Chapter 6: Equilibrium | Summary

Physical equilibria include solid-liquid, liquid-vapour, and solid-vapour equilibria, as well as the dissolution of solids or gases in liquids. In solid-liquid equilibrium, ice and water coexist at 273 K and atmospheric pressure; the rates of transfer of molecules from ice to water and from water to ice are equal. The normal melting point is the temperature at which solid and liquid phases are at equilibrium at atmospheric pressure. For liquid-vapour equilibrium, the vapour pressure remains constant at a given temperature; the equilibrium vapour pressure increases with temperature and is higher for more volatile liquids.

Solid-vapour equilibrium is illustrated by solid iodine subliming in a closed vessel. For dissolution equilibria, the solubility of a solid in a liquid is constant at a given temperature, confirmed by radioactive tracer experiments with sugar. The dissolution of gases in liquids follows Henry's law: the mass of gas dissolved in a given mass of solvent at any temperature is proportional to the pressure of the gas above the solvent. All physical equilibria are characterized by constant measurable properties at a given temperature, and are possible only in a closed system.

Chemical reactions also attain a state of dynamic equilibrium in which the rates of forward and reverse reactions are equal and there is no net change in composition. Equilibrium can be attained from either direction, whether starting from pure reactants or pure products. Haber's process for ammonia synthesis demonstrates dynamic equilibrium: using deuterium in place of hydrogen, scrambling of H and D atoms in the product molecules proves that both forward and reverse reactions continue at equilibrium.

The dynamic nature of chemical equilibrium is illustrated by the reaction H2(g) + I2(g) ⇌ 2HI(g), where the same equilibrium mixture is obtained whether starting from pure reactants or pure product, given the same total amounts of H and I atoms. A student activity using two measuring cylinders and glass tubes of different diameters also illustrates dynamic equilibrium analogously, where the level of coloured water becomes constant even as transfer between cylinders continues.

The Law of Chemical Equilibrium, proposed by Norwegian chemists Guldberg and Waage in 1864, states that at a given temperature, the product of concentrations of reaction products raised to their stoichiometric coefficients divided by the product of concentrations of reactants raised to their stoichiometric coefficients has a constant value called the equilibrium constant Kc. For the general reaction aA + bB ⇌ cC + dD, Kc = [C]c[D]d / [A]a[B]b. This is also called the law of mass action. The equilibrium constant for the reverse reaction is the inverse of Kc for the forward reaction. If the equation is multiplied by n, the new Kc is the nth power of the original Kc.

For gaseous reactions, the equilibrium constant Kp is expressed in terms of partial pressures and is related to Kc by Kp = Kc(RT)Δn, where Δn is the difference between the number of moles of gaseous products and gaseous reactants. In heterogeneous equilibria, concentrations of pure solids and liquids are excluded from the equilibrium constant expression because their molar concentrations are constant. Equilibrium constants can also be expressed as dimensionless quantities by referencing standard states (1 bar for gases, 1 M for solutes).

The equilibrium constant provides three important applications: predicting the extent of a reaction, predicting the direction of the reaction, and calculating equilibrium concentrations. When Kc > 103, products predominate and the reaction proceeds nearly to completion; when Kc < 10-3, reactants predominate; and when Kc is between 10-3 and 103, appreciable concentrations of both reactants and products are present. The reaction quotient Qc is defined in the same way as Kc but uses non-equilibrium concentrations. If Qc < Kc, the reaction proceeds forward; if Qc > Kc, the reaction proceeds in reverse; if Qc = Kc, the system is at equilibrium.

Equilibrium concentrations can be calculated by setting up an ICE (Initial, Change, Equilibrium) table, defining x as the concentration of one species that reacts, and substituting equilibrium concentrations into the equilibrium constant expression to solve for x. The relationship between Kc, the reaction quotient Q, and Gibbs energy G is given by ΔG = ΔG° + RT lnQ; at equilibrium ΔG = 0 and ΔG° = –RT lnK. If ΔG° < 0, K > 1 implying spontaneous forward reaction; if ΔG° > 0, K < 1 implying non-spontaneous forward reaction.

Le Chatelier's principle states that a change in any factor determining the equilibrium conditions of a system will cause the system to change so as to reduce or counteract the effect of the change. This principle governs the effect of concentration change, pressure change, inert gas addition, temperature change, and catalysts on equilibrium. Adding a reactant shifts equilibrium forward to consume it; removing a product shifts equilibrium forward to replenish it. Commercial applications include liquefying and removing ammonia in the Haber process and continuously removing CO2 in CaO production from CaCO3.

Increasing pressure favours the side with fewer moles of gas; decreasing pressure favours the side with more moles of gas. Addition of an inert gas at constant volume does not affect equilibrium because partial pressures and concentrations remain unchanged. Temperature increase favours the endothermic direction and changes the value of Kc, while a catalyst increases reaction rates without affecting equilibrium composition, by lowering the activation energy equally for forward and reverse reactions. In ammonia synthesis, the optimum conditions are about 500°C and 200 atm with an iron catalyst.

Ionic equilibrium involves equilibria between ions in aqueous solutions. Electrolytes conduct electricity in aqueous solution; strong electrolytes are completely ionized while weak electrolytes are only partially dissociated. According to the Arrhenius concept, acids produce H+ ions and bases produce OH– ions in water. The Brønsted-Lowry concept defines an acid as a proton donor and a base as a proton acceptor; each acid-base reaction involves two conjugate acid-base pairs differing by one proton. Strong acids have very weak conjugate bases and vice versa.

The Lewis concept defines an acid as an electron pair acceptor and a base as an electron pair donor, broadening the scope to include species without protons, such as BF3. The ionization constant of water, Kw = [H+][OH–] = 1 × 10–14 at 298 K. The pH scale is defined as pH = –log[H+]; acidic solutions have pH < 7, basic solutions have pH > 7, and neutral solutions have pH = 7. The relation pH + pOH = pKw = 14 always holds at 298 K. For weak acids, Ka = [H+][A–]/[HA], and for weak bases, Kb = [M+][OH–]/[MOH]; for a conjugate pair, Ka × Kb = Kw.

Salts of strong acid and strong base give neutral solutions (pH 7) since neither cation nor anion hydrolyses. Salts of weak acid and strong base (e.g., CH3COONa) give alkaline solutions because the acetate ion undergoes hydrolysis to produce OH– ions. Salts of strong acid and weak base (e.g., NH4Cl) give acidic solutions because the ammonium ion hydrolyses to produce H+ ions. For salts of weak acid and weak base, pH = 7 + ½(pKa – pKb). The common ion effect is a shift in equilibrium caused by adding a substance that provides an ionic species already present in the equilibrium, based on Le Chatelier's principle.

Buffer solutions resist changes in pH on dilution or on addition of small amounts of acid or alkali. An acidic buffer is prepared from a weak acid and its salt with a strong base; the Henderson-Hasselbalch equation gives pH = pKa + log([A–]/[HA]). A basic buffer is prepared from a weak base and its conjugate acid. Sparingly soluble salts establish a solubility equilibrium expressed by the solubility product constant Ksp = [Mp+]x[Xq–]y. Molar solubility S can be calculated from Ksp. The common ion effect reduces the solubility of sparingly soluble salts, while lower pH increases the solubility of salts of weak acids by protonating the anion.

Chapter 6 on Equilibrium covers the essential concept that both physical and chemical processes can reach a state of dynamic equilibrium in which opposing processes occur at equal rates and macroscopic properties remain constant. The equilibrium constant Kc (or Kp for gases) quantifies the extent of a reaction and enables prediction of the direction and extent of reaction using the reaction quotient. Le Chatelier's principle provides a qualitative tool to predict how changes in concentration, pressure, temperature, and catalysts affect equilibrium, with direct industrial relevance in processes such as ammonia synthesis.

The ionic equilibrium section is of great practical importance for board examinations. Topics such as Arrhenius, Brønsted-Lowry, and Lewis concepts of acids and bases; the pH scale and its calculation; Ka and Kb; the relationship Ka × Kb = Kw; the common ion effect; buffer solutions; hydrolysis of salts; and solubility product constants are all highly testable and form the backbone of analytical and biological chemistry. Students should practice numerical problems on calculating equilibrium concentrations, pH, degree of ionization, and solubility from Ksp to score well in board examinations.