
Effect of Concentration on Rate
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Effect of Concentration on Rate
Consider the reaction:
A + B → C + D
The rate equation can be expressed in several ways:

To find how the rate varies with [A] or [B] it is necessary to perform a series of experiments in which one of the concentrations is kept constant and the other varied.
Usually it is found that:
This is called the rate equation for the reaction.
k is the rate constant at a given temperature. x and y are orders of reaction with respect to A and B. They are usually whole numbers - 0, 1, 2, 3, but sometimes they can be fractions.
The order of a reaction with respect to a given reactant is defined as: 'power of its concentration in the rate equation'.
For example:
(CH3)3CCl(aq) + OH-(aq) → (CH3)3COH(aq) + Cl-(aq)
It has been found experimentally that the rate equation for the reaction is:
Therefore, the reaction is first order with respect to (CH3)3CCl(aq) (x = 1) and zero order with respect to OH- (y = 0).
For example, changing [OH-(aq)] has no effect on the reaction rate and so it does not appear in the rate equation.
The overall order of a reaction is defined as 'the sum of the powers of the concentrations of the reactants which appear in the rate equation'.
For the above reaction overall order = x + y = 1 + 0 = 1. This is a first order reaction.
Note: Rate equation and orders must be found experimentally. They cannot simply be deduced from the equation.
To find the order of a reaction with respect to one of the reactants A,
- Plot [A] against time.
- Calculate the rate at 5 or 6 different times by drawing tangents to the curve at these times and finding the gradients.
- Plot the rate against [A]. If this is a straight line then the reaction is first order in A. If not a straight line then, plot rate against [A]2. A straight line shows the reaction is second order in A.
Three examples of this type of graph (showing zero order, first order, then second order) are shown below:

This method is the same as the above. The rate is found for different concentrations of A. Then rate is plotted against [A], [A]2... until a straight line is obtained.
Since rate = k[A]
The value of k is found by taking the gradient of the graph.
The half-life (t1/2) of a reactant is the time taken for the initial concentration of a reactant to fall by half.
First order reactions have a constant half-life which is independent of the initial concentration.

Note: All radioactive decay processes are first order and have a constant half-life.
For second order reactions the half-life does depend upon the initial concentration. It can be shown that it is inversely proportional to it.