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# 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:

(CH_{3})_{3}CCl_{(aq)} + OH^{-}_{(aq)} → (CH_{3})_{3}COH_{(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 (CH_{3})_{3}CCl_{(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.