The criteria of chemical reaction
There is no denying the fact that kinetics is the
study of how fast (the rate) a reaction progresses. The rate of a reaction is a
physical property of a reaction and is measured by the change in some reaction
quantity (e.g. volume, mass, concentration) per unit time. The most common
method used to calculate the rate of reaction is to measure the change in
concentration of the reactant(s) per second. The rate becomes, rate = - ( change in concentration of reactant in
mol dm-3 ) / time in seconds {or, rate = change in concentration of product /
time}. This gives the unit of mol dm-3 s-1 for the rate of
a reaction.
The rate of a reaction may be represented by a
mathematical equation related to the chemical equation for a reaction, e.g. for the simple hydrolysis reactions of
haloalkanes,
SN1 : the most important reaction, or the rate
determining step, is the breaking of the C-halogen bond. The rate equation for this reaction is written as, where, k = the rate constant for the reaction
SN2 : the rate determining step here is the
displacement of the halogen atom with a hydroxyl group like the rate equation here is, in general for the mechanism equation
N.B.: k is a constant only for a particular
reaction and a particular set of reaction conditions.
Kinetics - Graphs and Calculations
(1) 0 order reaction graph:
If a reactant is said to be of 0 orders in a
reaction it doesn't effect the rate of the reaction. So graphical plots of
concentration vs. time and rate vs. concentration would look like this,
N.B.: The rate of reaction at any particular time
is found as the gradient of the concentration vs. time graph at the particular
time. The gradient of rate of reaction vs. concentration is zero as the
reactant has no effect on the overall reaction until after the rate determining
step.
(2) 1st order reaction
graph :
If a reactant is said to be of 1st order, it has a
uniform effect on the rate of reaction. So graphical plots of concentration vs.
time and rate vs. concentration would look like this,
N.B.: The gradient of the concentration vs. time
graph is not constant and gradually decreases as the concentration decreases.
This produces a rate vs. concentration graph that is a straight line. The
gradient of this line will be rate/concentration or k, the rate constant for
the reaction.
(3) Calculating initial
rate using concentrations :
For the following set of data about the change in
concentration of a reactant with time,
Time (s)
|
Concentration (mol
dm-3)
|
0
|
0.50
|
5
|
0.43
|
10
|
0.37
|
20
|
0.27
|
30
|
0.20
|
40
|
0.15
|
a graph can be plotted,
The rate of reaction at various times can be found
by taking tangents to the curve above and calculating their gradients.
(2) Calculating order of reaction from initial rates :
For a reaction involving three reactants, A, B and
C, the following experimental data was found,
Experiment
|
Concentration of A (mol
dm-3)
|
Concentration of B (mol
dm-3)
|
Concentration of C (mol
dm-3)
|
Initial rate (mol dm-3
s-1)
|
1
|
0.01
|
0.01
|
0.01
|
0.05
|
2
|
0.01
|
0.02
|
0.01
|
0.10
|
3
|
0.02
|
0.01
|
0.01
|
0.10
|
4
|
0.01
|
0.01
|
0.02
|
0.05
|
A comparison of successive experimental runs shows
that if the concentration of A is doubled (and all other concentrations are
kept constant) then the rate doubles. This would follow if rate = k[A],
therefore A must be a 1st order reactant.
If the concentration of B is doubled, with all the
other concentrations remaining constant, then the rate is also doubled. This
shows that B must be a 1st order reactant as well.
However, when C is looked at in a similar manner, a
change in concentration has no effect on the rate. C is therefore of 0 order
and takes no part in the rate determining step or the rate equation.
The rate equation for this reaction is, rA =
k[A][B].
The reaction is 1st order with respect to A, 1st
order with respect to B and 2nd order overall.
(3) Calculating a rate
constant from initial rates :
From the previous set of experimental data, rA =
k[A][B]. Taking the information from experimental run 1, [A] = 0.01 mol dm-3,
[B] = 0.01 mol dm-3 and rA = 0.05 mol dm-3 s-1,
therefore, k = 500 dm3 mol-1 s-1.
The same value of k is obtained no matter which set
of experimental data are used.
Kinetics - Half-lifes
The half-life of, t½, for a reaction is the time
taken for the concentration of a reactant (or reactants) to halve exactly. For a first-order reactant the half-life is both
(i) a constant for the reaction and (ii) independent of the initial concentration of the reactant.
Therefore, knowing the half-life for a first-order
reaction enables a graph of concentration vs. time to be plotted,
SN1 reactions and radioactive decay are typical
examples of first-order reactions.
For a second-order reactant the half-life is both
(i) not a constant for the reaction and (ii) dependent on the initial concentration of the reactant.
SN2 reactions are typical examples of second-order
reactions.
Kinetics - Reactions Mechanisms
Most reactions do not follow simple, single-step
pathways. They involve two, three or more individual steps. However, one of
these steps is always slower than the other and that individual stage is called
the rate determining step - it is a limiting factor for the reaction rate. Only
reactants appearing in the rate determining step, or in fast steps before the
rate determining step, appear in the rate equation.
So, for a reaction involving A, B and C following
the mechanism below,
The rate equation overall is,
rA = k[A2][B]
i.e. 1 moles of A2 and 1 mole of B are involved in
the critical rate determining step and previous fast steps.
Kinetics - Collision Theory
The simplest way to think of a reaction occurring
is with the collision between two atoms or molecules.
The easier or faster these collisions occur, the
faster the rate of reaction will be. As an example of this, an increase in the
concentration of the reactants increases the frequency of collisions between
species (there are more molecules present in a certain volume) and therefore
increases the reaction rate.
The rate constant, k, for a rate equation brings in
the idea of collisions between species into the rate equation itself. It gives
some measure of how easy/effective the collisions are in forming the desired
product.
Boltzmann distribution of
energies :
At a given temperature a collection of molecules do
not all have the same energy. Their energies follow the Boltzmann distribution,
A lot of molecules have a similar energy; however,
there are some with less and some with more than this average value.
As well as depending on the simple collision of two
molecules, the rate of reaction depends on the molecules having a certain
amount of energy for a successful reaction to occur. This energy value is
called the activation energy for a reaction - EA,
All the molecules in the shaded area have more than
enough energy for the a successful reaction to occur between them when they
collide.
As the temperature is increased the average energy
possessed by the molecules increases,
Now more molecules have energy greater than or
equal to EA so collisions are more effective. The molecules are moving faster,
so the frequency of collisions is also greater. Both these factors lead to an
increase in the rate constant, k, and thereby to an increase in the rate of
reaction.
In fact, the rate constant and the activation
energy are linked by this equation,
where, R = the gas constant, 8.314 J K-1 mol-1.
Kinetics - Catalysis
(1) General :
A catalyst is a compound that increases the rate of
a reaction by providing an alternative reaction mechanism, for a chemical
process. This alternative mechanism has a lower activation energy,
Now more molecules have energy greater then or
equal to EA and so any collisions will be more effective, so the rate constant
is higher and the rate of reaction is increased.
(2) Homogeneous catalysts
:
These are catalysts which are in the same phase as
the reactants e.g. catalysts that are soluble in the same solvents as the
reactants. With this sort of catalysis there is direct action between the
catalyst and reactant.
e.g. Crown ethers are an example of this type of
catalyst. They form complexes with ionic compounds, enabling the ionic
compounds to be dissolved in organic solvents so they can carry out reactions
there e.g. oxidation using potassium manganate(VII).
(3) Heterogeneous catalysts:
This process uses catalysts which are in a
different phase to the reactants e.g. a solid catalyst in a reaction between
gases or a solid catalyst in a reaction occurring in solution.
With this type of catalysis the reactants have to
be absorbed either into the solid or just onto the surface of the solid. The
reaction proper can then occur on/in the solid catalyst.
e.g. In the hydrogenation of alkenes a nickel
catalyst is used. The hydrogen gas is absorbed onto the surface of the nickel
and the H-H bonds break to form single hydrogen atoms bound to the nickel's
surface. These atoms are picked up by a passing alkenes molecule, turning it
into an alkane.
(4) Enzymes:
These are biological catalysts which are often
reaction specific. They have large, complex 3-D structures which provide sites
for only certain molecules to interact with them.
They may also require a certain level of pH,
moisture or other external factors.
(5) Uses of catalysts:
Nitrogen fixation
Haber process, fertilizer production
Petroleum processing, cracking/reforming
Immobilized enzymes in industry
Catalytic converters in cars, lead as a poison
It has values.
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