Mini-Lesson

How fast, how far — rate and equilibrium

5 missions. Guess, learn, then check. Your place is saved.

Mission 1A speed camera clocks a car at one instant. How do you clock a reaction at one instant?
Mission 2Why can a cloud of flour dust explode, when a heap of flour only smoulders?
Mission 3Hydrogen peroxide sits in a bottle for months, yet fizzes at once on a slice of raw potato. Why?
Mission 4Air is mostly nitrogen and oxygen, which can react to form NO. Why isn't the air turning into NO?
Mission 5Why do ammonia plants squeeze their gases to about 200 times atmospheric pressure?

Mission 1

Mission 1: A speed camera clocks a car at one instant. How do you clock a reaction at one instant?

Make a guess: A speed camera clocks a car at one instant. How do you clock a reaction at one instant?

Mission 1

What rate means

Rate of reaction: the change in concentration of a reactant or product per unit time.
Units: mol dm⁻³ s⁻¹. Rate is quoted as a positive value.
Reactant concentrations fall; product concentrations rise.
Other measures work too: gas volume (cm³ s⁻¹) or mass (g s⁻¹).

Quick check

?Hydrogen peroxide decomposes: 2H₂O₂(aq) → 2H₂O(l) + O₂(g). Which quantity is the rate of this reaction at a particular moment?

Mission 1

Following a reaction

Gas volume: collect the gas in a gas syringe; read it at set times.
Mass loss: a gas escapes from a flask on a balance, e.g. CO₂ from marble chips and acid.
Colour: a colorimeter follows a coloured species, such as bromine fading.
Change one variable; keep everything else the same.

Mission 1

Average rate or rate at an instant

Average rate = total change ÷ total time: the gradient of a straight line between two points.
Rate at an instant = gradient of the tangent to the curve at that time.
Initial rate: the tangent at t = 0, where the curve is steepest.
The curve flattens as reactants are used up: the rate falls.

Mission 1

Worked example: drawing a tangent

Marble chips + acid: mass of CO₂ lost (g) against time (s). At 60 s, 1.19 g has been lost.
The tangent at 60 s passes through (0 s, 0.46 g) and (120 s, 1.92 g).
Rate = (1.92 − 0.46) g ÷ (120 − 0) s = 1.46 ÷ 120 = 0.0122 g s⁻¹.
Average over the first 60 s is 1.19 ÷ 60 = 0.0198 g s⁻¹: larger, because the reaction was faster earlier.
Read two far-apart points on the tangent, not on the curve.

Quick check

?Magnesium ribbon reacts with excess hydrochloric acid, and the hydrogen is collected in a gas syringe. A graph of the volume of hydrogen (y-axis, cm³) against time (x-axis, s) is a curve that is steep at first, becomes less steep and levels off at 60 cm³ at 100 s. The curve passes through the point (20 s, 34 cm³). A tangent drawn to the curve at t = 20 s passes through the points (0 s, 10 cm³) and (40 s, 58 cm³). What is the rate of reaction at t = 20 s?

Calculate

1Bromine reacts with methanoic acid: Br₂(aq) + HCOOH(aq) → 2HBr(aq) + CO₂(g). A graph of [Br₂] (mol dm⁻³) against time (s) starts at 0.0130 mol dm⁻³ and curves downwards, passing through (80 s, 0.0087 mol dm⁻³). A tangent drawn at t = 80 s passes through (0 s, 0.0122 mol dm⁻³) and meets the time axis at (280 s, 0 mol dm⁻³). Calculate the rate of reaction at t = 80 s, in units of 10⁻⁵ mol dm⁻³ s⁻¹.

Mission check

?A reaction is followed by measuring the concentration of a reactant. Which gives the rate of reaction at exactly t = 30 s?

Mission 2

Mission 2: Why can a cloud of flour dust explode, when a heap of flour only smoulders?

Make a guess: Why can a cloud of flour dust explode, when a heap of flour only smoulders?

Mission 2

Collision theory

Particles must collide to react.
The collision needs energy at least equal to Ea, the activation energy.
It also needs a suitable orientation: the atoms that will bond must meet.
In HCl + C₂H₄, the H end of HCl must hit the C=C double bond.
Only a small fraction of collisions are successful.

Quick check

?Hydrogen chloride reacts with ethene: HCl(g) + C₂H₄(g) → C₂H₅Cl(g). Some collisions between HCl and C₂H₄ molecules have more energy than Ea, yet do not react. Why?

Mission 2

Temperature and kinetic energy

The particles in a sample have a range of kinetic energies.
Average kinetic energy is proportional to the temperature in kelvin.
Double the kelvin temperature: double the average kinetic energy.
At the same temperature, all gases have the same average kinetic energy; heavier particles move more slowly.
Celsius ratios mean nothing: use T/K = T/°C + 273.

Calculate

1A gas is heated from 27 °C to 327 °C. By what factor does the average kinetic energy of its particles increase?

Mission 2

Concentration, pressure, surface area

Higher concentration: more particles per unit volume → more frequent collisions.
Higher gas pressure: the same gas particles are closer together → more frequent collisions.
Larger surface area of a solid: more particles exposed → more frequent collisions.
These change collision frequency only, not the energy of each collision.

Mission 2

Temperature and catalysts

Higher temperature: a much larger fraction of collisions have energy ≥ Ea.
Collisions also become a little more frequent, but that is the smaller effect.
A catalyst lowers Ea, so more collisions succeed at the same temperature.
Mission 3 shows both on a graph.

Quick check

?Two experiments use equal masses of calcium carbonate and the same volume of excess hydrochloric acid of the same concentration at the same temperature. In experiment 1 the calcium carbonate is a single lump; in experiment 2 it is a fine powder. Which statement is correct?

Quick check

?Hydrogen iodide decomposes: 2HI(g) → H₂(g) + I₂(g). A sample of hydrogen iodide is compressed to half its volume at constant temperature. What is the effect on the rate of reaction, and why?

Quick check

?Sodium thiosulfate solution reacts with hydrochloric acid, and a cloudy precipitate of sulfur forms. The sodium thiosulfate concentration is doubled, at the same temperature. Why does the cloudiness appear sooner?

Quick check

?At constant temperature, a graph of a reactant's concentration against time becomes less steep as the reaction goes on. Why?

Mission check

?Flour dust spread through the air in a mill can explode, while a heap of the same flour only smoulders. Why?

Mission 3

Mission 3: Hydrogen peroxide sits in a bottle for months, yet fizzes at once on a slice of raw potato. Why?

Make a guess: Hydrogen peroxide sits in a bottle for months, yet fizzes at once on a slice of raw potato. Why?

Mission 3

Energy profiles

Activation energy, Ea: the minimum energy colliding particles need to react.
On an energy profile, Ea runs from the reactants up to the top of the barrier.
Exothermic: products below reactants, ΔH negative.
Endothermic: products above reactants, ΔH positive.
Ea is always positive, even for an exothermic reaction.

Quick check

?Which energy profile correctly shows an endothermic reaction?

Mission 3

The Maxwell–Boltzmann distribution

Number of particles (y) against kinetic energy (x), at one temperature.
Starts at the origin: no particles have zero energy.
Rises to a peak, then a long tail that never reaches the axis.
Area under the curve = the total number of particles.
Area to the right of Ea = the particles with enough energy to react.

Mission 3

Two temperatures

Hotter sample: peak lower and further right; the curve is broader.
Total area unchanged: same number of particles.
Area beyond Ea is much larger, so a much bigger fraction of collisions can succeed.
Ea does not change with temperature.

Quick check

?A Maxwell–Boltzmann distribution is plotted for a sample of gas at 300 K, with number of particles on the y-axis and kinetic energy on the x-axis. The curve starts at the origin, rises to a peak and falls to a long tail that approaches the energy axis. Which describes the curve for the same sample at 400 K?

Quick check

?The graph shows Maxwell–Boltzmann energy distributions, P and Q, for the same sample of a gas at two different temperatures. The activation energy, Ea, of a reaction of the gas is marked. Which statement is correct?

Mission 3

Catalysts

A catalyst provides an alternative pathway with a lower Ea. It is not used up.
Reactant and product energies are unchanged, so ΔH is unchanged.
The barrier is lower in both directions: forward and reverse reactions both speed up.
Biological catalysts are enzymes: catalase speeds up the breakdown of hydrogen peroxide.

Mission 3

The reverse reaction's barrier

The reverse reaction starts from the products: on D9, its Ea arrow runs from the products up to the peak.
Read it off the profile. As a check: Ea(reverse) = Ea(forward) − ΔH.
Example: Ea(forward) = 60 kJ mol⁻¹, ΔH = −90 kJ mol⁻¹, so Ea(reverse) = 60 + 90 = 150 kJ mol⁻¹.
A catalyst lowers Ea(forward) and Ea(reverse) by the same amount.

Quick check

?The diagram shows the energy profile of an exothermic reaction without a catalyst (solid line) and with a catalyst (dashed line). Which arrow represents the activation energy of the catalysed reverse reaction?

Quick check

?Which diagram correctly shows the energy profiles of an endothermic reaction with and without a catalyst?

Mission 3

A catalyst on the Maxwell–Boltzmann curve

Same temperature, so the same curve.
Mark a second, lower Ea(catalysed) to the left of Ea(uncatalysed).
The area beyond Ea(catalysed) is larger: more particles have enough energy.
The particles have no extra energy; the barrier is lower.

Quick check

?Which sketch correctly shows how a catalyst affects a Maxwell–Boltzmann distribution at constant temperature?

Mission check

?Catalase is an enzyme that catalyses the exothermic decomposition of hydrogen peroxide: 2H₂O₂(aq) → 2H₂O(l) + O₂(g). The energy profile of the uncatalysed reaction rises from the reactants to a maximum and falls to products that are lower in energy than the reactants. How does the profile differ when catalase is present?

Mission 4

Mission 4: Air is mostly nitrogen and oxygen, which can react to form NO. Why isn't the air turning into NO?

Make a guess: Air is mostly nitrogen and oxygen, which can react to form NO. Why isn't the air turning into NO?

Mission 4

Dynamic equilibrium

A reversible reaction in a closed system reaches equilibrium.
Forward rate falls as reactants are used; backward rate rises as products form.
At dynamic equilibrium the two rates are equal and not zero.
Concentrations are then constant, but not usually equal.

Mission 4

Signs of an equilibrium

Observable properties (colour, pressure, density) stay constant.
It needs a closed system: nothing enters or leaves.
Physical changes reach equilibrium too: Br₂(l) ⇌ Br₂(g) in a stoppered flask.
The same equilibrium can be reached from either direction (same T, same overall amounts).

Quick check

?Hydrogen and iodine are heated in a sealed flask at constant temperature until the amount of hydrogen iodide no longer changes: H₂(g) + I₂(g) ⇌ 2HI(g) Which statement must be true of the mixture at this point?

Quick check

?Some liquid bromine is placed in a flask, which is then stoppered and kept at constant temperature. The brown colour of the vapour above the liquid deepens at first and then stays constant. Which statement about the flask once the colour is constant is correct?

Mission 4

The equilibrium constant expression

For aA + bB ⇌ cC + dD: K = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ), using equilibrium concentrations.
Products on top; each coefficient becomes a power; terms are multiplied.
For homogeneous equilibria: every species in the same phase.
Worked: CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g) gives K = [CO][H₂]³ / ([CH₄][H₂O]).
Steam, H₂O(g), is a species like any other.

Quick check

?Which is the equilibrium constant expression for the following reaction? N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Quick check

?Which is the equilibrium constant expression for 4NH₃(g) + 5O₂(g) ⇌ 4NO(g) + 6H₂O(g)?

Mission 4

What the size of K tells you

K	At equilibrium
K ≫ 1	almost all products: reaction nearly complete
K > 1	products favoured
K = 1	neither side favoured: significant amounts of both
K < 1	reactants favoured
K ≪ 1	almost all reactants: hardly any reaction

K tells you how far a reaction goes, not how fast.
K changes only with temperature (Mission 5).

Quick check

?For the reaction X(g) ⇌ Y(g), K = 1.0 × 10¹⁵ at 298 K. Which statement about this reaction at 298 K is correct?

Quick check

?For the reaction A(g) ⇌ B(g), K = 1.0 × 10⁻⁸ at 298 K. Which statement about this reaction at 298 K is correct?

Mission 4

K for the reverse reaction

Reversing the equation swaps the top and bottom of the K expression.
So K(reverse) = 1 / K(forward), at the same temperature.
Worked: ethanoic acid + ethanol ⇌ ethyl ethanoate + water, K ≈ 4.0.
Ester + water ⇌ acid + alcohol: K = 1 ÷ 4.0 = 0.25.
K is never negative: reversing does not change its sign, as it does for ΔH.

Quick check

?At 298 K, K for N₂(g) + O₂(g) ⇌ 2NO(g) is 4 × 10⁻³¹. What is K for 2NO(g) ⇌ N₂(g) + O₂(g) at 298 K?

Mission check

?For N₂(g) + O₂(g) ⇌ 2NO(g), K ≈ 4 × 10⁻³¹ at 298 K. What does this tell you about air at equilibrium at 298 K?

Mission 5

Mission 5: Why do ammonia plants squeeze their gases to about 200 times atmospheric pressure?

Make a guess: Why do ammonia plants squeeze their gases to about 200 times atmospheric pressure?

Mission 5

Le Châtelier's principle

Disturb a system at equilibrium and the position shifts to partly oppose the change.
Position of equilibrium: the composition of the equilibrium mixture.
Concentration and pressure change the position, not K.
Temperature changes the position and K.
A catalyst changes neither.

Mission 5

Changing a concentration

N₂(g) + 3H₂(g) ⇌ 2NH₃(g).
Add N₂: the forward rate rises, so the position shifts right: more NH₃.
Remove NH₃: the position shifts right, replacing some of it.
The shift only partly uses up the added N₂.
K is unchanged.

Quick check

?An equilibrium mixture of ethanoic acid, ethanol, ethyl ethanoate and water is kept at constant temperature. Some ethyl ethanoate is removed. What is true once equilibrium is re-established?

Mission 5

Changing the pressure

Raise the pressure by reducing the volume: the position shifts to the side with fewer moles of gas.
N₂ + 3H₂ ⇌ 2NH₃: 4 mol of gas → 2 mol, so it shifts right.
Equal moles of gas on each side: no shift.
Only gases count. K is unchanged.

Quick check

?CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g). The pressure is increased at constant temperature. What happens?

Mission 5

Changing the temperature

Raise T: the position shifts in the endothermic direction.
Forward exothermic (ΔH < 0): heating shifts it left; K decreases.
Forward endothermic (ΔH > 0): heating shifts it right; K increases.
Temperature is the only change that alters K.

Quick check

?The forward reaction in the following equilibrium is exothermic: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g) The temperature of the equilibrium mixture is increased at constant pressure. How do the amount of SO₃ and the value of K at the new equilibrium compare with those at the original equilibrium?

Mission 5

Catalysts, and gases dissolving

A catalyst speeds up both directions equally: equilibrium is reached sooner, same composition, same K.
A gas dissolving is an equilibrium too: O₂(g) ⇌ O₂(aq).
More O₂ pressure above the water: the position shifts right; more O₂ dissolves.
Dissolving O₂ is exothermic, so warmer water holds less O₂.

Quick check

?In a pond, O₂(g) ⇌ O₂(aq), and the forward change is exothermic. On a hot day the water warms up. How does the amount of dissolved O₂ change once equilibrium is re-established?

Quick check

?For N₂(g) + 3H₂(g) ⇌ 2NH₃(g), which change alters the value of K?

Mission check

?An ammonia plant runs at about 200 atmospheres: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Why does high pressure increase the equilibrium yield of ammonia?

Recap

The big ideas

Rate is change in concentration per unit time; the rate at an instant is a tangent's gradient.
Reactions need collisions with energy ≥ Ea and a suitable orientation.
Concentration, pressure, surface area: more frequent collisions. Temperature: a far bigger fraction with E ≥ Ea.
A catalyst lowers Ea for both directions; ΔH is unchanged.
Dynamic equilibrium: equal rates, constant concentrations; K = products over reactants, with powers.
Le Châtelier: the position shifts to partly oppose a change; only temperature changes K.

🏆

Mini-lesson complete!

⭐⭐⭐

You've worked through How fast, how far — rate and equilibrium for IB Diploma Chemistry SL. 🎉

Mission 1A speed camera clocks a car at one instant. How do you clock a reaction at one instant?
Mission 2Why can a cloud of flour dust explode, when a heap of flour only smoulders?
Mission 3Hydrogen peroxide sits in a bottle for months, yet fizzes at once on a slice of raw potato. Why?
Mission 4Air is mostly nitrogen and oxygen, which can react to form NO. Why isn't the air turning into NO?
Mission 5Why do ammonia plants squeeze their gases to about 200 times atmospheric pressure?

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