If we wanted to calculate the rate at 60 seconds we would need to draw a tangent at 30 seconds and calculate the gradient, this is the rate.

Initial rate of reaction, a tangent drawn at 0, is an often used term you need to be familiar with.

Through experimentation a rate equation can be calculated, an example rate equation could be rate = k [A][B], if we know the rate constant, k, and the concentration of A and B we would be able to calculate the rate of reaction. The rate constant is different depending on the reaction and the temperature so both must be stated. The units for rate are moldm-3s-1, and the units for concentration are moldm-3, therefore the units of k will change depending on the rate equation.

The rate equation is not as simple as multiplying all of the reactants for example the reaction A + B + C —> D could have the rate equation rate = k[A][C]^2. This would mean the rate is in first order in respect to A, zeroth order in respect to B, and second order in respect to C.

If the concentration of A was to increase by x3 the rate of reaction would increase by x2^1 = x2

If the concentration of B was to increase by x3 the rate of reaction would increase by x2^0 = x1 therefore no change.

If the concentration of C was to increase by x3 the rate of reaction would increase by x2^2 = x4

The below table shows the effect on increasing concentration on initial rate of reaction.

To prove the orders of reaction we can plot the rate of reaction against concentration and we will get one of the following shapes. The A-level course is only concerned about orders of 0, 1, and 2.

The Rate Determining step

The rate equation can be used to help determine a rate determining step. Most reactions do not occur in one step, as seen in organic chemistry, they can take part in multiple steps like below.

In the above two A must combined first in to produce an intermediate D and then react to produce the product C.

If the rate equation was k[A]^2 this would indicate that the first step is the rate determining step as it is the slowest step so the rate of any steps after it is not relevant.

If the second step was the rate determining step the rate equation would be k[A]^2[B]. The rate equation will include all of the steps up to and including the rate determining step.

For the above reaction steps we can see that the rate equation does not including Z, which is involved in the third step but it does contain Y which is in the second step so the second step is the rate determining step.

The Arrhenius Equation

The Arrhenius equation can be used to calculate the activation energy given rates at different temperatures. There is two forms of the equation you need to be able to use. One with he exponential function and one with the natural log function.

k is rate constant

A is pre-exponential (a constant]

e is exponential function

Ea is Activation energy in J/mol

R is gas constant

T is temperature in kelvin

ln is natural logarithm

The equation can be used graphically, the axis will be ln k and 1/T.

The graph will be a straight line so has the equation y=mx + c which can be compared to the second version of the Arrhenius equation.

When -Ea/RT is equal to zero, on the axis ln k = ln A

Once the graph of ln k to 1/T has been plotted comparing it to y=mx+c, x is 1/T and m which is the gradient is -Ea/R. By multiplying the gradient by -R we get the activation energy.