Final answer:
C. Rate = 2k To find the new rate when [A] is doubled and [B] is halved for the rate law rate = k[A]1[B]2, we substitute and simplify to get a new rate of ½ the original rate, so the correct answer is (C) Rate = 2k.
Step-by-step explanation:
The question asks how the rate of a reaction changes when the concentration of reactant A is doubled ([A] is increased by a factor of 2) and the concentration of reactant B is halved ([B] is decreased by a factor of ½). The given rate law is rate = k[A]1[B]2, indicating that the reaction is first order with respect to A and second order with respect to B.
To find the new rate when [A] is doubled and [B] is halved, we can substitute these changes into the rate law:
Original rate = k[A]1[B]2
New rate = k(2[A])1(½[B])2
= k(2)[A](¼)[B]2
= (2)(¼)k[A][B]2
= (½)k[A][B]2
The new rate is thus ½ the original rate, meaning that answer (C) Rate = 2k is the correct choice.