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Ch.14 - Chemical Kinetics
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 35d
Chapter 14, Problem 35d

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?

Verified step by step guidance
1
Identify the rate law for the reaction. The rate law can be expressed as: Rate = k[BF3]^m[NH3]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to BF3 and NH3, respectively.
Use the experimental data to determine the reaction orders m and n. Compare experiments where only one concentration changes while the other remains constant to find the order with respect to each reactant.
For example, compare experiments 1 and 2 to find the order with respect to NH3. The concentration of BF3 is constant, so the change in rate is due to the change in NH3 concentration. Use the formula: (Rate1/Rate2) = ([NH3]1/[NH3]2)^n to solve for n.
Similarly, compare experiments 3 and 4 to find the order with respect to BF3. The concentration of NH3 is constant, so the change in rate is due to the change in BF3 concentration. Use the formula: (Rate3/Rate4) = ([BF3]3/[BF3]4)^m to solve for m.
Once the orders m and n are determined, use any experiment to solve for the rate constant k. Substitute the values of m, n, and the concentrations and rate from one experiment into the rate law equation to find k. Finally, use the rate law with the determined k, m, and n to calculate the rate for [BF3] = 0.100 M and [NH3] = 0.500 M.

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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 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, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders. Understanding the rate law is essential for predicting how changes in concentration affect the reaction rate.
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Rate Law Fundamentals

Reaction Order

Reaction order refers to the exponent in the rate law that indicates how the rate of reaction depends on the concentration of a particular reactant. It can be determined experimentally and can be zero, first, second, or even fractional. The overall order of the reaction is the sum of the individual orders, which helps in understanding the kinetics of the reaction.
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Method of Initial Rates

The method of initial rates involves measuring the initial rate of reaction at varying concentrations of reactants to deduce the rate law and reaction orders. By analyzing how the initial rate changes with different concentrations, one can derive the values of m and n in the rate law. This method is crucial for determining the kinetics of the reaction in question.
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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 

(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 

(c) Calculate the rate constant with proper units?

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.