6.10: Hess’s Law

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally determined enthalpy changes. Some reactions are difficult, if not impossible, to investigate and make accurate measurements for experimentally. And even when a reaction is not hard to perform or measure, it is convenient to be able to determine the heat involved in a reaction without having to perform an experiment.

This type of calculation usually involves the use of Hess’s law, which states: If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps. Hess’s law is valid because enthalpy is a state function: Enthalpy changes depend only on where a chemical process starts and ends, but not on the path it takes from start to finish. For example, the reaction of carbon with oxygen to form carbon dioxide occurs either directly or by a two-step process. The direct process is written as:

In the two-step process, first carbon monoxide is formed:

Then, carbon monoxide reacts further to form carbon dioxide:

The equation describing the overall reaction is the sum of these two chemical changes:

Because the CO produced in Step 1 is consumed in Step 2, the net change is:

According to Hess’s law, the enthalpy change of the reaction will equal the sum of the enthalpy changes of the steps.

ΔH of the overall reaction is the same, regardless of whether it occurs in one step or two. This finding (overall ΔH for the reaction = sum of ΔH values for reaction “steps” in the overall reaction) is true in general for chemical and physical processes.

There are two important features of ΔH that prove useful while solving problems using Hess’s law. This is based on the fact that ΔH is directly proportional to the quantities of reactants or products, and changing the reaction (or the thermochemical equation) in well-defined ways changes the ΔH accordingly.

For example, the enthalpy change for the reaction forming 1 mole of NO₂ (g) is +33.2 kJ:

When 2 moles of NO₂ (twice as much) are formed, the ΔH is twice as large:

In general, if multiplying or dividing a chemical equation, the change in enthalpy should also be multiplied or divided by the same number.

ΔH for a reaction in one direction is equal in magnitude and opposite in sign to ΔH for the reaction in the reverse direction. For example:

Then, for the reverse reaction, the enthalpy change is also reversed:

This text is adapted from Openstax, Chemistry 2e, Section 5.3: Enthalpy.

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.