Study Notes on Collision Theory and Chemical Equilibrium

Fundamentals of Collision Theory

• Criteria for an Effective Collision: In order for a collision between particles to be considered effective and result in a reaction, three specific conditions must be met:
      * Collision: The reacting particles must physically collide with one another.
      * Correct Orientation: The particles must be aligned in the correct geometric orientation at the moment of impact.
      * Sufficient Energy: The particles must collide with enough energy (activation energy) to break existing bonds and form new ones.

• The Impact of Temperature on Collisions: If the temperature of a system increases ($\uparrow$), the expected result is a higher frequency of collisions (more collisions) because particles move faster and with greater kinetic energy.

• Core Requirements for a Chemical Reaction to Occur: The two essential conditions that must be fulfilled are proper orientation and having enough energy.

Principles of Chemical Equilibrium

• Defining Chemical Equilibrium: Chemical equilibrium describes a state in which the chemical reaction is constant. This means the rate of the forward reaction equals the rate of the reverse reaction, leading to no net change in the concentrations of reactants and products.

• State of Matter Constraints: According to these notes, equilibrium expressions are written exclusively for substances in the gaseous state ($Gases\,only$).

Factors Affecting Chemical Equilibrium and Le Chatelier’s Principles

• Concentration Changes: Equilibrium can be disturbed and subsequently affected by:
      * The addition or removal of Reactants.
      * The addition or removal of Products.

• Volume and Pressure Changes: The equilibrium position is sensitive to changes in volume and pressure.
      * Relationship to Moles: The shift depends on the number of moles of gas present.
      * Note on Volume: The notes indicate a relationship between $\uparrow V$ (increased volume) and the side with the "least #moles."

• Temperature and Thermal Effects (Exothermic vs. Endothermic):
      * Exothermic Reactions:
          * Heat/Energy is released and is associated with the product side.
          * Representation: $A + B \rightarrow C + D + \text{kJ}$.
          * Entropy/Enthalpy sign: $- \text{kJ}$.
      * Endothermic Reactions:
          * Heat/Energy is absorbed and is associated with the reactant side.
          * Representation: $\text{Heat (kJ)} + A + B \rightarrow C + D$.
      * Directional Shifts: If a system "cools down," the equilibrium will shift to compensate (the opposite is true for heating up).

Mathematical Formulation of Equilibrium Expressions ($K_{eq}$)

• General Expression: The equilibrium constant ($K_{eq}$) is calculated using the ratio of the concentration of products ($[P]$) to the concentration of reactants ($[R]$).
      * Formula: $K_{eq} = \frac{[P]}{[R]}$

• Application of Coefficients: In the equilibrium expression, any coefficients from the balanced chemical equation become exponents for the respective chemical species concentrations.

• Phase Requirements: The $K_{eq}$ expression is written only for gases ($g$).

Utilizing Equilibrium Expressions for Calculations

• Determining $K_{eq}$ or Molarity: The equilibrium expression can be used to solve for the equilibrium constant or the molar concentration ($M$) of the compounds in a reaction using the following procedural steps:
      1. Set Up: Establish the equilibrium expression using the specific chemical equation provided in the problem.
      2. Substitution: Substitute the known numerical information (concentrations or constants) into the established expression.
      3. Solve: Use a calculator to perform the final mathematical calculation.

• Calculation Template:
      $K_{eq} = \frac{[P]}{[R]}$

Practice Problems

• Textbook References for Application:
      * Page 613: Numbers 18 and 19.
      * Page 627: Numbers 71 and 74.
      * Page 628: Numbers 75, 76, and 81.