Hess Law

Hess’s Law of Constant Heat Summation states the enthalpy change for a reaction is always the same irrespective of the path followed by reactants and intermediates to give the final products. In other words, the enthalpy of a reaction remains unchanged whether the reaction proceeds in one step or multiple steps.

The enthalpy of the overall reaction is the sum of the enthalpies of every individual reaction.

The law was revealed by Swiss-Russian chemist and doctor Germain Henri Hess. He introduced the law in its 1840’s publication.

Explanation

Consider reactant R undergoing a chemical change to form product P. reactant R can also form intermediate I, which further converts into product P—see the below diagram.

The Heat of reaction for reactant R to product P is ΔHrxn. And the heat of reactions for reactant R to intermediate I and intermediate I to product P are ΔHrxn1 and ΔHrxn2.

According to Hess’s law of constant heat summation:

ΔHrxn = ΔHrxn1 + ΔHrxn2

Thus, we can rephrase the law: the overall heat of reaction is the sum of the heat of reaction of every intermediate step. The enthalpy change for reactions is additive if the sum of all intermediate reactions leads to the final desired reaction.

The law is not a new idea or concept. Instead, it is the manifestation of the fact that enthalpy is a state function.

What does a state function mean? A quantity in thermodynamics is said to be a state function or function of state if its definition solely relies on its current thermodynamic state. A state function can be expressed by state variables, like temperature, pressure, volume.

The enthalpy of a system is a state function because we can estimate the enthalpy solely based on certain state variables. Irrespective of how the system is formed, the enthalpy for a given state is always going to be the same. Enthalpy is independent of the path followed by the system.

If we know the enthalpy of formation of all the components taking part in a series of reactions, we can estimate the heat of reaction of the overall reaction using the below formula.

ΔHrxn = ∑ΔHf(prod) − ∑ΔHf(react)

Here, ΔHrxn is the enthalpy change for a reaction, ∑ΔHf(react) is the sum of the enthalpy of formation of all reactants, and ∑ΔHf(prod) is the sum of the enthalpy of formation of all products.

If ΔHrxn is a negative value, then the reaction is exothermic, i.e., heat is evolved from the reaction. But if ΔHrxn is a positive value, the reaction is endothermic, which means the reaction absorbs the heat from its surroundings.

Example

Consider a simple reaction that produces hydrogen gas from hydrocarbons, e.g., methane (CH4):

CH4(g) + 2H2O(g) --> CO2(g) + 4H2(g)

This reaction takes place in two steps. The first step is steam reforming.

CH4(g) + H2O(g) --> CO(g) + 3H2(g)

Steam-methane reforming is an industrial reaction, whose main purpose is to produce hydrogen gas. In fact, the world’s most hydrogen gas is obtained by this reaction.

The heat of reaction for the steam reforming reaction is:

ΔHrxn1 = ∑ΔHf(prod) − ∑ΔHf(react) = ΔHf(CO) + 3ΔHf(H2) − (ΔHf(CH4) + ΔHf(H2O)) = −110.53 + 3*0 − (−74.53 − 241.82) = 205.82 KJ/mol.

ΔHrxn1 is positive, so the reaction is endothermic.

The second step is the water-gas shift reaction.

CO(g) + H2O(g) --> CO2(g) + H2(g)

In the water-gas shift reaction, carbon monoxide reacts with water vapor to form carbon dioxide and hydrogen gas. Hydrogen is liberated in this step too.

The heat of reaction for the water-gas shift reaction is:

ΔHrxn2 = ∑ΔHf(prod) − ∑ΔHf(react) = ΔHf(CO2) + ΔHf(H2) − (ΔHf(CO) + ΔHf(H2O)) = −393.51 + 0 − (−110.53 − 241.82) = −41.16 KJ/mol.

ΔHrxn2 is negative, so the reaction is mildly exothermic.

According to Hess’s law, the heat of reaction of the overall reaction is ΔHrxn = ΔHrxn1 + ΔHrxn2 = 205.82 − 41.16 = 164.66 KJ/mol.

For Hess’s law to be true, the addition of intermediate reactions should give the overall reaction. In the case of our example, this holds. Adding the last two reactions gives the first reaction.

CH4(g) + H2O(g) + CO(g) + H2O(g) --> CO(g) + 3H2(g) + CO2(g) + H2(g)

CH4(g) + 2H2O(g) --> 4H2(g) + CO2(g)

Other things to be considered for the validation of Hess’s law are conditions. We have used the standard heat of formation of species to calculate the heat of reaction. So, the enthalpy change for the reactions is valid only for standard conditions (T = 298.15 K, P = 1 bar). For non-standard conditions, we have to account for the effect of temperature or pressure on the assessed values.

Extension of the law to other state functions

Hess’s law is the manifestation of the fact that enthalpy is a state function. This concept can be extended to other state functions, like entropy, Gibbs free energy, and Helmholtz free energy.

The change in entropy of a reaction as follows:

ΔSrxn = ∑ΔS(prod) − ∑ΔS(react)

For the change in Gibbs free energy of a reaction,

ΔGrxn = ∑ΔG(prod) − ∑ΔG(react)

And for the change in Helmholtz free energy,

ΔArxn = ∑ΔA(prod) − ∑ΔA(react)