Chemical Equilibrium and Le Châtelier’s Principle: Effects of Concentration, Volume, and Temperature

Chapter 14: Chemical Equilibrium

Introduction to Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a closed system are equal, resulting in constant concentrations of reactants and products. The study of equilibrium is fundamental in understanding how chemical systems respond to changes in conditions.

• Dynamic Equilibrium: Both forward and reverse reactions continue to occur, but there is no net change in concentrations.

• Equilibrium Constant (K): Quantifies the ratio of product to reactant concentrations at equilibrium.

• Reaction Quotient (Q): Used to predict the direction a reaction will shift to reach equilibrium.

Calculating Equilibrium Constants

The equilibrium constant expression depends on the balanced chemical equation and the physical states of the reactants and products.

• General Form: For a reaction $aA + bB \rightleftharpoons cC + dD$:

$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• For Gaseous Reactions: Use partial pressures:

$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$

Le Châtelier’s Principle

Definition and Statement

Le Châtelier’s Principle states that if a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the system will shift its equilibrium position to counteract the disturbance.

• Henri Le Châtelier (1850–1936): "Any change to a chemical reaction at equilibrium causes the reaction to proceed in the direction that reduces the effect of the change."

Effects of Concentration Changes

Changing the concentration of reactants or products causes the system to shift in the direction that consumes the added substance or replaces the removed substance.

• Adding Reactant: Shifts equilibrium toward products (right).

• Adding Product: Shifts equilibrium toward reactants (left).

• Removing Reactant: Shifts equilibrium toward reactants (left).

• Removing Product: Shifts equilibrium toward products (right).

Example: For $N_2O_4(g) \rightleftharpoons 2 NO_2(g)$, adding $NO_2$ shifts equilibrium left, increasing $N_2O_4$.

Effects of Volume and Pressure Changes

Volume changes affect gaseous equilibria by altering the partial pressures of the gases. The system shifts to minimize the change in pressure.

• Decrease Volume (Increase Pressure): Shifts equilibrium toward the side with fewer moles of gas.

• Increase Volume (Decrease Pressure): Shifts equilibrium toward the side with more moles of gas.

• If both sides have equal moles of gas: No shift occurs.

• Adding Inert Gas at Constant Volume: No effect on equilibrium position.

Example: For $N_2(g) + 3 H_2(g) \rightleftharpoons 2 NH_3(g)$, decreasing volume shifts equilibrium right (toward fewer moles of gas).

Table: Effect of Volume Change on Equilibrium

Change	Shift Direction	Reason
Decrease Volume	Toward fewer moles of gas	Reduces pressure increase
Increase Volume	Toward more moles of gas	Compensates for pressure decrease
Add inert gas (constant V)	No shift	Partial pressures unchanged

Effects of Temperature Changes

Temperature changes affect equilibrium depending on whether the reaction is exothermic or endothermic.

• Endothermic Reaction ($\Delta H > 0$): Heat is a reactant. Increasing temperature shifts equilibrium toward products.

• Exothermic Reaction ($\Delta H < 0$): Heat is a product. Increasing temperature shifts equilibrium toward reactants.

Example: For $N_2O_4(g) + \text{heat} \rightleftharpoons 2 NO_2(g)$ ($\Delta H = 58$ kJ/mol), increasing temperature shifts equilibrium right, favoring $NO_2$ formation.

Table: Effect of Temperature on Equilibrium Constant (K)

Temperature (K)	Equilibrium Constant, K
298	4.39 × 107
800	1.38 × 102
1000	2.54 × 101
1200	3.92

Observation: For exothermic reactions, increasing temperature decreases K; for endothermic reactions, increasing temperature increases K.

Application: Predicting Shifts in Equilibrium

To predict how a system at equilibrium will respond to changes, apply Le Châtelier’s Principle and consider the reaction quotient (Q) relative to K.

• If Q < K: Reaction shifts right (toward products).

• If Q > K: Reaction shifts left (toward reactants).

Example: For $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$, adding $CaO$ does not affect equilibrium because solids are not included in K; $K = P_{CO_2}$.

Concept Checks and Practice Questions

• How can you increase the partial pressure of $N_2O_4$ in $N_2O_4(g) \rightleftharpoons 2 NO_2(g)$?

  • Add more $NO_2$ (shifts left).

  • Compress the mixture (shifts left).

• How can you increase the concentration of products in $N_2(g) + 3 H_2(g) \rightleftharpoons 2 NH_3(g)$ ($\Delta H = -46.19$ kJ)?

  • Increase pressure (decrease volume).

  • Add $N_2$ or $H_2$.

  • Decrease temperature (for exothermic reaction).

Summary Table: Le Châtelier’s Principle Effects

Change	Effect on Equilibrium
Add reactant	Shifts right (products)
Add product	Shifts left (reactants)
Remove reactant	Shifts left (reactants)
Remove product	Shifts right (products)
Decrease volume	Shifts to fewer moles of gas
Increase volume	Shifts to more moles of gas
Increase temperature (endothermic)	Shifts right (products)
Increase temperature (exothermic)	Shifts left (reactants)

Additional info:

• For reactions involving solids and liquids, only gases and aqueous species are included in equilibrium expressions.

• Inert gases do not affect equilibrium unless they change the total pressure at constant volume.

• Endothermic and exothermic reactions can be identified by the sign of $\Delta H$.