17.1.2 Gibbs Free Energy & the Equilibrium Constant

Gibbs Free Energy & the Equilibrium Constant

• The equilibrium constant, K_c, gives no information about the individual rates of reaction
  • It is independent of the kinetics of the reaction

• The equilibrium constant, K_c, is directly related to the Gibbs free energy change, ΔG^Ꝋ, according to the following (van't Hoff's) equation:

ΔG^Ꝋ = -RT lnK

• • ΔG^Ꝋ= Gibbs free energy change (kJ mol^–1)
  • R = gas constant (8.31 J K^-1 mol^-1)
  • T = temperature (Kelvin, K)
  • K = equilibrium constant
  • This equation is provided in section 1 of the data booklet

• This relationship between the equilibrium constant, K_c, and Gibbs free energy change, ΔG^Ꝋ, can be used to determine whether the forward or backward reaction is favoured

The relationship between the equilibrium constant, K_c, and Gibbs free energy change, ΔG^Ꝋ

• At a given temperature, a negative ΔG value for a reaction indicates that:
  • The reaction is feasible / spontaneous
  • The equilibrium concentration of the products is greater than the equilibrium concentration of the reactants
  • The value of the equilibrium constant is greater than 1

• As ΔG becomes more negative:
  • The forward reaction is favoured more
  • The value of the equilibrium constant increases

• The relationship between Gibbs free energy change, ΔG^Ꝋ, temperature and the equilibrium constant, K_c, is described by the equation:

ΔG^Ꝋ = -RT lnK

• The rearrangement of this equation makes it possible to:
  • Calculate the equilibrium constant
  • Deduce the position of equilibrium for the reaction

Answers

Answer 1:

Step 1: Convert any necessary values

• • ΔG^Ꝋ into J mol^-1:
    • -4.38 x 1000 = -4380 J mol^-1

  • T into Kelvin
    • 25 + 273 = 298 K

Step 2: Write the equation:

• • ΔG^Ꝋ = -RT lnK_c

Step 3: Substitute the values:

• • -4380 = -8.31 x 298 x lnK_c

Step 4: Rearrange and solve the equation for K_c:

• • lnK_c = -4380 ÷ (-8.31 x 298)
  • lnK_c = 1.77
  • K_c = e^1.77
  • K_c = 5.87

Answer 2:

From part (1), the value of K_c is 5.87

Therefore, the equilibrium lies to the right / products side because the value of K_c is positive