R2.2 How fast? The rate of chemical changeIB Chemistry HL: Revision notes

Section 1

Rate and collision theory

The rate of reaction is the change in concentration of a reactant or product per unit time (mol dm⁻³ s⁻¹). Particles react only when they collide with E ≥ Ea and the correct orientation. Average kinetic energy is proportional to temperature in kelvin.

Rate increases with concentration, pressure (gases), surface area, temperature and a catalyst. Concentration, pressure and surface area raise collision frequency; temperature mainly raises the proportion of collisions with E ≥ Ea; a catalyst lowers Ea.

Key termsactivation energycollision geometry

Section 2

Maxwell–Boltzmann curves and catalysts

At higher temperature the Maxwell–Boltzmann curve is flatter with its peak at higher energy and the same area, so more particles have E ≥ Ea. A catalyst provides an alternative pathway with lower Ea: the curve is unchanged but Ea moves left. On an energy profile the catalysed maximum is lower but ΔH is unchanged.

Key termsMaxwell–Boltzmann distributioncatalyst

Section 3

Mechanisms and the rate-determining step (HL)

Many reactions occur in a series of elementary steps, the mechanism. The slowest step is the rate-determining step (RDS). The molecularity of a step is the number of particles reacting in it: unimolecular (one), bimolecular (two), termolecular (three, rare because three-body collisions with the right energy and orientation are improbable).

A valid mechanism must add up to the overall equation and predict the experimental rate equation. Species in the RDS (and before it) appear in the rate equation; species that react only after it do not.

Key termsrate-determining stepmolecularityelementary step

Common mistake

Rate equations cannot be read from the overall balanced equation; they must be found by experiment.

Section 4

Intermediates, transition states and energy profiles (HL)

A transition state is at an energy maximum: partial bonds, momentary, cannot be isolated. An intermediate is formed in one step and used up in a later step; it sits in an energy minimum between two maxima and has a finite lifetime.

A multistep energy profile has one peak per step. The highest barrier (measured from the preceding minimum) belongs to the RDS, and its peak is the transition state of the RDS. Kinetic data (which step is slow, Ea values) can be used to construct such a profile.

Key termstransition stateintermediate

Section 5

Rate equations, orders and k (HL)

rate = k[A]ᵐ[B]ⁿ: m and n are the orders, found only by experiment; the overall order is m + n. Compare experiments where only one concentration changes: ×2 concentration giving ×1, ×2, ×4 rate means order 0, 1, 2.

Graphs: zero order — concentration falls linearly with time; rate is independent of concentration (horizontal line). First order — exponential decay with a constant half-life; rate proportional to concentration (straight line through origin). Second order — steeper initial fall, half-life increases; rate against concentration is an upward curve.

Units of k: zero order mol dm⁻³ s⁻¹; first s⁻¹; second dm³ mol⁻¹ s⁻¹; third dm⁶ mol⁻² s⁻¹. k increases with temperature.

Key termsorder of reactionrate constanthalf-life

Exam tip

Units of k: start from mol dm⁻³ s⁻¹ and divide by (mol dm⁻³) raised to the overall order.

Section 6

The Arrhenius equation (HL)

$k = Ae^{-E_a/RT}$ and its linear form $\ln k = -\frac{E_a}{RT} + \ln A$ are in the data booklet. As T rises, k increases (exponentially). A plot of ln k against 1/T is a straight line of gradient −Ea/R and intercept ln A. With two temperatures: $\ln\frac{k_1}{k_2} = \frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$ .

The Arrhenius factor, A, accounts for the frequency of collisions with the correct orientation; it has the same units as k.

Key termsArrhenius equationArrhenius factor

Common mistake

Ea from the gradient comes out in J mol⁻¹ because R is in J K⁻¹ mol⁻¹; divide by 1000 for kJ mol⁻¹.

Must know

Successful collision: E ≥ Ea and correct orientation; temperature raises the proportion with E ≥ Ea.
A catalyst lowers Ea, not ΔH.
(HL) RDS = slowest step; intermediate at a minimum, transition state at a maximum.
(HL) Orders only from experiment; units of k from overall order.
(HL) ln k vs 1/T: gradient −Ea/R, intercept ln A.

That's the notes covered.

Carry on to the next subtopic.