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Intro to Chemistry
Table of Contents
Unit 12 Overview: Kinetics
12.1 Chemical Reaction Rates
12.2 Factors Affecting Reaction Rates
12.3 Rate Laws
12.4 Integrated Rate Laws
12.5 Collision Theory
12.6 Reaction Mechanisms
12.7 Catalysis

Chemical reactions are all about collisions between particles. Collision theory explains how factors like temperature and concentration affect reaction rates. Understanding these concepts helps predict and control how fast reactions occur.

The key players are activation energy and the transition state. These represent the energy barrier particles must overcome to react. The Arrhenius equation ties it all together, showing how temperature impacts reaction rates exponentially.

Collision Theory and Reaction Rates

Collision theory and reaction rates

  • Collision theory states reactions occur when reactant particles collide with sufficient energy and proper orientation
    • Higher frequency of collisions with enough energy leads to faster reaction rates (doubling collision frequency doubles rate)
    • Effective collisions are those that result in a chemical reaction
  • Physical state affects collision frequency and reaction rates
    • Gases have highest collision frequency due to high molecular motion and large intermolecular distances
    • Liquids have lower collision frequency than gases due to closer intermolecular distances and less molecular motion
    • Solids have lowest collision frequency and slowest reaction rates due to fixed positions of particles and minimal molecular motion
  • Temperature influences average kinetic energy of particles and reaction rates
    • Higher temperatures increase average kinetic energy of particles
      • Particles move faster and collide more frequently (doubling temperature in Kelvin doubles collision frequency)
      • Larger fraction of collisions have sufficient energy to overcome activation energy barrier
    • Increasing temperature typically leads to faster reaction rates (rule of thumb: 10℃ rise doubles rate)
    • The Maxwell-Boltzmann distribution describes the distribution of molecular speeds at a given temperature
  • Concentration affects number of particles per unit volume and reaction rates
    • Higher concentrations of reactants increase probability of collisions
      • More particles per unit volume result in more frequent collisions (doubling concentration doubles collision frequency)
    • Increasing reactant concentrations generally leads to faster reaction rates

Activation energy and transition state

  • Activation energy ($E_a$) is minimum energy required for reactants to collide and form products
    • Represents energy barrier that must be overcome for reaction to occur
    • Reactant particles must possess kinetic energy ≥ $E_a$ for successful collision
  • Transition state is highest-energy intermediate formed during chemical reaction
    • Represents unstable configuration of atoms at peak of activation energy barrier
    • Has partial bonds between atoms, with bond breaking and bond forming occurring simultaneously
    • Rate of reaction depends on concentration of transition state complex

Collision factors

  • Collision cross-section represents the effective area within which particles must approach each other for a collision to occur
  • Steric factor accounts for the orientation requirement in successful collisions, affecting the overall reaction rate

Arrhenius equation for rate constants

  • Arrhenius equation relates rate constant ($k$) to temperature ($T$) and activation energy ($E_a$)
    • $k = Ae^{-E_a/RT}$
      • $A$ is pre-exponential factor, accounts for factors like collision frequency and orientation
      • $R$ is universal gas constant ($8.314 \text{ J mol}^{-1} \text{K}^{-1}$)
  • To calculate rate constants at different temperatures:
    1. Obtain values for $A$ and $E_a$ (usually determined experimentally)
    2. Substitute values for $A$, $E_a$, $R$, and desired $T$ into Arrhenius equation
    3. Solve equation for rate constant ($k$) at given temperature
  • Arrhenius equation shows increasing temperature leads to exponential increase in rate constant
    • Doubling temperature (in Kelvin) increases rate constant by factor of 2 to 4, depending on $E_a$

Key Terms to Review (29)

Arrhenius equation: The Arrhenius equation describes the temperature dependence of reaction rates. It shows how the rate constant $k$ increases exponentially with an increase in temperature.
Activation energy (Ea): Activation energy (Ea) is the minimum amount of energy required for a chemical reaction to occur. It determines the rate at which reactants transform into products.
Activated complex: The activated complex, also known as the transition state, is a temporary and unstable arrangement of atoms formed during a chemical reaction. It represents the highest energy point along the reaction pathway.
Collision theory: Collision theory explains how and why chemical reactions occur by describing the conditions under which reactant particles must collide. Effective collisions require proper orientation and sufficient energy to overcome activation energy.
Frequency factor: Frequency factor, also known as the pre-exponential factor, is a term in the Arrhenius equation that represents the frequency of collisions with proper orientation for a reaction to occur. It is denoted by $A$ and has units dependent on the order of the reaction.
Kinetic energy: Kinetic energy is the energy possessed by an object due to its motion. It is given by the formula $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.
Kelvin (K): Kelvin (K) is the SI unit of thermodynamic temperature. It is one of the seven base units in the International System of Units (SI).
Reaction diagrams: Reaction diagrams graphically represent the energy changes during a chemical reaction, typically showing the transition from reactants to products. They often include important features like activation energy and the transition state.
Rate constant: The rate constant, often denoted as $k$, is a proportionality factor in the rate equation that relates the reaction rate to the concentration of reactants. Its value is specific to a particular reaction and changes with temperature.
Transition state: The transition state is a high-energy, unstable configuration of atoms during a chemical reaction that represents the point of maximum energy. It is the state through which reactants must pass to be converted into products.
Kelvin: Kelvin is the base unit of temperature in the International System of Units (SI). It is named after the physicist William Thomson, also known as Lord Kelvin, who was the first to propose an absolute scale of temperature. The Kelvin scale is a fundamental quantity in various areas of chemistry, including measurements, the ideal gas law, collision theory, and the study of spontaneity.
Kinetic Energy: Kinetic energy is the energy of motion possessed by an object. It is the energy an object has by virtue of being in motion and is directly proportional to the mass of the object and the square of its velocity.
Maxwell-Boltzmann Distribution: The Maxwell-Boltzmann distribution describes the distribution of molecular speeds or kinetic energies in an ideal gas at a given temperature. It is a fundamental concept in the kinetic-molecular theory of gases and is crucial for understanding factors affecting reaction rates and collision theory.
Rate Constant: The rate constant is a measure of the speed or rate at which a chemical reaction occurs. It is a fundamental parameter that describes the intrinsic reactivity of the reactants and the reaction mechanism, and it is an essential component in understanding and predicting the kinetics of chemical processes.
Transition State: The transition state is a critical point in the course of a chemical reaction where the reactants have not yet fully transformed into the products, but rather exist in a high-energy, unstable intermediate configuration. This transient state is a key concept in understanding the factors that affect reaction rates and the mechanisms by which reactions occur.
$E_a$: $E_a$, also known as the activation energy, is the minimum amount of energy required to initiate a chemical reaction. It represents the energy barrier that reactants must overcome in order for the reaction to occur. The concept of $E_a$ is central to the understanding of reaction kinetics and the Collision Theory.
Activation Energy: Activation energy is the minimum amount of energy required to initiate a chemical reaction. It represents the energy barrier that must be overcome for the reaction to occur, acting as a catalyst for the transformation of reactants into products.
Reaction Rates: Reaction rates refer to the speed at which chemical reactions occur, measuring the change in the concentration of reactants or products over time. The rate of a chemical reaction is a crucial factor in understanding and predicting the behavior of chemical systems.
Arrhenius Equation: The Arrhenius equation is a mathematical formula that describes the relationship between the rate of a chemical reaction and the temperature at which the reaction occurs. It is a fundamental concept in the field of chemical kinetics and is widely used to understand and predict the behavior of chemical reactions.
Collision Theory: Collision theory is a model that explains how chemical reactions occur by describing the necessary conditions for reactant molecules to collide and form products. It is a fundamental concept in understanding the factors that affect the rates of chemical reactions.
Collision Frequency: Collision frequency refers to the number of collisions between reactant molecules per unit of time. It is a critical factor in determining the rate of a chemical reaction, as more frequent collisions between reactants increase the probability of successful reactions occurring.
$k = Ae^{-E_a/RT}$: $k = Ae^{-E_a/RT}$ is the rate constant equation, which describes the relationship between the rate constant $k$ and various factors that influence the rate of a chemical reaction. This equation is a fundamental component of collision theory, which explains how the frequency and energy of collisions between reactant molecules determine the overall reaction rate.
Pre-Exponential Factor: The pre-exponential factor, also known as the frequency factor or the collision factor, is a term that appears in the Arrhenius equation, which describes the relationship between the rate constant of a chemical reaction and the temperature at which the reaction occurs. It represents the frequency of collisions between reactant molecules and the likelihood that these collisions will result in a successful reaction.
Effective Collisions: Effective collisions refer to the specific type of molecular collisions that result in a chemical reaction occurring. These are the collisions where the reactants have sufficient energy and proper orientation to overcome the activation energy barrier and form the products of the reaction.
Universal Gas Constant: The universal gas constant, denoted as R, is a fundamental physical constant that represents the proportionality between the pressure, volume, amount of substance, and absolute temperature of an ideal gas. It is a crucial parameter in the study of gas behavior and thermodynamics.
Collision Cross-Section: The collision cross-section is a measure of the effective area of a target particle that determines the probability of a collision occurring between two particles. It is a crucial concept in the field of collision theory, which describes the interactions between particles during chemical reactions.
Intermolecular Distances: Intermolecular distances refer to the spatial separation between the centers of adjacent molecules in a substance. This characteristic is crucial in understanding the Collision Theory, which describes the factors that influence the rate of chemical reactions.
Molecular Orientation: Molecular orientation refers to the specific arrangement or positioning of atoms or molecules within a substance. It is a crucial concept in understanding the behavior and properties of materials at the molecular level, particularly in the context of collision theory.
Steric Factor: The steric factor, also known as the steric effect, refers to the influence of the spatial arrangement or geometry of molecules on the rate of a chemical reaction. It considers the physical hindrance or obstruction that the orientation and size of reactant molecules can have on their ability to effectively collide and undergo a reaction.