We know that the rate of a reaction is dependent on the kinetic energy of the colliding particles and whether those particles have sufficient energy to react. Other factors will be the orientation of those colliding particles and the actual mechanism for the chemical reaction.

These factors are linked together in an equation known as the Arrhenius expression.

It looks like this:

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 The Arrhenius expression can be tricky for students to grasp. This is because there seems to a be a lot of manipulation of numbers and coefficients before it can be used to get information.

At its simplest level it is a way of linking all the factors which will affect the rate of a reaction in one mathematical expression. By taking natural logarithms of the equation it can take the form

ln k= ln A - E_A/RT

Typically we rearrange the equation to make it fit the general expression for the equation of a straight line, 

 y = mx + c

like this

ln k=( - E_A/R x 1/T) + ln A  

We can now do something with it by plotting graphs and determining the activation energy or the temperature.

k gives us an indication of the rate of reaction. However, it is worth noting that because of the way that the rate constant depends on concentration then if the concentration of the reactants is 1 mol dm^-3 then the rate constant, k,is same as the rate. The reasoning is fully explored in another section.

At its simplest level, the Arrhenius expression links the temperature of the reactants to the rate of reaction whilst taking account of the activation energy (E_A).

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The expression also helps us understand why the shaded portion of Maxwell-Boltzmann graph which we saw earlier and which shows the proportion of reacting particles increases so significantly when the temperature is changed.