Reactivity 1.2.2 – Hess’s Law

Historical Context of Hess’s Law

• Hess’s Law was established in 1840 by the Russian chemist Germain Hess, who was among the first to systematically study energy changes in chemical reactions.
• The law provided one of the earliest formal expressions of energy conservation in chemistry, and it remains foundational to thermochemical calculations.
• It enables indirect determination of enthalpy changes by algebraically combining reactions with known enthalpy values, regardless of whether the direct route is feasible to measure experimentally.

Link to the First Law of Thermodynamics

• Hess’s Law reflects the First Law of Thermodynamics, which states that energy cannot be created or destroyed in an isolated system.
• All chemical reactions conserve energy — they merely convert it between different forms, such as potential, kinetic, or thermal energy.
• Because enthalpy is a state function, its value depends only on the initial and final conditions, not on the process taken to get there.
• This means that the enthalpy change for a chemical reaction is the same whether it occurs in one step or through multiple intermediates — which is the core principle behind Hess’s Law.

What Is Hess’s Law?

Hess’s Law states that the total enthalpy change for a chemical reaction is independent of the route or pathway taken, provided that the initial and final conditions are the same.

Formal Statement

“If a reaction can be carried out by more than one route, the total enthalpy change is the same for each route.”

Why Hess’s Law Works

• Enthalpy depends only on the energy difference between the reactants and products.
• It does not matter how many steps are involved or what intermediates form during the reaction.
• This allows us to construct enthalpy cycles or use algebraic methods to deduce unknown values.

Enthalpy Cycles (Hess Cycles)

In many applications, a triangle or cycle is used to visualize the different routes a reaction can take. These are called Hess cycles. They often involve standard enthalpy changes such as:

• Standard enthalpy of formation (\( \Delta H_f^\circ \))
• Standard enthalpy of combustion (\( \Delta H_c^\circ \))

We can apply Hess’s Law mathematically using simple addition and subtraction of enthalpy changes:

\( \Delta H_{\text{overall}} = \Delta H_1 + \Delta H_2 + \ldots \)

Applications of Hess’s Law

1. Calculating Enthalpy Changes That Cannot Be Measured Directly

Some reactions are difficult or dangerous to perform in a laboratory (e.g., combustion of toxic gases or reactions involving unstable intermediates). In such cases, Hess’s Law allows chemists to determine the enthalpy change indirectly using other known reactions.

2. Determining Enthalpy of Formation (\( \Delta H_f^\circ \))

If the enthalpy of formation of a compound is not available directly, it can be calculated using Hess’s Law with known combustion data or other formation enthalpies.

\( \Delta H^\circ_{\text{rxn}} = \sum \Delta H_f^\circ (\text{products}) – \sum \Delta H_f^\circ (\text{reactants}) \)

3. Calculating Enthalpy of Combustion (\( \Delta H_c^\circ \))

Hess’s Law is useful for calculating the enthalpy of combustion when direct measurements are difficult or when comparing combustion of different fuels for energy efficiency analysis.

\( \Delta H^\circ_{\text{rxn}} = \sum \Delta H_c^\circ (\text{reactants}) – \sum \Delta H_c^\circ (\text{products}) \)

Note: This is the reverse of the formation method because combustion data represent a reaction going to a common product (e.g., CO₂ and H₂O).

4. Thermochemical Cycles in Energetics

Hess’s Law is used to construct enthalpy cycles (or energy cycles), which help visualize and solve problems involving multiple steps and overlapping data. This is especially useful in problems involving:

• Lattice enthalpies

• Electron affinities

5. Comparing Stability of Compounds

Using enthalpy data calculated via Hess’s Law, chemists can compare relative stabilities of isomers, allotropes (e.g., graphite vs. diamond), and different molecular arrangements.

6. Verifying Experimental Data

Experimental enthalpy values can be cross-checked using Hess’s Law. If measured and calculated values don’t agree, this may point to experimental error, heat loss, or incorrect assumptions.

7. Supporting the Concept of State Functions

Hess’s Law reinforces the principle that enthalpy is a state function, helping students and researchers conceptually understand the independence of energy changes from reaction pathways.

How to Use Hess’s Law

When a target reaction cannot be measured directly, its enthalpy change can be determined by manipulating other known reactions and applying Hess’s Law.

General Strategy

1. Write the given reactions with known \( \Delta H \) values.
2. Modify these reactions (reverse or multiply) to match the overall target reaction.
3. Apply the same modifications to the \( \Delta H \) values:
   • Reversing a reaction: change the sign of \( \Delta H \).
   • Multiplying a reaction: multiply \( \Delta H \) by the same factor.
4. Add the modified equations and sum their enthalpy changes to get \( \Delta H_{\text{target}} \).