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The zero order reaction means that the rate of the reaction does not depend upon the concentration of the reactant. When the rate of the reaction depends on the first power of the reactant concentration in the rate equation, then the reaction is said to follow first order. When the rate of the reaction depends on the second power of the concentration term in the rate equation, then the reaction is called as the second order reaction. If there are two reactants in the rate equation and if the rate of reaction depends on the first power of the two reactants, then also it is called as the second order reaction.
To add to this, if we are strictly given time series graphs we can also describe their order based on the plot. For example, if there is a straight line plot for the graph of concentration vs time, it is a zero order reaction. A straight line plot for natural log concentration vs time means a 1st order reaction. Finally, a second order reaction is described by a straight line plot for a 1/concentration versus time graph.
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