So to find a rate equation, given the order of the reactants, we must know that the order with respect to each reactant is the exponent in the rate equation.
That being said, we are told that the reaction is first-order with respect to [X], and the reaction is second-order with respect to [Y]. So we are going to put a 1 as the exponent to [X] and a 2 as the exponent to [Y]:
\(R=k [X]^{1} [Y]^{2}\)
But since anything to the first power is itself, we can omit the exponent of 1 on the [X] reactant:
\(R=k[X] [Y]^{2}\)
So now we know that the answer is C) rate = k[X][Y]2.
