equilibrium

EQUILIBRIUM

Review of Thermodynamics

• Reaction: The transformation of nitrogen dioxide gas (NO₂) to dinitrogen tetroxide (N₂O₄)

  • Chemical Equation:
    $2NO<em>2(g) \rightleftharpoons N</em>2O_4(g)$

  • Standard Gibbs Free Energy Change (ΔG°):

  • Value: -12.7 kJ/mol

• Interpretation of ΔG:

  • A negative ΔG indicates that the reaction favors product formation at equilibrium.

  • Hypothetical Scenario: If ΔG = -3000 kJ/mol, it implies a strong favoring of the products (more N₂O₄ at equilibrium).

• Equilibrium Constant (K):

  • The ratio of N₂O₄ to NO₂ at equilibrium is dependent on the Gibbs Free Energy (ΔG).

  • Relationship:

  • If ΔG is negative, then K is greater than 1, indicating more products than reactants at equilibrium.

  • If ΔG is positive, then K is less than 1, indicating more reactants than products at equilibrium.

  • Note: The value of K is always positive and can only be affected by temperature changes.

  • Important Note: K has no units.

Law of Mass Action

• K Expression: For a general reaction
  \text{aA (aq) + bB (aq) \rightleftharpoons cC (aq) + dD (aq)}

  • The equilibrium constant ($K<em>c$) is given by: $K</em>c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

  • Pure solids and liquids (e.g., pure water) are not included in the K expression. Only aqueous solutions and gases are relevant.

• Equilibrium Condition:

  • The concentrations of all substances involved must already be at equilibrium for K to be calculated.

• Kp vs. Kc:

  • The equilibrium constant ($K<em>p$) is used when gaseous quantities are expressed in terms of pressure (atm), while $K</em>c$ is for concentrations (molarity).

  • A conversion between $K<em>c$ and $K</em>p$ may be necessary depending on the type of measurement.

What is Equilibrium?

• Equilibrium does not imply that no processes occur; rather, it indicates that the rates of the forward and backward reactions are equal.

  • Example of dynamic equilibrium:

  • Vapor Pressure: Comparison between closed versus open beakers, also with a fan.

  • Saturated Solutions: Reach equilibrium where solute dissolves and precipitates at equal rates.

• Equilibrium is inherently linked to thermodynamics, with only limited connections to kinetics.

Equilibrium Calculations

• Type 1: Calculations when equilibrium is established.

  • Example Reaction:
    $2O<em>3(g) \rightleftharpoons 2O</em>2(g) + O_2(g)$

  • $K_p = 7.81 \times 10^{-7}$

  • Experiment Data:
    | Experiment | Initial Pressure (atm) | Final Equilibrium Pressure (atm) |
    |------------|------------------------|-------------------------------|
    | 1 | O₃: 10.0, O₂: 0, O₂: 0 | O₃: 9.9464, O₂: 0.0536 |
    | 2 | O₃: 20.0, O₂: 0, O₂: 0 | O₃: 19.9148, O₂: 0.0852 |
    | 3 | O₃: 10.0, O₂: 0, O₂: 10.0 | O₃: 9.997206, O₂: 10.001397 |

  • Task: Calculate $K_p$ for each of the experiments.

• Type 2: Given $K$ and some equilibrium concentrations.

  • Example Reaction:
    $H<em>2(g) + Br</em>2(g) \rightleftharpoons 2HBr (g)$

  • Equilibrium constant (K) = 55.

  • Given concentrations: 3.0 M of H₂ and 0.45 M of Br₂.

  • Task: Calculate the moles of HBr at equilibrium.

• Type 3: Calculations with initial concentrations (not equilibrium).

  • Requires: ICE (Initial, Change, Equilibrium) tables.

  • Example Reaction:
    $2NO<em>2 \rightleftharpoons 2NO + O</em>2$

  • Initial NO₂ concentration: 0.800 M (NO and O₂ are initially 0).

  • $K_C = 0.50$

  • Task: Calculate the equilibrium concentrations of NO₂, NO, and O₂.

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