Chemical Kinetics (A-level physical chemistry)
Chemical kinetics
It is a branch of chemistry that deals with the measurement of reaction velocities/rates and determination of mechanisms by which reactants are converted into products.
The knowledge of chemical kinetics is useful when altering the rates of chemical reaction is needed. For instance, manufacturers of fertilizers aim at speeding up the formation of ammonia from nitrogen and hydrogen whereas a car manufacturer wishes to slow down the rate at which iron rust.
Rates of reaction
Reaction rate is the speed at which a chemical reaction proceeds. It is often expressed in terms of either the concentration (amount per unit volume) of a product that is formed in a unit of time or the concentration of a reactant that is consumed in a unit of time.
Consider the reaction
A → product (p) …………………………………………… (I)
The rate of the reaction or reaction velocity may be defined as the rate of disappearance of the reactant (A) or the rate of appearance or formation of the product (P) with respect to time.
Where, K, is the rate constant.
In general for a reaction
aA +bB → cC + dD ………………………………………(II)
The rate of reaction is given as
Since the reaction depends on the concentration of the reactants, the rate equation for the reaction in (II) can be expressed in a rate equation represented as
Rate = K[A]x[B]y.
Definitions terms in a rate law
(i) [A] is the molar concentration of reactant A
(ii) x is the order of reaction with respect to A
(iii) y is the order of reaction with respect to B.
(iv) The algebraic sum (x+y) is the overall order of the reaction. i.e. the order of the reaction is the sum of power dependence of the rate on the concentration of each reactant.
(v) K is the rate constant of the reaction is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate.
Stoichiometry of a reaction is the quantitative relationships of the amount of products and reactants in a given reaction
The values of x and y are often 1 or 2 and rarely 0, 3, fraction, or negative numbers.
These values x and y are experimentally determined values and cannot be predicted until one has carried out the experiment. The order of the reaction has nothing to do with the stoichiometry of the equation for the reaction.
For example, a simple reaction between bromated (V) ions, bromide ions and hydrogen ions to give bromine is represented by the equation:
BrO3–(aq) + 5Br–(aq) + 6H+(aq) → 3Br2(aq) + 3H2O(l)
This has a complex rate equation from kinetic measurements as expressed below:
Determining the order of reaction
The order of a reaction can be found by comparing the initial rates of two more or reactions at known initial concentrations.
Example 1
The following results obtained for a reaction between A and B; can be used to determine the order of reaction with respect to A and with respect to B and the rate constant.
Method
Rate equation = K[A]x[B]y
To obtain x, which compare reactions in which the concentrations of B are constant but those of A vary such as (d) and (e):
x = 1
To obtain y, which compare reactions in which the concentrations of A are constant but those of B vary such as (b) and (a):
Calculating the rate constant, K,
We substitute for x and y in any of the experiment above e.g. (a)
2 = K[0.5]1x [1.0]2
K = 4.0dm6mol-2s-1
Trial 1
(a) Explain terms:
(i) Rate of reaction
(ii) Order of reaction
(iii) Stoichiometry of reaction
(iii) Rate constant
(b) For the reaction
A+ B → C
The following results were obtained for kinetic runs at the same temperature.
Why do kinetic experiments carried out at a constant temperature
(c) Find
(i) the rate equation for the reaction,
(ii) the rate constant,
(iii) the initial rate of reaction, when [A]0 = 0.60moldm-3 and [B]0 = 0.3moldm-3.
Trial 2
Tabulated are values of initial rates for the reaction
2A + B → C +D
(a) Find the order of reaction with respect to A, the order of reaction with respect to B, and the overall order of the reaction.
(b) Find the value of the rate constant
(c) Find the initial rate of the reaction when [A]0 = 0.120 moldm-3 and [B]0 = 0.22 moldm-3.
Trial 3
The reaction between nitrous oxide and ozone is given by the equation
NO (g) + O3(g) → NO2 + O2
Was studied in the lab at 250C and the following results were obtained.
| Exp. 21 No. | [NO]moll-1 | [O3]moll-1 | Rate (moll-1s-1) |
| 1 | 1.00 x 10-6 | 3.00 x 10-6 | 0.66 x 10-4 |
| 2 | 2.00 x 10-6 | 3.00 x 10-6 | 1.32 x 10-4 |
| 3 | 1.00 x 10-6 | 9.00 x 10-6 | 1.98 x 10-4 |
| 4 | 2.00 x 10-6 | 9.00 x 10-6 | 3.96 x 10-4 |
| 5 | 3.00 x 10-6 | 9.00 x 10-6 | 5.9 x 10-4 |
(a) Write an expression for the rate equation for the reaction above.
(b) Determine the order of reaction with respect to NO and O3.
(c) Write the true rate equation for the reaction.
(d) Calculate the value of the rate constant.
Trial 4
The kinetic data for the reaction between X and Y are shown in the table below
(a) Determine the order of reaction with respect to
(i) X
(ii) Y
(b) Determine the overall order
(c) Calculate the rate constant for the reaction and indicate its units.
Trial 5
The rate equation for a certain reaction is:
Rate = K[P][Q]2[R]
(a) State what would happen to the rate of reaction if
(i) the concentration of P and Q is kept constant, but that of R is doubled.
(ii) the concentration of all species are halved
(iii) the concentration of all species are doubled
(b) the following were obtained in a study of reaction between peroxodisulphate and iodide ions
(i) Write the rate equation
(ii) Calculate the rate constant for the reaction and state its units
Reactions of various orders
1. First-order reaction
A reaction is said to be first order if the rate is proportional to the first power of concentration of reactants on which the reaction kinetics depends. That is, the rate law for the first order reaction is given by
Rate = K[A]
Identification of a first-order reaction
The first-order reaction can be identified from the shapes of the following graphs.
All these graphs that show that the rate of reaction is proportional to the concentration of the reactant in the chemical reaction.
(i) Rate of reaction against concentration
A straight line with a positive gradient shows that the rate is proportional concentration of the reactant and that the reaction is thus first order.
(ii) The concentration of the reactant against time.
Hyperbola shows that the rate of reaction is proportional to the concentration of the reactant and thus the first-order reaction
(iii) For a first-order reaction, a plot logarithm of concentration against time gives a straight line with a negative gradient.
A typical example of a reaction that follows a first-order reaction mechanism is a radioactive disintegration process.
Definitions
Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic loses energy by radiation.
The integrated rate law for the first-order reaction
Consider the first-order reaction
A→ P
If the initial concentration [A] of reactant (A) at the time, t=0, is a moldm-3 and the concentration of the product, P, after time t is x moldm-3; then concentration of A at time, t, will be (a-x) moldm-3.
Then, the rate of reaction as the rate of formation of the product is represented as
Half-life of the first order reactions
The half-life of the reaction is the time taken by a reactant to reduce to half of its initial concentration.
The expression for the half-life of a first-order reaction is obtained from the integrated rate law: i.e.
This shows that in the first-order reaction, the half-life is independent of the initial concentration of the reactants. The time necessary for the reactants to decrease to any other given fraction can be derived in a similar manner.
Trial 6
(a) The rate of a chemical reaction is given by the relationship:
Rate = K[A]a[B]b
State
(i) What each of the following stands for
[A] …………………………………………………
a ………………………………………………….
b ……………………………………………………
(ii) One factor that can affect the constant K.
(b) Write an equation for the decomposition of dinitrogen oxide
(c) At 858K, the half-life of dinitrogen oxide is 75.09hours
Calculate
(i) The rate constant for the decomposition of
dinitrogen oxide
(ii) the total pressure after 75.09hours at 858K, if the initial pressure was one atmosphere.
Trial 7
(b) The half-life of a first-order reaction is 100s
(i) calculate the rate constant.
(ii) Determine the percentage of the reactant that has reacted after 250s.
2. Zero-order reactions
In a zero-order reaction, the rate is independent of the concentration of the reactants.
A plot of the concentration [A] of the reactant against time has the form below:
The rate equation for a zero-order reaction:
Rate = K[A]0 or Rate = K s-1
Example, the reaction between iodine and propanone is a zero-order with respect to iodine.
Pseudo-order reaction
A pseudo order reaction is a reaction that is truly higher-order but can be approximated to a lower order under special circumstances.
For instance, an elementary reaction between two reactants A and B is normally expected to be a second-order; for example, hydrolysis of an ester and inversion of sucrose.
However, if one of the reactant B is present at a very much greater concentration than that of A or else only acts as a catalyst, the concentration of B is considered constant ad the rate law becomes
Rate = K’[A]
Such a reaction is said to be pseudo-first order since the rate is proportional to the concentration of A raised to the first power. Nevertheless, it must be remembered that the new constant (K’) is not a true constant because it also depends on the concentration of B. Since water is usually found in excess, the reactions are given above are in practice found to be pseudo-first-order.
Note that:
(1) For a zero-order reaction, any change in concentration of the reactant does not affect the rate of reaction.
(2) For a first-order reaction increasing the concentration of the reactant two or three times also increase the rate two or three times.
Trial 8
(a) State what is meant by the term order of a reaction
(b) Methylethanoate is hydrolysed by water in the presence of an acid according to the following reaction:
CH3COOCH3 + H2O (l) ↔ CH3CH2OH +C H3OH
(i) State the molecularity of the reaction
(ii) State the conditions under which the reaction can be the overall first order
(c) The table below shows some kinetic data for the following reaction:
(i) Write the overall order of reaction
(ii) Calculate the rate constant and give its units.
Measuring the rates of reactions
The rate of a chemical reaction can be obtained by following some property which alters with the extent of the reaction. By analyzing the reaction mixture at suitable intervals, it’s possible to determine the concentration of both the reactant and/or the product at different times and hence obtaining the rate (i.e. the rate at which the concentration of a particular substance changes with time).
In practice, the rates may be measured by observing the rate of change of physical properties such as refractive index, volume, color, and if the reaction is sufficiently slow, its rate may be found by frequent withdrawal of small portion of the reacting mixture and analyse then chemically at intervals.
Examples,
1. An experiment to measure the rate of chemical reaction in which a gas is produced such as
Mg (s) + 2HCl (aq) → MgCl2 (g) + H2 (g)
Or 2H2O2 (aq) → 2H2O (l) + O2 (g)
The volume of a gas is recorded at intervals
(a) H2O2 solution and catalyst.
(b) The plunger of the syringe moves outwards.
(c) Oxygen: Volume is recorded at certain times after the start of the reaction
(d) Thermostat bath maintains temperature.
(e) The rate of reaction is given by where V is the volume of the gas.
2. An experiment to determine the order reaction with respect to iodine in the reaction of iodine with propanone in presence of an acid catalyst.
- A fixed volume of standard Iodine solution is added to an excess of propanone solution in a flask.
- To this mixture is added a fixed volume of dilute sulphuric acid and a stop clock started immediately.
- At intervals of time say (every 10 minutes for 50 minutes), a specified portion is pipetted from the mixture and into a flask containing sodium hydrogen carbonate which stops the reaction.
- The resultant mixture is titrated with standard sodium thiosulphate using a starch indicator.
- The volume (Vt) of thiosulphate used on the portion of the mixture after a specified time (t) is proportional to the amount of iodine remaining in the mixture.
- The initial amount of iodine (V0) is obtained by titrating a similar portion of the original mixture with sodium thiosulphate solution.
- A plot of the graph of Vt against time gives a straight line as shown below showing that the order of reaction with respect to iodine is zero.
NB. The gradient gives the rate constant whose units is molcm-3 s-1.
Activated complex
With the exception of radioactive disintegration all elementary reaction occurs via a transition state, for example, substitution reaction is expected to proceed as below
A + BC ↔ [A….B…..C] ↔ AB + C
In order to form the transition state, the reactants must first acquire activation energy i.e. This is the minimum energy required for the reaction to take place. Being energy-rich, the transition species is unstable and cannot be isolated and is usually referred to as the activation complex. This may decompose either to give the product or original reactants. The energy variation during the above process may be represented by the figures below:
Definition
An activated complex is the structure that results in the maximum energy point along the reaction path.
The energy diagram for the reaction for an exothermic reaction
The energy diagram for the reaction for an endothermic reaction
The difference between the energy of the reactants and the product is the enthalpy of the reaction (∆Hr) which is negative for exothermic reaction (i.e. energy given out during the reaction and the reaction mixture heats up) or positive for endothermic reaction (i.e. energy is required for the reaction to take place.)
Definition
The molecularity of a reaction is defined as the number of molecules or ions that participate in the rate-determining step.
The activation energy of a chemical reaction is the difference between the energy of the activated complex and the energy of the reactants.
Factors that affect the rate of reaction
The main factors which influence reaction rate are
(i) concentration of the reactant
(ii) temperature
(iii) Pressure
(iv) presence of light
(v) the size of the particles for solid reactants.
(vi) Catalyst
1. Particle size
The smaller the particle sizes the faster the reaction in the solid state because of increased surface area for contact. e.g.
CaCO3(s) + 2HCl (aq) → CO2(g) + CaCl2(aq) + H2O(l)
The reaction is faster when CaCO3 is in powder form than big chips.
2. Concentration
The higher the concentration of reactants; the faster is the rate of reaction due to the increase in the rate of collision among the reacting molecules..
3. Pressure
Pressure increases the rate of reaction when the reactants are in the gaseous phase because it increases the proximity and the rate of collision of the reacting molecules.
4. Temperature
Temperature increases the rate of reaction because
- Particles gain kinetic energy which increases the rate collision
- it increases the fraction of molecules with energy equal or higher than the activation energy that enables the reaction to take place in case collision take place between molecules.
The graph below shows the distribution of kinetic energies of molecules of a gas at temperatures T1 and T2; T2 being higher than T1.
The number of molecules with energy equal to or greater then Ea increases rapidly with temperature as shown by the shaded area under graph above
5. Light
Some reactions are catalyzed by light such as photosynthesis and formation of silver from silver salts that take place when a photographic film is exposed to light. The higher the light intensity, the higher the rate of reaction will be.
6. Surface area
Increasing surface area of the reactant increases the rate of reaction because it brings the reacting substances into more intimate contact to facilitate their interaction.
7. Catalyst
Increase the rate of reaction by lowering the activation energy
The energy diagram for the reaction for exothermic reaction in the absence and presence of a catalyst.
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Compiled by Dr. Bbosa Science
The notes are good for A’Level students in Uganda. However, some parts of the topic like mechanism, collision theory are lacking