Determining a Rate Law by the Method of Initial Rates
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Determining a rate law by the method of initial rates means comparing trials in which one reactant's concentration changes while the others are held constant, using the ratio of rates and the ratio of concentrations to solve for each reaction order, then substituting one full trial back in to solve for the rate constant.
For NO + O3, when [O3] doubles with [NO] held constant, the rate doubles, so the order in O3 is one; when [NO] doubles with [O3] held constant, the rate also doubles, so the order in NO is one. Substituting one trial's concentrations and measured rate into rate = k[NO][O3] then isolates the numerical value of k.
Comparing two trials in which more than one concentration changes at once makes the resulting order impossible to isolate — only a pair differing in exactly one reactant's concentration determines that reactant's order.