Hess’s Law (OpenStax Chemistry 2e)
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, we can think of the reaction of carbon with oxygen to form carbon dioxide as occurring either directly or by a two-step process. The direct process is written:
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.
The result is shown in Figure 1. We see that ΔH of the overall reaction is the same 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.
The two important features of ΔH are the following:
- ΔH is directly proportional to the quantities of reactants or products. 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 will be twice as large:
In general, if we multiply or divide an equation by a number, then the enthalpy change should also be multiplied or divided by the same number.
2. 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, given that:
Then, for the “reverse” reaction, the enthalpy change is also “reversed”:
We also can use Hess’s law to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products are available. The stepwise reactions we consider are: (i) decompositions of the reactants into their component elements (for which the enthalpy changes are proportional to the negative of the enthalpies of formation of the reactants), followed by (ii) re-combinations of the elements to give the products (with the enthalpy changes proportional to the enthalpies of formation of the products). The standard enthalpy change of the overall reaction is therefore equal to: (ii) the sum of the standard enthalpies of formation of all the products plus (i) the sum of the negatives of the standard enthalpies of formation of the reactants. This is usually rearranged slightly to be written as follows, with ∑ representing “the sum of” and n standing for the stoichiometric coefficients:
Flowers, P., Theopold, K., Langley, R., & Robinson, W. R. (2019, February 14). Chemistry 2e. Houston, Texas: OpenStax. Access for free at: https://openstax.org/books/chemistry-2e
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