Ch.14 - Chemical Kinetics

Problem 125

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Chapter 14, Problem 125

Concentration–time data for the conversion of A and B to D are listed in the following table. (c) What is the rate law?

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Identify the rate law expression: Rate = k[X]^m[Y]^n[Z]^p[A]^q.

Compare experiments where only one reactant concentration changes while others remain constant to determine the order with respect to each reactant.

For example, compare Experiment 1 and Experiment 2 to determine the order with respect to [X].

Compare Experiment 1 and Experiment 3 to determine the order with respect to [A].

Compare Experiment 1 and Experiment 4 to determine the order with respect to [Y].

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of its reactants. It is typically expressed in the form rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B, respectively. Understanding the rate law is crucial for predicting how changes in concentration affect the reaction rate.

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by the concentration of that reactant. The overall order is the sum of the individual orders, and it helps in determining the relationship between concentration and reaction rate, which is essential for analyzing experimental data.

Integrated Rate Laws

Integrated rate laws provide a mathematical relationship between the concentration of reactants and time. They are derived from the differential rate laws and can be used to determine the concentration of reactants at any given time. Understanding integrated rate laws is important for interpreting concentration-time data, such as that presented in the table, to deduce the rate law and reaction order.

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Rate Law Fundamentals

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Related Practice

Textbook Question

Consider the reaction H₂(g) + I₂(g) → 2 HI(g). The reaction of a fixed amount of H₂ and I₂ is studied in a cylinder fitted with a movable piston. Indicate the effect of each of the following changes on the rate of the reaction. (a) An increase in temperature at constant volume

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl^-). The products are chloride ion and hypoiodite ion (OI^-).

(a) Write a balanced equation for the reaction.

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Textbook Question

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl^-). The products are chloride ion and hypoiodite ion (OI^-).

(b) Determine the rate law, and calculate the value of the rate constant.

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Textbook Question

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl^-). The products are chloride ion and hypoiodite ion (OI^-).

(d) Propose a mechanism that is consistent with the rate law, and express the rate constant in terms of the rate constants for the elementary steps in your mechanism. (Hint: Transfer of an H⁺ ion between H₂O and OCl^- is a rapid reversible reaction.)

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