The rate equation of a reaction represents the relationship between the concentration of the reactants and the rate of the chemical reaction.

Take: A + 2B ? 3C + 2D

The rate at which this reaction occurs is given by:

rate = k[A]^x[B]^y

In which:

• [A] = concentration of A
• [B] = concentration of B
• x = order of reaction with respect to A
• y = order of reaction with respect to B
• k = the rate constant of the reaction

The order of reaction with respect to a reactant is the strength of that reactant’s concentration within the rate equation.

The overall order of reaction can be calculated by adding the powers of the reactant concentrations together (x+y).

The rate constant is the rate equation’s constant of proportionality.

Rate of reaction

When a chemical reaction takes place the:

• concentration of the reactants decreases
• concentration of the products increases

In other words, the rate of a reaction is the decrease in concentration of reactants per unit time or the increase in concentration of products per unit time.

The units of rate of reaction are moldm^-3s^-1.

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Determining Orders of Reaction

In order to work out the orders of reaction in terms of each reactant in a reaction you need to carry out the reaction using different initial concentrations and then measuring the change in the initial rate of reaction. It is then possible to determine the orders of reaction either graphically or arithmetically.

• To determine the order of reaction in terms of one reactant you should only change the concentration of one reactant and keep all others constant.
• To determine the overall order you should change all reactants by the same factor.

The arithmetic method

With the arithmetic method (which you will need for your exam):

change of concentration ^{order of reaction} = change in rate

• For a reaction that is first order: by doubling the concentration the rate will double, by tripling the concentration the rate will triple, and so on.
• For a reaction that is second order: by doubling the concentration the rate will quadruple, by tripling the concentration the rate with increase ninefold, and so on.
• For a reaction that is zero order: changing the concentration will have no effect on the rate of reaction.

For example: take the reaction RX + OH^– ? ROH + X^–

Keeping the temperature constant, the following rate data was collected:

0.15

0.0750.06

0.12

0.064 x 10^-4

2 x 10^-4

2 x 10^-4

From the second to the first experiment there is a doubling of the concentration of hydroxide ions while the concentration of RX does not change. The rate also doubles which means that the order of reaction with respect to OH^–is 1.

From the third to the first experiment there is a doubling of the concentration of RX while the concentration of hydroxide ions does not change. The rate also doubles which means that the order of reaction with respect to RX is 1.

Therefore, the rate equation is: rate = k[RX][OH^–]

Using the data from one of the experiments it is now possible to work out the rate constant. For example, taking the data from experiment 1:

k = rate / ([RX][OH^–]) = 4 x 10^-4 / (0.06 x 0.15) = 0.044 moldm^-3dm³ s^-1

Graphical method

The graphical method (which you will use in practicals) can be used for concentrations which are not simple whole number rations of one another. A graph is plotted of concentration against initial rate.

For first order reactions, in which rate = k[A], the plot will be a straight line through the origin of gradient (k).

For second order reactions, in which rate = k[A]², the plot will be a curve through the origin of gradient.

For zero order reactions, in which rate = k, the plot will be a horizontal line.

If you plot log (rate of reaction) against log (concentration) you should always get a straight line. The gradient of this line is equal to the order of reaction.

Measuring initial rates of reaction

The rate of reaction is not always easy to measure directly. In these cases it is easier to use the time taken for a certain stage to be reached in the reaction. For example:

• the time it takes for a certain amount of gas to be released
• the time it takes for absorbance to change for a particular amount
• using a clock reaction (the appearance of a particular coloured product is delayed if a fixed amount of another species is added)

The rate of a reaction is the change in concentration per unit time therefore it is inversely proportional to time taken. A graph in which 1/t is plotted against initial concentration will produce a curve.

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Explaining the Orders of Reaction

A chemical equation’s order of reactions do not always match the coefficients of the reaction and so you cannot predict the rate equation of a reaction in this way.

A lot of reactions are composed of a number of steps: some of these steps are slow while others are fast. The speed of a reaction can be determined by the slowest step. This step is known as the rate-determining step. If the rate of this step is altered then the whole rate of reaction is affected. However, altering the speed of the fast steps will not. The rate equation of a chemical reaction is determined by how many species are involved in this rate-determining step.

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Effect of Changing Condition on the Rate Constant

The rate equation is a representation of how the concentration of reactants and the rate of reaction relate to one another.

When the concentration of a reactant is increased, the rate of reaction also increases but the rate constant (k) does not change.

When the pressure is increased, the concentration of reactants will also increase thereby increasing the rate of reaction. However the rate constant will not change.

Therefore: the rate constant, k, is independent of both concentration and pressure.

When the temperature is increased, the rate of reaction increases without an increase in concentration. Therefore, it is clearly the rate constant that changes.

When a catalyst is added, the rate of reaction again increases without an increase in concentration. Therefore, it is clearly the rate constant that changes.

Therefore: the rate constant, k, changes with a change in temperature and with the addition of a catalyst.