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OCR A-level Chemistry A (H432) · Module 5: Physical chemistry and transition elements
Mini-Lesson

Physical Chemistry & Transition Elements

Module 5 is the most mathematically demanding part of the A-level. Everything here is quantitative: rate equations, Kc and Kp, pH and Ka, Born–Haber cycles, entropy, Gibbs and electrode potentials.

Then transition elements pull it together — complexes, ligand substitution, colour, catalysis and redox titrations.

Work through each screen, answer the questions as you go (several are full A-level calculations) and collect ⭐ stars. Press Start when you're ready.

5.1.1 How fast?

Rate equations, orders and the rate-determining step

rate = k[A]m[B]nm and n are the orders — found only by experiment, never from the balanced equation
  • Zero order in X — changing [X] has no effect on rate.
  • First order — rate ∝ [X]. Doubling [X] doubles the rate. Its half-life is constant.
  • Second order — rate ∝ [X]². Doubling [X] gives the rate.

The overall order is the sum of the individual orders. The units of k depend on the overall order: 1st order → s⁻¹; 2nd order → mol⁻¹ dm³ s⁻¹; 3rd order → mol⁻² dm⁶ s⁻¹.

The rate-determining step (RDS) is the slowest step. Only species involved in or before the RDS appear in the rate equation — and the order in each species equals the number of its molecules in the RDS. This is how a rate equation reveals a mechanism.

Arrhenius: k = Ae−Ea/RT, or ln k = −Ea/RT + ln A. A plot of ln k against 1/T gives a straight line of gradient −Ea/R.

Calculate

Your turn — calculation 1

1For a reaction, rate = k[A][B]². When [A] = 0.100 mol dm⁻³ and [B] = 0.200 mol dm⁻³, the rate is 2.00 × 10⁻³ mol dm⁻³ s⁻¹. Calculate k, in mol⁻² dm⁶ s⁻¹.
mol⁻² dm⁶ s⁻¹
Hint: k = rate ÷ ([A][B]²) = 2.00 × 10⁻³ ÷ (0.100 × 0.200²).
Method

[B]² = 0.0400. [A][B]² = 0.100 × 0.0400 = 4.00 × 10⁻³. k = 2.00 × 10⁻³ ÷ 4.00 × 10⁻³ = 0.500 mol⁻² dm⁶ s⁻¹. (Overall order 3 → units mol⁻² dm⁶ s⁻¹.)

Quick check

Think it through

?A reaction is first order in A and zero order in B. The overall equation is A + 2B → C. What does this tell you about the mechanism?
Sort it

What order is it?

Tap an observation, then tap the order in X that it indicates.

0️⃣ Zero order

1️⃣ First order

2️⃣ Second order

5.1.2 How far?

Kc and Kp

Kc uses equilibrium concentrations; Kp uses partial pressures for gases.

partial pressure = mole fraction × total pressuremole fraction = moles of that gas ÷ total moles of gas

For aA + bB ⇌ cC + dD, Kp = (pCc × pDd) ÷ (pAa × pBb).

Only temperature changes K. Changing pressure or concentration shifts the position of equilibrium so that K stays the same. A catalyst changes neither. For an exothermic forward reaction, raising the temperature decreases K.

5.1.3 Acids and bases

pH, Ka and Kw

A Brønsted–Lowry acid is a proton donor; a base is a proton acceptor. Every acid has a conjugate base.

pH = −log₁₀[H⁺]and [H⁺] = 10−pH

For a strong monobasic acid, dissociation is complete, so [H⁺] = [acid].

For a weak acid HA ⇌ H⁺ + A⁻:

Ka = [H⁺][A⁻] ÷ [HA]so [H⁺] = √(Ka × [HA])  ·  pKa = −log Ka

Two approximations are built into that: [H⁺] = [A⁻] (we ignore water's own dissociation) and [HA]eqm ≈ [HA]initial (little dissociates).

Kw = [H⁺][OH⁻] = 1.00 × 10⁻¹⁴ mol² dm⁻⁶ at 298 Kuse this to get [H⁺] for a base from its [OH⁻]
Calculate

Your turn — calculation 2

2Calculate the pH of 0.0500 mol dm⁻³ hydrochloric acid, a strong monobasic acid, to 2 decimal places.
pH
Hint: HCl fully dissociates, so [H⁺] = 0.0500. pH = −log(0.0500).
Method

[H⁺] = 0.0500 mol dm⁻³. pH = −log₁₀(0.0500) = 1.30.

Calculate

Your turn — calculation 3

3Calculate the pH of 0.100 mol dm⁻³ ethanoic acid. Ka = 1.74 × 10⁻⁵ mol dm⁻³. Give your answer to 2 decimal places.
pH
Hint: [H⁺] = √(Ka × [HA]) = √(1.74 × 10⁻⁵ × 0.100). Then pH = −log[H⁺].
Method

[H⁺] = √(1.74 × 10⁻⁶) = 1.319 × 10⁻³ mol dm⁻³. pH = −log(1.319 × 10⁻³) = 2.88. Compare with 1.00 for 0.100 mol dm⁻³ HCl — the weak acid is far less dissociated.

5.1.3 Buffers

Buffers and titration curves

A buffer resists a change in pH when small amounts of acid or base are added. An acidic buffer is a weak acid plus its conjugate base (e.g. CH₃COOH + CH₃COONa).

  • Add acid: the added H⁺ is removed by the conjugate base: A⁻ + H⁺ → HA.
  • Add alkali: the added OH⁻ is removed by the weak acid: HA + OH⁻ → A⁻ + H₂O.
  • Both reservoirs are large, so the ratio [HA]/[A⁻] barely changes and pH barely moves.
[H⁺] = Ka × ([HA] ÷ [A⁻])

Choosing an indicator: the indicator must change colour entirely within the vertical section of the titration curve. Strong acid–strong base: any (both work). Strong acid–weak base: methyl orange. Weak acid–strong base: phenolphthalein. Weak acid–weak base: no suitable indicator — there is no vertical section.

Calculate

Your turn — calculation 4

4A buffer contains 0.200 mol dm⁻³ ethanoic acid and 0.100 mol dm⁻³ sodium ethanoate. Ka(CH₃COOH) = 1.74 × 10⁻⁵ mol dm⁻³. Calculate the pH to 2 decimal places.
pH
Hint: [H⁺] = Ka × [HA] ÷ [A⁻] = 1.74 × 10⁻⁵ × (0.200 ÷ 0.100). Then pH = −log[H⁺].
Method

[H⁺] = 1.74 × 10⁻⁵ × 2.00 = 3.48 × 10⁻⁵ mol dm⁻³. pH = −log(3.48 × 10⁻⁵) = 4.46.

Quick check

Think it through

?Which indicator is suitable for titrating ethanoic acid (weak) with sodium hydroxide (strong)?
5.2.1 Lattice enthalpy

Born–Haber cycles

Lattice enthalpy of formation is the enthalpy change when one mole of an ionic compound is formed from its gaseous ions. It is always exothermic and cannot be measured directly — hence the Born–Haber cycle.

By Hess's law, going round the cycle:

ΔHf = ΔHat(metal) + IE + ΔHat(non-metal) + EA + ΔHLE

Rearranged: ΔHLE = ΔHf − (all the other steps).

What makes a lattice enthalpy more exothermic: smaller ionic radii and greater ionic charges, both of which increase the electrostatic attraction. MgO (2+ and 2−, small ions) has a far more exothermic lattice enthalpy than NaCl. The same two factors make hydration enthalpies more exothermic.

Calculate

Your turn — calculation 5

5Construct a Born–Haber cycle for NaCl. ΔHf(NaCl) = −411; ΔHat(Na) = +107; 1st IE(Na) = +496; ΔHat(½Cl₂) = +122; 1st EA(Cl) = −349, all in kJ mol⁻¹. Calculate the lattice enthalpy of formation of NaCl (include the sign).
kJ mol⁻¹
Hint: ΔH_LE = ΔHf − (ΔHat(Na) + IE + ΔHat(Cl) + EA) = −411 − (107 + 496 + 122 − 349).
Method

Sum of the other steps = 107 + 496 + 122 + (−349) = +376 kJ mol⁻¹. ΔHLE = −411 − 376 = −787 kJ mol⁻¹.

5.2.2 Entropy and Gibbs

Entropy and free energy

Entropy (S) measures the number of ways energy and particles can be arranged — the dispersal of energy. Solids < liquids << gases. Producing more moles of gas raises entropy sharply.

ΔS = Σ S(products) − Σ S(reactants)S is in J K⁻¹ mol⁻¹ — note the joules
ΔG = ΔH − TΔSa reaction is feasible when ΔG ≤ 0

The unit trap that ruins Gibbs calculations: ΔH is in kJ mol⁻¹ but ΔS is in J K⁻¹ mol⁻¹. Convert ΔS to kJ (divide by 1000) before substituting, or you will be out by a factor of 1000.

At the temperature where ΔG = 0, the reaction is just becoming feasible, so T = ΔH ÷ ΔS.

Calculate

Your turn — calculation 6

6For CaCO₃(s) → CaO(s) + CO₂(g), the standard entropies are: CaCO₃ = 92.9, CaO = 39.7, CO₂ = 213.8 J K⁻¹ mol⁻¹. Calculate ΔS in J K⁻¹ mol⁻¹, to 1 decimal place.
J K⁻¹ mol⁻¹
Hint: ΔS = (39.7 + 213.8) − 92.9.
Method

ΔS = (39.7 + 213.8) − 92.9 = 253.5 − 92.9 = +160.6 J K⁻¹ mol⁻¹. It is strongly positive because a gas is produced from a solid.

Calculate

Your turn — calculation 7

7For the same decomposition, ΔH = +178 kJ mol⁻¹ and ΔS = +160.6 J K⁻¹ mol⁻¹. Calculate the minimum temperature, in K, at which the reaction becomes feasible. Give your answer to the nearest 10 K.
K
Hint: Feasible when ΔG ≤ 0, so at the limit T = ΔH ÷ ΔS. Convert ΔS to kJ: 0.1606 kJ K⁻¹ mol⁻¹.
Method

T = ΔH ÷ ΔS = 178 ÷ 0.1606 = 1108 K (about 835 °C). Below this, ΔG is positive and limestone does not decompose — which is why lime kilns run so hot.

5.2.3 Redox and electrode potentials

E° values, cells and feasibility

A standard electrode potential, E°, is measured against the standard hydrogen electrode (E° = 0.00 V) under standard conditions: 298 K, 100 kPa, all solutions 1.00 mol dm⁻³.

cell = E°(reduced species, the positive electrode) − E°(oxidised species, the negative electrode)equivalently: E°(right-hand half-cell) − E°(left-hand half-cell)
  • The more positive E° half-cell is reduced (it gains electrons) and forms the positive electrode.
  • The less positive half-cell runs in reverse — it is oxidised, and is the negative electrode.
  • A reaction is feasible if E°cell is positive.

Two limitations of E° feasibility that carry marks: (1) E° values apply only under standard conditions — change the concentrations and the potential changes. (2) A positive E°cell shows the reaction is thermodynamically feasible, but says nothing about the rate. A very high activation energy can leave a feasible reaction not happening at all.

Fuel cells: H₂ + ½O₂ → H₂O, producing only water. They convert chemical energy directly to electrical energy and do not need recharging while fuel is supplied — but the H₂ has to be produced and stored, which usually consumes energy.

Calculate

Your turn — calculation 8

8Zn²⁺(aq) + 2e⁻ ⇌ Zn(s), E° = −0.76 V. Cu²⁺(aq) + 2e⁻ ⇌ Cu(s), E° = +0.34 V. Calculate E°cell for the zinc–copper cell, in V, to 2 decimal places.
V
Hint: The more positive half-cell (Cu) is reduced. E°cell = (+0.34) − (−0.76).
Method

cell = (+0.34) − (−0.76) = +1.10 V. Positive, so the reaction Zn + Cu²⁺ → Zn²⁺ + Cu is feasible; zinc is the negative electrode.

Quick check

Think it through

?A reaction has E°cell = +1.20 V but no reaction is observed when the reactants are mixed at room temperature. What is the best explanation?
5.3.1 Transition elements

Complexes, colour, catalysis and redox titrations

A transition element forms at least one stable ion with a partially filled d sub-shell. (Sc and Zn are therefore d-block but not transition elements: Sc³⁺ is d⁰ and Zn²⁺ is d¹⁰.)

Their characteristic properties all flow from that partly-filled d sub-shell:

  • Variable oxidation states — the 4s and 3d energies are very close, so several electrons are available.
  • Coloured ions — ligands split the d orbitals into two energy levels. An electron absorbs a photon of visible light and jumps the gap (a d–d transition): ΔE = hν. The colour you see is the complement of the light absorbed. Change the ligand, the coordination number or the oxidation state and the gap — and so the colour — changes.
  • Catalysis — variable oxidation states let them accept and donate electrons (e.g. Fe²⁺/Fe³⁺ in the persulfate–iodide reaction).

A ligand is a species that donates a lone pair into a vacant orbital on the metal — a dative covalent (coordinate) bond. The coordination number is the number of coordinate bonds.

Ligand substitution to remember: [Cu(H₂O)₆]²⁺ (pale blue) + excess concentrated HCl → [CuCl₄]²⁻ (yellow-green) — note the coordination number falls from 6 to 4 because Cl⁻ is much larger. With excess NH₃ you get the deep blue [Cu(NH₃)₄(H₂O)₂]²⁺, where only four water ligands are replaced.

Redox titration with MnO₄⁻ is self-indicating — the end-point is the first permanent pale pink from a trace of excess MnO₄⁻:

MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O
Calculate

Your turn — calculation 9

925.0 cm³ of an Fe²⁺(aq) solution is titrated with 0.0200 mol dm⁻³ KMnO₄ in excess dilute sulfuric acid. The mean titre is 22.40 cm³. Using MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O, calculate the concentration of Fe²⁺ in mol dm⁻³, to 3 significant figures.
mol dm⁻³
Hint: n(MnO₄⁻) = 0.02240 × 0.0200. Ratio is 1 MnO₄⁻ : 5 Fe²⁺. Then c = n(Fe²⁺) ÷ 0.0250.
Method

n(MnO₄⁻) = 0.02240 × 0.0200 = 4.48 × 10⁻⁴ mol. n(Fe²⁺) = 5 × 4.48 × 10⁻⁴ = 2.24 × 10⁻³ mol. c = 2.24 × 10⁻³ ÷ 0.0250 = 0.0896 mol dm⁻³.

Match it

Match the species to its colour

Tap a species on the left, then its colour on the right.

Species
Colour
Quick check

Think it through

?Zinc is in the d-block but is not classed as a transition element. Why?
Recap

The big ideas to know

Rates: rate = k[A]^m[B]^n — orders come from experiment; only species in or before the RDS appear; ln k vs 1/T has gradient −Ea/R

Kc and Kp: partial pressure = mole fraction × total pressure; only temperature changes K

Acids: pH = −log[H⁺] · Ka = [H⁺]²/[HA] for a weak acid · Kw = 1.00 × 10⁻¹⁴ · buffer [H⁺] = Ka[HA]/[A⁻]

Thermodynamics: Born–Haber for lattice enthalpy · ΔS = ΣS(products) − ΣS(reactants) · ΔG = ΔH − TΔS (convert ΔS to kJ!)

Electrode potentials: E°cell = E°(positive) − E°(negative); positive = feasible, but says nothing about rate

Transition elements: partially filled d sub-shell → variable oxidation states, colour (d–d transitions), catalysis, complex formation

That is Module 5 — the quantitative core of the A-level. Press Finish to see your score.

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