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A zero order reaction means that any change in the concentration does not affect the rate. A first order reaction means that any change in the reactant concentration will lead to the same change in the rate (concentration doubles means rate will double)
Another way to tell the difference between zero and first is that for a zero order reaction, the plot of [Reactant] vs t is a straight line graph while for a first order reaction, the plot of ln[Reactant] vs t is a straight line graph.
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