## 1.9 Rate equations (Kinetics A2)

In rate equations, the mathematical relationship between rate of reaction and concentration gives information about the mechanism of a reaction that may occur in several steps.

The rate expression is an experimentally determined relationship

Species that appear in the chemical equation do not necessarily appear in the rate expression.
Conversely, a species that is not in the chemical equation may appear in the rate equation (e.g. a catalyst).

The rate of a chemical reaction is related to the concentration of reactant species, that have been experimentally determined, in a rate equation of the form:

Rate = k[A]m [B]n
rate is expressed as mol dm−3 s−1
m and n are the orders of reaction with respect to reactants A and B
κ is the rate constant; units depend on the overall order of the reaction (1st order s−1, 2nd order mol−1 dm3 s−1,
3rd order mol−2 dms−1 )
the overall order of the reaction is m+n.
[The orders m and n in this module are restricted to the values 0, 1, and 2].

Example

In chemical reaction,                                                 CH3COCH3 + I2 → CH2ICOCH3 + HI
However, experimentally determined rate expression is     Rate=k[CH3COCH3][H+]
Reaction is:
zero order with respect to [I2] ; first order with respect to [CH3COCH3] and [H+]; [H+] acts as a catalyst.

Rate of Reaction at any instant

The gradient of the tangent of a plot of [Reactant species] vs time, at the times required, provides the rate of reaction at that time, measured as  mol dm−3 s−1 .

Rate constant κ increases with increasing temperature

As the temperature increases, a greater proportion of reacting particles have sufficient energy (activation energy Ea ) to successfully collide and react. For every 10K rise, the rate of reaction approximately doubles. Given [species] is unaffected by increasing temperature, according to the rate equation, the rate constant k must therefore increase with temperature.

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Beyond A2

Arrhenius’ equation gives the quantitative basis of the relationship between the activation energy and the reaction rate at which a reaction proceeds. The rate constant is then given by

$\kappa =A{ e }^{ -{ E }_{ a }/RT }$

At temperature T the molecules have energies according to a Boltzmann distribution, thus the proportion of collisions with energy greater than Ea will vary according to eEa/RT.

Rate determining step and mechanism

The order of a reaction with respect to a particular reactant may give some information as to the mechanism of the reaction. Most reactions take place by a number of simple steps, the sequence being known as the reaction mechanism. The reaction cannot proceed faster than the slowest of these simple steps. The slowest step in the mechanism is called the rate-determining step.

Consider the following reactions which compare the rates of hydrolysis of primary and tertiary haloalkanes and the iodination of propanone.

From experimental data,

1. Rate = k[CH3CH2CH2CH2Br][OH]

Primary haloalkanes undergo hydrolysis via a bimolecular process where there are two species in the slow (rate determining step)-this reaction is classified as SN2 nucleophilic substitution.

2. Rate = k[(CH3)3CBr]

Tertiary haloalkanes undergo hydrolysis by a unimolecular process where there is one species in the slow (rate determining step)-this reaction is classified as SN1 nucleophilic substitution.

3. Rate=k[CH3COCH3][H+]

The rate equation shows that the reaction is first order with respect to CH3COCH3 and first order with respect to H+,
i.e. the concentrations of both affect the rate of reaction. As the rate of a reaction is determined by its slowest step, it is reasonable to assume that the correct reaction mechanism will include a rate-determining step that involves both CH3COCH and H+.

Mechanism of hydrolysis of haloalkanes and iodination of propanone

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