Consider this second-order reaction: (a b c and rate = k[a]2). what will happen to the reaction rate if the concentration of a is doubled?

The reaction rate will be multiplied by four.

Explanation:

The reaction rate is the measure of how fast a reaction is happening, and it can be calculated by how fast the reactants are disappearing, or how fast the products are being formed.

For a generic reaction:

A → B + C

The rate (r) is:

-r = k*[A]ⁿ

The minus signal refers to the disappearing of the reactant, k is the velocity constant of the reaction, and n is the reaction order. So, for a second-order reaction:

-r = k*[A]²

If the concentration of A is doubled: [A]' = 2[A]

-r' = k*(2[A])²

-r' = k*4*[A]

-r' = 4*k*[A]

-r' = 4*(-r)