3.4.4 Hess' Law

Calculating ΔH_r from ΔH_f using Hess’s Law energy cycles

• The products can be directly formed from the elements = ΔH₂

   OR

• The products can be indirectly formed from the elements = ΔH₁ + ΔH_r

The enthalpy change from elements to products (direct route) is equal to the enthalpy change of elements forming reactants and then products (indirect route)

• Equation

ΔH₂ = ΔH₁ + ΔH_r

   Therefore,

ΔH_r = ΔH₂ – ΔH₁

 

Worked Example

Answer

Step 1: Write the balanced equation at the top

Step 2: Draw the cycle with the elements at the bottom

Step 3: Draw in all arrows, making sure they go in the correct directions. Write the standard enthalpy of formations

Step 4: Apply Hess’s Law

• • ΔH_r = ΔH₂ - ΔH₁ 
    • ΔH₂ = ΔH_f [Na₂CO₃ (s)] + ΔH_f [CO₂ (g)] + ΔH_f [H₂O (l)]
    • ΔH₁ = 2 x ΔH_f [NaHCO₃ (s)]
  • ΔH_r = ((-1130.7) + (-393.5) + (-285.8)) - (2 x (-950.8))
  • ΔH_r = +91.6 kJ mol^-1 

• You must make sure that you can apply Hess' Law effectively and calculate enthalpy changes in different situations
• Remember - it is the data that is important
• Check whether the data you have been given is formation data or combustion data, and then complete the cycle or calculation according to that

Worked Example

Answer

Step 1: Write the equation for enthalpy change of formation at the top and add oxygen on both sides

Step 2: Draw the cycle with the combustion products at the bottom

Step 3: Draw all arrows in the correct direction

Step 4: Apply Hess’s Law

• • ΔH_f = ΔH₁ - ΔH₂ 
    • ΔH₂ = ΔH_c [C₂H₆ (g)] 
    • ΔH₁ = 2 x ΔH_c [C_graphite (s)] + 3 x ΔH_c [H₂ (g)]
  • ΔH_r = (2 x (-393.5) + 3 x (-285.8)) - (-1559.7)
  • ΔH_r = -84.7 kJ mol^-1 

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