Hess’s Law (Constant Heat Summation)

What is Hess’s Law?

Hess’s law is one of the important outcomes of the first law of thermodynamics.

The enthalpy change in a chemical or physical process is the same whether the process is carried out in one step or in several steps.

The law for constant heat summation was derived in the year 1840, a Swiss-born Russian chemist and physician, Germain Hess, derived a relationship in thermochemistry for calculating the standard reaction enthalpy for multistep reactions. It basically exploits the properties of state functions, that is the value of state functions does not depend on the path taken for formation or dissociation rather it depends only on state at the moment (temperature, pressure, volume, etc).

As we know enthalpy is a state function, hence, it is independent of the path taken to reach the final state starting from the initial state. According to Hess’s law, for a multistep reaction, the standard reaction enthalpy is independent of the pathway or number of steps taken, rather it is the sum of standard enthalpies of intermediate reactions involved at the same temperature.

The purpose of Hess’s law is to measure the enthalpies of neutralization for several acid-base reactions, then use that information and Hess’s law to determine the reaction enthalpies for two salts in aqueous solution.

Table of Contents

• • Application of Hess’s Law
  • Determination of Enthalpy of Formation
  • Calculation of Standard Enthalpies of Reaction
  • Solved Example
  • Frequently Asked Questions – FAQs

Application of Hess’s Law

Let us look at some practical areas where Hess’s law is applied, for example, the formation of Sulphur Trioxide gas from Sulphur is a multistep reaction involving the formation of Sulphur Dioxide gas. Let us find out the standard reaction enthalpy for the formation of Sulphur Trioxide gas from Sulphur.

Step 1: Formation of Sulphur Dioxide gas

Step 2: Conversion of Sulphur Dioxide gas to Sulphur Trioxide gas

Standard reaction enthalpy as per Hess’s Law:

Net reaction:

Hence, in simple words we can state:

Determination of Enthalpy of Formation

There are many compounds such as C6H6, Co, C2H6 etc, whose direct synthesis from their constituent elements is not possible. Their ΔH values can be determined indirectly by Hess’s law.

As with enthalpy, Hess’s Law can be used to determine other state functions such as free energy and entropy, for example, Bordwell thermodynamic cycle which takes advantage of easily measured equilibriums and Redox potentials to determine experimentally inaccessible Gibbs free energy values.

As entropy can be measured as an absolute value, hence in case of entropy there is no need to use the entropy of formation.

Calculation of Standard Enthalpies of Reaction

From the standard enthalpies of formation of reactants and products, the standard enthalpy of reaction can be calculated using Hess’s law. In general, the Hess’s law cycle representing the formation of reactants and products from their respective elements in the standard state is considered as

According to Hess’s law,

Solved Example

Question:

Calculate the standard enthalpy change for a reaction
CO₂(g) + H₂(g) → CO(g) + H₂O(g)
Given that Δ_rH^o for CO2(g), CO(g) and H₂O(g) as -393.5, -110.5 and 241.8kJ/mol respectively.

Solution:

Δ_rH^o for the reaction is given as

Substituting the given values, we get

= + 41.2 kJ

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