Chapter 16: Equilibrium, Kinetics, and Electrochemistry

Chemical equilibrium

At equilibrium, the forward and reverse rates are equal and concentrations are constant. For , the equilibrium constant is

and is the same in terms of partial pressures, with where is the change in moles of gas. Compare the reaction quotient with : if the reaction proceeds forward; if , in reverse. Le Chatelier’s principle: a system at equilibrium responds to a disturbance so as to oppose it. Adding reactant shifts the position to the right; raising temperature favours the endothermic direction; raising pressure favours the side with fewer moles of gas; a catalyst does not change .

Worked example (ICE table). For H₂ + I₂ ⇌ 2HI with , start with 1.0 mol dm⁻³ each of H₂ and I₂. At equilibrium, let react: and . Then , so , which gives and mol dm⁻³.

Acids, bases, and buffers

An acid donates a proton and a base accepts one (Brønsted–Lowry). . The ionic product of water at 25 °C is . For a weak acid HA, and, when dissociation is small, . Example: 0.10 mol dm⁻³ ethanoic acid () has , so pH .

A buffer resists pH change; it contains a weak acid and its conjugate base. The Henderson–Hasselbalch equation is

For ethanoic acid (p), equal concentrations of acid and salt give pH 4.76; a tenfold excess of salt gives 5.76. In titrations, the choice of indicator depends on the pH at the equivalence point (phenolphthalein for strong base with weak acid; methyl orange for strong acid with weak base). The solubility product governs sparingly soluble salts: for AgCl, , so the solubility mol dm⁻³.

Chemical kinetics

The rate is the change in concentration per unit time. The rate law is determined by experiment: , where are the orders and the overall order. For a first-order reaction, and (for , min). The initial-rates method compares rates when concentrations are changed one at a time.

Collision theory: reaction requires collisions with sufficient energy () and correct orientation. The Arrhenius equation is , or , so a plot of against is a line with gradient . Example: with kJ mol⁻¹, raising from 300 K to 310 K gives , so increases by a factor of about 1.9. Catalysts provide a path with lower and are not consumed. A mechanism is a sequence of elementary steps; the slowest step (rate-determining) controls the rate law.

Electrochemistry

In a galvanic cell, a spontaneous redox reaction generates electrical energy; oxidation occurs at the anode (negative), reduction at the cathode (positive). The standard cell potential is . Example: Daniell cell, V and V give V. Free energy: with ( kJ mol⁻¹). The Nernst equation gives the potential under non-standard conditions:

Electrolysis drives non-spontaneous reactions with an external current. Faraday’s laws: the charge and the mass deposited . Example: 2.0 A for 30 min deposits g of copper. Applications include electroplating, refining copper, and the production of aluminium, chlorine, and sodium hydroxide.

Common mistakes

Including pure solids and liquids in expressions.

Using the approximation without checking that dissociation is small.

Confusing the order of a reaction with its stoichiometric coefficients.

Reversing the cathode and anode in .

Practice questions

Calculate the pH of mol dm⁻³ HCl. [2.00]

A first-order reaction has half-life 20 min. What fraction remains after 60 min? [1/8]

How long does it take to deposit 1.00 g of silver () at 0.50 A? [≈29.8 min]