How fast? The rate of chemical change

The **change in concentration** of a reactant or product **per unit time**.

**mol dm⁻³ s⁻¹** — a concentration (mol dm⁻³) divided by a time (s).

It is the **gradient** (steepness) of the curve — the tangent at a point gives the instantaneous rate.

The **reactant concentration is highest** at t = 0, so effective collisions are most frequent and the curve is **steepest**.

**Average** = total change ÷ total time (slope of the **chord**); **instantaneous** = slope of the **tangent** at one moment.

Particles must **collide** to react, but only **effective** collisions (enough energy + correct orientation) lead to a reaction.

Energy **≥ the activation energy Eₐ**, AND the particles collide in the **correct orientation**.

The **minimum energy** that colliding particles must have for a reaction to occur.

Reactants are **used up**, so their concentration falls and effective collisions become **less frequent**; rate drops to zero when reactants run out.

Measure the **volume of gas** collected vs time, or the **mass lost** vs time.

Use a **colorimeter** to measure the **light absorbed** as it changes with time.

The rate at t = 0 — the **slope of the tangent drawn at the start** of a concentration–time graph (the steepest point).

Energy **≥ the activation energy (E_{a})** AND the **correct orientation**.

The **minimum** energy a colliding pair of particles must have for a reaction to occur.

**Concentration, pressure, surface area, temperature** and a **catalyst**.

They put more particles in the reaction space, so collisions are **more frequent** (the energy per collision is unchanged).

Particles move faster (collisions **more frequent**) AND the distribution shifts right so a **greater fraction** have energy ≥ E_{a} — the second effect is the main one.

A substance that speeds up a reaction by providing an **alternative pathway of lower E_{a}**, and is **not used up** itself.

**No** — the reactant and product energy levels are unchanged, so ΔH is the same.

How the **kinetic energies** of particles are **spread out**; only those to the right of E_{a} can react.

**Lower and shifted to the right** (broader/flatter), but with the **same area** underneath.

The **fraction of particles** with enough energy to react (energy ≥ E_{a}).

The curve is **unchanged**; the **E_{a} line moves left**, so a larger fraction lies to the right of it.

The reaction goes **faster**, AND the solid is **recovered unchanged** (same mass/nature) at the end.

**rate = k[A]^{m}[B]^{n}** — the rate equals the rate constant k times the reactant concentrations, each raised to its order.

The **power** to which that reactant's concentration is raised in the rate equation (found by **experiment**).

The **sum** of the individual orders (m + n).

**Experimentally** — from how the initial rate responds to changing each concentration; **never** from the stoichiometric equation.

**Zero order** (× 1 = 2⁰) — that reactant is not in the rate equation.

**First order** (× 2 = 2¹).

**Second order** (× 4 = 2²).

The proportionality constant in the rate equation; **fixed at a given temperature** (it changes only with temperature).

**s⁻¹** — from k = rate ÷ [A] = (mol dm⁻³ s⁻¹) ÷ (mol dm⁻³).

**mol⁻¹ dm³ s⁻¹** — from k = rate ÷ [A]².

**mol⁻² dm⁶ s⁻¹** — from k = rate ÷ [A]³.

The **slowest** step in a multi-step mechanism; it sets the overall rate. The rate equation shows the species **up to and including** the RDS.

**k = A·e^{−E_{a}/RT}** — it gives the rate constant in terms of the frequency factor A, the activation energy E_{a}, the gas constant R and the absolute temperature T.

The **frequency of collisions** and whether they occur with the **correct orientation** (the steric factor). A has the **same units as k**.

The **activation energy** — the minimum collision energy needed to react. It sits in the **exponent**, so it has a large effect on k.

R = the **gas constant** = **8.31 J K⁻¹ mol⁻¹**; T = the **absolute temperature in kelvin** (°C + 273).

Because E_{a}/RT shrinks as T rises and the term is **exponential** — a small T increase makes a large k increase (often k roughly doubles per 10 K).

**ln k = ln A − (E_{a}/R)(1/T)** — the equation of a straight line for ln k against 1/T.

**y-axis = ln k**, **x-axis = 1/T** (T in kelvin).

**−E_{a}/R** — a negative value (because E_{a} > 0).

**ln A** — the value of ln k when 1/T = 0; so A = e^{intercept}.

**E_{a} = −gradient × R**, then **÷ 1000** to convert J mol⁻¹ → kJ mol⁻¹.

**ln(k₂/k₁) = −(E_{a}/R)(1/T₂ − 1/T₁)** — used to find E_{a} from rate constants at two temperatures.

**(1)** Forgetting the minus sign — E_{a} = −gradient × R. **(2)** Forgetting to ÷ 1000, since R is in **J** K⁻¹ mol⁻¹, so E_{a} comes out in J mol⁻¹.