The mathematical expression used for expressing the rates of chemical reaction is given below by taking two different set of chemical reactions.
    
Reactions involving same stoichiometric coefficients of all the reactants and products: let us consider the gaseous reaction between nitrogen dioxide and carbon monoxide.
                                        
NO₂(g) + CO(g)  CO₂(g) + NO(g)

In this case, as the reactants and products appear in same stoichiometric proportions, therefore, the rate of the reactions may be expressed in terms of rate of disappearance of nitrogen dioxide or carbon monoxide or alternatively, by the rate of appearance of carbon dioxide or nitric oxide whichever may be convenient.

Thus, the rate of reaction is given by:

Rate of reaction = [rate of disappearance of NO₂]

= [rate of disappearance of CO] = [rate of appearance of CO₂] = rate of appearance of CO] 
                               


Since, nitrogen dioxide is a deep raddish brown gas, the rate of this reaction can be followed more easily by measuring the change in the intensity of colour in the gaseous mixture in a given interval of time.

Now consider another reaction
                                           
Hg(l) + Cl₂(g)  HgCl₂(s)

How stoichiometric coefficients of the reactants and products are same and therefore rate of the reaction is given as



i.e. rate of disappearance of any of the reactants is same as the rate of appearance of the product.

2. Reactions involving different stoichiometric coefficients of reactants and products:

Consider another gaseous reaction between hydrogen and iodine to give hydro-iodic acid.
                                      
H₂(g) + I₂(g)  2HI(g)

The rate of this reaction can also be given in terms of rate of disappearance of one of the reactants H₂ or I₂ or in terms of the rate of formation of HI.

Now, in the present case, as the reactants (H₂ and I₂) and products (HI) have different stoichiometric coefficients, this means that for every mole of H₂ or I₂ reacting we get two moles of HI. Thus, the rate of formation of HI will be twice the rate of disappearance or H₂ or I₂, to get a unique value of the reaction rate irrespective of the species selected, we divide the rate of change of concentration by the stoichiometric coefficient of reactant or product involved in the reaction. Thus, we have



Similarly, for the reaction

5Br^-(aq) + BrO₃^- (aq) + 6H⁺(aq)  3 Br (aq) + 3H₂O(l)

Rate of reaction:



It is important to note here that for a gaseous reaction at constant temperature, concentration is directly proportional to the partial pressure of a species and hence, rate can also be expressed as rate of change in partial pressure of the reactant or the product.