1.8.4 Hess Cycles

• In 1840, the Russian chemist Germain Hess formulated a law which went on to be known as Hess’s Law
• This went on to form the basis of one of the laws of thermodynamics. The first law of thermodynamics relates to the Law of Conservation of Energy
• It is sometimes expressed in the following form:

Energy cannot be created or destroyed, it can only change form

• This means that in a closed system, the total amount of energy present is always constant
• Hess’s law can be used to calculate the standard enthalpy change of a reaction from known standard enthalpy changes
• Hess’s Law states that:

"The total enthalpy change in a chemical reaction is independent of the route by which the chemical reaction takes place as long as the initial and final conditions are the same."

• This means that whether the reaction takes place in one or two steps, the total enthalpy change of the reaction will still be the same

The diagram above illustrates Hess’ Law: the enthalpy change of the direct route, going from reactants (A+B) to product (C) is equal to the enthalpy change of the indirect routes

• Hess’ Law is used to calculate enthalpy changes which can’t be found experimentally using calorimetry, e.g.:

3C (s) + 4H₂ (g) → C₃H₈(g)

• Δ_fH (propane) can’t be found experimentally as hydrogen and carbon don’t react under standard conditions

Calculating Δ_rH from Δ_fH using Hess’s Law energy cycles

• You can see the relationships on the following diagram:

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

 

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

OR

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

• Equation

ΔH₂ = ΔH₁ + ΔH_r

Therefore for energy to be conserved,

ΔH_r = ΔH₂ – ΔH₁

• Hess cycles can be used to calculate various enthalpy changes as long as sufficient information about the other sides of the cycle is known

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

• • Δ_rH = ΔH₂ - ΔH₁
    • It is minus ΔH₁ because you have to go in the opposite direction of the arrow
  • ΔH₂ is Δ_fH [Na₂CO₃ (s)] + Δ_fH [CO₂ (g)] + Δ_fH [H₂O (l)]
  • ΔH₁ is 2 x Δ_fH [NaHCO₃ (s)]
  • Δ_rH = (Δ_fH [Na₂CO₃ (s)] + Δ_fH [CO₂ (g)] + Δ_fH [H₂O (l)]) - (2Δ_fH [NaHCO₃ (s)])
  • Δ_rH = ((-1130.7) + (-393.5) + (-285.8)) - (2 x (-950.8))
  • Δ_rH = +91.6 kJ mol^-1