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Ch.14 - Chemical Kinetics
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 37b
Chapter 14, Problem 37b

Consider the gas-phase reaction between nitric oxide and bromine at 273°C: 2 NO(g) + Br2(g) → 2 NOBr(g). The following data for the initial rate of appearance of NOBr were obtained:
Experiment [NO] (M) [Br2] (M) Initial Rate (M/s)
1 0.10 0.20 24
2 0.25 0.20 150
3 0.10 0.50 60
4 0.35 0.50 735 
(b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets.

Verified step by step guidance
1
Write the rate law expression for the reaction based on the stoichiometry given in the balanced chemical equation. For the reaction 2 NO(g) + Br2(g) → 2 NOBr(g), the rate law can be expressed as Rate = k[NO]^m[Br2]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to NO and Br2, respectively.
Use the given data from each experiment to set up an equation based on the rate law. For example, from Experiment 1, substitute the concentrations of NO and Br2 and the initial rate into the rate law equation: Rate = k[0.10]^m[0.20]^n = 24 M/s.
Solve the system of equations obtained from the data for each experiment to find the values of m and n. This typically involves taking logarithms of both sides of each equation and using linear algebra techniques to solve for the reaction orders m and n.
Once m and n are known, substitute these values back into the rate equations for each experiment to solve for k. For instance, using the values of m and n, calculate k from the equation for Experiment 1: k = 24 / (0.10^m * 0.20^n).
Calculate the average value of the rate constant k by averaging the k values obtained from each experiment. This gives a representative value of k for the reaction under the given conditions.

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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 as the change in concentration of a reactant or product per unit time. Understanding how to interpret and calculate reaction rates is essential for analyzing experimental data and determining the kinetics of a reaction.
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Average Rate of Reaction

Rate Law

The rate law is an equation that relates the rate of a 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. Determining the rate law from experimental data allows chemists to understand the relationship between concentration and reaction rate, which is crucial for calculating the rate constant.
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Rate Law Fundamentals

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that is specific to a given reaction at a specific temperature. It reflects the intrinsic speed of the reaction and is influenced by factors such as temperature and the presence of catalysts. Calculating the average value of the rate constant from multiple experiments provides insight into the overall kinetics of the reaction being studied.
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Related Practice
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 

(c) Calculate the rate constant with proper units?

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?

Textbook Question

Consider the reaction of peroxydisulfate ion (S2O82-) with iodide ion (I-) in aqueous solution:

S2O82-(aq) + 3 I-(aq) → 2 SO42-(aq) + I3-(aq)

 At a particular temperature, the initial rate of disappearance of S2O82- varies with reactant concentrations in the following manner:

Experiment [S2O82-] (M) [I-] (M) Initial Rate (M/s)

1 0.018 0.036 2.6 × 10-6

2 0.027 0.036 3.9 × 10-6

3 0.036 0.054 7.8 × 10-6

4 0.050 0.072 1.4 × 10-5

(a) Determine the rate law for the reaction and state the units of the rate constant.

Textbook Question

(a) For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

Textbook Question

(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?