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As mentioned above, the order is the power to which the concentration of the reactant or product is raised in the rate law. The overall order of the reaction also helps you know what the time versus concentration graph is going to look like for that reaction, which I think we are going to cover more extensively in upcoming lectures.
To add on, the order also reveals something about the rate of reaction. For example, a first-order reaction is one in which the rate of it is directly proportional to the concentration of the reactant concentration. A second-order reaction's rate is proportional to the second power of the concentration.
The textbook briefly talks about fractional order reactions (page 621). I believe that if the fractional order is in the denominator, it means that the reaction slows down as the concentration of it increases. On the other hand, if the fractional order is in the numerator, the reaction rate increases as the concentration increases.
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