Chapter14.4. Genchem

Factors Affecting the Rate of Chemical Reactions

• Temperature

  • Affects the rate of chemical reactions through collisions.

  • Core concept: More collisions lead to faster chemical reactions.

  • Higher temperature causes particles to absorb heat, resulting in:

  • Increased kinetic energy (energy of movement).

  • Faster particle movement.

  • More frequent collisions.

  • Not every collision will result in a reaction; other factors must also be considered.

• Differential Rate Law

  • The rate of a reaction can be described by the equation:
    $\text{Rate} = k[A]^x$

  • where:

    • $k$ is the rate constant.

    • $[A]$ is the concentration of reactant A.

    • $x$ is the order with respect to reactant A.

  • Temperature affects the value of $k$ (the rate constant) rather than the concentration of reactants.

  • As temperature increases, $k$ also increases.

  • Understanding the value of $k$ is crucial, especially in integrated rate laws where temperature is mentioned explicitly.

• Collision Frequency

  • The frequency of collisions among particles also plays a crucial role.

  • Faster particle movement leads to increased collision frequency.

• Orientation of Molecules

  • The spatial orientation of colliding molecules affects the likelihood of reaction.

  • For a reaction to occur, particles must collide in the correct orientation.

  • Bonds need to break in reactants, requiring energy (endothermic process) before new bonds can form (exothermic process).

• Activation Energy (EA)

  • The minimum energy required for a reaction to occur.

  • The concept of the activated complex (or transition state) is key: a short-lived, high-energy state that occurs after the reactants collide but before products are formed.

  • The activation energy can be sketched on an energy diagram:

  • Activation energy is the energy needed to move from reactants to the activated complex.

  • Example values might be:

    • Reactants: 10 kJ

    • Activated Complex: 100 kJ

    • Activation Energy ($EA$) = 100 kJ - 10 kJ = 90 kJ

  • If products have lower energy than the reactants, the reaction is exothermic, and vice versa.

• Energetics of Chemical Bonds

  • Energy profile for reactions:

  • Endothermic Reaction Example:

    • Products at higher energy than reactants.

    • $\Delta H =\text{Energy of Products} - \text{Energy of Reactants}$

    • For instance: Products (40 kJ) - Reactants (10 kJ) = +30 kJ (endothermic)

  • Exothermic Reaction Example:

    • Products at lower energy than reactants.

    • $\Delta H = 10 kJ - 30 kJ = -20 kJ$ (exothermic)

• Catalysts

  • Substances that speed up reactions by lowering the activation energy.

  • They provide a surface for reactants to collide effectively.

  • Effect on Energy Diagram:

  • Catalysts lower the height of the activation energy barrier, thus speeding up the reaction.

  • Represented by dashed lines in illustrations.

• Arrhenius Equation

  • Describes how the rate constant $k$ varies with temperature $T$.

  • General form:
    $k = Ae^{-\frac{EA}{RT}}$

  • Linear form often used for experiments:
    $\ln(k) = -\frac{EA}{R} \cdot \frac{1}{T} + \ln(A)$

  • where:

    • $y = \ln(k)$

    • $x = \frac{1}{T}$ (temperature in Kelvin)

    • $R = 8.314 \, \text{J/mol·K}$ (gas constant)

    • $A$ is the frequency factor related to orientation.

  • Calculation of Activation Energy:

  • Could be calculated with two data points using:
    $\ln(\frac{k<em>1}{k</em>2}) = \frac{EA}{R}(\frac{1}{T<em>2} - \frac{1}{T</em>1})$

• Summary of Energy Changes

  • Concept of Gibbs Free Energy: Enthalpy change ($\Delta H$) where

  • Positive change indicates energy absorbed (endothermic).

  • Negative change indicates energy released (exothermic).

• Chemistry of Bonds

  • Breaking bonds requires energy (endothermic process).

  • Forming bonds releases energy (exothermic process).

  • Stability context: Higher energy states are unstable; systems tend to move towards lower energy states.