Ch.14 - Chemical Kinetics

Problem 33a

Chapter 14, Problem 33a

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl^- + I^- → OI^- + Cl^- . This rapid reaction gives the following rate data:
[OCl₄^-] (M) [I^-] (M) Initial Rate (M,s)
1.5 * 10-3 1.5 * 10-3
1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4
(a) Write the rate law for this reaction.

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Identify the general form of the rate law: \( \text{Rate} = k [\text{OCl}^-]^m [\text{I}^-]^n \), where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to OCl\(^-\) and I\(^-\), respectively.

Use the given data to determine the reaction orders \( m \) and \( n \). Compare experiments where only one concentration changes to isolate the effect of each reactant.

For example, compare the first and second experiments to determine \( m \) by keeping \([\text{I}^-]\) constant and changing \([\text{OCl}^-]\).

Similarly, compare the first and third experiments to determine \( n \) by keeping \([\text{OCl}^-]\) constant and changing \([\text{I}^-]\).

Once \( m \) and \( n \) are determined, write the rate law using these values.

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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, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders with respect to each reactant. Understanding the rate law is essential for predicting how changes in concentration affect the reaction rate.

Reaction Order

Reaction order 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 of a reaction is the sum of the individual orders, and it can be determined experimentally by analyzing how the rate changes with varying concentrations of reactants.

Method of Initial Rates

The method of initial rates involves measuring the initial rate of a reaction at different concentrations of reactants to deduce the rate law. By comparing how the rate changes with varying concentrations, one can determine the reaction orders for each reactant. This method is particularly useful for complex reactions where direct observation of the rate law is not feasible.

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Rate Law Determination

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Textbook Question

The reaction between ethyl bromide (C₂H₅Br) and hydroxide ion in ethyl alcohol at 330 K, C₂H₅Br(alc) + OH^-(alc) → C₂H₅OH(l) + Br^-(alc), is first order each in ethyl bromide and hydroxide ion. When [C₂H₅Br] is 0.0477 M and [OH^-] is 0.100 M, the rate of disappearance of ethyl bromide is 1.7×10^-7 M/s. (a) What is the value of the rate constant?

Textbook Question

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Textbook Question

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl - + I - ¡OI - + Cl - . This rapid reaction gives the following rate data:

[OCl₄^-] (M) [I^-] (M) Initial Rate (M,s)

1.5 * 10-3 1.5 * 10-3

1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4

1.5 * 10-3 3.0 * 10-3 2.72 * 10-4

(b) Calculate the rate constant with proper units.

Textbook Question

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl^- + I^- → OI^- + Cl^- . This rapid reaction gives the following rate data:

[OCl₄^-] (M) [I^-] (M) Initial Rate (M,s)

1.5 * 10-3 1.5 * 10-3

1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4

1.5 * 10-3 3.0 * 10-3 2.72 * 10-4 (c) Calculate the rate when [OCl^-] = 2.0 * 10-3 M and [I^-] = 5.0 * 10 - 4 M.