Chemical Equilibrium: Principles and Calculations

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Chemical Equilibrium

The Concept of Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry describing a state in which the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. This balance is dynamic, meaning reactions continue to occur, but there is no net change in the amounts of substances.

Equilibrium State: At equilibrium, the system's composition remains unchanged over time.
Dynamic Nature: Both forward and reverse reactions proceed, but at equal rates.
Example: The dissociation of dinitrogen tetroxide (N2O4) into nitrogen dioxide (NO2) illustrates equilibrium as color changes stop when equilibrium is reached.

N2O4 and NO2 equilibrium color change and molecular representation Graphs showing concentration and rate changes as equilibrium is achieved

Equilibrium Constant and Its Expression

The equilibrium constant quantifies the ratio of product and reactant concentrations at equilibrium. It is denoted as K and depends on the balanced chemical equation.

Notation: The double arrow () indicates a reversible reaction.
General Expression: For a reaction aA + bB → cC + dD, the equilibrium constant expression is:

Pressure-based Equilibrium: For gaseous reactions, equilibrium can also be expressed in terms of partial pressures (Kp).

Kc symbol Kp symbol

Magnitude and Interpretation of K

The value of the equilibrium constant indicates the extent to which a reaction favors products or reactants.

K >> 1: Products predominate at equilibrium; equilibrium "lies to the right".
K << 1: Reactants predominate; equilibrium "lies to the left".

Diagram showing K >> 1 favors products, K << 1 favors reactants

Stoichiometry and Equilibrium Constants

Changing the stoichiometry of a reaction affects the equilibrium constant:

Multiplying Equation: Raise K to the corresponding power.
Dividing Equation: Take the appropriate root of K.
Reversing Equation: Use the reciprocal of K.

Combining Equilibrium Expressions

When reactions are added, their equilibrium constants are multiplied to obtain the new constant for the overall reaction.

Example: If two reactions have constants K1 and K2, the combined reaction has K = K1 × K2.

Homogeneous and Heterogeneous Equilibria

Equilibria can involve substances in the same phase (homogeneous) or different phases (heterogeneous).

Homogeneous Equilibrium: All reactants and products are in the same phase.
Heterogeneous Equilibrium: At least one component is in a different phase. Concentrations of pure solids and liquids are omitted from the equilibrium expression.
Example: The decomposition of calcium carbonate:

CaCO3 decomposition equilibrium with solid and gas phases

Calculating Equilibrium Constants

To determine the equilibrium constant from experimental data:

Tabulate initial and equilibrium concentrations.
Calculate changes in concentration.
Use stoichiometry to relate changes among species.
Find equilibrium concentrations.
Substitute into the equilibrium expression to solve for K.

Table of initial and equilibrium concentrations for NO2 and N2O4 Graph showing equilibrium concentration of NO2

Reaction Quotient (Q) and Predicting Direction

The reaction quotient (Q) is calculated using current concentrations or pressures and compared to K to predict the direction of the reaction.

Q < K: Reaction proceeds toward products.
Q = K: System is at equilibrium.
Q > K: Reaction proceeds toward reactants.

Calculating Equilibrium Concentrations

Given initial concentrations and K, equilibrium concentrations can be found by setting up a table and solving for the change variable (often "x") using stoichiometry and the equilibrium expression.

Quadratic Equations: Sometimes, solving for x requires the quadratic formula.
Physical Meaning: Only positive, physically meaningful values for concentrations are accepted.

Le Châtelier’s Principle

Le Châtelier’s Principle states that if a system at equilibrium is disturbed, it will shift to counteract the disturbance and re-establish equilibrium.

Change in Concentration: Adding/removing reactants or products shifts equilibrium to use up or produce the component.
Change in Volume/Pressure: For gases, increasing volume (decreasing pressure) favors the side with more moles; decreasing volume favors the side with fewer moles.
Change in Temperature: For endothermic reactions, adding heat shifts equilibrium toward products (K increases); for exothermic reactions, adding heat shifts equilibrium toward reactants (K decreases).
Catalysts: Catalysts speed up attainment of equilibrium but do not affect the equilibrium composition or constant.

Summary Table: Types of Equilibrium and Effects

Type	Description	Effect on K
Homogeneous	All substances in same phase	No effect
Heterogeneous	Substances in different phases; solids/liquids omitted from K	No effect
Change in Concentration	Shifts equilibrium position	K unchanged
Change in Pressure/Volume	Shifts equilibrium for gases	K unchanged
Change in Temperature	Shifts equilibrium; affects K	K changes
Catalyst	Speeds up equilibrium attainment	K unchanged

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