Textbook Question
(b) Write the balanced reaction that corresponds to the data in the graph.
Ch.14 - Chemical Kinetics
Chapter 14, Problem 40b
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)?
Verified step by step guidance1
Identify the reaction order: The reaction is first order in A and first order in B, which means the overall reaction order is 2.
Understand the rate law: The rate law for this reaction is given by Rate = k[A][B], where k is the rate constant, and [A] and [B] are the concentrations of reactants A and B, respectively.
Compare the concentrations: To determine the relative values of the rate constant k for different vessels, compare the concentrations of A and B in each vessel.
Analyze the rate: Since the rate is directly proportional to the product of the concentrations of A and B, the vessel with higher concentrations of A and B will have a higher rate, assuming k is constant.
Conclude the relative values: If the concentrations of A and B are the same across vessels, then the rate constant k is the same. If they differ, the vessel with higher concentrations will have a higher rate, but k remains constant as it is a characteristic of the reaction at a given temperature.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 the rate of reaction is directly proportional to the concentration of each reactant. This implies that if the concentration of either A or B is doubled, the reaction rate will also double.
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Average Bond Order
Rate Constant (k)
The rate constant, denoted as k, is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. It is specific to a given reaction at a particular temperature and is influenced by factors such as temperature and the presence of catalysts. The value of k can vary between different vessels depending on conditions like temperature and pressure.
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Concentration and Reaction Rate
The concentration of reactants plays a crucial role in determining the rate of a chemical reaction. For a reaction that is first order in both A and B, the rate is affected by the product of their concentrations. This means that the relative values of k in different vessels can be compared by analyzing how the concentrations of A and B differ in those vessels, impacting the overall reaction rate.
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Related Practice
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]
(a) What are the relative rates of this reaction in vessels (1)–(4)? Each vessel has the same volume.
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)?
Textbook Question
Consider the first-order reaction AS B in which A molecules(red spheres) are converted to B molecules (blue spheres).(a) Given the pictures at t = 0 min and t = 1 min, drawpictures that show the number of A and B moleculespresent at t = 2 min and t = 3 min.