Lesson 12 of 12 · 17 min

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Must-know facts

20 facts

1Equilibrium is dynamic: forward and backward rates are equal, not zero.
2Normal boiling point: vapour pressure = 1.013 bar (1 atm).
3Reverse reaction: K' = 1/K; equation multiplied by n: K' = Kⁿ.
4Kp = Kc(RT)^Δn with Δn = gaseous products − gaseous reactants; R = 0.0831 bar L mol⁻¹ K⁻¹.
5Pure solids and liquids are omitted from K; CaCO₃ ⇌ CaO + CO₂ has Kp = p(CO₂).
6Q < K forward; Q > K backward; Q = K equilibrium.
7ΔG° = −RT ln K = −2.303 RT log K.
8Only temperature changes K; a catalyst changes neither K nor composition.
9Inert gas added at constant volume: no shift.
10Haber process: N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92.38 kJ mol⁻¹.
11Kw = 1.0 × 10⁻¹⁴ at 298 K; it rises with temperature.
12pH + pOH = 14 at 298 K.
13Ka × Kb = Kw; pKa + pKb = 14.
14Weak acid (small α): [H⁺] = √(Ka c).
15Lewis acids: BF₃, AlCl₃, Co³⁺, Mg²⁺; Lewis bases: NH₃, OH⁻, F⁻.
16Acid strength: HF < HCl < HBr < HI (bond strength); CH₄ < NH₃ < H₂O < HF (electronegativity).
17Salt of weak acid + weak base: pH = 7 + ½(pKa − pKb).
18Buffer: pH = pKa + log([salt]/[acid]); pH = pKa when they are equal.
19Ksp for M₂X or MX₂ = 4S³; for MX = S².
20Common ion lowers solubility; NaCl is purified by HCl gas.

Common traps

Where marks are lost

Computing Δn as reactants minus products.

Δn is gaseous products minus gaseous reactants; for PCl₅ ⇌ PCl₃ + Cl₂ it is +1, so Kp = Kc(RT).

Putting moles directly into Kc when Δn ≠ 0.

Divide by volume to get mol L⁻¹ first; only when Δn = 0 does the volume cancel.

Thinking adding more reactant changes K.

Concentration and pressure changes shift the position; only temperature changes K.

Expecting an inert gas to shift equilibrium whenever it is added.

At constant volume partial pressures of reacting gases are unchanged, so there is no shift.

Taking [OH⁻] = c for Ba(OH)₂ or Ca(OH)₂.

Each formula unit releases two OH⁻, so [OH⁻] = 2c.

Writing Ksp = S² for every salt.

Raise each ion's concentration to its coefficient: M₂X gives (2S)²(S) = 4S³.

Comparing solubilities of AgCl-type and Ag₂CrO₄-type salts by Ksp values alone.

Calculate S for each; salts with different formula types can reverse the order.

Believing neutral water always has pH 7.

pH 7 is neutral only at 298 K; Kw increases with temperature, so neutral pH falls when hot.

Treating a mixture of excess weak base with a strong acid as a simple salt solution.

Find what is left after neutralisation; leftover weak base plus its salt is a buffer, solved with the pOH equation.

Using ΔG° in kJ with R = 8.314 J K⁻¹ mol⁻¹.

Convert ΔG° to J mol⁻¹ before computing ln K.

Formulas

12 to know

Equilibrium constant (concentrations)

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

For aA + bB ⇌ cC + dD; pure solids and liquids omitted.

Kp and Kc

Kp = Kc(RT)^Δn

Δn = gaseous product moles − gaseous reactant moles; R = 0.0831 bar L mol⁻¹ K⁻¹ with p in bar.

Gibbs energy and Q

ΔG = ΔG° + RT ln Q

At equilibrium ΔG = 0 and Q = K.

Gibbs energy and K

ΔG° = −RT ln K = −2.303 RT log K

K = e^(−ΔG°/RT).

Ionic product of water

Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ (298 K)

pKw = 14 at 298 K.

pH = −log[H₃O⁺] ; pH + pOH = 14

The sum is 14 only at 298 K.

Weak acid ionisation

Ka = cα² / (1 − α) ≈ cα² ; [H₃O⁺] = cα ≈ √(Ka c)

Approximation valid when α is small.

Conjugate pair

Ka × Kb = Kw ; pKa + pKb = pKw

Applies to an acid and its own conjugate base.

Salt of weak acid and weak base

pH = 7 + ½(pKa − pKb)

At 298 K; independent of salt concentration.

Acidic buffer

pH = pKa + log([A⁻]/[HA])

Henderson-Hasselbalch equation.

Basic buffer

pOH = pKb + log([BH⁺]/[B])

Then pH = 14 − pOH at 298 K.

Solubility product

Ksp = xˣ yʸ S^(x+y) for MₓXᵧ

MX: S²; M₂X or MX₂: 4S³; S in mol L⁻¹.

Key terms

13 terms

Dynamic equilibrium: State where opposing processes run at equal rates so the composition stays constant.
Law of mass action: Reaction rate is proportional to the product of reactant active masses, leading to the K expression.
Reaction quotient (Q): The K-type ratio evaluated at any moment, used to predict the direction of change.
Heterogeneous equilibrium: An equilibrium involving species in more than one phase.
Le Chatelier's principle: A disturbed equilibrium shifts to partly undo the disturbance.
Conjugate acid-base pair: Two species differing by one proton.
Lewis acid: A species that accepts an electron pair.
Amphoteric: Able to act as either an acid or a base, as water does.
Degree of ionisation (α): Fraction of a weak electrolyte present as ions at equilibrium.
Common ion effect: Suppression of a weak electrolyte's ionisation, or of a salt's solubility, by an added shared ion.
Hydrolysis: Reaction of a salt's ions with water that makes the solution acidic or basic.
Buffer solution: A solution that resists pH change on adding small amounts of acid or base.
Solubility product (Ksp): Equilibrium constant for a sparingly soluble salt dissolving into its ions.

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