Textbook Question
What fraction of the molecules in a gas at 300 K collide with an energy equal to or greater than Ea when Ea equals 50 kJ/mol? What is the value of this fraction when Ea is 100 kJ/mol?
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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 92b
Consider three reactions with different values of Ea and ΔE:
Reaction 1. Ea = 20 kJ>mol; ΔE = -60 kJ/mol
Reaction 2. Ea = 10 kJ>mol; ΔE = -20 kJ/mol
Reaction 3. Ea = 40 kJ>mol; ΔE = +15 kJ/mol
(b) Assuming that all three reactions are carried out at the same temperature and that all three have the same frequency factor A, which reaction is the fastest and which is the slowest?
Verified step by step guidance1
Identify the given values for each reaction: Activation energy (E_a) and change in energy (ΔE).
Recall that the rate of a reaction is influenced by the activation energy (E_a) according to the Arrhenius equation: k = A * e^(-E_a/RT), where k is the rate constant, A is the frequency factor, R is the gas constant, and T is the temperature.
Understand that a lower activation energy (E_a) results in a higher rate constant (k), making the reaction faster, assuming the frequency factor (A) and temperature (T) are constant.
Compare the activation energies of the three reactions: Reaction 1 (E_a = 20 kJ/mol), Reaction 2 (E_a = 10 kJ/mol), and Reaction 3 (E_a = 40 kJ/mol).
Determine that Reaction 2, with the lowest activation energy (E_a = 10 kJ/mol), is the fastest, and Reaction 3, with the highest activation energy (E_a = 40 kJ/mol), is the slowest.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Activation Energy (E<sub>a</sub>)
Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to transform into products. A lower activation energy typically indicates that a reaction can proceed more quickly, as fewer energy collisions are needed to reach the transition state.
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02:02
Speed of Reactions
Change in Energy (ΔE)
The change in energy (ΔE) of a reaction indicates the difference in energy between the reactants and products. A negative ΔE signifies an exothermic reaction, where energy is released, while a positive ΔE indicates an endothermic reaction, where energy is absorbed. This energy change can influence the spontaneity and rate of the reaction.
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01:53Chemical Changes
Arrhenius Equation
The Arrhenius equation relates the rate constant of a reaction to its activation energy and temperature. It is expressed as k = A * e^(-E<sub>a</sub>/RT), where k is the rate constant, A is the frequency factor, R is the gas constant, and T is the temperature in Kelvin. This equation shows that a lower activation energy and higher temperature lead to a faster reaction rate.
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01:20Arrhenius Equation
Related Practice
Textbook Question
If the rate of a reaction increases by a factor of 2.5 when the temperature is raised from 20 °C to 30 °C, what is the value of the activation energy in kJ/mol? By what factor does the rate of this reaction increase when the temperature is raised from 120 °C to 130 °C?
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Textbook Question
Consider three reactions with different values of Ea and ΔE:
Reaction 1. Ea = 20 kJ>mol; ΔE = -60 kJ/mol
Reaction 2. Ea = 10 kJ>mol; ΔE = -20 kJ/mol
Reaction 3. Ea = 40 kJ>mol; ΔE = +15 kJ/mol
(c) Which reaction is the most endothermic, and which is the most exothermic?
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Textbook Question
A certain first-order reaction has a rate constant of 1.0 * 10-3 s-1 at 25 °C. (b) What is the Ea (in kJ/mol) if the same temperature change causes the rate to triple?
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Textbook Question
The values of Ea = 248 kJ>mol and ΔE = 41 kJ>mol have been measured for the reaction H21g2 + CO21g2S H2O1g2 + CO1g2 (b) Considering the geometry of the reactants and products, suggest a plausible structure for the transition state.
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Textbook Question
When the temperature of a gas is raised by 10 °C, the collision frequency increases by only about 2%, but the reaction rate increases by 100% (a factor of 2) or more. Explain.
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