Chapter 14.5-14.6

Finding k1 Instead of Activation Energy

  • Focus on k1: The objective is to find the variable k1 instead of activation energy.

  • Nature of Variables:

    • The variables include k1, k2, t1, t2, and activation energy (EA).

    • If four variables are provided, the task is to calculate the fifth variable.

    • R, the constant, is always provided.

Calculating Constants and Energy

  • Equation Setup:

    • The equation is set up as:
      ln⁡(k1k2)=EAR⋅T\ln\left(\frac{k1}{k2}\right) = \frac{EA}{R \cdot T}

    • Given that ln⁡(k1k2)=−3.18\ln\left(\frac{k1}{k2}\right) = -3.18 and k2=2.5×10−5k2 = 2.5 \times 10^{-5}.

    • Convert EA from kilojoules to joules for consistency in units.

    • 1 kilojoule = 1000 joules.

  • Calculation of Activation Energy:

    • Initially provided as:

    • EA=160 kJ=160 000 JEA = 160\,\text{kJ} = 160\,000\,\text{J}

    • Substitute into the equation:
      160,000 J8.314 J/mol K(1T<em>2−1T</em>1).\frac{160,000\,\text{J}}{8.314\,\text{J/mol K}} \left(\frac{1}{T<em>2} - \frac{1}{T</em>1}\right).

Solving for k1

  • After Calculating with the Equation:

    • Substituting values gave us:
      ln⁡(k12.5×10−5)=−3.18\ln\left(\frac{k1}{2.5 \times 10^{-5}}\right) = -3.18

    • Eliminating the logarithm leads to:
      k1=2.5×10−5⋅e−3.18.k1 = 2.5 \times 10^{-5} \cdot e^{-3.18}.

    • This results in:
      k1=1×10−6s−1.k1 = 1 \times 10^{-6} s^{-1}.

    • Overall Order of Reaction: This means the overall order is 1 since molarity is absent, indicated by only a rate constant of s−1s^{-1}.

Implications for Future Assessments

  • Quiz/Test Expectation: Understanding how to calculate any of the variables is essential for quizzes and tests.

Reaction Mechanisms

  • Definition: Reactions often occur in multiple steps, where each individual step is an elementary step.

  • Representation of Reactions:

    • Often simplified as: a+b→c+d.a + b \rightarrow c + d.

    • However, complex reactions involve more than one elementary step.

  • Elementary Steps: Each step contributes to the overall reaction mechanism, which specifies what happens during the reaction.

  • Example of Reaction Steps:

    1. In Step 1: A reacts with B to form C and D.

    2. In Step 2: A interacts with D, forming F.

    • Here, D acts as an intermediate: formed in Step 1 and used in Step 2.

Recognizing Intermediates and Catalysts

  • Intermediates: Substances formed in one step and consumed in the subsequent step; can occur at any step.

  • Catalysts: Substances that appear in the first step as reactants and in the last step as products, remaining unchanged during the process.

Types of Elementary Reactions

  • Unimolecular Reactions: Involve one molecule.

  • Bimolecular Reactions: Involves two molecules, which can be the same or different. For example, reactions can be represented as:

    • A+AA + A or A+B.A + B.

  • Termolecular Reactions: Rarely occur involving three molecules.

Rate Determining Step

  • Concept: In a multi-step reaction, the slowest step determines the overall reaction rate.

  • Analogy: Using a swim team where the slowest swimmer determines the race outcome.

  • Rate Laws for Steps:

    • Each reaction step has its rate law, for example, for a reaction involving A:

    • First step can be characterized by:
      Rate=k⋅[A]x.\text{Rate} = k \cdot [A]^x.

Important Considerations for Rate Laws

  • If the First Step is Slow:

    • The rate law of the first step equals the overall reaction rate law.

  • If the First Step is Fast:

    • Finding the overall rate law requires accounting for intermediates, which can complicate calculations.

Example of a Reaction Mechanism**:

  • For the mechanism:

    1. Reaction of NO2 with another NO2 to form products (O and NO3).

    2. NO3 reacts with CO to regenerate some NO2 and form CO2.

    • The rate law for the slow step would then serve as the rate law for the overall reaction.

  • Example Rate Law:

    • For the slow step reaction, written as:
      Rate=k⋅[NO2]2.\text{Rate} = k \cdot [NO2]^2.

Final Notes on Assessments

  • Upcoming Assessment Schedule:

    • A math exam will be opened right away, due next Monday at midnight.

    • A quiz will be administered on the following Tuesday.

    • Preparation resources include worksheets and mastering chemistry exercises.

  • Reassurance on Assessment Content: Questions will reflect taught material, ensuring no unexpected content.

  • Be aware of potential technical discrepancies with online platforms; address issues promptly.