8.1 Equilibrium Constants and Reaction Extent

Chemical equilibrium is a crucial concept in reactive processes. It determines maximum product yield and influences process design. Understanding equilibrium constants and how to calculate them is key to predicting reaction behavior and completeness.

Reaction extent helps determine equilibrium concentrations, while factors like temperature, pressure, and concentration changes affect equilibrium. Le Chatelier's Principle explains how systems respond to these disturbances, guiding our understanding of reaction dynamics and process optimization.

Chemical Equilibrium Fundamentals

Definition of chemical equilibrium

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• Chemical equilibrium occurs when forward and reverse reaction rates become equal resulting in no net change in concentrations of reactants and products
• Significance in reactive processes determines maximum product yield influences process design and operating conditions helps predict reaction behavior and completeness
• Equilibrium constant ($K$) quantifies reaction extent at equilibrium relates concentrations of reactants and products

Calculation of equilibrium constants

• Concentration-based equilibrium constant ($K_c$) calculated using $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ for reaction $aA + bB \rightleftharpoons cC + dD$ with concentrations in mol/L
• Pressure-based equilibrium constant ($K_p$) used for gas-phase reactions calculated as $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$ with partial pressures in atm or bar
• Relationship between $K_c$ and $K_p$ expressed as $K_p = K_c(RT)^{\Delta n}$ where $\Delta n$ represents change in moles of gas

Reaction Extent and Equilibrium Analysis

Determination of equilibrium concentrations

• Reaction extent ($\xi$) measures reaction progress calculated using $\xi = \frac{n_i - n_{i,0}}{\nu_i}$ where $n_i$ is moles at equilibrium $n_{i,0}$ is initial moles and $\nu_i$ is stoichiometric coefficient
• Equilibrium concentrations determined by $[A] = [A]_0 - \nu_A\xi$ $[B] = [B]_0 - \nu_B\xi$ $[C] = [C]_0 + \nu_C\xi$ $[D] = [D]_0 + \nu_D\xi$
• Solving for equilibrium concentrations involves:
  1. Substituting expressions into equilibrium constant equation
  2. Solving for reaction extent
  3. Calculating final concentrations using reaction extent

Factors affecting equilibrium

• Le Chatelier's Principle states system responds to minimize effects of disturbances (temperature, pressure, concentration changes)
• Temperature effects:
  • Endothermic reactions: $K$ increases with temperature (e.g., N2 + O2 ⇌ 2NO)
  • Exothermic reactions: $K$ decreases with temperature (e.g., N2 + 3H2 ⇌ 2NH3)
  • van 't Hoff equation describes temperature dependence: $\frac{d\ln K}{dT} = \frac{\Delta H^\circ}{RT^2}$
• Pressure effects only impact gas-phase reactions with change in moles:
  • Increase in pressure favors side with fewer moles of gas (e.g., N2 + 3H2 ⇌ 2NH3)
  • Decrease in pressure favors side with more moles of gas (e.g., PCl5 ⇌ PCl3 + Cl2)
• Concentration effects:
  • Adding reactants shifts equilibrium towards products (e.g., adding H2 to N2 + 3H2 ⇌ 2NH3)
  • Removing products shifts equilibrium towards reactants (e.g., removing NH3 from N2 + 3H2 ⇌ 2NH3)
  • Inert gases affect equilibrium only by changing total pressure (e.g., adding Ar to N2 + 3H2 ⇌ 2NH3)