Ch.14 - Chemical Kinetics

Problem 34

Chapter 14, Problem 34

The reaction 2 ClO2(aq) + 2 OH-(aq) → ClO3-(aq) + ClO2-(aq) + H2O(l) was studied with the following results: Experiment [ClO2] (M) [OH-] (M) Initial Rate (M/s) 1 0.060 0.030 0.0248 2 0.020 0.030 0.00276 3 0.020 0.090 0.00828. (c) Calculate the rate when [ClO2] = 0.100 M and [OH-] = 0.050 M.

Verified step by step guidance

Step 1: Write the rate law expression for the reaction. The general form of the rate law is Rate = k [ClO2]^m [OH-]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to ClO2 and OH-, respectively.

Step 2: Determine the order of the reaction with respect to ClO2 by comparing experiments 1 and 2. Notice that [OH-] is constant, so any change in rate is due to the change in [ClO2]. Calculate the ratio of rates and the ratio of concentrations to find the order m.

Step 3: Determine the order of the reaction with respect to OH- by comparing experiments 2 and 3. Notice that [ClO2] is constant, so any change in rate is due to the change in [OH-]. Calculate the ratio of rates and the ratio of concentrations to find the order n.

Step 4: Calculate the rate constant k using the rate law and the data from one of the experiments. Substitute the known values of rate, [ClO2], and [OH-] into the rate law and solve for k.

Step 5: Use the rate law with the determined values of k, m, and n to calculate the rate when [ClO2] = 0.100 M and [OH-] = 0.050 M. Substitute these concentrations into the rate law and solve for the rate.

Key Concepts

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

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as 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. Understanding the rate law is essential 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 can be determined experimentally and indicates how the rate is affected by the concentration of that reactant. For example, if a reaction is first order with respect to ClO2, doubling its concentration will double the reaction rate, highlighting the importance of determining the order for accurate rate predictions.

Initial Rate Method

The initial rate method involves measuring the rate of a reaction at the very beginning, before significant changes in concentration occur. By analyzing initial rates from different experiments, one can deduce the reaction order with respect to each reactant. This method is crucial for calculating the rate under new conditions, as seen in the question, where initial rates help establish the relationship needed to predict the rate at different concentrations.

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Rate Law Determination

Related Practice

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

(a) Write the rate law for this reaction.

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.

Textbook Question

The following data were measured for the reaction BF₃(g) + NH₃(g) → F₃BNH₃(g):

Experiment [BF₃] (M) [NH₃] (M) Initial Rate (M/s)

1 0.250 0.250 0.2130

2 0.250 0.125 0.1065

3 0.200 0.100 0.0682

4 0.350 0.100 0.1193

5 0.175 0.100 0.0596

(b) What is the overall order of the reaction?

Textbook Question

The following data were measured for the reaction BF₃(g) + NH₃(g) → F₃BNH₃(g):

Experiment [BF₃] (M) [NH₃] (M) Initial Rate (M/s)

1 0.250 0.250 0.2130

2 0.250 0.125 0.1065

3 0.200 0.100 0.0682

4 0.350 0.100 0.1193

5 0.175 0.100 0.0596

Textbook Question

The following data were measured for the reaction BF₃(g) + NH₃(g) → F₃BNH₃(g):

Experiment [BF₃] (M) [NH₃] (M) Initial Rate (M/s)

1 0.250 0.250 0.2130

2 0.250 0.125 0.1065

3 0.200 0.100 0.0682

4 0.350 0.100 0.1193

5 0.175 0.100 0.0596

(d) What is the rate when [BF₃] = 0.100 M and [NH₃] = 0.500 M?