Every chemical reaction can be associated with a rate law that describes mathematically the dependence of rate of reaction on the concentrations of the reactants. This is derived through exhaustive experiments involving concentration of various species with respect to time. The overall order of a reaction is the sum of exponents or powers to which the concentration terms are raised in the equation that expresses the rate law. Therefore, order of a reaction is also a purely experimental quantity and can not be written from the balanced chemical equation. That is the reason, order of a chemical reaction can not be determined without doing some sort of experiment.
There are several experimental methods to determine the order of a chemical reaction.
However, there are ways to determine the order if some experimentaly determined parameters like unit of the rate constant of the reaction, or half-life of the reactants, are supplied. For example, the units of rate constant (k) for a reaction of n-th order will be
`(mol * L^-1)^(1-n) * s^-1`