Reaction rate graphs

By drawing a suitable graph we can determine the order of reaction for a particular reactant in a chemical reaction. This is a popular task set in exams. However, you must be careful to check on the axes for the graph you are using. Different axes will lead to different shapes.

 In a zero order reaction the reactant has no effect on the rate of reaction. This means that as the concentration changes, the rate stays the same. A graph of rate of reaction against concentration is therefore a straight, horizontal line (constant reaction rate). This is shown in the top graph. Given that the gradient of a concentration-time graph represents the rate of reaction, this gradient must be constant for a zero order graph. So a concentration-time graph for a zero order graph is a straight line with a negative gradient (the reactant is being used up as the reaction proceeds).
 In a first order reaction the reaction rate is proportional to the concentration of the reactant. So a graph of rate of reaction against concentration is a straight line with a positive gradient (a graph showing proportionality). A first order concentration-time graph has a constant half-life. This means that the time it takes for the concentration to fall to half its original value remains constant. It is best to take two consecutive half-lives, for example from 2 M to 1 M then from 1 M to 0.5 M. Bear in mind that with real data it is unlikely that the two half-lives will be identical, but they should be similar.
 In a second order reaction the reaction rate is proportional to the square of the concentration of the reactant. So a graph of rate of reaction against concentration is of the type y = x2. A second order concentration-time graph has an increasing half-life. The half life will clearly increase. If you measure two consecutive half-lives and they turn out to be 40 s and 42 s, this is almost certainly a first order relationship with a little experimental error.

An alternative graph uses log10 [rate] (this will be log10 [1/time] for an initial rate method) against log10 [concentration]. This should give a straight line whose gradient is the order of the reaction.

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