Chemical Reaction Equilibria Notes

Chemical Reaction Equilibria Overview

• Introduction to Chemical Equilibrium

  • Topic 9: Focus on chemical reaction equilibria, intersecting with reaction kinetics and solution thermodynamics.
  • Importance in chemical engineering for reactor design and operation.

• Fundamentals of Reaction Equilibrium

  • Reaction rates and equilibrium conversions depend on:
    • Temperature
    • Pressure
    • Composition
  • Concept of equilibrium conversion and reaction rates changes with these thermodynamic properties.

Key Concepts

• Thermodynamic Properties Influence

  • Different thermodynamic properties impact equilibrium conversion.
  • This lecture discusses how varying temperature, pressure, and initial composition can influence equilibrium conversions in chemical reactions.

• Reaction Stoichiometry

  • General Reaction Format: $\nu<em>1 A</em>1 + \nu<em>2 A</em>2 + \ldots \rightarrow \nu<em>3 A</em>3 + \nu<em>4 A</em>4 + \ldots$
    • Where $\nu_i$ (stoichiometric coefficients) indicates the amount of each reactant and product.
  • Sign Convention:
    • Reactants have negative coefficients; products have positive coefficients.

• Example of Stoichiometric Coefficients:

  • For the reaction of methane ($CH<em>4$) reacting with water to produce carbon monoxide ($CO$) and hydrogen ($H</em>2$):
    • $C H<em>4 + H</em>2 O \rightarrow CO + 3 H_2$
    • Coefficients: $\nu<em>{CH</em>4} = -1, \nu<em>{H</em>2O} = -1, \nu<em>{CO} = +1, \nu</em>{H_2} = +3$

Reaction Coordinate and Changes in Moles

• Defining Reaction Coordinate (Epsilon):
  • Defines the extent of reaction, often referred to as degree of reaction or progress variable, denoted as $\epsilon$.
  • Relates the change in moles of species to the reaction coordinate:
    $\frac{d n<em>1}{\nu</em>1} = \frac{d n<em>2}{\nu</em>2} = \ldots$
  • Derives the relationship of the number of moles in relation to the reaction coordinate.

Mole Fraction and Reaction Coordinates

• Mole Fraction Relations to Reaction Coordinate:

  • $y<em>i = \frac{n</em>i}{n_{total}}$ where:
    • $n<em>{total} = n</em>{i0} + \nu_i \epsilon$
  • Use the stoichiometric coefficients to express each species mole fraction as a function of $\epsilon$.

• Example Calculation (for a specific reaction involving methane, water, carbon monoxide, hydrogen)

  • Determine expressions for mole fractions utilizing initial moles and stoichiometric coefficients derived from the balanced reactions.

Equilibrium Criteria

• Equilibrium Condition:

  • Total Gibbs free energy ($G$) must be minimized at equilibrium, which involves
    • $\frac{d G}{d \epsilon} = 0$ at constant temperature and pressure.
  • Relates Gibbs energy change to the equilibrium constant ($K$).

• Derivation of Equilibrium Constant:

  • The equilibrium constant ($K$) relates to standard Gibbs free energy ($\Delta G^0$):
    $K = e^{-\frac{\Delta G^0}{RT}}$
  • Determines how transformations between reactants/products occur at equilibrium.

Application to Problems

• Calculating Equilibrium Constant:
  • Use the law of mass action, consider both gas and liquid phases, and solve equations through integral calculations involving heat capacities and Gibbs energy.
  • Use provided data for coefficient constants to determine the equilibrium conditions and constants.

Self-Assessment Problems

• Three problems addressing:
  1. Mole fraction equations as functions of reaction coordinate.
  2. Multiple independent reactions occurring simultaneously.
  3. Finding the equilibrium constant for a specified chemical reaction and conditions (500°C, 1 bar).