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The process is obviously more involved than it sounds, but here's the basic process. When particles of the reactant collide with enough force and at the right orientation, the reactant bonds briefly break. For a split second they're in a state known as the activated complex. Then the bonds reform between different particles that once formed the reactants. New bonds are formed, and you've got the product, usually with a change of energy in the form of heat as well.

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