Hess's Law

Hydrogen gas leaking from electric cars can react with the ozone layer in the atmosphere and produce water. For reactions like this, directly measuring the enthalpy change in a laboratory setting is difficult.

However, this reaction can be carried out in the lab in two steps to measure the enthalpy of each step.

In step 1, oxygen gas is converted to ozone gas, and ΔH₁ = +285.4 kJ. In step 2, hydrogen and oxygen gases combine to produce water vapor, and ΔH₂ = −483.6 kJ.

As enthalpy is a state function, the enthalpy change of a reaction depends only on the initial state of the system, hydrogen and ozone, and the final state, water, regardless of the intermediate steps.

Hess’s Law of constant heat summation states that if a chemical equation can be written in multiple steps, then the net enthalpy change for the equation can be written as a sum of enthalpies associated with each step.

Often, thermochemical reactions must be manipulated in order to make the reactions sum to a given reaction. The stoichiometric quantities and the direction of the reaction can be changed and a new enthalpy of each manipulated reaction can be determined.

In this example, the two steps with known changes in enthalpy cannot directly be added to find the unknown enthalpy of reaction.

This is because the first equation has ozone as a product, while the reaction of interest has ozone as a reactant.

To account for this, the first equation, an endothermic reaction, must be converted into the reverse exothermic reaction where ozone decomposes into oxygen and releases 285.4 kJ. The new ΔH has the same value but the opposite sign.

Still, adding the reverse of step 1 and step 2 does not yield the 3 moles of water as in the conversion of ozone to water because the stoichiometric coefficients are different.

To account for this, the stoichiometric coefficients of each of the reactions and their associated enthalpy changes must be multiplied by factors that allow the coefficient to match the reaction of interest or cancel out. Because enthalpy change depends on the amounts of reactants and products, the ratio between the coefficients and the enthalpy change remains constant.

To obtain 3 moles of water, step 2 must be multiplied by 3 over 2 giving a new ΔH₂ of −725.4 kJ.

To consume 1 mole of ozone, the reverse of step 1 must be multiplied by 1 over 2, giving a new ΔH₁ of −142.7 J.

Summing the modified thermochemical equation and canceling all compounds that appear in both reactants and products, yields the reaction of interest. When the new ΔH₁ and ΔH₂ are added, the enthalpy change for the reaction between hydrogen and ozone is −868.1 kJ.