Reaction kinetics,part-3

5. Integrated rate laws

A rate law is a differential equation that describes the rate of change of a reactant (or product)
concentration with time. If we integrate the rate law then we obtain an expression for the
concentration as a function of time, which is generally the type of data obtained in an experiment.
In many simple cases, the rate law may be integrated analytically....

6.Half lives

The half life, t1/2, of a substance is defined as the time it takes for the concentration of the
substance to fall to half of its initial value...

7.Determining the rate law from experimental data

A kinetics experiment consists of measuring the concentrations of one or more reactants or
products at a number of different times during the reaction

8.Complex reactions

In kinetics, a ‘complex reaction’ simply means a reaction whose mechanism comprises more than
one elementary step. In the previous sections we have looked at experimental methods for
measuring reaction rates to provide kinetic data that may be compared with the predictions of
theory. In the following sections, we will look at a range of different types of complex reactions and
the rate laws that may be predicted from their kinetic mechanisms. Disagreement of a predicted
rate law with the experimental data is enough to rule out the corresponding proposed mechanism,
while agreement inspires some confidence that the proposed mechanism is the correct one. It
should be noted though that agreement between the predicted and measured kinetics is not
always enough to assign a mechanism. The proposed mechanism must be able to account for all
other properties of the reaction, which may include quantities such as the product distribution,
product stereochemistry, kinetic isotope effects, temperature dependence, and so on.
The types of complex mechanisms that we will cover are: consecutive (or sequential) reactions;
competing reactions; pre-equlibria; unimolecular reactions; third order reactions; enzyme reactions;
chain reactions; and explosions.

9.Consecutive reactions

If the rate constants for the following reaction are $k_1$ and $k_2$ ; $A \rightarrow \; B \rightarrow \; C$ , then the rate equation is:

For reactant A:
$\frac{d[A]}{dt} = -k_1 [A]$

For reactant B:
$\frac{d[B]}{dt} = k_1 [A] - k_2 [B]$

For product C:

$\frac{d[C]}{dt} = k_2 [B]$