Final answer:
The rate law for the elementary reaction 2A(g) + B(g) → C(g) + D(g) is rate = k[A]^2[B], which indicates that the reaction is second order with respect to A and first order with respect to B.
Step-by-step explanation:
To write the rate law for the given elementary reaction, 2A(g) + B(g) → C(g) + D(g), we need to know the molecularity of the reaction. In the given elementary reaction, two molecules of A and one molecule of B are colliding. Therefore, the rate law is determined directly from the stoichiometry of the reactants in the elementary step. As the molecularity suggests bimolecular for A and unimolecular for B, the rate law is given by:
Rate = k[A]^2[B]
This means the reaction is second order with respect to A, because two A molecules are involved, and first order with respect to B, making it third order overall.