# Hess's Law Hess's law, also known as the heat summation law, is a fundamental principle in chemistry and thermodynamics that allows predicting changes in the enthalpy of a chemical reaction based on enthalpy information from previous chemical reactions.

This law, named after the Russian-German chemist Germain Henri Hess, has been a pillar in the understanding of the energy involved in chemical reactions and has played a crucial role in the formulation of theories and prediction of chemical reactions.

## Definition: What Does Hess's Law Say? Hess's law is based on the fundamental principle that the change in the enthalpy of a chemical reaction is an extensive magnitude, which means that its value does not depend on the way in which the final reaction is reached, but only on the initial and final states.

In other words, if a chemical reaction can be divided into several intermediate stages, the change in total enthalpy will be equal to the sum of the changes in enthalpy of those intermediate stages.

### Explanatory Example

To better understand this concept, let's consider the following example.

Suppose we want to determine the change in enthalpy of the reaction A → C, but we do not have the direct information for this reaction. However, we have information about the reactions A → B and B → C, and we can use Hess's law to calculate the change in enthalpy of A → C.

Hess's law states that:

ΔH(A → C) = ΔH(A → B) + ΔH(B → C)

In other words, the change in enthalpy of the reaction A → C is equal to the sum of the changes in enthalpy of the reactions A → B and B → C. This principle is valid even if the intermediate reactions are not real and only They are used as a way to break down the desired reaction into smaller steps.

## Hess's Law Formula

Hess's law is expressed by the following formula:

ΔH_total = ΣΔH_products - ΣΔH_reagents

Where:

• ΔH_total is the change in the enthalpy of the chemical reaction in question.

• Σ (sigma) indicates the sum of the terms.

• ΔH_products is the sum of the enthalpies of the reaction products.

• ΔH_reagents is the sum of the enthalpies of the reactants of the reaction.

## Examples of Applications of Hess's Law Hess's law has a wide variety of applications in chemistry and thermodynamics. Some of the most notable applications include:

• Calculation of changes in the standard enthalpy of formation : The standard enthalpy of formation is the enthalpy of a reaction that forms one mole of a substance from its elements in its most stable state at 25°C and 1 atmosphere of pressure. Hess's law is used to calculate these standard enthalpies of formation, which provides crucial information about the stability of chemical compounds.
• Predicting the feasibility of chemical reactions : By knowing the changes in the enthalpy of the chemical reactions involved, it is possible to determine whether a reaction will be exothermic (releases heat) or endothermic (absorbs heat). This is essential to predict whether a reaction is thermodynamically favorable or unfavorable.
• Optimization of industrial processes : In the chemical industry, Hess's law is used to optimize production processes, ensuring that the chemical reactions involved are as efficient as possible in terms of energy and resource consumption.
• Calculating the enthalpy of non-experimental reactions : In many cases, it is not possible to directly measure the change in enthalpy of a reaction. Hess's law allows these values ​​to be estimated from experimentally related reactions.

## Hess's Law Exercises

Below we show two exercises that demonstrate how Hess's law is used to calculate changes in the enthalpy of chemical reactions based on information from related reactions.

### Exercise 1: Calculate the Change in Enthalpy for the Following Reaction

2H₂(g) + O2(g) → 2H₂O(g)

Based on the following information:

ΔH1: H₂(g) + 1/2O₂(g) → H₂O(g) has a value of -286 kJ/mol. ΔH₂: H₂(g) + 1/2O₂(g) → H₂O₂(g) has a value of -196 kJ/mol.

Solution

To calculate the change in enthalpy of the given reaction, you can apply Hess's law. The given reaction can be decomposed into two stages:

Step 1: 2H₂(g) + O₂(g) → 2H₂O₂(g) (multiplying ΔH₂ by 2)

Step 2: 2H₂O₂(g) → 2H₂O(g) (multiplying ΔH₁ by 2)

Then the change in total enthalpy is the sum of ΔH1 and ΔH₂:

ΔH_total = (2 * ΔH₂) + (2 * ΔH₁) = (2 * -196 kJ/mol) + (2 * -286 kJ/mol) = -392 kJ/mol - 572 kJ/mol = -964 kJ/mol

Therefore, the change in enthalpy for the given reaction is -964 kJ.

### Exercise 2: Calculate the Change in Enthalpy for the Following Reaction

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g)

Use the following information:

ΔH₁: C(s) + O₂(g) → CO₂(g) has a value of -393.5 kJ/mol. ΔH₂: H₂(g) + 1/2O₂(g) → H₂O(g) has a value of -285.8 kJ/mol. ΔH₃: C₃H₈(g) + 5/2O₂(g) → 3CO₂(g) + 4H₂O(g) has a value of -2045 kJ/mol.

Solution

To calculate the change in enthalpy of the given reaction, we will decompose the reaction into its intermediate steps using Hess's law:

• C₃H₈(g) → 3C(s) + 4H₂(g)

• 3C(s) + 4H₂(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g)

ΔH_total = ΔH₁ + ΔH₂ + ΔH₃

ΔH_total = (-393.5 kJ/mol) + [4 * (-285.8 kJ/mol)] + (-2045 kJ/mol)

ΔH_total = -393.5 kJ/mol - 1143.2 kJ/mol - 2045 kJ/mol

ΔH_total = -3581.7 kJ/mol

Therefore, the change in enthalpy for the given reaction is -3581.7 kJ.

## Limitations of the Law

Although Hess's law is a powerful tool in chemistry and thermodynamics, it has some important limitations.

One of the key limitations is that this law only applies to changes in enthalpy and does not provide information about other thermodynamic parameters such as entropy or Gibbs free energy.

Furthermore, Hess's law assumes that changes in enthalpy are additive and do not depend on the specific conditions of the reaction, which may not be completely accurate in certain situations, especially at high pressures or extremely low temperatures.

## Conclusion

Hess's law is a fundamental principle in chemistry and thermodynamics that allows predicting changes in the enthalpy of chemical reactions using information about related reactions.

This law has been crucial in the formulation of theories and in the prediction of chemical reactions in a wide variety of applications, from the determination of the enthalpy of formation to the optimization of industrial processes.

Despite some limitations, Hess's law remains an essential tool in the field of chemistry and thermodynamics.

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Published: November 1, 2023
Last review: November 1, 2023