Chemical Equilibrium

The Concept of Equilibrium

Chemical equilibrium is the state in which the concentrations of all reactants and products in a closed system remain constant over time, as the forward and reverse reactions occur at equal rates. This dynamic balance means that, although reactions continue to occur, there is no net change in the amounts of substances present.

• Dynamic equilibrium: Both forward and reverse reactions continue, but their rates are equal.

• Constant concentrations: The amounts of reactants and products do not change once equilibrium is reached.

• Double arrow notation: Equilibrium reactions are represented with a double arrow () to indicate reversibility.

Approaching Equilibrium

As a reaction mixture approaches equilibrium, the concentrations of reactants and products change until the rates of the forward and reverse reactions become equal. The path to equilibrium can be monitored experimentally by measuring concentration changes over time.

Equilibrium from Either Direction

Equilibrium can be established whether the reaction starts with only reactants, only products, or a mixture of both. Regardless of the starting point, the system will reach the same equilibrium concentrations under identical conditions.

The Equilibrium Constant

Defining the Equilibrium Constant

The equilibrium constant () quantifies the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their coefficients in the balanced equation. For a general reaction:

The equilibrium constant expression is:

• : Uses concentrations in molarity (M).

• : Used for gases, based on partial pressures.

For reactions involving gases, is related to by:

where is the change in moles of gas (), is the gas constant, and is temperature in Kelvin.

Interpreting the Value of K

• If : The reaction is product-favored; products predominate at equilibrium.

• If : The reaction is reactant-favored; reactants predominate at equilibrium.

Visualizing Equilibrium Systems

Different systems at equilibrium can be compared by examining the relative numbers of reactant and product particles.

Manipulating Equilibrium Constants

Rules for Manipulating K

• Reversing a reaction: The new is the reciprocal of the original.

• Multiplying a reaction by a factor : The new is the original raised to the th power.

• Adding reactions: The overall is the product of the individual values.

Heterogeneous Equilibria

Solids and Liquids in Equilibrium Expressions

The concentrations of pure solids and pure liquids are constant and do not appear in equilibrium constant expressions. Only the concentrations of gases and aqueous species are included.

• Example: For ,

Calculating Equilibrium Concentrations

ICE Tables

ICE tables (Initial, Change, Equilibrium) are used to organize data and solve for unknown concentrations at equilibrium.

Quadratic Equation in Equilibrium Calculations

When solving for equilibrium concentrations, you may need to solve a quadratic equation:

The Reaction Quotient (Q) and Predicting Direction

Definition and Use of Q

The reaction quotient () is calculated using the same expression as , but with initial (not necessarily equilibrium) concentrations. Comparing to predicts the direction the reaction will proceed:

• If : The system is at equilibrium.

• If : The reaction will proceed forward (toward products).

• If : The reaction will proceed in reverse (toward reactants).

Le Châtelier’s Principle

Response to Disturbances

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

• Adding reactant: Shifts equilibrium toward products.

• Removing product: Shifts equilibrium toward products.

• Changing pressure (gases): Increasing pressure favors the side with fewer moles of gas.

• Changing temperature: For endothermic reactions, increasing temperature favors products; for exothermic, it favors reactants.

The Haber Process Example

The synthesis of ammonia from nitrogen and hydrogen is an industrially important equilibrium process. Manipulating conditions such as concentration, pressure, and temperature can shift the equilibrium to increase ammonia yield.

Catalysts and Equilibrium

Effect of Catalysts

Catalysts increase the rate at which equilibrium is achieved by lowering the activation energy for both the forward and reverse reactions. However, they do not affect the equilibrium position or the value of the equilibrium constant.

Practice and Application

Writing Equilibrium Constant Expressions

For the reaction: , the correct equilibrium constant expression is:

• Solids and liquids are omitted from the expression.

Summary Table: Key Relationships in Equilibrium

Additional info: For more complex equilibrium calculations, especially when is very small or very large, approximations or the quadratic formula may be used to solve for unknown concentrations.