n_\mathrm{gas} = (c + d) - (a + b)
$$
Then, for a decrease in volume (increase in pressure) at constant temperature:
- If $\Delta n_\mathrm{gas} < 0$: the system “prefers” the side with fewer moles of gas. The equilibrium shifts toward the side with fewer gas particles to reduce pressure.
- If $\Delta n_\mathrm{gas} > 0$: the system “prefers” the side with more moles of gas. The equilibrium shifts toward the side with fewer moles of gas, i.e., toward the opposite side.
- If $\Delta n_\mathrm{gas} = 0$: the total mole number of gas is the same on both sides; a volume change (pressure change) has much less effect on equilibrium composition.
More concretely:
- Increase of pressure (by decreasing volume):
Equilibrium shifts to the side with fewer gas moles. - Decrease of pressure (by increasing volume):
Equilibrium shifts to the side with more gas moles.
The equilibrium constant $K_p$ itself does not change when you compress or expand the system at constant temperature; instead, the actual partial pressures change, and the composition readjusts until $K_p$ is satisfied again at the new pressure.
Changing the Total Pressure by Adding an Inert Gas
An inert gas is a gas that does not participate in the reaction (e.g., helium introduced to a mixture of reacting gases).
Two situations must be distinguished:
- Constant volume, add inert gas
- The total pressure increases.
- The partial pressures of the reacting gases, however, remain the same because their amounts and the volume do not change.
- Since the equilibrium expression $K_p$ only involves partial pressures of the reacting gases, nothing in the $K_p$ expression changes.
⇒ No shift in the position of equilibrium. - Constant pressure, add inert gas and allow volume to change
- The system expands (increase in volume) to keep total pressure constant.
- The partial pressures of all existing gases (including the reacting ones) decrease.
- This is similar to an increase of volume for the reacting mixture:
Equilibrium shifts to the side with more moles of gas.
Thus, whether adding an inert gas affects the equilibrium depends on whether the volume or the pressure is held constant.
Effect of Pressure on Heterogeneous Equilibria
In heterogeneous equilibria, where gases coexist with pure solids or pure liquids, only the gaseous components appear in $K_p$ (and $K_c$). The activities of pure solids and pure liquids are taken as unity and do not depend directly on pressure in the ordinary range.
Consequently:
- Pressure changes affect only the gas-phase species, through their partial pressures.
- The direction of the shift again follows the rule based on $\Delta n_\mathrm{gas}$ for the gaseous components.
Combined Influence of Temperature and Pressure
In many practical systems, both temperature and pressure can change, and they may affect the equilibrium in different directions.
For example, a reaction could be:
- Exothermic: lowering temperature favors products.
- Producing fewer moles of gas: increasing pressure favors products.
Operating conditions in industrial processes (such as the ammonia synthesis, treated elsewhere) are chosen as a compromise between:
- thermodynamic favorability of the desired equilibrium position with respect to temperature and pressure,
- and kinetic and technical constraints (reaction rates, costs, materials, safety).
The important conceptual separation is:
- Temperature changes: alter the value of the equilibrium constant $K$ (due to $\Delta_\mathrm{r}H^\circ$ dependence).
- Pressure/volume changes (at fixed temperature): do not change $K$ itself but change actual concentrations/partial pressures, which pushes the composition to a new equilibrium that still satisfies the same $K$.