Equilibrium

Learning Objectives

• Understand the dynamic nature of chemical equilibrium and how it is established when the rate of the forward reaction equals the rate of the reverse reaction.
• Apply the law of mass action to write equilibrium constant expressions for various chemical reactions.
• Calculate equilibrium constants ($K_c$ and $K_p$) and understand their dependence on stoichiometric coefficients.
• Predict the effects of changes in concentration, pressure, and temperature on the position of equilibrium using Le Chatelier's Principle.
• Analyze the temperature dependence of equilibrium constants and how it affects the direction of exothermic and endothermic reactions.
• Explore heterogeneous equilibria involving multiple phases and understand the exclusion of pure solids and liquids in equilibrium constant expressions.
• Use the reaction quotient ($Q_c$) to predict the direction of reaction shifts to reach equilibrium.
• Relate Gibbs free energy change ($\Delta G$) to the equilibrium constant to determine reaction spontaneity.
• Investigate equilibrium in physical processes, such as phase changes and solubility, including the application of Henry's law.
• Utilize equilibrium constants to predict the extent of reactions, direction of reaction shifts, and calculate equilibrium concentrations from initial data.
• Classify acids and bases using Arrhenius, Bronsted-Lowry, and Lewis concepts, and calculate ionization constants for weak acids and bases.
• Explain the ionization of water, the ionic product ($K_w$), and the relationship between $pH$ and $pOH$.
• Evaluate the strength of acids and bases using $pK_a$ and $pK_b$ values.
• Understand the function and calculations related to buffer solutions and their resistance to $pH$ changes.

Chapter Notes

Dynamic Chemical Equilibrium

• Definition: A state where the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products.
• Dynamic Nature: At equilibrium, reactions continue to occur at the molecular level, but no net change is observed in the concentrations.
• Law of Mass Action: The rate of a chemical reaction is proportional to the product of the masses of the reacting substances, each raised to a power equal to the coefficient in the balanced chemical equation.

Equilibrium Constant Expressions

• Kc: Equilibrium constant in terms of concentration.
• Kp: Equilibrium constant in terms of partial pressures.
• Expression: For a reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant is given by: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Dependence on Stoichiometry: The powers in the expression are the stoichiometric coefficients from the balanced equation.

Le Chatelier's Principle

• Principle: If a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the system will adjust to counteract the effect of the change and a new equilibrium will be established.
• Concentration: Adding a reactant or product shifts the equilibrium to consume the added substance.
• Pressure: Increasing pressure shifts the equilibrium towards the side with fewer moles of gas.
• Temperature: Increasing temperature favors the endothermic direction.

Temperature Dependence of Equilibrium

• Exothermic Reactions: Increase in temperature decreases $K$.
• Endothermic Reactions: Increase in temperature increases $K$.

Heterogeneous Equilibria

• Definition: Equilibria involving more than one phase.
• Expression: Pure solids and liquids do not appear in the equilibrium constant expression.

Reaction Quotient (Qc)

• Definition: A ratio similar to the equilibrium constant but for non-equilibrium conditions.
• Use: Predicts the direction of the reaction shift to reach equilibrium by comparing $Q_c$ with $K_c$.

Gibbs Free Energy and Equilibrium

• Relationship: $\Delta G = \Delta G^\circ + RT \ln Q$
• Equilibrium: At equilibrium, $\Delta G = 0$ and $Q = K$, so $\Delta G^\circ = -RT \ln K$.

Equilibrium in Physical Processes

• Examples: Solid-liquid, liquid-vapour, solid-vapour, solid-in-liquid, and gas-in-liquid equilibria.
• Vapour Pressure: At equilibrium, the vapour pressure is constant.

Applications of Equilibrium Constant

• Extent of Reaction: Large $K$ indicates products predominate; small $K$ indicates reactants predominate.
• Direction: Compare $Q$ with $K$ to predict the direction of the reaction.
• Equilibrium Concentrations: Calculate using initial concentrations and $K$.

Acids and Bases: Arrhenius, Bronsted-Lowry and Lewis Concepts

• Arrhenius: Acids produce $H^+$ in water, bases produce $OH^-$.
• Bronsted-Lowry: Acids are proton donors, bases are proton acceptors.
• Lewis: Acids accept electron pairs, bases donate electron pairs.

Ionisation Constants of Weak Acids and Weak Bases

• Ka and Kb: Measure the strength of weak acids and bases.
• Ostwald's Dilution Law: Relates degree of ionization to concentration.

Ionisation of Water, Kw, pH and pOH

• Kw: Ionic product of water, $Kw = [H^+][OH^-]$.
• pH and pOH: $pH + pOH = pKw$.

pKa, pKb and Strength of Acids/Bases

• Relation: $pKa = -\log Ka$, $pKb = -\log Kb$.
• Strength: Lower $pKa$ or $pKb$ indicates stronger acid or base.

Buffer Solutions

• Definition: Solutions that resist changes in pH upon addition of small amounts of acid or base.
• Components: Typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid.