19.1 Chemical equilibrium and reaction coordinates

Chemical equilibrium is a balancing act in reactions. It's when forward and reverse reactions happen at the same speed, keeping concentrations steady. The Gibbs free energy change hits zero at this point, showing the system's found its sweet spot.

Reaction coordinate diagrams map out a reaction's energy journey. They show how Gibbs free energy changes as the reaction progresses, helping us predict if a reaction will happen on its own and how far it'll go.

Chemical Equilibrium and Reaction Coordinates

Concept of chemical equilibrium

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• Dynamic state forward and reverse reactions occur at equal rates resulting in no net change in concentrations of reactants and products
• At equilibrium Gibbs free energy change ($\Delta G$) equal to zero represents minimum Gibbs free energy for system at constant temperature and pressure
• Relationship between Gibbs free energy change and equilibrium constant ($K$) given by equation $\Delta G^\circ = -RT \ln K$
  • $\Delta G^\circ$ standard Gibbs free energy change
  • $R$ universal gas constant (8.314 J/mol·K)
  • $T$ absolute temperature (K)

Interpretation of reaction coordinate diagrams

• Plot Gibbs free energy of system as function of reaction progress
  • Reactants represented on left side products on right side
  • Transition state highest point represents energy barrier that must be overcome for reaction to occur
• Direction of chemical reaction determined by comparing Gibbs free energy of reactants and products
  • Products lower than reactants reaction spontaneous in forward direction (exothermic)
  • Reactants lower than products reaction spontaneous in reverse direction (endothermic)
• Extent of chemical reaction determined by difference in Gibbs free energy between reactants and products
  • Larger difference results in greater extent of reaction (higher yield)

Calculations with law of mass action

• Law of mass action equilibrium constant ($K$) equal to product of concentrations of products raised to stoichiometric coefficients divided by product of concentrations of reactants raised to stoichiometric coefficients
  • General reaction $aA + bB \rightleftharpoons cC + dD$, equilibrium constant $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
  • Square brackets denote concentrations of respective species at equilibrium (mol/L or M)
• Equilibrium concentrations calculated using equilibrium constant and initial concentrations of reactants and products
  1. Set up equilibrium constant expression using law of mass action
  2. Substitute initial concentrations into equilibrium constant expression
  3. Solve resulting equation for equilibrium concentrations (quadratic formula or ICE table)

Effects on equilibrium state

• Le Chatelier's principle system at equilibrium subjected to change in temperature pressure or concentration will shift equilibrium position to counteract change and re-establish equilibrium
• Effect of temperature depends on whether reaction is endothermic or exothermic
  • Endothermic reaction increasing temperature shifts equilibrium towards products (favors forward reaction)
  • Exothermic reaction increasing temperature shifts equilibrium towards reactants (favors reverse reaction)
• Effect of pressure depends on stoichiometry of reaction
  • Increasing pressure shifts equilibrium towards side with fewer moles of gas (favors reaction that decreases number of gas molecules)
  • Decreasing pressure shifts equilibrium towards side with more moles of gas (favors reaction that increases number of gas molecules)
• Effect of concentration predicted using equilibrium constant expression
  • Increasing concentration of reactant shifts equilibrium towards products (favors forward reaction)
  • Increasing concentration of product shifts equilibrium towards reactants (favors reverse reaction)
  • Adding inert gas at constant volume has no effect on equilibrium (does not change partial pressures)