Hess’ Law & Enthalpy Cycles
Calculating ΔHr from ΔHf 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 + ΔHr
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 + ΔHr
Therefore,
ΔHr = ΔH2 – ΔH1
Worked example
Calculating the enthalpy change of reaction
Calculate the ΔHf for the following reaction:
2NaHCO3 (s) → Na2CO3 (s) + CO2 (g) + H2O (I)
The table below shows the standard enthalpy of formations (ΔHf) relevant to this reaction:
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
-
- ΔHr = ΔH2 - ΔH1
- ΔH2 = ΔHf [Na2CO3 (s)] + ΔHf [CO2 (g)] + ΔHf [H2O (l)]
- ΔH1 = 2 x ΔHf [NaHCO3 (s)]
- ΔHr = ((-1130.7) + (-393.5) + (-285.8)) - (2 x (-950.8))
- ΔHr = +91.6 kJ mol-1
- ΔHr = ΔH2 - ΔH1
- 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
Calculating the enthalpy change of formation of ethane
Calculate ΔHf [ethane]. The relevant change in standard enthalpy of combustion (ΔHc) values are shown in the table below:
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
-
- ΔHf = ΔH1 - ΔH2
- ΔH2 = ΔHc [C2H6 (g)]
- ΔH1 = 2 x ΔHc [Cgraphite (s)] + 3 x ΔHc [H2 (g)]
- ΔHr = (2 x (-393.5) + 3 x (-285.8)) - (-1559.7)
- ΔHr = -84.7 kJ mol-1
- ΔHf = ΔH1 - ΔH2
Exam Tip
There are two rules that you can use to help with your calculations using enthalpy changes of formation and combustion
- Using enthalpy changes of formation, ΔHf
- ΔrH = ∑ΔHf(products) - ∑ΔHf(reactants)
- Using enthalpy changes of combustion, ΔHc
- ΔrH = ∑ΔHc(reactants) - ∑ΔHc(products)
