Textbook Question
Why don't all collisions between reactant molecules lead to a chemical reaction?
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Ch.14 - Chemical Kinetics
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement143
- Ch.2 - Atoms, Molecules & Ions134
- Ch.3 - Mass Relationships in Chemical Reactions149
- Ch.4 - Reactions in Aqueous Solution157
- Ch.5 - Periodicity & Electronic Structure of Atoms92
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory73
- Ch.7 - Covalent Bonding and Electron-Dot Structures47
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure51
- Ch.9 - Thermochemistry: Chemical Energy104
- Ch.10 - Gases: Their Properties & Behavior138
- Ch.11 - Liquids & Phase Changes43
- Ch.12 - Solids and Solid-State Materials56
- Ch.13 - Solutions & Their Properties98
- Ch.14 - Chemical Kinetics79
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Aqueous Equilibria: Acids & Bases94
- Ch.17 - Applications of Aqueous Equilibria125
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium66
- Ch.19 - Electrochemistry130
- Ch.20 - Nuclear Chemistry73
- Ch.21 - Transition Elements and Coordination Chemistry122
- Ch.22 - The Main Group Elements155
- Ch.23 - Organic and Biological Chemistry43
Chapter 14, Problem 87
Two reactions have the same activation energy, but their rates at the same temperature differ by a factor of 10. Explain.
Verified step by step guidance1
Understand that the rate of a chemical reaction is influenced by the activation energy and the frequency factor (A) in the Arrhenius equation: k = A * e^(-Ea/RT).
Recognize that since the activation energies (Ea) are the same for both reactions, the difference in reaction rates must be due to the frequency factor (A).
Recall that the frequency factor (A) represents the number of times that reactants approach the activation barrier per unit time, which is influenced by factors such as molecular orientation and collision frequency.
Conclude that the reaction with the higher rate constant (k) has a higher frequency factor (A), meaning that the reactants are more likely to collide in the correct orientation to overcome the activation energy barrier.
Therefore, even with the same activation energy, the difference in reaction rates by a factor of 10 is due to a difference in the frequency factors of the two reactions.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Activation Energy
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. Even if two reactions have the same activation energy, other factors can influence their rates, such as the frequency of collisions and the orientation of reactants during those collisions.
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Rate of Reaction
The rate of a reaction refers to how quickly reactants are converted into products. It is influenced by several factors, including concentration, temperature, and the presence of catalysts. In this case, even with the same activation energy, differences in the rate can arise from variations in these factors, particularly the frequency of effective collisions between reactant molecules.
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Arrhenius Equation
The Arrhenius equation describes the relationship between the rate constant of a reaction and temperature, incorporating activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. The pre-exponential factor can vary significantly between reactions, leading to differences in rates even when activation energies are identical.
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Related Practice
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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Textbook Question
Consider the following concentration–time data for the decomposition reaction AB → A + B.
(b) What is the molarity of AB after a reaction time of 192 min?
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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
Trans-cycloheptene 1C7H122, a strained cyclic hydrocarbon, converts to cis-cycloheptene at low temperatures. This molecular rearrangement is a second-order process with a rate constant of 0.030 M-1 s-1 at 60 °C. If the initial concentration of trans-cycloheptene is 0.035 M: (c) What is the half-life of trans-cycloheptene at an initial concentration of 0.075 M?
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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
(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?
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