In a first-order reaction, the rate of the reaction is directly proportional to the concentration of one of the reactants. This means that if the concentration of the reactant is doubled, the rate of the reaction will also double. Conversely, if the concentration is halved, the rate of the reaction will be halved as well. This relationship can be represented mathematically by the rate law equation:Rate = k[A]^1where Rate is the rate of the reaction, k is the rate constant, and [A] is the concentration of the reactant.Experimental evidence to support this relationship can be obtained by conducting a series of experiments in which the concentration of the reactant is varied while keeping other factors, such as temperature and pressure, constant. By measuring the rate of the reaction at different concentrations, a plot of the reaction rate versus the concentration of the reactant can be created. For a first-order reaction, this plot will show a linear relationship with a slope equal to the rate constant k .One classic example of a first-order reaction is the decomposition of N2O5:2 N2O5 4 NO2 + O2In a study conducted by R. L. Shriner and F. R. Smith Journal of the American Chemical Society, 1933, 55, 5104-5107 , the decomposition of N2O5 was investigated at various concentrations. They found that the rate of the reaction was directly proportional to the concentration of N2O5, confirming that it is a first-order reaction. The linear relationship between the rate of the reaction and the concentration of N2O5 provided strong experimental evidence for the first-order nature of this reaction.