Introductory Chemistry: A Foundation - Zumdahl S.S., DeCoste D.J. 2019

Hess’s Law


· To understand Hess’s law.

One of the most important characteristics of enthalpy is that it is a state function. That is, the change in enthalpy for a given process is independent of the pathway for the process. Consequently, in going from a particular set of reactants to a particular set of products, the change in enthalpy is the same whether the reaction takes place in one step or in a series of steps. This principle, which is known as Hess’s law , can be illustrated by examining the oxidation of nitrogen to produce nitrogen dioxide. The overall reaction can be written in one step, where the enthalpy change is represented by .

This reaction can also be carried out in two distinct steps, with the enthalpy changes being designated as and :

Note that the sum of the two steps gives the net, or overall, reaction and that

The importance of Hess’s law is that it allows us to calculate heats of reaction that might be difficult or inconvenient to measure directly in a calorimeter.

Characteristics of Enthalpy Changes

To use Hess’s law to compute enthalpy changes for reactions, it is important to understand two characteristics of for a reaction:

1. If a reaction is reversed, the sign of is also reversed.

2. The magnitude of is directly proportional to the quantities of reactants and products in a reaction. If the coefficients in a balanced reaction are multiplied by an integer, the value of is multiplied by the same integer.

Both these rules follow in a straightforward way from the properties of enthalpy changes. The first rule can be explained by recalling that the sign of indicates the direction of the heat flow at constant pressure. If the direction of the reaction is reversed, the direction of the heat flow also will be reversed. To see this, consider the preparation of xenon tetrafluoride, which was the first binary compound made from a noble gas:

This reaction is exothermic, and kJ of energy flows into the surroundings as heat. On the other hand, if the colorless crystals are decomposed into the elements, according to the equation

the opposite energy flow occurs because kJ of energy must be added to the system to produce this endothermic reaction. Thus, for this reaction, .

The second rule comes from the fact that is an extensive property, depending on the amount of substances reacting. For example, because kJ of energy is evolved for the reaction

then for a preparation involving twice the quantities of reactants and products, or

twice as much heat would be evolved:

Critical Thinking

· What if Hess’s law were not true? What are some possible repercussions this would have?

Interactive Example 10.6. Hess’s Law

Two forms of carbon are graphite, the soft, black, slippery material used in “lead” pencils and as a lubricant for locks, and diamond, the brilliant, hard gemstone. Using the enthalpies of combustion for graphite ( kJ/mol) and diamond ( kJ/mol), calculate for the conversion of graphite to diamond:


Where Are We Going?

We want to determine for the conversion of graphite to diamond.

What Do We Know?

The combustion reactions are

How Do We Get There?

Note that if we reverse the second reaction (which means we must change the sign of ) and sum the two reactions, we obtain the desired reaction:

Thus kJ of energy is required to change mole of graphite to diamond. This process is endothermic.

Self-Check: Exercise 10.6

· From the following information

calculate for the reaction

See Problems 10.45, 10.46, 10.47, and 10.48.