R2.2Reactivity 2 — How much, how fast, how far?

How fast? The rate of chemical change — IB Chemistry HL Revision Notes & Topical Questions

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R2.2 How fast? The rate of chemical change — IB CHEMISTRY HL notes: Measure and explain reaction rates with collision theory, and use rate equations, mechanisms and the Arrhenius equation (HL).Definition — the change in concentration of a reactant or product per unit time, in mol…

Rate at a time
Gas volume
Colorimetry
Conductivity
Clock reaction
Requirement

Section 1 of 66Rate of reaction

Definition

Definition the change in concentration of a reactant or product per unit time, in mol dm⁻³ s⁻¹.

Graph

Graph the steeper the concentration–time graph, the faster the rate.

Rate at a time

Rate at a time the gradient of the tangent to the curve at that time.

Sign

Sign the rate is positive, so the negative gradient of a reactant graph is changed to positive.

Tangent

Tangent draw a large gradient triangle using gridline intersections to reduce error.

Section 2 of 66Measuring rates

Principle

Principle follow a property proportional to concentration, such as mass, volume or colour.

Mass loss

Mass loss a balance records escaping gas; the gas must be dense enough, so CO₂ works but H₂ does not.

Gas volume

Gas volume a gas syringe or an inverted measuring cylinder over water, the latter only for gases of low solubility.

Colorimetry

Colorimetry measures light passing through a coloured solution, but not for coloured precipitates.

Titration

Titration samples are taken and quenched, then titrated.
- (the reaction is stopped)

Conductivity

Conductivity follows changing ion concentration.

Clock reaction

Clock reaction times a fixed visible point, as in the disappearing cross with sodium thiosulfate and acid, giving one data point per run.

Section 3 of 66Collision theory

Requirement

Requirement particles must collide with enough energy and the correct orientation.

Collision frequency

Collision frequency how often particles collide, changed by concentration, pressure, temperature and surface area.

Collision energy

Collision energy the combined energy of the colliding particles.

Activation energy

Activation energy the minimum energy for a successful collision, fixed for a given route.

Collision geometry

Collision geometry orientation matters most for large molecules such as proteins.

Success

Success most collisions fail because of insufficient energy rather than wrong orientation.

Rate

Rate depends on the number of successful collisions per unit time.

Section 4 of 66Factors affecting rate

Concentration

Concentration more particles per unit volume give more collisions and more successful collisions.

Pressure

Pressure in gases, it acts like concentration.

Temperature

Temperature particles collide more often and a larger proportion have energy ≥ E_a;
- the second effect is more important.

Surface area

Surface area more surface particles of a solid can collide, so powders react faster than lumps.

Catalyst

Catalyst provides a lower-E_a pathway, so a greater proportion of collisions succeed.

Section 5 of 66Energy profiles and catalysts

Energy profiles and catalysts

Exothermic profile

Exothermic profile reactants are higher than products.

Endothermic profile

Endothermic profile reactants are lower than products.

Reverse Ea

Reverse Ea exothermic E_a(reverse) = E_a(forward) + |ΔH|; endothermic E_a(reverse) = E_a(forward) − ΔH.

Catalyst

Catalyst lowers the peak but leaves ΔH and the start and end levels unchanged, and is chemically unchanged.

Homogeneous

Homogeneous same phase as the reactants; heterogeneous — different phase.

Industry

Industry catalysts lower energy needs, reduce waste and increase selectivity.

Enzymes and transition metals

Enzymes and transition metals enzymes are biological catalysts;
- transition metals are catalysts because of variable oxidation states.

Section 6 of 66Maxwell–Boltzmann curves

Curve

Curve shows how particle energies are distributed at a temperature, starting at the origin and never touching the x-axis.

Peak

Peak the most probable energy.

Area

Area the area under the curve to the right of E_a is the number of particles able to react;
- the total area stays constant.

Higher temperature

Higher temperature the curve flattens, the peak lowers and shifts right, and more particles exceed E_a;
- the curves cross once.

Catalyst

E_a moves left on the same curve, so more particles exceed it.

Section 7 of 66Rate equations (HL)

Rate equation

Rate equation rate = k[A]^m[B]ⁿ, found experimentally and not from the stoichiometric equation.
What the symbols mean: rate (mol dm⁻³ s⁻¹) · k = rate constant · [ ] = concentration (mol dm⁻³) · each power is the order with respect to that reactant
- (units depend on the overall order)

Order

Order the power of a concentration;
- zero order has no effect, first order doubles the rate when concentration doubles, second order quadruples it.

Overall order

Overall order m + n.

Initial rates

Initial rates compare experiments in which only one concentration changes: ^order = rate factor.
- (concentration factor)

Rate constant

Rate constant k = rate ÷ concentration terms, with units depending on overall order (s⁻¹ for first order, mol⁻¹ dm³ s⁻¹ for second).

Temperature

Temperature k increases with temperature; the rate roughly doubles for each 10 K rise.

Section 8 of 66Mechanisms (HL)

1Mechanism

Mechanism a sequence of elementary steps summing to the overall equation.

2Intermediate

Intermediate made in one step and used in another, so it does not appear in the overall equation or the rate equation.

3Rate-determining step

Rate-determining step the slowest step; its reactants appear in the rate equation.

4Molecularity

Molecularity the number of particles in an elementary step: unimolecular, bimolecular or termolecular (rare).

5Energy profile

Energy profile each step has a peak; the step with the greatest activation energy is rate-determining.

6Kinetics

Kinetics it can disprove a mechanism but not prove it.

Section 9 of 66The Arrhenius equation (HL)

Equation

Equation k = Ae^−E_a/RT.
What the symbols mean: k = rate constant · A = pre-exponential (frequency) factor · E_a = activation energy (J mol⁻¹) · R = 8.31 J mol⁻¹ K⁻¹ · T = temperature (K)

Terms

A the frequency factor, E_a the activation energy, R = 8.31 J K⁻¹ mol⁻¹ and T in kelvin.

Logarithmic form

Logarithmic form ln k = −E_a/RT + ln A.

Graph

Graph ln k against 1/T is a straight line with gradient −E_a/R and intercept ln A.

Calculation

E_a = −gradient × R, and A = e^intercept.

Effects

Effects higher E_a gives a lower k, and higher T gives a higher k.

Section 10 of 66More from the specification

1Reaction order with respect to reactant

The power to which a reactant concentration is raised in the experimental rate equation.
- (rate = k [A]^m [B]^n)

2Maxwell-Boltzmann distribution curves

Energy distribution graphs showing the fraction of molecules possessing sufficient kinetic energy (>= Ea) at a given temperature.

3Effect of temperature on distribution

Higher temperature flattens and broadens the curve to the right, dramatically increasing the proportion of particles with energy exceeding activation energy.

4Catalyst mechanism on distribution

Catalysts provide an alternative pathway with lower activation energy, shifting Ea to the left without altering curve shape.

5Hydrogen

A gas that gives a squeaky pop with a lighted splint.

6Maxwell-Boltzmann distribution

A graph showing how particle energies are spread at a given temperature.

Section 11 of 66Rate of reaction

Definition

Definition change in concentration of a reactant or product per unit time, in mol dm⁻³ s⁻¹.

Progress

Progress reactant concentration falls and product concentration rises.

Reversible reactions

Reversible reactions concentrations stay constant once dynamic equilibrium is reached.

Measuring

Measuring follow a property that changes with time and is proportional to the concentration.

Section 12 of 66Measuring rate with gas volume

Gas syringe

Gas syringe records the volume of gas every few seconds.

Inverted cylinder

Inverted cylinder collects gas over water, only for gases of low solubility such as hydrogen.

Graph

Graph volume measures the amount of product, and a plateau shows the reaction has stopped.

Section 13 of 66Titration, conductivity and clock reactions

Titration

Titration taking a sample can change the rate and cannot be continuous, so samples are taken at intervals and quenched.

Quenching

Quenching the reaction is deliberately stopped, for example by dilution or cooling, before titrating.

Conductivity

Conductivity changes as the ion concentration changes, for example in HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l).

Clock reaction

Clock reaction a non-continuous method timing a fixed visible point.

Examples

Examples a magnesium ribbon dissolving, or the disappearing cross where sulfur from Na₂S₂O₃ and HCl hides a cross.

Limitation

Limitation only one piece of data per run.

Section 14 of 66Rate from the gradient of a graph

Steepness

Steepness the steeper the graph, the faster the reaction.

Rate at a time

Rate at a time the gradient of the tangent, Δy / Δx.

Sign

Sign the rate is positive, so a reactant graph's negative gradient is reversed.

Rate from the gradient of a graph

Draw a tangent touching the curve at the chosen time.

Make the gradient triangle large, using gridline intersections.

Read Δy and Δx and divide.

Section 15 of 66Collision theory

Collision theory

Requirement

Requirement particles must collide with enough energy and the correct orientation.

Rate

Rate depends on the number of successful collisions per unit time.

Collision frequency

Collision frequency changed by concentration, pressure, temperature and surface area.

Collision energy

Collision energy the combined energy of the two particles.

Kinetic energy

KE = ½mv²,
so at the same temperature lighter particles move faster and diffuse faster.
What the symbols mean: E_k = kinetic energy (J) · m = mass (kg) · v = speed (m s⁻¹)

Particle energies

Particle energies particles have a range of kinetic energies due to random motion.

Section 16 of 66Activation energy and orientation

Activation energy

Activation energy the minimum collision energy; below it particles bounce apart.

At or above Ea

At or above Ea the collision can be successful.

Catalyst

Catalyst does not change E_a of a given route but provides an alternative route with lower E_a.

Geometry

Geometry particles must collide in a suitable orientation, especially large molecules whose active sites are reached from one direction.

Why collisions fail

Why collisions fail most fail because energy is too low rather than orientation.

Section 17 of 66More from the specification

Rate Equations and Reaction Orders

A rate equation expresses the mathematical relationship between reactant concentrations and reaction rate: Rate = k [A]^m [B]^n,
where m and n are the reaction orders with respect to each reactant,
and their sum equals the overall order.

Elementary Steps in Reaction Mechanisms

Complex chemical reactions proceed through a sequence of elementary steps; the stoichiometry of the slowest elementary step directly reflects the exponents in the empirical rate equation.
- (rate-determining step)

Kinetic Graphs for Deducing Reaction Orders

Reaction orders are deduced from concentration-time and rate-concentration graphs: a zero-order reactant gives a horizontal line on a rate-concentration graph, a first-order reactant gives a straight line passing through the origin,
and a second-order reactant produces an upward curve.

Arrhenius Equation and Rate Constant Temperature Dependence

As temperature increases, the rate constant k rises exponentially according to the Arrhenius equation: k = A e^(-Ea / RT), reflecting a greater proportion of collisions with sufficient activation energy.

Maxwell-Boltzmann distribution

A graph showing how particle energies are spread at a given temperature.

Energy profile

Diagram showing energy during a reaction

Elementary step

A single stage in a reaction mechanism.

Reaction order

Exponent of a reactant concentration in the rate law.

Arrhenius factor

The pre-exponential factor A.

Mechanism

The sequence of steps by which reactants form products.

Arrhenius equation

K = Ae^−E_a/RT, relating the rate constant to temperature and activation energy.

Section 18 of 66Pressure and concentration

Pressure

Pressure in gases it has the same effect as higher concentration.

Mechanism

Mechanism particles have less space, collide more often, so there are more successful collisions per second.

Concentration

Concentration more particles per unit volume give more collisions and more successful collisions.

Section 19 of 66Temperature

Kinetic energy

Kinetic energy rises, so particles move faster.

More collisions

More collisions collision frequency increases.

Larger proportion

Larger proportion a larger proportion of collisions have energy ≥ E_a.

Importance

Importance the second effect is the more important one.

Section 20 of 66Surface area

Surface area

Surface only

Surface only only surface particles of a solid can collide with the other reactant.

Powder

Powder has a much larger surface area than lumps, so more collisions occur.

Particle size

Particle size increasing the particle size decreases the surface area and reduces the rate.

Section 21 of 66Activation energy and energy profiles

Activation energy

Activation energy the minimum energy reactant particles need to react.

Exothermic

Exothermic reactants are higher in energy than products.

Endothermic

Endothermic reactants are lower in energy than products.

Successful collision

Successful collision correct orientation and energy ≥ E_a.

Reverse reaction

Reverse reaction exothermic E_a(reverse) = E_a(forward) + |ΔH|; endothermic E_a(reverse) = E_a(forward) − ΔH.

Section 22 of 66Catalysts

Effect

Effect an alternative pathway with a lower activation energy, so more collisions are successful.

Unchanged

Unchanged the catalyst is chemically unchanged at the end and ΔH is not changed.

Profile

Profile the catalysed route has a lower peak but the same start and end levels.

Homogeneous

Homogeneous same phase as the reactants.

Heterogeneous

Heterogeneous different phase, for example a solid catalyst with gaseous reactants.

Section 23 of 66Catalysts in industry and biology

Energy

Energy lower temperatures and pressures are needed.

Waste

Waste small, reusable amounts reduce waste and raise atom economy.

Selectivity

Selectivity side reactions are suppressed.

Enzymes

Enzymes biological catalysts that control cell reactions and allow industrial reactions at lower temperature and pressure.

Transition metals

Transition metals often catalysts because variable oxidation states give alternative pathways in redox reactions.

Section 24 of 66Explaining rate changes

Explaining rate changes

State the change in the frequency of collisions or the proportion of particles with enough energy.

Link it to the number of successful collisions per unit time.

Conclude that the rate increases or decreases.

1Concentration, pressure, surface area

Concentration, pressure, surface area only collision frequency changes.

2Temperature

Temperature the proportion of particles with E ≥ E_a changes as well as frequency.

3Catalyst

E_a changes while collision frequency is unchanged.

4Wording

Wording do not say particles "have more activation energy"; activation energy is a property of the reaction.

Section 25 of 66More from the specification

Rate equations and reaction orders

A rate equation expresses the relationship between reaction rate and reactant concentrations: rate = k [A]^m [B]^n,
where m and n represent orders with respect to individual reactants,
and (m+n) gives the overall order.

Graphical determination of orders

On a concentration-time graph, a straight line indicates zero order,
while an exponential decay curve with constant half-life indicates first order;
- plotting rate against concentration gives a horizontal line for zero order and a proportional straight line for first order.

Rate-determining elementary steps

Complex reactions occur via multiple elementary steps;
- the molecularity of the slowest elementary step matches the reaction orders in the experimental rate equation.

Arrhenius equation and rate constant

The rate constant k is temperature-dependent according to the Arrhenius equation ln(k) = -Ea / (RT) + ln(A),
where plotting ln(k) against 1/T yields a straight line with gradient -Ea / R.

Rate equations and reaction orders

A rate equation expresses the relationship between reaction rate and reactant concentrations: rate = k [A]^m [B]^n,
What the symbols mean: rate (mol dm⁻³ s⁻¹) · k = rate constant (units depend on the overall order) · [ ] = concentration (mol dm⁻³) · each power is the order with respect to that reactant
where m and n represent orders with respect to individual reactants,
and (m+n) gives the overall order.

Graphical determination of orders

On a concentration-time graph, a straight line indicates zero order,
while an exponential decay curve with constant half-life indicates first order;
- plotting rate against concentration gives a horizontal line for zero order and a proportional straight line for first order.

Rate-determining elementary steps

Complex reactions occur via multiple elementary steps;
- the molecularity of the slowest elementary step matches the reaction orders in the experimental rate equation.

Arrhenius equation and rate constant

The rate constant k is temperature-dependent according to the Arrhenius equation ln(k) = -Ea / (RT) + ln(A),
where plotting ln(k) against 1/T yields a straight line with gradient -Ea / R.

Hydrogen

A gas that gives a squeaky pop with a lighted splint.

Arrhenius equation

K = Ae^−E_a/RT, relating the rate constant to temperature and activation energy.

Maxwell-Boltzmann distribution

A graph showing how particle energies are spread at a given temperature.

Elementary step

A single stage in a reaction mechanism.

Reaction order

Exponent of a reactant concentration in the rate law.

Arrhenius factor

The pre-exponential factor A.

Gradient

The change in y divided by the change in x on a graph.

Molecule

Two or more atoms held together by covalent bonds.

Section 26 of 66The Maxwell–Boltzmann distribution

The Maxwell–Boltzmann distribution

Meaning

Meaning shows how particle energies are spread at a given temperature.

Shape

Shape a few particles have very low or very high energy, and many have values in between.

Peak

Peak the most probable energy, E_MP.

Axis

Axis the curve starts at the origin and approaches but never touches the x-axis.

Reacting particles

Reacting particles only particles to the right of E_a can react.

Area

Area the area to the right of E_a is the number of particles able to react.

Section 27 of 66Effect of temperature

Curve

Curve flattens, with a lower peak shifted right.

Tail

Tail the high-temperature tail is higher and the two curves cross once.

Ea unchanged.

Result

Result a higher proportion of particles have energy ≥ E_a, and collisions are more frequent.

Exam questions

Exam questions often ask about lowering the temperature, so apply the theory in reverse.

Section 28 of 66Effect of a catalyst

Curve

Curve unchanged.

Ea lowered by the alternative pathway.

Result

Result a higher proportion of particles have energy ≥ the lower E_a.

Shading

Shading shade the whole area to the right of the new E_a, not just the extra area.

Section 29 of 66Rate and concentration

Measuring

Measuring rate comes from the fall in reactant concentration or rise in product concentration, in mol dm⁻³ s⁻¹.

Direct proportion

Direct proportion a rate against concentration graph that is a straight line through the origin means rate ∝ [A].

Gradient

Gradient rate ÷ concentration is then constant, giving rate = k[A].

Effect

Effect doubling [A] doubles the rate and halving it halves the rate.

Not general

Not general not all reactions behave like this, so orders are needed.

Section 30 of 66The rate equation

1Form

Form rate = k[A]^m[B]ⁿ, where m and n are orders with respect to each reactant.

2Species

Species catalysts or products may appear, but intermediates do not.

3Zero order

Zero order changing the concentration has no effect.

4First order

First order rate changes by the same factor as concentration.

5Second order

Second order rate changes by the square of the factor, so doubling [A] quadruples the rate and tripling gives a factor of nine.

6Several changes

Several changes multiply the separate effects.

Section 31 of 66The rate constant

Constant

Constant k does not change with concentration.

Changes

Changes k changes with temperature and with a catalyst.

Check

Check k calculated from any experiment at one temperature should be the same, which checks the orders.

Section 32 of 66More from the specification

Arrhenius equation and activation energy

Arrhenius equation and activation energy linear Arrhenius plots of rate constant logarithms versus reciprocal temperature yield activation energy from graph slopes.

Elementary steps in reaction mechanisms

Elementary steps in reaction mechanisms complex chemical transformations proceed through sequences of elementary unimolecular or bimolecular steps that determine overall reaction kinetics.

Collision theory and successful collisions

Collision theory and successful collisions raising absolute temperature increases kinetic energy of reactant molecules, yielding higher proportions of successful collisions exceeding activation barriers.

Reaction rate equations and orders

The rate equation rate = k [A]^m [B]^n relates reaction velocity to reactant concentrations,
where exponents m and n represent partial orders of reaction.

Arrhenius equation and activation energy

The rate constant varies with absolute temperature according to k = A * exp(-Ea / RT);
- plotting ln(k) against 1/T yields a straight line with gradient -Ea / R.

Rate-determining step in multi-step mechanisms

The slowest elementary step in a reaction mechanism governs overall reaction rate, matching reactant stoichiometry found in the experimental rate law.

Arrhenius equation

K = Ae^−E_a/RT, relating the rate constant to temperature and activation energy.

Maxwell-Boltzmann distribution

A graph showing how particle energies are spread at a given temperature.

Energy profile

Diagram showing energy during a reaction

Elementary step

A single stage in a reaction mechanism.

Arrhenius factor

The pre-exponential factor A.

Kinetic energy

The energy of motion of a particle.

Successful collision

A collision with the correct orientation and enough energy to react.

Mechanism

The sequence of steps by which reactants form products.

Molecule

Two or more atoms held together by covalent bonds.

Hydrogen

A gas that gives a squeaky pop with a lighted splint.

Activation energy

The minimum energy colliding particles need to react.

Section 33 of 66Order of reaction

Rate equation

Rate equation rate = k[A]^m[B]ⁿ, found by experiment because it depends on the mechanism.
What the symbols mean: rate (mol dm⁻³ s⁻¹) · k = rate constant · [ ] = concentration (mol dm⁻³) · each power is the order with respect to that reactant
- (units depend on the overall order)

Order

Order the power to which a reactant's concentration is raised.

Possible values

Possible values positive, negative or fractional; fractional orders suggest a multi-step mechanism.

Calculations

Calculations only 0, 1 or 2 are used.

Overall order

Overall order the sum of the individual orders, m + n.

Section 34 of 66Zero, first and second order

Order	Effect of doubling concentration	In the rate equation
Zero	No change in rate	Reactant does not appear
First	Rate doubles (directly proportional)	[A]
Second	Rate quadruples (proportional to the square)	[A]²

Fractional examples
- ethanal decomposition rate = k[CH₃CHO]^3/2, H₂ with Br₂ rate = k[H₂][Br₂]^1/2.

Section 35 of 66Using a given rate equation

1First order

First order any change in concentration causes the same change in rate.

2Several reactants

Several reactants multiply the effects, so doubling a first-order reactant and halving another first-order reactant leaves the rate unchanged.

3Overall order

Overall order add the powers of each reactant.

Section 36 of 66Deducing orders from initial rates

Choose two experiments in which only one concentration changes.

Work out the factor by which that concentration changes.

Work out the factor by which the rate changes.

Use (concentration factor)^order = rate factor.

Repeat for each reactant and write the rate equation.

Powers of ten

Powers of ten failing to notice a factor of ten between values is the most common error.

Units

Units data may be given in standard form.

Section 37 of 66Checking a rate equation

Test

Test after finding the orders, test the equation on another experiment.

Same k

Same k a correct rate equation gives the same k for every experiment at the same temperature.

Different k

Different k means the orders are wrong.

Zero order

Zero order a zero-order reactant is absent from the equation.

Catalyst

Catalyst it may appear in the rate equation though not in the balanced equation.

Section 38 of 66More from the specification

Reaction mechanism elementary steps

Reaction mechanism elementary steps multi-step chemical reactions proceed through a sequential series of molecular collisions termed elementary steps.

Activation Energy and Reaction Profiles

The activation energy represents the threshold energy barrier that colliding particles must overcome for chemical bonds to break and reaction to occur.

Arrhenius Rate Constant Relation

The rate constant k increases exponentially with temperature according to k = A exp(-Ea/RT), reflecting a greater fraction of energetic collisions.

Catalytic Lowering of Activation Energy

Adding a catalyst provides an alternative elementary pathway with a lower activation energy, visible as a reduced peak height on reaction energy graphs.

Elementary Reactions and Collision Dynamics

In an elementary step, the rate of reaction depends directly on the frequency of successful molecular collisions between reactant particles.

Activation Energy and Reaction Profiles

The activation energy represents the threshold energy barrier that colliding particles must overcome for chemical bonds to break and reaction to occur.

Arrhenius Rate Constant Relation

The rate constant k increases exponentially with temperature according to k = A exp(-Ea/RT), reflecting a greater fraction of energetic collisions.

Catalytic Lowering of Activation Energy

Adding a catalyst provides an alternative elementary pathway with a lower activation energy, visible as a reduced peak height on reaction energy graphs.

Elementary Reactions and Collision Dynamics

In an elementary step, the rate of reaction depends directly on the frequency of successful molecular collisions between reactant particles.

Kinetic energy

The energy of motion of a particle.

Successful collision

A collision with the correct orientation and enough energy to react.

Collision frequency

Number of collisions per second

Product

A substance formed in a reaction.

Hydrogen

A gas that gives a squeaky pop with a lighted splint.

Activation energy

The minimum energy colliding particles need to react.

Arrhenius equation

K = Ae^−E_a/RT, relating the rate constant to temperature and activation energy.

Maxwell-Boltzmann distribution

A graph showing how particle energies are spread at a given temperature.

Energy profile

Diagram showing energy during a reaction

Elementary step

A single stage in a reaction mechanism.

Arrhenius factor

The pre-exponential factor A.

Particle

A tiny portion of matter, too small to see.

Gradient

The change in y divided by the change in x on a graph.

Molecule

Two or more atoms held together by covalent bonds.

Section 39 of 66Concentration–time graphs

1Zero order

Zero order concentration falls at a constant rate, a straight downward line whose gradient is the rate;
- rate = k.

2First order

First order concentration falls exponentially, a curve that flattens; rate = k[A].
What the symbols mean: rate (mol dm⁻³ s⁻¹) · k = rate constant · [ ] = concentration (mol dm⁻³) · each power is the order with respect to that reactant
- (units depend on the overall order)

3Second order

Second order concentration falls more steeply at first, a steep curve; rate = k[A]².

Section 40 of 66Rate–concentration graphs

Order	Rate against concentration	Effect of doubling concentration
Zero	Horizontal line (rate = k)	No change
First	Straight line through the origin	Rate doubles
Second	Upward curve from the origin	Rate quadruples

Avoid confusion

Avoid confusion do not mix the straight line of a zero-order concentration–time graph with the straight line of a first-order rate–concentration graph.

Avoid confusion

Avoid confusion do not mix the curve of a first-order concentration–time graph with the curve of a second-order rate–concentration graph.

Section 41 of 66Graph plus table

1Combined question

Combined question a graph often gives the order for one reactant and the table gives the others.

2Half-life

Half-life constant for first order, shortening for zero order and lengthening for second order.

3Tangents

Tangents drawing tangents at two concentrations shows that rate ∝ concentration for first order.

4Final step

Final step combine the orders into the rate equation to calculate k with units.

Section 42 of 66Calculating k and its units

Calculating k and its units

Rearrange the rate equation to make k the subject.

Substitute an initial rate and the initial concentrations.

Substitute the units into the rate equation and cancel to find the units of k.

Overall order	Units of k
0	mol dm⁻³ s⁻¹
1	s⁻¹
2	mol⁻¹ dm³ s⁻¹
3	mol⁻² dm⁶ s⁻¹

Same k
- every measurement at one temperature gives the same value.

Section 43 of 66Temperature and the rate constant

Effect

Effect raising the temperature increases k, so the rate rises even at the same concentrations.

Trend

Trend k increases exponentially with temperature.

Rule of thumb

Rule of thumb the rate roughly doubles for each 10 °C rise;
- it could be 9 °C or 11 °C, the interval changes gradually and it does not apply to every reaction.

Yield

Yield a higher rate does not mean a higher yield, which depends on whether the reaction is exothermic or endothermic (Le Châtelier).

Section 44 of 66A first look at mechanisms

1Elementary steps

Elementary steps most reactions occur in a series of simple steps, the reaction mechanism.

2Intermediates

Intermediates species made in one step and used in another.

3Sum

Sum the steps must add up to the overall equation.

4Evidence

Evidence kinetics can disprove a proposed mechanism but cannot prove it.

Section 45 of 66More from the specification

Section 46 of 66Proposing a mechanism

1Mechanism

Mechanism a set of elementary steps whose sum is the overall equation.

2Intermediates

Intermediates produced in one step and used in another, so they cancel.

3One-step mechanism

One-step mechanism the overall equation itself.

4Catalysed route

NO catalyses SO₂ oxidation: step 1 2NO + O₂ → 2NO₂, step 2 NO₂ + SO₂ → NO + SO₃.

5Check

Check the steps must add up to the overall equation or the mechanism is wrong.

Section 47 of 66Rate-determining step

1Definition

Definition the slowest step; the reaction can go no faster than it.

2Rate equation

Rate equation includes species in the rate-determining step.
- (and those needed to make an intermediate in it)

3Order

Order for a reactant, the number of its particles in the rate-determining step.

4Stoichiometry

Stoichiometry there is no direct link between the orders and the coefficients of the overall equation.

5Intermediate

Intermediate cannot appear in the rate equation; the reactants that form it are used instead.

Section 48 of 66Predicting a mechanism from a rate equation

1NO₂ + CO → NO + CO₂ with rate

NO₂ + CO → NO + CO₂ with rate k[NO₂]2

the slow step contains two NO₂ and no CO.

2Step 1 (slow)

2NO₂ → NO + NO₃.

3Step 2 (fast)

NO₃ + CO → NO₂ + CO₂.

4Check

Check cancelling NO₃ and one NO₂ gives the overall equation.

Section 49 of 66Deducing a rate equation from a mechanism

12NO + 2H₂ → N₂ + 2H₂O

2NO + 2H₂ → N₂ + 2H₂O step 1 NO + NO → N₂O₂ (fast).

2Step 2 (slow)

N₂O₂ + H₂ → H₂O + N₂O.

3Step 3 (fast)

N₂O + H₂ → N₂ + H₂O.

4Rate-determining step

Rate-determining step contains N₂O₂ (from two NO) and one H₂.

5Rate equation

Rate equation rate = k[NO]²[H₂], third order overall.
What the symbols mean: rate (mol dm⁻³ s⁻¹) · k = rate constant · [ ] = concentration (mol dm⁻³) · each power is the order with respect to that reactant
- (units depend on the overall order)

Section 50 of 66The transition state

Transition state

Transition state an unstable, high-energy arrangement higher than reactants or products, whose energy above the reactants is E_a.

Example H₂ + I₂

H–I bonds begin to form while H–H and I–I bonds lengthen and weaken.

Two outcomes

Two outcomes the new bonds strengthen to form HI, or the original bonds re-form to give back the reactants.

Requirement

HI forms only if molecules collide with energy ≥ E_a and in the correct orientation.

Section 51 of 66Energy profiles of multi-step reactions

1Peaks

Peaks each step has its own peak, with intermediates in the valleys.

2Rate-determining step

Rate-determining step the step with the greatest activation energy.

3Greatest, not highest

Greatest, not highest it is the largest barrier, not necessarily the highest peak.

4Overall energy

Overall energy exothermic reactions end lower than they start.

Section 52 of 66Multi-step example: NO<sub>2</sub> and F<sub>2</sub>

1Reaction

2NO₂ + F₂ → 2NO₂F is exothermic and unlikely in one step, as three molecules would have to collide.

2Rate equation

Rate equation rate = k[NO₂][F₂].

3Proposed steps

NO₂ + F₂ → NO₂F + F, then NO₂ + F → NO₂F.

4Rate-determining step

Rate-determining step step 1, because only its reactants match the rate equation, so it has the larger E_a.

5After step 1

After step 1 the species present are NO₂, NO₂F and F, at the energy level of the valley.

Section 53 of 66More from the specification

1Collision theory and temperature

According to collision theory, a reaction occurs when reacting particles collide with energy exceeding the activation energy;
increasing temperature shifts the Maxwell-Boltzmann distribution curve to higher kinetic energies, greatly increasing the proportion of successful collisions.

2Reaction order and concentration

The order of reaction with respect to a specific reactant indicates how rate changes as its concentration varies.
- (e.g. rate is independent of concentration for zero order, directly proportional for first order)

3Concentration-time and rate-concentration graphs

In a first-order reaction, a concentration-time graph exhibits a constant half-life,
while a rate against concentration graph is a straight line through the origin whose gradient equals the rate constant k.

4Arrhenius equation and rate constant

The rate constant k increases exponentially with temperature according to the Arrhenius relationship ln(k) = -Ea / (R * T) + ln(A), yielding a straight-line plot of ln(k) versus 1 / T.

5Arrhenius equation

K = Ae^−E_a/RT, relating the rate constant to temperature and activation energy.

6Maxwell-Boltzmann distribution

A graph showing how particle energies are spread at a given temperature.

7Arrhenius factor

The pre-exponential factor A.

8Successful collision

A collision with the correct orientation and enough energy to react.

9Collision frequency

Number of collisions per second

10Temperature

A measure of the average kinetic energy of the particles.

11Gradient

The change in y divided by the change in x on a graph.

12Hydrogen

A gas that gives a squeaky pop with a lighted splint.

Section 54 of 66Molecularity

Definition

Definition the number of reacting particles taking part in an elementary step.

Unimolecular

Unimolecular one particle reacts.

Bimolecular

Bimolecular two particles collide and react.

Termolecular

Termolecular three particles must collide at once; very unlikely and rare.

Example

CH₃Br + OH⁻ → CH₃OHBr⁻ is bimolecular and CH₃OHBr⁻ → CH₃OH + Br⁻ is unimolecular;
- CH₃OHBr⁻ is the intermediate.

Section 55 of 66The rate constant and temperature

Meaning

Meaning k reflects collision frequency and energy requirements, not just concentrations.

Constant

Constant fixed at a given temperature.

Change

Change increases with temperature because a larger proportion of molecules exceed E_a.

Effect

Effect both the rate and the rate constant increase.

Section 56 of 66The Arrhenius equation

1Equation

Equation k = A e^−E_a/RT, in section 1 of the data booklet.
What the symbols mean: k = rate constant · A = pre-exponential (frequency) factor · E_a = activation energy (J mol⁻¹) · R = 8.31 J mol⁻¹ K⁻¹ · T = temperature (K)

2Applies to

Applies to reactions in gases, in solution and on a catalyst surface.

k the rate constant.

A the Arrhenius (frequency or pre-exponential) factor, related to collision frequency and orientation; characteristic of the reaction.

5Ea

Ea activation energy per mole, in J mol⁻¹ or kJ mol⁻¹.

8.31 J K⁻¹ mol⁻¹ (data booklet section 2).

T temperature in kelvin; e ≈ 2.718.

8Effects

Effects higher E_a gives lower k; higher T gives higher k.

Section 57 of 66Logarithmic form

Equation

Equation ln k = −E_a/RT + ln A, also in the data booklet.

Use

Use easier to rearrange for E_a, A or T.

Rearranged

E_a = (ln A − ln k) × RT.

Units

Units convert J mol⁻¹ to kJ mol⁻¹ by dividing by 1000 at the end.

Common task

Common task calculate E_a from k and T.

Section 58 of 66The Arrhenius graph

Plot

Plot ln k (y) against 1/T (x), a straight line matching y = mx + c.

Gradient

−E_a/R, so E_a = −gradient × R, and the minus signs cancel to give a positive E_a.

Intercept

Intercept ln A, so A = e^intercept.

Axis not from zero

Axis not from zero the intercept cannot be read;
- substitute one point and the gradient into ln k = gradient × (1/T) + ln A.

Units

Units use T in kelvin and calculate 1/T in K⁻¹.

Sign check

Sign check the gradient is negative because k increases with temperature.

Gradient accuracy

Gradient accuracy use two well-separated points on the best-fit line.

Section 59 of 66More from the specification

Section 60 of 66The graph and its gradient

Equation

Equation ln k = −(E_a/R)(1/T) + ln A.

Straight line

Straight line y = mx + c when ln k is on the vertical axis and 1/T on the horizontal axis.

Gradient

−E_a/R.

Intercept

Intercept ln A on the vertical axis.

Units

Units temperature in kelvin and 1/T in K⁻¹.

Negative gradient

Negative gradient because k usually increases as temperature increases.

Section 61 of 66Activation energy from the gradient

Rearrangement

E_a = −gradient × R.

8.31 J K⁻¹ mol⁻¹.

Unit conversion

Unit conversion divide by 1000 only at the end to give kJ mol⁻¹.

Sign

Sign the minus signs cancel, so E_a is positive.

Section 62 of 66Arrhenius factor from a point

Method

Method take a plotted point and substitute it with the gradient into ln k = gradient × (1/T) + ln A.

Solve

Solve rearrange for ln A, then A = e^{ln A}.

Units

A has the same units as the rate constant k.

When needed

When needed the intercept cannot be read directly if the x-axis does not start at zero.

Section 63 of 66Checking the calculation

Separation

Separation find the gradient from two well-separated points on the best-fit line to reduce uncertainty.

Axis check

Axis check the horizontal axis is 1/T, not T.

Size check

Size check a gradient of about −3.7 × 10³ K gives E_a of about 30 kJ mol⁻¹.

Sign check

Sign check a negative E_a indicates a sign error.

Section 64 of 66More from the specification

Section 65 of 66Key terms

Term	Meaning
Rate of reaction	Change in concentration per unit time.
Activation energy	Minimum energy for a successful collision.
Order of reaction	The power of a concentration in the rate equation.
Rate constant	The constant k in the rate equation, dependent on temperature.
Rate-determining step	The slowest elementary step in a mechanism.
Intermediate	A species formed and used up within a mechanism.
Arrhenius factor	The pre-exponential factor A.

Term	Meaning
Quenching	Deliberately stopping a reaction to analyse a sample.
Clock reaction	A method timing the reaction to a fixed visible point.
Collision frequency	Number of collisions per unit time.
Successful collision	A collision with sufficient energy and the correct orientation.
Tangent	A straight line touching a curve at one point.

Term	Meaning
Activation energy	Minimum energy for reactant particles to react.
Catalyst	A substance that lowers E_a and is not used up.
Homogeneous catalyst	A catalyst in the same phase as the reactants.
Heterogeneous catalyst	A catalyst in a different phase from the reactants.
Enzyme	A biological catalyst.

Term	Meaning
Maxwell–Boltzmann distribution	A graph of the distribution of particle energies.
Most probable energy	The energy at the peak of the curve.
Rate constant	The constant k in the rate equation.
Rate equation	The expression relating rate to concentrations.

Term	Meaning
Order of reaction	Power of a concentration in the rate equation.
Overall order	Sum of the individual orders.
Initial rate	Rate at the start of a reaction.
Zero order	Rate independent of concentration.
First order	Rate proportional to concentration.

Term	Meaning
Half-life	The time for the concentration of a reactant to halve.
Rate constant	The proportionality constant k in the rate equation.
Units of k	Depend on the overall order of reaction.
Elementary step	A single step in a mechanism.
Reaction mechanism	The sequence of elementary steps in a reaction.

Term	Meaning
Elementary step	A single step in a mechanism involving a few particles.
Intermediate	A species formed in one step and used in a later step.
Rate-determining step	The slowest step, which controls the rate.
Transition state	The highest-energy arrangement along a reaction step.
Termolecular	A step involving three particles colliding together.

Term	Meaning
Molecularity	The number of particles in an elementary step.
Arrhenius factor	The pre-exponential factor A.
Arrhenius equation	k = A e^−E_a/RT.
Unimolecular	A step involving one particle.
Bimolecular	A step involving two particles.

Term	Meaning
ln A	The vertical intercept of the Arrhenius graph.
Gradient	−E_a/R on a ln k against 1/T graph.
Arrhenius factor	A, which has the same units as k.
Reciprocal temperature	1/T in K⁻¹.

Section 66 of 66Exam technique

Giving the rate of a reactant graph as negative.

Saying a catalyst changes ΔH or increases the particles' energy — it lowers E_a.

Reading orders from the stoichiometric coefficients.

Using temperature in °C in the Arrhenius equation.

Saying the rate-determining step has the highest peak rather than the greatest activation energy.

Giving a negative value for a reaction rate.

Drawing a small triangle for a tangent gradient.

Using a gas syringe for a very soluble gas or a balance for a very light gas such as hydrogen.

Saying a catalyst changes the activation energy of the original route.

Explaining a temperature effect only by more frequent collisions.

Saying a catalyst changes ΔH or collision frequency.

Saying particles "have more activation energy".

Saying increased particle size increases rate.

Drawing the higher-temperature curve with a higher peak.

Showing the catalysed curve with a different shape — only E_a moves.

Shading only the extra area to the left of the original E_a for a catalyst.

Assuming the orders equal the coefficients of the balanced equation.

Writing orders from the coefficients of the balanced equation.

Missing a factor of ten when reading standard form data.

Adding the orders of the products to the overall order.

Using experiments where two concentrations change at once.

Confusing zero-order concentration–time lines with first-order rate–concentration lines.

Quoting the wrong units for k for the overall order.

Saying a faster rate always gives a greater yield.

Using the rate for the half-life without checking whether it is constant.

Allowing an intermediate to appear in the rate equation.

Proposing steps that do not add up to the overall equation.

Taking the orders from the overall coefficients.

Identifying the rate-determining step as the step at the highest energy rather than the step with the greatest activation energy.

Using the wrong unit for E_a — R is in J, so the result is in J mol⁻¹ before conversion.

Plotting ln k against T instead of 1/T.

Reading the intercept when the x-axis does not start at zero.

Calling a three-particle step common — termolecular steps are rare.

Using the gradient as positive E_a/R without the minus sign.

Dividing by 1000 before multiplying by R.

Plotting k instead of ln k.

Reading the intercept from a graph whose x-axis does not start at zero.

Last updated: 14 October 2026

Section 1 of 66Rate of reaction

Section 2 of 66Measuring rates

Section 3 of 66Collision theory

Section 4 of 66Factors affecting rate

Section 5 of 66Energy profiles and catalysts

Section 6 of 66Maxwell–Boltzmann curves

Section 7 of 66Rate equations (HL)

Section 8 of 66Mechanisms (HL)

Section 9 of 66The Arrhenius equation (HL)

Section 10 of 66More from the specification

Section 11 of 66Rate of reaction

Section 12 of 66Measuring rate with gas volume

Section 13 of 66Titration, conductivity and clock reactions

Section 14 of 66Rate from the gradient of a graph

Section 15 of 66Collision theory

Section 16 of 66Activation energy and orientation

Section 17 of 66More from the specification

Section 18 of 66Pressure and concentration

Section 19 of 66Temperature

Section 20 of 66Surface area

Section 21 of 66Activation energy and energy profiles

Section 22 of 66Catalysts

Section 23 of 66Catalysts in industry and biology

Section 24 of 66Explaining rate changes

Section 25 of 66More from the specification

Section 26 of 66The Maxwell–Boltzmann distribution

Section 27 of 66Effect of temperature

Section 28 of 66Effect of a catalyst

Section 29 of 66Rate and concentration

Section 30 of 66The rate equation

Section 31 of 66The rate constant

Section 32 of 66More from the specification

Section 33 of 66Order of reaction

Section 34 of 66Zero, first and second order

Section 35 of 66Using a given rate equation

Section 36 of 66Deducing orders from initial rates

Section 37 of 66Checking a rate equation

Section 38 of 66More from the specification

Section 39 of 66Concentration–time graphs

Section 40 of 66Rate–concentration graphs

Section 41 of 66Graph plus table

Section 42 of 66Calculating k and its units

Section 43 of 66Temperature and the rate constant

Section 44 of 66A first look at mechanisms

Section 45 of 66More from the specification

Section 46 of 66Proposing a mechanism

Section 47 of 66Rate-determining step

Section 48 of 66Predicting a mechanism from a rate equation

Section 49 of 66Deducing a rate equation from a mechanism

Section 50 of 66The transition state

Section 51 of 66Energy profiles of multi-step reactions

Section 52 of 66Multi-step example: NO<sub>2</sub> and F<sub>2</sub>

Section 53 of 66More from the specification

Section 54 of 66Molecularity

Section 55 of 66The rate constant and temperature

Section 56 of 66The Arrhenius equation

Section 57 of 66Logarithmic form

Section 58 of 66The Arrhenius graph

Section 59 of 66More from the specification

Section 60 of 66The graph and its gradient

Section 61 of 66Activation energy from the gradient

Section 62 of 66Arrhenius factor from a point

Section 63 of 66Checking the calculation

Section 64 of 66More from the specification

Section 65 of 66Key terms

Section 66 of 66Exam technique

Marked practiceQuizzes for this lesson