Understanding the Calculation of Hess’s Law Cycle (Hess’s Law)

Hess’s Law calculation determines enthalpy changes using indirect reaction pathways. It simplifies complex thermochemical problems efficiently.

This article explores detailed formulas, common values, and real-world applications of Hess’s Law cycles for expert understanding.

• Calculate the enthalpy change for the reaction: C + O₂ → CO₂ using Hess’s Law cycle.
• Determine ΔH for the formation of NH₃ from N₂ and H₂ using given enthalpies of intermediate reactions.
• Use Hess’s Law to find the enthalpy change of combustion of methane from standard enthalpies of formation.
• Calculate the enthalpy change for the reaction of graphite to diamond using Hess’s Law cycle data.

Comprehensive Table of Common Enthalpy Values for Hess’s Law Calculations

These values represent standard enthalpies of formation (ΔH°f) at 298 K, essential for Hess’s Law cycle calculations. The zero values correspond to elemental standard states.

Fundamental Formulas for Calculation of Hess’s Law Cycle

Hess’s Law states that the total enthalpy change for a reaction is the same, regardless of the pathway taken. This principle allows calculation of unknown enthalpy changes by combining known reactions.

The core formula for Hess’s Law is:

Where:

• ΔH_reaction = Enthalpy change of the overall reaction (kJ/mol)
• Σ ΔH_steps = Sum of enthalpy changes of individual steps (kJ/mol)

When using standard enthalpies of formation, the enthalpy change of a reaction can be calculated as:

Where:

• n = Stoichiometric coefficient of each species
• ΔH°_f = Standard enthalpy of formation of each species (kJ/mol)

For Hess’s Law cycle involving intermediate reactions, the enthalpy change is calculated by algebraic addition of the enthalpy changes of the steps, considering the direction of each reaction:

Each ΔH_step must be multiplied by -1 if the reaction is reversed.

Explanation of Variables and Common Values

• ΔH°_f: Standard enthalpy of formation is the enthalpy change when one mole of a compound forms from its elements in their standard states at 298 K and 1 atm. Values are tabulated and widely available.
• n: Stoichiometric coefficients are derived from balanced chemical equations.
• ΔH_reaction: The target enthalpy change, either known or to be calculated.
• Temperature and Pressure: Standard values are at 298 K and 1 atm; deviations require corrections.

Real-World Application Examples of Hess’s Law Cycle Calculation

Example 1: Calculating the Enthalpy Change for the Formation of Carbon Monoxide (CO)

Given the following reactions and their enthalpy changes:

• C (graphite) + O₂ (g) → CO₂ (g), ΔH° = -393.5 kJ/mol
• CO (g) + 1/2 O₂ (g) → CO₂ (g), ΔH° = -283.0 kJ/mol

Calculate the enthalpy change for the reaction:

C (graphite) + 1/2 O₂ (g) → CO (g)

Solution:

Step 1: Write the target reaction:

C (graphite) + 1/2 O₂ (g) → CO (g)

Step 2: Use Hess’s Law by manipulating the given reactions:

• Reverse the second reaction to get CO₂ → CO + 1/2 O₂, changing the sign of ΔH°:
CO₂ (g) → CO (g) + 1/2 O₂ (g), ΔH° = +283.0 kJ/mol
• Add this reversed reaction to the first reaction:
C (graphite) + O₂ (g) → CO₂ (g), ΔH° = -393.5 kJ/mol
CO₂ (g) → CO (g) + 1/2 O₂ (g), ΔH° = +283.0 kJ/mol

Step 3: Add the reactions and their enthalpy changes:

Cancel CO₂ (g) on both sides:

Step 4: Calculate ΔH°:

Result: The enthalpy change for the formation of CO is -110.5 kJ/mol.

Example 2: Determining the Enthalpy Change for the Combustion of Methane (CH₄)

Given the standard enthalpies of formation:

• CH₄ (g): ΔH°_f = -74.8 kJ/mol
• CO₂ (g): ΔH°_f = -393.5 kJ/mol
• H₂O (l): ΔH°_f = -285.8 kJ/mol
• O₂ (g): ΔH°_f = 0 kJ/mol (elemental standard state)

Calculate the enthalpy change for the combustion reaction:

CH₄ (g) + 2 O₂ (g) → CO₂ (g) + 2 H₂O (l)

Solution:

Step 1: Apply the formula for enthalpy change using standard enthalpies of formation:

Step 2: Substitute values:

Result: The combustion of methane releases -890.3 kJ/mol of energy.

Additional Considerations and Advanced Insights

Hess’s Law is foundational in thermochemistry, enabling indirect determination of enthalpy changes that are difficult to measure directly. It relies on the state function property of enthalpy, meaning the path taken does not affect the total enthalpy change.

When applying Hess’s Law, it is critical to ensure:

• All reactions are balanced correctly, including physical states.
• Enthalpy values correspond to the same temperature and pressure conditions.
• Reactions reversed have their enthalpy changes sign inverted.
• Stoichiometric coefficients are applied as multipliers to enthalpy changes.

For reactions at temperatures other than 298 K, corrections using heat capacities (C_p) and Kirchhoff’s equation may be necessary:

Where ΔC_p is the difference in heat capacities between products and reactants.

Summary of Key Points for Expert Application

• Hess’s Law allows calculation of unknown enthalpy changes by summing known reaction enthalpies.
• Standard enthalpies of formation are essential data, available in authoritative thermodynamic tables.
• Careful manipulation of reaction equations (reversing, scaling) is required to construct Hess’s Law cycles.
• Temperature corrections may be necessary for non-standard conditions.
• Real-world applications include combustion analysis, synthesis enthalpy determination, and phase change energetics.

References and Further Reading

• NIST Chemistry WebBook – Standard Enthalpies of Formation
• Thermopedia – Hess’s Law and Thermochemical Cycles
• LibreTexts – Hess’s Law