15.2.2 Calculating Entropy Change

• The standard molar enthalpy values, S^ꝋ, relate to standard conditions of temperature and pressure
• The entropy change, ΔS^ꝋ, can be calculated from thermodynamic data using the following equation:

ΔS^ꝋ₂₉₈(reaction) = ΣS^ꝋ₂₉₈(products) - ΣS^ꝋ₂₉₈(reactants)

• • This equation is provided in the data booklet

• The units of ΔS_system^ꝋ are in J K^-1 mol^–1
• Entropy will change depending on the state of the matter
• Taking water as an example the values for S^ꝋ will be different for the liquid and gaseous phases
  • S^ꝋ₂₉₈(H₂O (l)) = 70.0 J K^-1 mol^–1
  • S^ꝋ₂₉₈(H₂O (g)) = 188.8 J K^-1 mol^–1

• When calculating ΔS^ꝋ, the coefficients used to balance the equation must be applied when calculating the overall entropy change
• For example, when calculating the ΔS^ꝋ for the reaction below we need to double the value for S^ꝋ (NO (g))
  • N₂O₄ (g) → 2NO₂ (g)
  • ΔS^ꝋ₂₉₈(reaction) = ΣS^ꝋ₂₉₈(products) - ΣS^ꝋ₂₉₈(reactants)
  • ΔS^ꝋ = [(2 x S^ꝋ₂₉₈(NO₂)] - S^ꝋ₂₉₈(N₂O₄)

Answer:

Step 1: Write out equation to calculate ΔS^ꝋ₂₉₈(reaction)

• • • ΔS^ꝋ₂₉₈(reaction) = ΣS^ꝋ₂₉₈(products) - ΣS^ꝋ₂₉₈(reactants)

Step 2: Substitute in formulas and then values for S^ꝋ

• • • ΔS^ꝋ₂₉₈(reaction) = [S^ꝋ₂₉₈(CaO) + S^ꝋ₂₉₈(CO₂)] - S^ꝋ₂₉₈(CaCO₃)
    • ΔS^ꝋ(reaction) = (39.7 + 213.6) - 92.9
    • ΔS^ꝋ(reaction) = +160.4 J K^-1 mol^–1

Answer:

Step 1: Write out equation to calculate ΔS^ꝋ₂₉₈(reaction)

• • • ΔS^ꝋ₂₉₈(reaction) = ΣS^ꝋ₂₉₈(products) - ΣS^ꝋ₂₉₈(reactants)

Step 2: Substitute in formulas and then values for S^ꝋ taking into account the coefficients

• • • ΔS^ꝋ₂₉₈(reaction) = [2 x S^ꝋ₂₉₈(NH₃)] - [S^ꝋ₂₉₈(N₂)+ (3 x S^ꝋ₂₉₈(H₂ ))]
    • ΔS^ꝋ₂₉₈(reaction) = [2 x 192.3] - [191.6 + (3 x 131)]
    • ΔS^ꝋ₂₉₈(reaction) = 384.6 - 584.6
    • ΔS^ꝋ₂₉₈(reaction) = -200 J K^-1 mol^–1