Chemical Equilibrium and Le Chatelier’s Principle

Introduction

Key Concepts

Definition of Chemical Equilibrium

Chemical equilibrium occurs in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products over time. It signifies a state of balance where no net change occurs, although both reactions continue to proceed at the molecular level.

Dynamic Nature of Equilibrium

Despite the appearance of a static state, equilibrium is dynamic. Reactant molecules continually transform into products and vice versa. This perpetual motion ensures that the overall concentrations of reactants and products remain unchanged, but individual molecules are constantly undergoing transformation.

The Equilibrium Constant (K)

The equilibrium constant, denoted as $K$, quantitatively expresses the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients. For a general reaction:

$aA + bB \rightleftharpoons cC + dD$

the equilibrium constant is given by:

The magnitude of $K$ indicates the position of equilibrium. A large $K$ value suggests a reaction that favors products, while a small $K$ value indicates a reaction that favors reactants.

Factors Affecting Equilibrium

Chemical equilibrium is influenced by several factors, as outlined by Le Chatelier’s Principle:

• Concentration: Changes in the concentration of reactants or products can shift the equilibrium position to restore balance.
• Pressure: Applicable to gaseous reactions, altering pressure can shift the equilibrium towards the side with fewer or more moles of gas.
• Temperature: Changing the temperature affects the position of equilibrium, favoring either the endothermic or exothermic direction of the reaction.
• Catalysts: While catalysts speed up the attainment of equilibrium, they do not alter the position of equilibrium.

Le Chatelier’s Principle

Le Chatelier’s Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust itself to counteract the imposed change and establish a new equilibrium.

Application of Le Chatelier’s Principle

Le Chatelier’s Principle can predict how a change in conditions affects the equilibrium position. For example:

• Concentration Changes: Adding more reactant shifts equilibrium towards products, while adding more product shifts it towards reactants.
• Pressure Changes: Increasing pressure shifts equilibrium towards the side with fewer moles of gas.
• Temperature Changes: For exothermic reactions, increasing temperature shifts equilibrium towards reactants; for endothermic reactions, towards products.

Calculating Equilibrium Concentrations

To determine equilibrium concentrations, an ICE (Initial, Change, Equilibrium) table is often used. This method involves:

1. Setting up the balanced equation for the reaction.
2. Listing initial concentrations, changes in concentrations, and equilibrium concentrations.
3. Substituting equilibrium concentrations into the equilibrium expression to solve for unknowns.

For example, consider the reaction:

$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

With an initial concentration of $N_2 = 1 \text{ M}$ and $H_2 = 3 \text{ M}$, and initially no $NH_3$ present.

At equilibrium, let the change in $N_2$ be $-x$, so $H_2$ changes by $-3x$, and $NH_3$ changes by $+2x$.

The equilibrium concentrations are:

• $[N_2] = 1 - x$
• $[H_2] = 3 - 3x$
• $[NH_3] = 2x$

Substituting into the equilibrium expression:

Solving this equation allows determination of the equilibrium concentration of $NH_3$.

Common Ion Effect

The common ion effect refers to the shift in equilibrium position when a common ion is added to a system in equilibrium. It results in the suppression of the dissociation of a weak electrolyte by the addition of a strong electrolyte that shares a common ion.

Solubility Product (Ksp)

The solubility product, $K_{sp}$, is a special type of equilibrium constant for the dissolution of sparingly soluble salts. For a salt $AB$ dissolving in water:

$AB (s) \rightleftharpoons A^+ (aq) + B^- (aq)$

the solubility product is:

Understanding $K_{sp}$ is crucial for predicting precipitation and solubility in various chemical reactions.

Theorems and Calculations

Several theorems assist in solving equilibrium problems, including:

• The ICE Method: A systematic approach to calculate changes in concentrations.
• Le Chatelier’s Principle: Predicting the direction of equilibrium shift in response to changes.
• Mass Action Law: The principle underpinning the equilibrium constant expression.

Example Problem

Consider the exothermic reaction:

$N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

At equilibrium, the partial pressures are as follows:

• $P_{N_2} = 1.0 \text{ atm}$
• $P_{H_2} = 3.0 \text{ atm}$
• $P_{NH_3} = 2.0 \text{ atm}$

Calculate the equilibrium constant $K_p$ for the reaction.

Using the equilibrium expression for partial pressures:

Graphical Representation of Equilibrium

Equilibrium can be visually represented through graphs showing concentrations or pressures over time. These graphs demonstrate how reactant and product concentrations level off, indicating dynamic balance. Additionally, graphs can illustrate shifts in equilibrium in response to changes in conditions, aligning with Le Chatelier’s Principle.

Distinguishing Between Homogeneous and Heterogeneous Equilibria

Chemical equilibria can be classified based on the phases of reactants and products:

• Homogeneous Equilibrium: All reactants and products are in the same phase, typically gaseous or aqueous.
• Heterogeneous Equilibrium: Reactants and products exist in different phases, such as solid and gas.

Understanding the type of equilibrium is important for correctly applying the equilibrium constant expressions and predicting system behavior.

Temperature and Equilibrium Constants

Temperature variations affect the value of the equilibrium constant. For exothermic reactions, increasing temperature decreases $K$, shifting equilibrium towards reactants. Conversely, for endothermic reactions, increasing temperature increases $K$, favoring product formation.

Effect of Catalysts on Equilibrium

Catalysts speed up the attainment of equilibrium by lowering the activation energy for both forward and reverse reactions equally. However, catalysts do not affect the position of equilibrium or the equilibrium constant.

Common Mistakes in Understanding Equilibrium

Students often confuse changes in conditions with changes in equilibrium position. It is crucial to differentiate between shifts that restore equilibrium and actual changes in concentrations. Additionally, misapplying the equilibrium constant expression by neglecting stoichiometric coefficients leads to incorrect calculations.

Comparison Table

Summary and Key Takeaways