For the reaction x + 2 y → xy₂, if the reaction occurs in a single elementary step as proposed, what is the correct rate law?

• A. rate = k[xy₂]
• B. rate = k[x]^2[y]
• C. rate = k[x][y]^2
• D. rate = k[x][y]

Answer: (C)

Verified step by step guidance

1. Identify that the reaction is given as an elementary step: x + 2 y → xy₂. For elementary reactions, the rate law can be written directly from the molecularity of the reactants involved in that step.
2. Write the rate law as proportional to the concentration of each reactant raised to the power of its stoichiometric coefficient in the elementary step. Here, the reactants are x and y, with coefficients 1 and 2 respectively.
3. Express the rate law as: \(rate = k[\text{x}]^{1}[\text{y}]^{2}\), where \(k\) is the rate constant, \([\text{x}]\) is the concentration of species x, and \([\text{y}]\) is the concentration of species y.
4. Understand that this rate law reflects the molecularity of the elementary step, meaning the reaction rate depends on the collision frequency of one x molecule with two y molecules simultaneously.
5. Confirm that the rate law is not based on the product concentration or any other powers of reactants, but strictly on the stoichiometry of the elementary step reactants.