In the reaction a + b c, doubling the concentration of a doubles the reaction rate and doubling the concentration of b does not affect the reaction rate. what is the rate law for this reaction?

The rate law for the reaction wherein you double the concentration of A doubles the reaction rate and doubling the concentration of B does not affect the reaction rate would be rate = k[A]2. This is because if 2 is multiplied by the concentration, the rate also doubles.

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What are the choices?

For a collision to be successful you need 2 different objects