Chemistry Practice Problems: Gibbs Free Energy

Gibbs Free Energy

• Gibbs free energy (∆G) can be expressed in several different equations:
  • ∆G° = ∑ G° (products) - ∑ G° (reactants)
  • ∆G° = -nFE°
  • ∆G = ∆G° + RT lnQ
• ∆G° is the standard Gibbs free energy, and K is the equilibrium constant
• At equilibrium, ∆G = 0, and Q = K

Chemical Equilibrium

• Chemical equilibrium is a state where the rate of the forward reaction equals the rate of the backward reaction
• It is the state where the concentrations of all reactants and products remain constant with time at any given temperature
• Any chemical reaction carried out in a closed vessel will reach equilibrium
• Many reactions do not go to completion, and the products react to form the original reactants once more

Le Chatelier's Principle

• This principle states that if a stress is applied on a system at equilibrium, the equilibrium will tend to shift in a direction to relieve that stress
• Examples of stresses include changes in concentration, pressure, and temperature
• A shift is a net reaction of reactants to form products or of products to form reactants

Chemical Kinetics

• Chemical kinetics is the area of chemistry that deals with the study of the rate (speed) and mechanism of reactions
• One of the main goals of chemical kinetics is to understand the steps by which a reaction takes place

Law of Mass Action

• The law of mass action states that the rate of a chemical reaction is proportional to the product of the molar concentrations of the reacting substances
• For the general reaction: A + B ⇌ C + D, the rate of forward reaction (RF) is proportional to [A][B], and the rate of reverse reaction (RR) is proportional to [C][D]
• RF = kF[A][B] and RR = kR[C][D], where kF and kR are constants of proportionality or rate constants

Equilibrium Constant

• The equilibrium constant (Kc) is a ratio of the product of the molar concentrations of the products to the product of the molar concentrations of the reactants
• Kc = [C]r [D]s / [A]p [B]q, where p, q, r, and s are the numbers of moles of A, B, C, and D respectively
• The equilibrium constant indicates the position of equilibrium, such that:
  • If K > 1, the equilibrium lies to the right, and products predominate
  • If K < 1, the equilibrium lies to the left, and reactants predominate
  • If K = 1, the equilibrium mixture contains equal amounts of products and reactants

Equilibrium Expression for Gases

• For gases, the equilibrium constant may be more usefully interpreted in terms of their partial pressures
• Kp = 𝑝C 𝑝D / 𝑝A 𝑝B, where Kp is the equilibrium constant in terms of partial pressure

Factors that Affect the Equilibrium Constant

• Composition of equilibrium mixture:
  • Concentration of reactant increased: shift to right, no effect on K
  • Concentration of reactant decreased: shift to left, no effect on K
• Pressure:
  • Increased or decreased: no effect on K, unless reaction involves a volume change
• Temperature:
  • Increased or decreased: change in K depends on the sign of ∆H
• Addition of catalyst: no effect on K
• Solving equilibrium problems:
  • Write the balanced equation for the reaction
  • Write the equilibrium expression using the law of mass action
  • List the initial concentrations
  • Apply the changes to the initial concentrations
  • Substitute the equilibrium concentrations into the equilibrium expression
  • Solve for the unknown