# Collision Theory

by Yuqing
Tags: collision, theory
 P: 218 I was reading a derivation of the rate equation from collision theory and there is one thing which confuses me a bit. In the derivation we assume that a particle will collide with every particle within its "collision volume" but it seems to me that this is a gross overestimate of the actual number of collisions. My reasoning is that if the particle successfully reacts during the first collision, then it will have only made 1 collision, and similarly with successive collisions. So shouldn't we instead be using an expected number of collisions rather than just saying the particle will collides with everything it has access to. This problem is then emphasized because we next multiple the number of collisions by the number of particles which seems to just blow up the error further. Am I getting confused on something here?
 Other Sci Sci Advisor P: 1,317 Collision theory is predicting the initial rate of reaction before a significant amount of reactant has reacted. Obviously as the concentration of reactant decreases as it is depleted by the reaction, the rate of reaction will decrease.
 P: 218 I realize that, but the problem I'm describing appears to be different. Suppose a particle makes 1000 collisions per second and that 10% of these are "successful" collisions (i.e. reactive). In theory, a single particle can only make 1 successful collision since it'll have reacted and will be unable to perform additional reactions. But this theory seems to suggest that there will be 100 successful collisions, that is a single particle can produce 100 reactant molecules.
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