General Chemistry II

Chemical Kinetics

• Instructor: Jong Moon Lee

Introduction to Chemical Kinetics

• Chemical Kinetics: Concerned with the rate at which chemical reactions occur.
  • Thermodynamics: Addresses if a reaction is spontaneous (e.g.,
  • 2H_2 (g) + O_2 (g)
    ightarrow 2H_2O (l)
  • H_2 (g) + Cl_2 (g)
    ightarrow 2HCl (g)
  • N_2 (g) + 3H_2 (g)
    ightarrow 2NH_3 (g))
  • Kinetics: Focuses on how fast these reactions happen and the mechanisms involved.
  • Example: The Haber process for ammonia synthesis:
    N_2 (g) + 3H_2 (g)
    ightleftharpoons 2NH_3 (g)
    Conditions: 450°C, 200 atm, iron catalyst.

Reaction Mechanism

• Definition: The sequence of elementary steps that describes how reactants convert into products.
  • Rate-determining step: The slowest step that controls the overall reaction rate.
  • Example:
  • Balanced chemical equation: A_2 + 2B
    ightarrow 2AB
  • Step 1: A_2 + B
    ightarrow A_2B (slow)
  • Step 2: A_2B + B
    ightarrow 2AB (fast)
  • Intermediate: A species formed in one step and consumed in another (e.g., $A_2B$).

Collision Theory

• For a reaction to occur:
  • Molecules must collide.
  • More collisions per second lead to a higher reaction rate.
  • Proper Orientation: Molecules must collide in the correct alignment.
  • Sufficient Energy: Collisions must provide enough energy to overcome the activation energy (Ea).
• Graph: Displays potential energy versus reaction progress, showing the activation energy requirement for reactions.

Arrhenius Equation

• The mathematically defines the factors of collision theory:
  • $k = pZe^{-Ea/RT}$
  • Where:
    • $k$: rate constant
    • $p$: probability of correct orientation
    • $Z$: collision frequency
    • $A$: frequency factor
    • $e$: Euler’s number (approximately 2.718)
    • $Ea$: activation energy
    • $R$: universal gas constant
    • $T$: temperature
  • Implications:
  • Increasing temperature ($T$) increases the reaction rate ($k$).
  • Decreasing activation energy ($Ea$) increases the reaction rate ($k$).

Transition State Theory

• Occurs when reactants with sufficient kinetic energy collide:
  • Energy converts into potential energy as bonds break and atoms rearrange.
  • Lowering the energy of the transition state decreases Ea, leading to a higher rate of reaction.

Reaction Energy Profiles

• Endergonic Reactions: Absorb energy, not spontaneous.
• Exergonic Reactions: Release energy, spontaneous.

Reaction Rate & Rate Equation

• Conceptual Reaction Rate: Rate at which reactants convert to products.
• Rate Law: For the reaction aA + bB ightarrow ext{products}:
  • General form: $ext{Rate} = k[A]^m[B]^n$
  • Where:
    • $k$: rate constant
    • $[A], [B]$: concentrations of reactants
    • $m, n$: reaction orders (determined experimentally)
• Relationship:
  • $ext{Rate} ext{ (M/s)} = -\frac{∆[A]}{∆t} = \frac{∆[B]}{∆t}$

Factors Affecting Reaction Rate

• Concentration: Higher concentration means more collisions.
• Temperature: Higher temperature results in more molecules having sufficient energy.
• Surface Area: Larger surface area (especially for solids) leads to more effective collisions.
• Steric Effects: Bulky molecules may impede effective collisions.
• Catalysts: Provide an alternative pathway, lowering the activation energy (Ea) and increasing the reaction rate.

Rate Expression and Reaction Orders

• Rate proportionality:
  • $ext{Rate} = k[A]^m[B]^n$
  • Reaction orders ($m$, $n$) are not the same as stoichiometric coefficients and must be determined experimentally.
  • Rate constant ($k$) can change with conditions.

Practice Problem – Rate Law

• Determine Rate Law: For the reaction aA + bB ightarrow cC + dD at 300 K:
  • Data Provided: Initial concentrations and reaction rates across trials.
  • Calculate rate constants from initial conditions for all trials given.

Integrated Rate Law – Zero-Order

• Zero-Order Reaction:
  • Basic form: aA
    ightarrow ext{Product}
  • Integrated form:
    $[A] = -kt + [A]_0$
  • Constants:
  • Rate constant ($k$): Units of $M ext{s}^{-1}$.

Integrated Rate Law – First-Order

• First-Order Reaction:
  • Form: aA
    ightarrow ext{Product}
  • Integrated form:
    $ext{ln}([A]) = -kt + ext{ln}([A]_0$
  • Constants:
  • Rate constant ($k$): Units of $s^{-1}$.

Integrated Rate Law – Second-Order

• Second-Order Reaction:
  • Basic form: aA
    ightarrow ext{Product}
  • Integrated form:
    $\frac{1}{[A]} = kt + \frac{1}{[A]_0}$
  • Constants:
  • Rate constant ($k$): Units of $M^{-1} ext{s}^{-1}$.

Integrated Rate Laws – Summary

Half-Life (t½)

• Definition: The time it takes for a reactant's concentration to reduce to half its initial amount.
• Half-Life Relations:
  • Zero-order:
    $t_{1/2} = \frac{[A]_0}{2k}$
  • First-order:
    $t_{1/2} = \frac{0.693}{k}$
  • Second-order:
    $t_{1/2} = \frac{1}{k[A]_0}$

Practice Problems – Integrated Rate Law

• Example 1: For a first-order reaction with known initial concentration and rate constant, calculate concentration after a set time.
• Example 2: Calculate time needed for 90% of reactant to react from a given half-life.

Integration and Logarithm Rules

• Integration Rules: Basic rules needed for calculus applied to kinetics equations.
• Logarithmic Rules: Understanding for manipulating logarithmic expressions is crucial in rate laws and calculations.