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?
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Ch.14 - Chemical Kinetics
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement170
- Ch.2 - Atoms, Molecules & Ions160
- Ch.3 - Mass Relationships in Chemical Reactions169
- Ch.4 - Reactions in Aqueous Solution199
- Ch.5 - Periodicity & Electronic Structure of Atoms102
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory92
- Ch.7 - Covalent Bonding and Electron-Dot Structures61
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure59
- Ch.9 - Thermochemistry: Chemical Energy122
- Ch.10 - Gases: Their Properties & Behavior155
- Ch.11 - Liquids & Phase Changes54
- Ch.12 - Solids and Solid-State Materials73
- Ch.13 - Solutions & Their Properties120
- Ch.14 - Chemical Kinetics98
- Ch.15 - Chemical Equilibrium125
- Ch.16 - Aqueous Equilibria: Acids & Bases110
- Ch.17 - Applications of Aqueous Equilibria147
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium86
- Ch.19 - Electrochemistry154
- Ch.20 - Nuclear Chemistry96
- Ch.21 - Transition Elements and Coordination Chemistry156
- Ch.22 - The Main Group Elements187
- Ch.23 - Organic and Biological Chemistry51
Chapter 14, Problem 42
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.
Verified step by step guidance1
Step 1: Observe the initial state at t = 0 s where all molecules are A (gray spheres).
Step 2: Observe the state at t = 30 s where some A molecules have been converted to B molecules (red spheres).
Step 3: Determine the number of A and B molecules at t = 30 s. Count the gray and red spheres.
Step 4: Use the observed conversion rate from t = 0 s to t = 30 s to predict the number of A and B molecules at t = 60 s (1 min).
Step 5: Continue using the same conversion rate to predict the number of A and B molecules at t = 90 s (1.5 min) and t = 120 s (2 min).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
First-Order Reaction
A first-order reaction is a type of chemical reaction where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of reactant A decreases, the rate at which it converts to product B also decreases. The rate law for a first-order reaction can be expressed as rate = k[A], where k is the rate constant.
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02:29
First-Order Reactions
Reaction Progress Over Time
In a first-order reaction, the conversion of reactants to products occurs over time, and the concentration of reactants decreases while the concentration of products increases. The graphical representation of this process typically shows an exponential decay for reactants and an exponential growth for products. Understanding this progression is crucial for predicting the amounts of A and B at any given time.
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02:16Electrochemical Stoichiometric Chart (Time)
Stoichiometry
Stoichiometry involves the calculation of reactants and products in chemical reactions based on their molar ratios. In this context, it helps determine how many molecules of A are converted to B over time. For a first-order reaction, knowing the initial concentration of A allows for the calculation of remaining A and formed B at any time, which is essential for drawing the required pictures.
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01:16Stoichiometry Concept
Related Practice
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)?
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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)?
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Textbook Question
The following pictures represent the progress of a reaction in which two A molecules combine to give a more complex molecule A2, 2 AS A2. (b) What is the rate law?
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Textbook Question
The following pictures represent the progress of the reaction AS B in which A molecules (red spheres) are converted to B molecules (blue spheres).
(c) Suppose that each sphere represents 6.0⨉1021 molecules and that the volume of the container is 1.0 L. What is the rate constant for the reaction in the usual units?
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Textbook Question
The following pictures represent the progress of the reaction AS B in which A molecules (red spheres) are converted to B molecules (blue spheres).
(b) Draw a picture that shows the number of A and B molecules present at t = 3 min.
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