Key Concepts

• Reaction Rate vs. Disappearance/Appearance Rates:

  • The rate of a chemical reaction can be determined by monitoring either the disappearance of reactants or the appearance of products.

  • Important: When reactants or products appear in the balanced equation with a coefficient other than 1, you must adjust the measured rate.

    • Example: For the reaction
      \[ 2\,\mathrm{NO} \rightarrow \text{products} \] if the disappearance rate of NO is measured, then the actual rate of the reaction is the measured rate divided by 2.

• Integrated Rate Equations:

  • First-Order Reactions:
    The integrated rate law is given by: \[ \ln \left(\frac{[A]_t}{[A]_0}\right) = -kt \] where \([A]_0\) is the initial concentration, \([A]_t\) is the concentration at time \(t\), and \(k\) is the rate constant.

  • Second-Order Reactions:
    The integrated rate law is: \[ \frac{1}{[A]_t} - \frac{1}{[A]_0} = kt \]

• Why Stoichiometry Matters:

  • When writing the rate expression from experimental data, ensure you convert between the rate of disappearance of a reactant and the rate of the overall reaction if the reactant’s stoichiometric coefficient is not 1.

  • The coefficients in the balanced equation do not necessarily equal the reaction orders; these must be determined experimentally (often using the method of initial rates).

How to Approach Problems

1. Identify the Measured Rate:
   • Determine if the data are given in terms of reactant disappearance or product formation.
   • Adjust the rate using the stoichiometric coefficient when necessary.
2. Determine the Order:
   • Use experimental data (often comparing different trials) to establish how changes in concentrations affect the rate.
   • For example, if doubling a reactant’s concentration doubles the rate, that reactant is first order in the rate law.
3. Apply the Integrated Rate Law:
   • Decide whether the reaction is first or second order.
   • Use the appropriate equation to calculate the rate constant or predict the concentration at a given time.
4. Check Units:
   • Ensure that the units for your rate constant \(k\) are consistent with the order of the reaction (e.g., for first order, units are s\(^{-1}\); for second order, M\(^{-1}\) s\(^{-1}\)).

Intermolecular Forces and Boiling Points

• Boiling Point Fundamentals:

  • The boiling point of a substance is influenced by the strength of intermolecular forces (IMFs).

  • Hydrogen Bonding:

    • A specific, strong form of dipole–dipole attraction.
    • Most effective when the hydrogen is bonded to highly electronegative atoms like N, O, or F.

  • General Tip:

    • Recognize that increased hydrogen bonding generally leads to higher boiling points due to the extra energy required to overcome these attractions.

Chemical Kinetics Overview

• Definition:
  Kinetics is the study of the rates of chemical reactions and the factors affecting these rates.

• Important Factors Influencing Reaction Rates:

  • Concentration: Higher concentrations often lead to higher collision frequencies.
  • Surface Area (for solids): Increased surface area can increase the reaction rate.
  • Temperature: Higher temperatures increase the kinetic energy of molecules, leading to more effective collisions.
  • Catalysts: Catalysts provide an alternative reaction pathway with a lower activation energy.

Determining Reaction Orders and Rate Laws

Reaction Mechanisms and Validation

• Reaction Mechanism:

  • A proposed step-by-step pathway that explains how reactants turn into products at the molecular level.

  • Key Points:

    • The individual elementary steps must add up to give the overall balanced equation.
    • Intermediates (species that are formed and then consumed) and catalysts must be identified.
    • The experimentally determined rate law should match the rate law predicted by the mechanism.

• Example Mechanism Discussion from the Slides:

  • Reaction: \[ \mathrm{Br}_2(g) + 2\,\mathrm{NO}(g) \rightarrow 2\,\mathrm{BrNO}(g) \]

  • Proposed Steps:

    1. \(\mathrm{Br}_2(g) + \mathrm{NO}(g) \rightleftharpoons \mathrm{Br_2NO}(g)\)
       
    2. \(\mathrm{Br_2NO}(g) + \mathrm{NO}(g) \rightarrow 2\,\mathrm{BrNO}(g)\)

  • Validation:

    • Ensure the sum of the steps equals the overall reaction.
    • Compare the predicted rate law with the experimental data to check for consistency.

Arrhenius Equation and Activation Energy

• Concept:

  • For a reaction to occur, colliding molecules must have energy equal to or greater than the activation energy (\(E_a\)).

  • Arrhenius Equation: \[ k = A e^{-E_a/RT} \] where:

    • \(k\) is the rate constant,
    • \(A\) is the frequency factor,
    • \(E_a\) is the activation energy,
    • \(R\) is the gas constant,
    • \(T\) is the temperature in Kelvin.
• Key Idea:
  • Increasing the temperature increases the fraction of molecules that have energy above \(E_a\), thus increasing the reaction rate.

How to Approach Kinetics Problems Step-by-Step

1. Write the Balanced Equation:
   • Clearly write the overall reaction and note the stoichiometric coefficients.
2. Identify the Method:
   • Determine whether you will use the initial rate method or an integrated rate law (first or second order).
3. Set Up the Rate Law Expression:
   • Write the general form:
     \[ \text{Rate} = k [\text{Reactant}_1]^a [\text{Reactant}_2]^b \dots \]
   • Use experimental data to determine the exponents \(a\), \(b\), etc.
4. Determine the Reaction Order:
   • Compare data from different trials (holding one reactant constant) to deduce the order with respect to each reactant.
5. Calculate the Rate Constant (\(k\)) and Half-Life (if applicable):
   • For first order, use \(\ln [A]\) vs. time; for second order, use \(1/[A]\) vs. time.
   • Calculate half-life using: \[ t_{1/2} = \frac{0.693}{k} \quad \text{(first order)} \]
6. Analyze Reaction Mechanisms:
   • For multi-step reactions, identify intermediates and determine which step is rate-determining.
   • Validate the mechanism by ensuring that the predicted rate law matches experimental observations.
7. Double-Check Units and Calculations:
   • Verify that the units for \(k\) match the reaction order.
   • Review any approximations (e.g., when assuming one reactant concentration is in excess).