About the enthalpy of formation $\Delta H_f$

As you already know, a chemical reaction needs thermal energy to occur. This is has already been introduced as a change on enthalpy $\Delta H$.

The proper name for $\Delta H$ is heat of reaction or enhtalpy of formation. Also, its nomenclature is more commonly found as $\Delta H_f$. 

However, since the compounds  involved in chemical reactions are to be used at the same conditions (must be) it is common practice to use enthalpy data at 1 atm and 25 °C. This is called standard condition. In this way, what we will be treating is in fact the standard enthalpy of formation $\Delta H_f^{\circ}$.

How to identify (or write) a reaction of formation

First, a reaction of formation is one that produces 1 mol of product from the corresponding elements. These type of reactions have a thermodynamical meaning, because of $\Delta H$, and are at the foundations of more complex reactions. 

Fig. 1 A sketch of important features of a reaction of formation

Identification and formulation of reactions of formation can be done if one follows the below observations and/or features,

Reactions of  formation are restricted to a single product

This a key feature of a reaction of this type. In contrast with other variations of chemical reactions, these are restricted to a single compound as the product.

A reaction of formation only produces 1 mole of product

This means that on the side of the products, the coefficient before the compound is 1. For example, if we consider the reaction of formation for HBr(g), this would be written as,

$\frac{1}{2}$H$_2$(g) + $\frac{1}{2}$Br$_2$(l) $\rightarrow$ HBr(g)        Eq. (01)

Notice that the coefficient of HBr(g) is 1.

Reactants should be elements

On the side of the reactants, compounds are not allowed. The idea of a reaction of formation is based on elements solely. For example, the following reaction aiming to form 1mol of N$_2$O$_5$(g),

2NO$_2$(g) + $\frac{1}{2}$O$_2$(g) $\rightarrow$ N$_2$O$_5$(g)        Eq. (02)

is not a reaction of formation.The reason? On the reactants side the first one is not an element but a compound. Perhaps, it would be better written in terms of N$_2$ and O$_2$.

Fig. 2 Detail on the features of a reaction of formation.

Only the most stable forms of the elements are allowed

This could require a memory exercise and good database of elements and its typical simplest forms. Only the smallest and most stable forms of the elements, at standard conditions (1atm,25 °C), are permitted. For example:

• for oxygen three different molecular species exist. These are: O, O$_2$ and O$_3$. However, since O$_2$(g) is the most stable form of oxygen, this shall be the one to be used;
• for hydrogen two different molecular species exist. These are: H and H$_2$. Since H$_2$(g) is the most stable form of hydrogen, this shall be the one to be used.

For the sake of simplicity you may identify the most stable form, among several availables, from data tables. The most stable molecular specie of a given element is the one with $\Delta H_f^{\circ}=0$.

Fractionary coefficients are allowed

Since the reaction of formation is forced to produce 1 mol of product a price is to be paid. As a consequence, the coefficients of the reactants may be fractionary numbers. Equations (01-02) are examples of this.

Test your knowledge

You can check if you have carefully read this post. Answer the quizz below and find out!

What you know about reactions of formation

Any question? Write in the comments and I shall try to help.

Other stuff of interest

• Some basic concepts on thermodynamics
• Who was Clausius?
• Processes at constant volume and pressure
• Composition variables in mixtures
• The first law of thermodynamics and some concepts
• Partial and total derivatives (for thermodynamics)
• First law of thermodynamics for chemical reactions
• Solving the Colebrook equation

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Ildebrando.