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Chemistry 3% exam weight

High-yield pointers

Part of the UNEB UACE (Uganda) study roadmap. Chemistry topic chemis-009 of Chemistry.

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High-yield pointers

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Rate of reaction measures how fast reactants are consumed (or products formed), in mol dm⁻³ s⁻¹. For a reaction A + B → products, the rate equation takes the form rate = k[A]ᵐ[B]ⁿ, where k is the rate constant and m, n are the orders, found experimentally (not from the equation).

The half-life of a first-order reaction is t₁/₂ = 0.693/k (constant, independent of concentration). The Arrhenius equation links k to temperature: k = A·exp(−Eₐ/RT), where Eₐ is the activation energy in J mol⁻¹ and R = 8.314 J mol⁻¹ K⁻¹.

A reversible reaction reaches dynamic equilibrium when forward and reverse rates equalise. Le Chatelier’s principle says the system shifts to oppose any change in concentration, pressure, or temperature. The equilibrium constant Kc = [products]ᶜᵒᵉᶠᶠ / [reactants]ᶜᵒᵉᶠᶠ, written products over reactants, omitting pure solids and liquids.

High-yield pointers

  • A catalyst lowers Eₐ and speeds both directions equally; it does not change Kc or yield.
  • The Haber process: N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹, Fe catalyst, ~450 °C, 200 atm.
  • The Contact process: 2SO₂ + O₂ ⇌ 2SO₃, ΔH = −197 kJ mol⁻¹, V₂O₅ catalyst, ~450 °C, 1–2 atm.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Measuring rate and determining order

Rate is tracked by following a changing quantity over time: mass loss (for gases), gas volume at constant T and P, colour intensity (colorimetry), or pH. From initial-rates experiments, the order in each reactant is found by varying one concentration while holding others constant. If doubling [A] doubles the initial rate, the reaction is first order in A (order = 1). If doubling [A] quadruples the rate, it is second order in A. If changing [A] has no effect, the reaction is zero order in A.

The overall order (m + n) determines the units of k: first order → s⁻¹, second order → dm³ mol⁻¹ s⁻¹, third order → dm⁶ mol⁻² s⁻¹. A common trap is to quote k with the wrong units.

Temperature, catalysts, and the Arrhenius equation

Raising temperature increases rate because a larger fraction of molecules exceed Eₐ on collision. Quantitatively, ln k = ln A − Eₐ/RT, so a plot of ln k against 1/T gives a straight line of slope −Eₐ/R. The two-temperature form ln(k₂/k₁) = (Eₐ/R)·(1/T₁ − 1/T₂) is the calculation examiners favour.

Mnemonic: “Catalyst speeds the road, never changes the destination” — Kc stays the same.

Reversible reactions and Le Chatelier’s principle

At equilibrium, macroscopic properties (colour, concentration, pressure) stay constant because forward and reverse rates are equal — this is dynamic, not static. A change in concentration shifts the position to consume the added species; a pressure increase shifts toward the side with fewer moles of gas; a temperature increase favours the endothermic direction and changes Kc.

Writing Kc expressions

Kc always places products over reactants, each raised to its stoichiometric coefficient. Pure solids (e.g. C(s), CaCO₃(s)) and pure liquids (e.g. H₂O(l)) are omitted because their “concentrations” are constant.

EquilibriumKc expression
N₂ + 3H₂ ⇌ 2NH₃Kc = [NH₃]² / ([N₂][H₂]³)
2SO₂ + O₂ ⇌ 2SO₃Kc = [SO₃]² / ([SO₂]²[O₂])
CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂OKc = ([ester][H₂O]) / ([acid][alcohol])

Industrial applications

The Haber process uses compromise conditions — moderate temperature (~450 °C) gives a reasonable rate even though a lower temperature would give a higher yield (exothermic forward reaction). High pressure (~200 atm) favours the side with fewer gas moles (2 mol NH₃ vs 4 mol reactants), and the Fe catalyst with Mo/K₂O promoter allows the rate to be acceptable. The unreacted N₂ and H₂ are recycled. The Contact process uses lower pressure (1–2 atm) because the cost of compressing SO₂/O₂ outweighs the modest yield gain, and a V₂O₅ catalyst gives a fast rate at ~450 °C.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Homogeneous vs heterogeneous equilibria

A homogeneous equilibrium has all species in the same phase (e.g. all gases, or all in solution), so every term appears in Kc. A heterogeneous equilibrium involves more than one phase; pure solids and liquids are excluded. Example: CaCO₃(s) ⇌ CaO(s) + CO₂(g) gives Kc = [CO₂] only, because the activities of the two solids equal 1.

Edge cases and examiner traps

  • Pressure changes only shift equilibria with Δn(gas) ≠ 0. For H₂(g) + I₂(g) ⇌ 2HI(g), Δn = 0, so pressure has no effect.
  • Adding an inert gas at constant volume does not change partial pressures, so the equilibrium position is unaffected.
  • Order of reaction is not stoichiometry. For 2N₂O₅ → 4NO₂ + O₂, the rate equation is rate = k[N₂O₅] (first order), even though the coefficient is 2.
  • Kc changes with temperature but not with concentration or (for ideal gases) pressure.
  • A reaction that is exothermic in the forward direction is endothermic in the reverse; the Eₐ values differ by ΔH.

Worked micro-example

For the decomposition of N₂O₅ at 45 °C, rate = k[N₂O₅], k = 6.2 × 10⁻⁴ s⁻¹. Half-life = 0.693 / (6.2 × 10⁻⁴) = 1118 s ≈ 18.6 min. If k doubles when temperature rises from 318 K to 328 K, find Eₐ: ln 2 = (Eₐ/8.314)(1/318 − 1/328) = (Eₐ/8.314)(9.58 × 10⁻⁵), giving Eₐ ≈ 6.0 × 10⁴ J mol⁻¹ = 60 kJ mol⁻¹.

Practice prompts

  1. For 2A + B → C + D, initial-rate data shows [A] doubled (rate ×2), [B] doubled (rate ×2). Write the rate equation, state the overall order, and give the units of k.
  2. For 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), ΔH = −197 kJ mol⁻¹, predict and explain the effect on equilibrium yield of (i) raising temperature, (ii) increasing pressure, (iii) adding more O₂.

Exam relevance

On the UACE paper, Topic 9 contributes around 3% and usually appears as one structured calculation (initial-rates table → rate equation → k units → Arrhenius Eₐ) worth 12–15 marks, plus a shorter 6–8 mark question linking Le Chatelier to the Haber or Contact process.

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