Hess’s Law

We know that enthalpy is a state function therefore the change in enthalpy is is independent of the path between initial state and final state in other words enthalpy change for the reaction is the same whether it occurs in one step or in a series of multiple step this may be stated as follows in the form of hayes law. If a chemical reaction takes place in multiple steps then it's standard enthalpy of reaction is the sum of the standard enthalpies of the intermediate reactions into which the net chemical reaction can be divided at the same temperature. 

Define Hess Law

Hess’s law, also called Hess law of constant heat summation, is one of the important outcomes of the first law of thermodynamics. The enthalpy change in a chemical or physical process is similar whether it is carried out in one step or in several steps.

Hess's law of constant heat summation was derived in 1840, from a Swiss-born Russian chemist and physician, where, Germain Hess, derived a thermochemistry relationship for calculating the standard reaction enthalpy for the multi-step reactions. In general, it exploits the state functions’ properties, where the state functions’ value does not depend on the path taken for dissociation or formation. Rather, it depends only on the state at the moment (pressure, formation volume, and more related).

Enthalpies for Different Types of Reactions

• Standard Enthalpy of  Combustion - Combustion reactions are exothermic in nature; these are important in industry rocketry and other works of life. standard enthalpy of combustion is defined as the enthalpy change when one mole of substance undergoes combustion at a constant temperature. for example cooking gas in cylinders contains mostly butane during complete combustion of one mole of butane 2658 kilo joule of heat is released

• Enthalpy of Atomisation - Consider the following example of atomization of dihydrogen in 2H you can see that h atoms are formed by breaking h/h bonds in dihydrogen the enthalpy change in this process is known as enthalpy of atomisation it is the enthalpy change on breaking one mole of bonds completely to obtain atoms in the gas phase in case of diatomic molecules live the hydrogen the enthalpy of atomization is also the bond dissociation enthalpy.

• Bond Enthalpy - Chemical reactions involved the breaking and making of chemical bonds energy required to break a bond and energy is released when a bond is formed it is possible to delete heat of a reaction to changes in energy associated with breaking and making of chemical bonds with reference to the enthalpy changes associated with chemical bonds two different terms are used in Thermodynamics bond dissociation enthalpy and mean Bond enthalpy.

• Lattice Enthalpy - The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociate into its ions in gaseous state since it is impossible to determine lattice enthalpy directly by experiment we can use and indirect method where we construct an enthalpy diagram called born Haber cycle.

• Enthalpy of Solution - Enthalpy of solution of a substance is the enthalpy change when 1 mole of it dissolves in a specified amount of solvent the enthalpy of solution is at infinite dilution is the enthalpy change observed on dissolving the substance in an infinite amount of solvent when the interaction between ions are negligible.

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Illustration of Hess’s Law

As we all know that enthalpy is a state function, and thereby, it is independent of the path taken to reach the final state from the initial state. Hess’s law says that for a multistep reaction, the standard reaction enthalpy is independent of either the pathway or the number of steps taken, rather being the sum of standard enthalpies of intermediate reactions that are involved at a similar temperature.

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

Application of Hess Law

Let us discuss some practical areas where Hess’s law is applied. As an example, let us take the formation of Sulphur Trioxide gas from Sulphur, which is a multistep reaction involved in Sulphur Dioxide gas formation. Let us find the enthalpy of the standard reaction for the Sulphur Trioxide gas formation from Sulphur.

Step 1: Sulphur Dioxide gas Formation

S + O2 → SO2, where, △H1=−70.96 KCal/mol

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

SO2 + 12O2 → SO3, where, △H2 = −23.49KCal/mol

Standard reaction enthalpy according to Hess’s Law:

△HR = △H2 + △H1 = (-70.96) + (-23.49) = -94.95KCal/mol

Net Reaction:

S + 32O2 → SO3, where, △HR=−94.95KCal/mol

Therefore, in simple words, we can state as follows.

△HR = △H2 + △H1 + △H3 + △H4 + ….

Formation of Enthalpy Determination

There are various compounds including Co, C6H6, C2H6, and more, whose direct synthesis from their constituent elements cannot be possible. Their △H values are determined indirectly using Hess’s law.

Hess’s Law can be used to determine other state functions with enthalpies like free energy and entropy. The Bordwell thermodynamic cycle can be taken as an example, which takes advantage of Redox potentials and easily measured equilibriums to experimentally determine the inaccessible Gibbs free energy values.

△G(reaction) = Σ△G(product) -  Σ△G(reactants)

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

△S(reaction) = ΣS(product)- ΣS(reactants)

Calculating Standard Enthalpies of Reaction

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

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According to Hess’s law,

Σ△fHo(P) = Σ△fHo(R) + Σ△RHo△RHo

= Σ△fHo(P) - Σ△fHo(R)

= Sum of the standard enthalpies of products’ formation − Sum of the standard enthalpies of reactants’ formation.

Uses of Hess’s Law

Hess's law of constant heat summation can be useful to determine the enthalpies of the following.

• Heats of unstable intermediates formation such as NO(g) and CO(g).

• The ionic substances’ lattice energies by constructing the Born-Haber cycles, if the electron affinity is known to form the anion.

• Heat changes in allotropic transitions and phase transitions.

• Electron affinities with a Born-Haber cycle using theoretical lattice energy.

Example of Hess’s Law

Hess’s Law, which is also called Hess’s Constant Heat Summation Law states, the overall change in enthalpy for the solution can be given by the sum of all changes independent of the various steps or phases of a reaction. This particular rule is a discovery, where enthalpy is a part of the state.

Problem

Calculate the reaction’s standard enthalpy change using the following reaction.

CO2(g) + H2(g) → CO(g) + H2O(g)

Given that, ΔrHo for CO(g), CO2(g), and H2O(g) as -110.5, -393.5, and 241.8kJ/mol respectively.

Solution

ΔrHo for the reaction can be given as 

△rHo = Σ△fHo (Products) - Σ△fHo(Reactants) 

= [△fHo (H2O) + △fHo(CO)] - [△fHo (CO2) + △fHo (H2)]  

Substituting the values that are given, we get the result as follows.

△rHo = −241.8−110.5 = −241.8−110.5 = −393.5+0 

=-352.3 + 393.5, = 41.2 kJ.

Did You Know?

• Hess’s law allows the enthalpy shift (even if it cannot be determined directly) to be estimated for any of the reactions. This can be achieved by carrying simple algebraic operations depending on the Hess’s law equation of the reactions by using the values, which are defined previously for the formation enthalpies.