Final answer:
The rate law for the reaction X + 2Y → XY₂ cannot be conclusively determined without experimental data or insights into the reaction mechanism. However, based on the stoichiometry and assuming Y participates in a bimolecular step, options D or E could reflect the rate dependence on both X and Y.
Step-by-step explanation:
The question is asking to determine the rate law for the reaction X + 2Y → XY₂ based on the proposed mechanism. To establish the rate law, one needs to understand the concept of reaction order and how it relates to the concentration of the reactants in the mechanism of the reaction. In the example reaction of A + B → C, where both A and B affect the rate of reaction, the rate law based on experimental findings will be rate = k[A][B]. In the case of the question's reaction, since X and Y are not identical and it's not specified how the concentrations of X and Y affect the reaction rate, we can't be certain of the exact rate law without experimental data.
However, given the stoichiometry of the reaction, it's likely that Y is involved in an elementary bimolecular step since it appears to collide with something twice. If Y reacts with itself, then its concentration would be squared in the rate law. If Y reacts with X in a single elementary step, the rate law might reflect a dependence on both [X] and [Y], possibly leading to a rate law similar to rate = k[X][Y] or rate = k[X][Y]². Without more information, we can't conclusively determine the rate law, but option D, rate = k[X][Y], and E, rate = k[X][Y]², would reflect a bimolecular relationship with respect to Y, consistent with the given stoichiometry in the reaction.