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First order means that the concentration of a single reactant is raised to the first power. For a second order reaction, the concentration of 2 reactants is raised to the first power or the concentration of a single reactant is raised to the second power. The order of a reaction is determined by the sum of the powers of the concentrations of reactants in the rate law equation.
If you have a graph, you can differentiate based on what graph shows a straight line (ln [A] vs ). If you have the rate laws or chemical equations, you can determine which order the reactions are based on the numbers and ratios of the reactants.
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