IMAT Chemistry · Equilibrium, Kinetics and Energetics

Reaction Rate, Collision Theory, Catalysts and Rate Laws

A reaction goes faster when particles collide more often or when more of the collisions carry at least the activation energy; the exact dependence on concentration has to be measured.

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Why this matters

Rates appear in the 2014, 2018, 2025 and 2026 papers: the effect of a more concentrated reactant on rate and on the amount of product, why higher pressure speeds up a gas reaction, what the activation energy is, and the fact that a rate law must be found by experiment.

Concept 1 of 4: Measuring the rate of a reaction

The rate of a reaction is how quickly a reactant is used up or a product appears, just as speed is how quickly distance changes. You can follow anything that changes as the reaction goes: the volume of gas given off, the mass lost from a flask, a colour, the pH. The rate is fastest at the start and slows as the reactants run out.

Definition

Rate of reaction = change in concentration (or amount, volume, mass) divided by the time taken. For concentrations the unit is $\text{mol dm}^{-3}\,\text{s}^{-1}$ .
A more concentrated reactant usually reacts faster; the next concept explains why.
The rate falls as the reaction proceeds, because the reactants are used up. The initial rate is the gradient of the curve at time zero.
Rate and yield are different things. How fast the product forms depends on the conditions. How much product forms in the end depends on the amount of the limiting reactant.

Average rate

\text{rate} = \frac{\Delta[\text{reactant or product}]}{\Delta t}

$\Delta[\ ]$ change in concentration, in mol/dm³ (taken as positive)
$\Delta t$ time taken, in s

Worked example

In a reaction, the concentration of a reactant falls from 0.80 mol/dm³ to 0.50 mol/dm³ in the first 60 s. What is the average rate over this time?

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A faster reaction does not make more product

Speeding a reaction up gets to the end sooner, but the amount of product is fixed by the limiting reactant. Doubling the amount of the limiting reactant doubles the product; doubling only the rate does not.

Concept 2 of 4: Collision theory and the factors that change the rate

Particles can only react when they meet, and most meetings are too gentle to break any bonds. Only collisions with at least the activation energy, and with the particles the right way round, lead to a reaction. So there are two ways to speed a reaction up: make collisions more frequent, or make a larger fraction of them energetic enough.

Definition

Collision theory: particles react only if they collide with energy at least equal to the activation energy and in a suitable orientation.

Concentration, pressure (for gases) and surface area raise the frequency of collisions. They do not change the fraction of particles with enough energy.
Temperature raises the collision frequency a little, but mainly increases the fraction of particles with energy at least $E_a$ . Many reactions roughly double in rate for a 10 °C rise.
A catalyst gives a route with a lower activation energy, so a larger fraction of collisions succeed.
The spread of particle energies is the Maxwell-Boltzmann distribution: at higher temperature the curve flattens and shifts right, and the area beyond $E_a$ grows sharply.

Factor increased	Effect on rate	Why
Concentration of a solution	Faster	More particles per volume, so more frequent collisions
Pressure of a gas	Faster	Particles closer together, so more frequent collisions
Surface area of a solid	Faster	More particles exposed, so more frequent collisions
Temperature	Faster	Mainly a larger fraction of collisions with energy at least $E_a$
Catalyst added	Faster	Lower activation energy, so more collisions succeed

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Pressure and concentration change how often particles collide, not how hard

Raising the pressure of a gas at constant temperature speeds a reaction because collisions become more frequent. It does not give more molecules energy above the activation energy: only a rise in temperature does that, and a catalyst lowers the barrier instead.

Concept 3 of 4: Catalysts: a lower-energy route, not more product

A catalyst is like a tunnel through a mountain. It offers the reactants a different route with a lower barrier, so more of them get through each second. The start and the end of the journey are unchanged, so the catalyst changes neither the energy released nor how far the reaction finally goes.

Definition

A catalyst increases the rate of a reaction without being used up overall.

It provides an alternative pathway with a lower activation energy.
It is regenerated at the end, so a small amount works for a long time.
It does not change $\Delta H$ , the position of equilibrium, the equilibrium constant, or the yield.
In a reversible reaction it speeds up the forward and reverse reactions equally, so equilibrium is reached sooner.
Enzymes are biological catalysts (catalase breaks down hydrogen peroxide in cells).

Feature	What a catalyst does
Activation energy	Lowers it, for both the forward and the reverse reaction
Rate	Increases the rates of both directions equally
ΔH	No change
Equilibrium position, K and yield	No change; equilibrium is reached sooner
Amount at the end	Same as at the start
Examples	$\mathrm{MnO_2}$ for $\mathrm{H_2O_2}$ decomposition, iron in ammonia synthesis, enzymes

Practice this conceptself-check · 3 quick reps

A catalyst never increases the yield

A catalyst gets a reversible reaction to equilibrium faster, but the equilibrium mixture is exactly the same as without it. Options saying a catalyst increases the yield, shifts the equilibrium or changes K are always wrong.

Concept 4 of 4: Rate laws and orders of reaction are found by experiment

Most reactions do not happen in one collision of all the reactants. They go through several steps, and the slowest step controls the rate. Since the balanced equation hides those steps, it cannot tell you how the rate depends on each concentration: that has to be measured.

Definition

The rate law (rate equation) has the form $\text{rate} = k[\mathrm{A}]^m[\mathrm{B}]^n$ .
$m$ and $n$ are the orders with respect to A and B; the overall order is $m + n$ . They are found experimentally and are usually 0, 1 or 2.
The orders are not the coefficients of the balanced equation in general. They match only for a single-step (elementary) reaction.
Doubling a concentration: order 0, no change; order 1, rate doubles; order 2, rate goes up four times.
The rate constant $k$ depends on temperature (and on a catalyst), not on concentration. It rises with temperature and is smaller when the activation energy is larger.

Rate law

\text{rate} = k\,[\mathrm{A}]^m\,[\mathrm{B}]^n

$k$ rate constant, fixed at a given temperature
$m, n$ orders with respect to A and B, found by experiment

Worked example

For A + B → products, three initial-rate experiments gave: [A] = 0.10, [B] = 0.10, rate

2.0 \times 10^{-4}

; [A] = 0.20, [B] = 0.10, rate

8.0 \times 10^{-4}

; [A] = 0.10, [B] = 0.20, rate

2.0 \times 10^{-4}

(concentrations in mol/dm³, rates in mol dm⁻³ s⁻¹). Find the rate law and k.

Practice this conceptself-check · 4 quick reps

Orders are not the coefficients of the equation

The rate law of a reaction cannot be read from its balanced equation, because most reactions go through several steps. Options like rate = k[A][B] written straight from A + B → C are guesses; the right answer is that the rate law is found by experiment. For a simple reaction, the products do not normally appear in it.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Measuring the rate of a reaction
Average rate
$\text{rate} = \frac{\Delta[\text{reactant or product}]}{\Delta t}$
Rate laws and orders of reaction are found by experiment
Rate law
$\text{rate} = k\,[\mathrm{A}]^m\,[\mathrm{B}]^n$

Reference tables (2)

Collision theory and the factors that change the rate5 rows

Factor increased	Effect on rate	Why
Concentration of a solution	Faster	More particles per volume, so more frequent collisions
Pressure of a gas	Faster	Particles closer together, so more frequent collisions
Surface area of a solid	Faster	More particles exposed, so more frequent collisions
Temperature	Faster	Mainly a larger fraction of collisions with energy at least $E_a$
Catalyst added	Faster	Lower activation energy, so more collisions succeed

Catalysts: a lower-energy route, not more product6 rows

Feature	What a catalyst does
Activation energy	Lowers it, for both the forward and the reverse reaction
Rate	Increases the rates of both directions equally
ΔH	No change
Equilibrium position, K and yield	No change; equilibrium is reached sooner
Amount at the end	Same as at the start
Examples	$\mathrm{MnO_2}$ for $\mathrm{H_2O_2}$ decomposition, iron in ammonia synthesis, enzymes

Watch out for (4)

A faster reaction does not make more product
→ Measuring the rate of a reaction
Pressure and concentration change how often particles collide, not how hard
→ Collision theory and the factors that change the rate
A catalyst never increases the yield
→ Catalysts: a lower-energy route, not more product
Orders are not the coefficients of the equation
→ Rate laws and orders of reaction are found by experiment

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