A Level Chemistry Revision: Physical Chemistry – Rate Equations

by Lucy Bell-Young

Determining the rate of chemical reactions can be done using rate equations, no matter what type of chemical reaction is taking place.

Rate equations are crucial diagnostic tools that are used to analyse the efficiency of chemical reactions. For example, rate equations can be used by chemical manufacturing companies who need their processes to be as efficient as possible so that they can maximise profits while minimising waste, time, and effort.

This goal can be achieved if the chemical reactions are optimised. While the rate of reactions may vary, it can be optimised based on the concentration of the reactants, the temperature and pressure, the intensity of agitation (e.g. stirring or shaking), and the presence of catalysts. 

What Are Chemical Reactions?

Chemical reactions are both destructive and creative processes: the bonds among the atoms of the reactants are destroyed in order to create new products. To chemically react, molecules must collide with one another and overcome certain energy barriers. Some types of reactions are faster than others.

Chemical reactions can be classified into five basic types of reaction:

  1. Combination Reactions

Also known as synthesis reactions, these happen when two or more reactants form a single product:

A + B → AB

Typically, reactions between elements are combination reactions, such as when sodium reacts with chlorine:

2Na (s) + Cl2 (g) → 2NaCl (s)

  1. Decomposition Reactions

These are the reverse of combination reactions. Put simply, a compound breaks down into its simpler constituent elements or simpler compounds under certain conditions. The simplest type is a binary compound that decomposes into its elements:

AB → A + B

A good example of this reaction is the decomposition of sodium hydroxide, under heat, into sodium oxide and water:

2NaOH (s) → NaO (s) + H2O (g)

  1. Single-Replacement Reactions

These are also known as single-displacement reactions, wherein one element displaces a similar element in a compound. If the element is metallic, it’s replaced by a metallic element with a higher reactivity:

A + BC → AC + B

An example of this type of reaction is the reaction between magnesium and an aqueous solution of copper (II) nitrate:

Mg (s) + Cu(NO3)2 (aq) → Mg(NO3)2 + Cu (s)

  1. Double-Replacement Reactions

These reactions only occur between ionic compounds. The positive and negative ions in two compounds exchange places to form new compounds:

AB + CD → AD + CB

  1. Combustion Reactions

Combustion reactions can be considered a special form of chemical reaction, which can be either a combination or replacement reaction. The main distinction is that it always involves oxygen. Combustion reactions produce energy in the form of light and heat. In other words, it’s the process of burning. It could also be explosive in nature, such as in the case of burning the gunpowder inside dynamite:

Substance + O2 → Oxide remains + Other byproducts

One of the simplest examples of combustion is the reaction between hydrogen and oxygen in the presence of a spark:

2H2 (g) + O2 (g) → 2H2O (g)

Most combustion reactions occur with hydrocarbons or organic compounds. One simple example of this is the combustion of propane. The complete combustion of hydrocarbons always produces water and carbon dioxide:

C3H8 (g) + 5O2 (g) → 3CO2 (g) + 4H2O (g)

Illustration of the five types of chemical reactions

What is the Generic Form of Rate Equation?

During a chemical reaction, the reactants are consumed as products are produced. More often than not, more than one product is produced. The rate or speed of chemical reactions is simply the speed by which the reactants are converted into products. This varies depending on several factors, like concentration or the type of reactants.

Rate equations are based on the balanced chemical equations of reactants and products. They also include the proportionalities of the chemical species involved. However, these rates are experimentally determined based on the available empirical data. They cannot easily be deduced from the chemical formulas of the reactants unless they have been previously tested.

Each of the five categories of chemical reactions has a comparable rate of reaction. In a combustion reaction, for instance, the rate of reaction can be very fast and explosive if it’s not properly controlled. Combustion reactions are almost always comparably faster than other types of chemical reactions.

The rate of reaction of each balanced chemical equation varies depending on the specific conditions and restrictions involved. However, comparable reactions can be analysed using the generalised formula for rate equations:

A generalised formula for rate equations

In this reaction, k is the constant. It’s not really an absolute constant, but based on specific conditions that are maintained at constant for a particular reaction analysis.

The rate constant of the reaction is directly proportional to the temperature, although the proper unit for k is not a unit of temperature, but instead involves mole, volume, and unit of time, usually in seconds. It varies depending on the derivation from the order of reaction. The value of k as directly proportional to temperature can be predicted by this equation:

k = AeEa/RT

A – the Arrhenius constant

Ea– the activation energy

T – the temperature in Kelvin

Meanwhile, the square brackets indicate the quantity of a particular chemical species inside the brackets. The exponents are the powers of the concentration, indicating how the rate is dependent on the individual reactant. It’s also known as the order of reaction.

How to Deduce the Order of Reaction Based on Data

While the order of reaction can also have decimal values, this is a rare occurrence. Typically, in exams, you’ll only encounter zero, first, and second orders of reaction:

  • Zero order means that a reactant’s concentration has no effect on the rate of reaction
  • A first order value means that the rate of reaction is directly proportional to the concentration of the reactant with the order value. So, if the concentration of that reactant is doubled, the reaction rate also doubles
  • A reactant with a second order reaction value has quadruple the effect on the rate of reaction if its concentration is doubled

It’s important to understand that the order of reaction and the k value are experimentally determined. You cannot simply look at a balanced chemical equation and deduce the values of k and the order of reaction for a particular chemical species. Therefore, in your exams, the data is always given so that you only need to compute the unknown.

Here is a sample problem with a solution on how to determine the order of reaction based on the given data. Although this is just a collection of mock data, it’s fairly useful to illustrate the process:

Sample problem on how to determine the order of reaction based on given data

Based on the table of data, it’s easy to deduce that reactant A is first order. This is because when the concentration of A is doubled while maintaining the concentrations of B and C, the rate of reaction also doubles.

By comparing experiments 1 and 3 in the table, we can conclude that reactant B is second order, because the rate of reaction quadruples as the concentration of reactant B is doubled.

We can also deduce that reactant C is zero order. By comparing experiments 1 and 4, you can clearly see that when the concentration of reactant C is doubled, while maintaining the concentrations of A and B the same as control, the rate of reaction did not change.

How Are the Values in Rate Equations Determined?

As we touched on earlier, the values in rate equations are experimentally determined. Various experimental methodologies can be used, requiring precise measurements of changes over time, such as the following:

  • Measuring the evolution of gases by volume through water displacement
  • Measuring the proportions of reactants and products, as shown in the generalised graph of a combination reaction that we’ve included below
  • Measuring the temperature change of the reaction until one of the reactants is fully consumed
  • Observing how long before colour change occurs after mixing the two reactants

A graph showing rate equations


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