Ch.14 - Chemical Kinetics

Problem 33b

Chapter 14, Problem 33b

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.

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Write down the rate law expression for the reaction based on the provided data. The rate law for a reaction can generally be expressed as Rate = k[A]^x[B]^y, where A and B are reactants, x and y are their respective orders, and k is the rate constant.

Use the given rate data to set up equations based on the rate law. For each set of concentrations and their corresponding rate, plug in the values into the rate law equation.

Solve the system of equations to find the values of x and y, which are the orders of the reaction with respect to OCl- and I-, respectively.

Once the orders of the reaction (x and y) are known, use any of the sets of data to solve for the rate constant k. Substitute the known values of concentrations, rate, x, and y into the rate law equation to solve for k.

Determine the units of the rate constant k based on the overall order of the reaction (sum of x and y). The units of k can be derived using the formula M^(1-n) s^-1, where n is the overall order of the reaction.

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Key Concepts

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

Rate of Reaction

The rate of reaction refers to the speed at which reactants are converted into products in a chemical reaction. It is typically expressed in terms of concentration change over time, such as molarity per second (M/s). Understanding how the concentration of reactants affects the rate is crucial for analyzing reaction kinetics and determining the rate law.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of its reactants, typically 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 each reactant. This concept is essential for determining how changes in concentration affect the reaction rate and for calculating the rate constant.

Units of the Rate Constant

The units of the rate constant (k) depend on the overall order of the reaction. For a first-order reaction, the units are s^-1, while for a second-order reaction, they are M^-1s^-1. Understanding how to derive the correct units for k based on the rate law is important for ensuring that calculations are accurate and meaningful in the context of the reaction.

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Rate Constant Units

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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. (b) What are the units 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

(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 (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?