A reaction was performed in which compounds A and B were combined to form compound C. The table below shows an analysis of the kinetics for the reaction with changing reagent concentration. Based on the kinetic data shown in the table, which overall reaction order and rate law best describe this reaction?

Question

A reaction was performed in which compounds A and B were combined to form compound C.  The table below shows an analysis of the kinetics for the reaction with changing reagent concentration.  Based on the kinetic data shown in the table, which overall reaction order and rate law best describe this reaction?

Quizplus · Accepted Answer

11ecba2d_11c3_7763_a3bf_1f2889db14f8_MD0008_00 The rate law of a reaction relates the rate of reaction to the concentration of each reactant. When two reactants are present, the rate law is expressed generally by the equation: Rate = k[A]^m[B]ⁿ where k is a constant, m and n are the order of the respective reactants, and (m + n) is the overall reaction order. To determine the actual rate law, the values of m and n must be found by comparing the given reactant concentrations and initial rates. Comparing Trial 2 to Trial 1, [A] is left unchanged but [B] is doubled relative to Trial 1, causing the reaction rate to double. Therefore, the rate has a first-order dependence upon [B], and n = 1. Similarly, when comparing Trial 3 to Trial 1, [A] is doubled but [B] is left unchanged, and the rate doubles; so, the reaction rate also has a first-order dependence upon [A], and m = 1. This result is further verified by comparing Trial 4 with Trial 1; doubling both [A] and [B] gives a rate four times greater than that seen for Trial 1. Therefore, the overall reaction rate must be a second-order expression (m + n = 2) involving variable terms for both [A] and [B]. (Choices A and B) These are rate laws that depend on only one chemical species but not the other (either m or n equals zero). However, the data show that the rate depends on both [A] and [B]. (Choice D) A fourth-order reaction (m + n = 4) is inconsistent with the second-order (m + n = 2) rate law expression given. In a fourth-order reaction (i.e., Rate = k[A][B]³, Rate = k[A]³[B], or Rate = k[A]²[B]²), kinetic data would show a four-fold or an eight-fold rate increase upon doubling the reagent with the higher order. Educational objective: Kinetic data can be used to determine rate laws and reaction orders. If doubling a reagent's concentration doubles the reaction rate, the reaction is first-order with respect to that reagent. If doubling the concentration quadruples the rate, the reaction is second-order with respect to the reagent, and so on. The overall order of a reaction is the sum of the reaction orders of each rate-influencing reagent.

A Reaction Was Performed in Which Compounds a and B