Hess’s Law

Full Notes

What is Hess’s Law?

Many chemical and physical processes occur in multiple steps, each with its own enthalpy change (ΔH).

Definition:
Hess’s Law states: “The total enthalpy change for a reaction is the same, regardless of the pathway taken, provided the initial and final conditions are the same.”

This means we can calculate the overall enthalpy change by adding the ΔH values of individual steps:

ΔH°_Overall = ΔH₁ + ΔH₂ + ΔH₃ + …

Why It Works

Hess’s Law is a consequence of the first law of thermodynamics: energy cannot be created or destroyed.

The total energy change (ΔH) depends only on the initial and final states — not on how the reaction gets there. Whether a process happens in one step or several, the total ΔH will be the same if start and end points are the same.

Matt’s exam tip

Hess’s Law only applies when the starting and ending conditions — like temperature and pressure — are the same in each path. Always double-check this before applying the law.

How to Use Hess’s Law – Key Rules

1. Reversing a reaction → reverse the sign of ΔH
   If a reaction is endothermic in one direction, it becomes exothermic in the reverse.
   

   Example:
   If A → B ΔH = +50 kJ
   then B → A ΔH = −50 kJ

2. Multiplying a reaction → multiply ΔH by the same factor
   Enthalpy is an extensive property, so it scales with the amount of substance.
   

   Example:
   If A → B ΔH = +50 kJ
   then 2A → 2B ΔH = +100 kJ

3. Adding reactions → add their ΔH values
   The overall enthalpy change is the sum of steps.
   

   Example:
   If A → B ΔH = +50 kJ
   and B → C ΔH = −20 kJ
   then A → C ΔH = +30 kJ

Worked Example: Using Hess’s Law

Matt’s exam tip

Be methodical and don't rush! Always check that your final equation matches the target before summing ΔH values. Keep workings very clear!

Other Uses of Hess’s Law

Hess’s Law is useful when direct measurement is difficult – we can use enthalpy cycles to calculate ΔH indirectly.

• Enthalpy of formation (ΔH_f) calculations
• Enthalpy of combustion (ΔH_c) calculations

2. Hess’s Law for Enthalpy of Formation

See Topic 6.8 for more detail.

ΔH_f = enthalpy change when one mole of a compound is formed from its elements in standard states.
For elements in standard states, ΔH_f = 0.

Formula: ΔH_r = ΣΔH_f(products) − ΣΔH_f(reactants)

Example: Formation of CO₂

• C(s) + O₂(g) → CO₂(g)
• ΔH_f(CO₂) = −393 kJ mol⁻¹
• ΔH_f(O₂) = 0

ΔH_r = −393 − (0 + 0) = −393 kJ mol⁻¹

3. Hess’s Law for Enthalpy of Combustion

ΔH_c = enthalpy change when one mole of a substance is completely burned in oxygen.

Example: Using enthalpies of combustion to find ΔH_f of propane (C₃H₈)

Data:
ΔH_c(C) = −394 kJ mol⁻¹
ΔH_c(H₂) = −286 kJ mol⁻¹
ΔH_c(C₃H₈) = −2220 kJ mol⁻¹

We can combust 3C(s) + 4H₂(g) to form 3CO₂(g) + 4H₂O(l), or combust C₃H₈(g) to form the same products.

By Hess’s Law: route 1 = route 2

ΔH₁ = ΔH? + ΔH₂
ΔH? = ΔH₁ − ΔH₂
ΔH? = (−2326) − (−2220) = −106 kJ mol⁻¹

4. Constructing and Using Hess’s Cycles

• Identify known enthalpy values (formation or combustion).
• Draw an enthalpy cycle showing different pathways.
• Apply Hess’s Law equations to calculate the unknown enthalpy change.

Summary

• Hess’s Law simplifies thermodynamic calculations by breaking a reaction into steps.
• Apply known enthalpy values and combine them to find total ΔH.
• You don’t need to run the full reaction — just combine known reactions!