Textbook Question
The relative rates of the reaction A + B S AB in vessels(1)–(3) are 4:4:1. Red spheres represent A molecules, andblue spheres represent B molecules.(1)-(3) (a) What is the order of the reaction in A and B?
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 43c
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?
Verified step by step guidance1
Determine the initial concentration of A molecules by counting the number of red spheres in the initial picture and multiplying by 6.0\(\times\)10^{21} to find the number of molecules. Divide by Avogadro's number to convert to moles, and then divide by the volume (1.0 L) to find the concentration in mol/L.
Determine the concentration of B molecules at a later time by counting the number of blue spheres in the later picture, multiplying by 6.0\(\times\)10^{21}, converting to moles, and dividing by the volume (1.0 L) to find the concentration in mol/L.
Use the change in concentration of A or B over time to calculate the rate of the reaction. The rate can be expressed as \(-\frac{\Delta [A]}{\Delta t}\) or \(\frac{\Delta [B]}{\Delta t}\), where \([A]\) and \([B]\) are the concentrations of A and B, respectively, and \(\Delta t\) is the time interval.
Assume a reaction order (e.g., first-order or second-order) based on the context or additional information provided. For a first-order reaction, the rate law is \(\text{Rate} = k[A]\), and for a second-order reaction, it is \(\text{Rate} = k[A]^2\).
Solve for the rate constant \(k\) using the rate law equation and the calculated rate and concentration values. Ensure the units of \(k\) are consistent with the assumed reaction order.
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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 is typically expressed in terms of concentration change over time, such as moles per liter per second (mol/L/s). Understanding the rate of reaction is crucial for determining how fast the conversion of A to B occurs in the given scenario.
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Average Rate of Reaction
Rate Constant (k)
The rate constant (k) is a proportionality factor in the rate law equation that relates the rate of a reaction to the concentration of reactants. It is specific to a particular reaction at a given temperature and has units that depend on the overall order of the reaction. For a first-order reaction, the units are typically s⁻¹, while for a second-order reaction, they are L/(mol·s).
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Concentration and Molarity
Concentration refers to the amount of a substance in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution. In this question, knowing that each sphere represents a specific number of molecules allows us to calculate the concentration of A and B in the 1.0 L container, which is essential for determining the rate constant.
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Related Practice
Textbook Question
What is the molecularity of each of the following elementary reactions?(a) (b) (c)
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
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?
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.
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.