Reaction rate, the factors that change it, the rate law & order, collision theory, activation energy and catalysis — exam-focused for the BIEK / Sindh Board paper. Read it, or open the interactive lecture and drive the rate simulator.
1 — Rate of a reaction
- Rate of reaction — the change in concentration of a reactant or product per unit time. Unit: mol dm⁻³ s⁻¹.
Raterate = − Δ[reactant]/Δt = + Δ[product]/Δt
The rate is fastest at the start (most reactant) and slows as reactants are used up.
2 — Factors affecting the rate
| Factor | Effect (increase →) |
|---|
| Concentration (of reactant) | faster — more collisions |
| Temperature | much faster — more energetic & frequent collisions |
| Surface area (solid) | faster — more contact |
| Catalyst | faster — lowers activation energy |
| Pressure (gases) | faster — molecules closer |
| Nature of reactants / light | varies |
3 — Rate law & rate constant
For aA + bB → productsrate = k [A]ᵐ [B]ⁿ
k = rate constant · m, n = orders (found by experiment)
The rate constant k is independent of concentration but increases with temperature. Its units depend on the overall order.
4 — Order of reaction
- Order — the power to which a reactant's concentration is raised in the rate law. Overall order = m + n. It is found experimentally, not from the equation.
| Order | Rate | Units of k |
|---|
| zero | rate = k | mol dm⁻³ s⁻¹ |
| first | rate = k[A] | s⁻¹ |
| second | rate = k[A]² | mol⁻¹ dm³ s⁻¹ |
5 — Molecularity vs order
| Molecularity | Order |
|---|
| number of species in one elementary step | experimental power in the rate law |
| always a whole number (1, 2, 3) | can be 0, fractional, or whole |
| theoretical (for a step) | determined by experiment |
The slowest step in a mechanism is the rate-determining step — it controls the overall rate.
6 — Collision theory
For a reaction to occur, particles must collide. But not every collision reacts — an effective collision needs:
- enough energy (≥ the activation energy, Ea), and
- the correct orientation.
Anything that increases the frequency or energy of collisions increases the rate.
7 — Activation energy & the energy profile
- Activation energy (Ea) — the minimum energy colliding particles must have to react.
- Activated complex (transition state) — the high-energy, unstable arrangement at the top of the energy barrier.
On an energy profile, reactants climb the Ea barrier to the transition state, then fall to products. Exothermic: products lower than reactants; endothermic: higher.
8 — Effect of temperature
A rise of ~10 °C roughly doubles the rate. Higher temperature gives molecules more kinetic energy, so a much larger fraction have energy ≥ Ea (the Maxwell–Boltzmann distribution shifts right).
Arrhenius equationk = A e^(−Ea/RT)
A = frequency factor · R = gas constant · T = kelvin
9 — Effect of a catalyst
- Catalyst — a substance that speeds up a reaction by providing an alternative path with a lower activation energy, and is not used up itself.
| Type | Description | Example |
|---|
| Homogeneous | same phase as reactants | acid in ester hydrolysis |
| Heterogeneous | different phase (usually solid) | Fe in Haber, Pt in catalytic converters |
A catalyst lowers Ea for both directions equally — it speeds up the approach to equilibrium but does not change the position or K.
10 — Measuring the rate
- Measure a gas volume produced over time (e.g. CO₂, H₂).
- Measure mass loss (gas escaping) on a balance.
- Measure colour / light absorbed (colorimetry).
- Measure conductivity or pH if ions change.
- Time how long a precipitate takes to obscure a mark.
11 — Worked numericals
order from data
When [A] doubles, the rate doubles. What is the order in A?
rate ∝ [A]¹ → first order
rate constant
A first-order reaction has rate = 4×10⁻³ mol dm⁻³ s⁻¹ when [A] = 0.2 M. Find k.
k = rate/[A] = (4×10⁻³)/0.2 = 0.02 s⁻¹
temperature
If a reaction's rate doubles per 10 °C, how much faster is it 30 °C hotter?
2 × 2 × 2 = 8 times faster
12 — Exam recap
- Rate definition & units; rate is fastest at the start.
- Factors: concentration, temperature, surface area, catalyst.
- Rate law rate = k[A]ᵐ[B]ⁿ; order & rate constant.
- Molecularity vs order; rate-determining step.
- Collision theory; activation energy & energy profile.
- Arrhenius (temperature); how a catalyst lowers Ea.