Consider the case of a generic chemical reaction:
$$a\ A + b\ B\ \rightleftharpoons\ c\ C + d\ D$$
Of all the variables that affect the reaction rate, the most emphasis is usually placed on the concentrations of the substances that take part in the reaction. If variable such as temperature, pressure, and others are held constant, then it can be determined experimentally that the rate of a reaction is a simple function of those concentrations. Experimentally, it can be verified that, in most cases, the speed is directly proportional to the product of certain integer powers of the concentrations:
$$v = k\ \cdot\ [A]^{\alpha}\ \cdot\ [B]^{\beta}\ \cdot\ [C]^{\gamma}\ \cdot\ ...$$
where $\alpha$, $\beta$, $\gamma$, ... are constants (usually integers) and $k$ is a constant of proportionality that we will call the specific rate constant . The exponents of the concentrations of each species that appear in this equation are called the order of reaction with respect to the given species. In other words, according to the expression we have written, the reaction is of order $\alpha$ with respect to the species $A$, of order $\beta$ with respect to $B$, and so on. The total order of the reaction is the sum of the orders with respect to each of the species that appear in the rate equation, that is, the total order of the reaction will be $\alpha + \beta + \gamma + .. .$
But things are not always that simple... The species that appear in the experimental reaction rate equation do not have to be reactants or products of the reaction. A reaction rate can be a function of the concentration of any substance present in the medium, whether it is a reactant, a product or substances that do not appear in the stoichiometry of the reaction (it can be an intermediate product, a catalyst, . .. etc.). Negative reaction orders are also possible, that is, that the concentration of some species appears dividing in the equation, and there are also reaction rate equations much more complicated than the equation written above, with two or more terms on the right side of The equation.