Rate of Reaction for Elementary Reactions
Intuitively, a reaction between A and B to give C will go twice as fast when you double the concentration of A (because collisions between A and B will occur twice as frequently). Similarly, doubling the concentration of B will also double the reaction rate. But what about the specific case where A and B are the same substance (A + A -> C)? When you double the concentration of A, the rate is quadrupled; when you triple the concentration of A, the rate goes up by a factor of 9, etc.