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Ch.14 - Chemical Kinetics
All textbooksMcMurry 8th EditionCh.14 - Chemical KineticsProblem 40a
Chapter 14, Problem 40a

The following reaction is first order in A (red spheres) and first order in B (blue spheres): A + B → Products Rate = k[A][B]
(a) What are the relative rates of this reaction in vessels (1)–(4)? Each vessel has the same volume.

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1
Identify the rate law for the reaction: Rate = k[A][B].
Understand that the reaction is first order in A and first order in B, meaning the rate depends linearly on the concentration of both A and B.
For each vessel, determine the concentration of A and B. Since the volume is the same for all vessels, you can count the number of red and blue spheres to find the concentrations.
Calculate the rate for each vessel using the rate law: Rate = k[A][B]. Since k is constant, the relative rates depend on the product of the concentrations of A and B.
Compare the calculated rates for each vessel to determine their relative rates.

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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 of a reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. For the given reaction, the rate law is Rate = k[A][B], indicating that the rate is directly proportional to the concentrations of both A and B. This means that if the concentration of either reactant changes, the rate of the reaction will change accordingly.
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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. In this case, the reaction is first order in both A and B, meaning that doubling the concentration of either reactant will double the rate of the reaction. Understanding the order helps predict how changes in concentration affect the reaction rate.
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Relative Rates

Relative rates compare the rates of reaction under different conditions, such as varying concentrations of reactants. By analyzing the concentrations of A and B in vessels (1)–(4), one can determine how the rate of reaction changes in each vessel. This concept is crucial for understanding how different setups influence the overall reaction speed.
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Related Practice
Textbook Question
To answer questions 13–15, refer to the mechanism: H2O21aq2 + I-1aq2¡OH-1aq2 + HOI1aq2 Slower, rate-determining HOI1aq2 + I-1aq2¡OH-1aq2 + I21aq2 Faster 2 OH-1aq2 + 2 H3O+1aq2¡4 H2O1l2 FasterIdentify the catalyst and intermediate(s) in the mechanism.(LO 14.12, 14.16)(a) Catalyst = I-, intermediates = OH-, HOI(b) Catalyst = H3O+, intermediate = HOI(c) No catalyst, intermediate = I2(d) No catalyst, intermediates = OH-, HOI
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Textbook Question
(b) Write the balanced reaction that corresponds to the data in the graph.

Textbook Question

The following reaction is first order in A (red spheres) and first order in B (blue spheres): A + B → Products Rate = k[A][B]

(b) What are the relative values of the rate constant k for vessels (1)–(4)?

Textbook Question
Consider the first-order decomposition of A molecules (red spheres) in three vessels of equal volume. (1)-(3)

(c) How will the rates and half-lives be affected if the volume of each vessel is decreased by a factor of 2?
Textbook Question

Consider the first-order decomposition of A molecules (red spheres) in three vessels of equal volume. (1)-(3)

(b) What are the relative half-lives of the reactions in vessels (1)–(3)?