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

Consider the gas-phase reaction between nitric oxide and bromine at 273 _x001E_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 (c) How is the rate of appearance of NOBr related to the rate of disappearance of Br2? (d) What is the rate of disappearance of Br2 when [NO] = 0.075 M and [Br2] = 0.25 M?

Verified step by step guidance
1
Step 1: Understand the stoichiometry of the reaction. The balanced chemical equation is 2 NO(g) + Br2(g) → 2 NOBr(g). This indicates that for every 2 moles of NO consumed, 1 mole of Br2 is consumed, and 2 moles of NOBr are produced.
Step 2: Relate the rate of appearance of NOBr to the rate of disappearance of Br2 using stoichiometry. Since 2 moles of NOBr are produced for every 1 mole of Br2 consumed, the rate of appearance of NOBr is twice the rate of disappearance of Br2. Mathematically, this can be expressed as: -d[Br2]/dtd[NOBr2]/dt=1/2
Step 3: Use the rate law to determine the rate of disappearance of Br2. The rate law for the reaction can be expressed as: Rate=k[NO]^x[Br2]^y, where k is the rate constant, and x and y are the orders of the reaction with respect to NO and Br2, respectively.
Step 4: Determine the reaction orders (x and y) using the experimental data. Compare experiments where one concentration is held constant while the other changes to find the order with respect to each reactant. For example, comparing experiments 1 and 2, where [Br2] is constant, can help determine the order with respect to NO.
Step 5: Calculate the rate of disappearance of Br2 using the determined rate law and the given concentrations [NO] = 0.075 M and [Br2] = 0.25 M. Substitute these values into the rate law equation to find the rate of disappearance of Br2.

Key Concepts

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

Rate of Reaction

The rate of a chemical reaction is a measure of how quickly reactants are converted into products. It can be expressed in terms of the change in concentration of a reactant or product over time. In this case, the rate of appearance of NOBr and the rate of disappearance of Br2 are related through the stoichiometry of the balanced equation, which indicates how the concentrations of reactants and products change relative to one another.
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Stoichiometry

Stoichiometry refers to the quantitative relationship between the amounts of reactants and products in a chemical reaction, as dictated by the balanced chemical equation. For the reaction 2 NO(g) + Br2(g) → 2 NOBr(g), the coefficients indicate that for every 1 mole of Br2 that reacts, 2 moles of NOBr are produced. This relationship is crucial for determining how changes in the concentration of one species affect the others.
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Rate Law

The rate law expresses the relationship between the rate of a reaction and the concentration of its reactants. It is typically formulated 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 each reactant. Understanding the rate law allows us to predict how changes in concentration will affect the rate of reaction, which is essential for calculating the rate of disappearance of Br2 in this scenario.
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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 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.

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.