Final answer:
The rate law for the reaction given is rate = K[X][Y]^2, where the rate is proportional to the concentration of X and proportional to the square of the concentration of Y.
Step-by-step explanation:
The rate law for a reaction that is first order with respect to reactant X and second order with respect to reactant Y would be expressed as rate = K[X][Y]^2. This is because the rate is directly proportional to the concentration of reactant X and proportional to the square of the concentration of reactant Y. The rate law can only be determined experimentally, and it reflects how changes in reactant concentrations affect the reaction rate.
This means that the reaction rate is directly proportional to the concentrations of both reactant X and reactant Y, raised to the power of their respective orders.