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The data in Table 1 were collected for Reaction I:

2X + Y –> Z

Reaction I

What is the rate law for the reaction?

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Correct Answer: **C.** *Rate = k[X][Y]*^{2}

This is a common MCAT-type question. By looking at Table 1, we can see that when the concentration of X is quadrupled (factor of 4^{1}) while [Y] is unchanged (Exp. 1 and 3), the rate is increased by a factor of 4 = 4^{1}. Thus the order of the reaction with respect to X is 1 (= “first order with respect to X”).

When the concentration of Y is doubled (factor of 2^{1}) while [X] remains the same (Exp. 1 and 2), the rate of reaction is quadrupled (factor of 4 = 2^{2}). Thus, the order of reaction with respect to Y is 2 (= “second order with respect to Y”).

The rate equation is Rate = [X][Y]^{2}. Since the overall rate of reaction is the sum of exponents, we can say that the reaction is (1 + 2) a third order reaction overall.

{Notice that the stoichiometric coefficients are not relevant; the order of reaction being based on data.}

Additional learning point: In Organic Chemistry, an SN2 reaction is typical of a second order reaction where the rate must be equally proportional to the concentration of both reactants; for example, first order with respect to the alkyl halide and first order with respect to the nucleophile, so overall second order.

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