Mechanism
A2 = 2A fast
A + B --> AB slow
Rate = k[A2][B]
Rate = k[A2][B]1/2
Rate = k [A2]1/2[B]
Rate = k[A2]
Rate = k[A][B]
2A +B will become A2B,
but the reaction rate will be limited by the slowest step, here 2A becoming A2.
rate= k[A]^2
hope it helps
