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This is the more important effect from an A' level point of view. Suppose you have a reaction which happens in a series of small steps. These steps are likely to have widely different rates - some fast, some slow.
For example, suppose two reactants A and B react together in these two stages:
The overall rate of the reaction is going to be governed by how fast A splits up to make X and Y. This is described as the rate determining step of the reaction.
If you increase the concentration of A, you will increase the chances of this step happening for reasons we've looked at above.
If you increase the concentration of B, that will undoubtedly speed up the second step, but that makes hardly any difference to the overall rate. You can picture the second step as happening so fast already that as soon as any X is formed, it is immediately pounced on by B. That second reaction is already "waiting around" for the first one to happen.
Note: The overall rate of reaction isn't entirely independent of the concentration of B. If you lowered its concentration enough, you will eventually reduce the rate of the second reaction to the point where it is similar to the rate of the first. Both concentrations will matter if the concentration of B is low enough.
However, for ordinary concentrations, you can say that (to a good approximation) the overall rate of reaction is unaffected by the concentration of B.
The best specific examples of reactions of this type comes from organic chemistry. These involve the reaction between a tertiary halogenoalkane (alkyl halide) and a number of possible substances - including hydroxide ions. These are examples of nucleophilic substitution using a mechanism known as SN1.
Note: If you are interested in exploring nucleophilic substitution reactions further, you could follow this link.
Otherwise, you can find more about how the relationship between concentration and rate of reaction is affected by reaction mechanisms by exploring the topics at the bottom of the rates of reaction menu (link below).
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The catalytic decomposition of hydrogen peroxide | | | The key importance of activation energy |