T - Standard Enthalpies of Formation and Hess's Law (Lesson)

Standard Enthalpies of Formation and Hess's Law

Enthalpies of Formation

Thus far, this module has discussed the energy changes associated with various chemical and physical processes. The heat energy associated with these changes has been expressed in the form of heats of reaction ($\Delta$H_rxn) and can be thought of as a stoichiometric factor as previous examples have shown. In this lesson, the energy changes associated with a very specific type of chemical reaction will be explored. Namely, enthalpy of formation reactions will be investigated.

A formation reaction is defined as a chemical reaction that occurs to produce exactly 1 mole of a substance from its constituent elements in their elemental forms. For example, the formation reaction for magnesium bromide is shown below:

Mg (s) + Br₂ (l)  $\longrightarrow$  MgBr₂ (s)

Notice in this example that the reactants are the elements that are found in the compound magnesium bromide.  Also, it should be noted that these elements are presented in their elemental forms at standard temperature and pressure.  Magnesium metal would be a solid at STP while bromine is a diatomic element that would exist as a liquid under those same conditions.

Because of the way a formation reaction is defined, the coefficients used to balance these equations can sometimes be a bit odd. Formation reactions are required to have a coefficient of 1 for the product; therefore, the reactants must sometimes utilize fractional coefficients, if necessary, to balance the reaction. For example, consider the formation reaction of water:

H₂ (g) + $\frac{1}{2}$O₂ (g)  $\longrightarrow$  H₂O (l)

The enthalpy change associated with any formation reaction is referred to as the standard enthalpy of formation ($\Delta H_f^{^{\circ}}$) for the particular reaction being studied. Another important aspect of formation reactions is that, by definition, the standard enthalpy of formation for any element is zero due to the fact that no formation reaction can be written for an element. Using the formation reaction of water, it can be understood that the $\Delta H_f^{^{\circ}}$ for hydrogen and oxygen are both zero, and any enthalpy change for the reaction would therefore be the $\Delta H_f^{^{\circ}}$ of water itself. This allows for the tabulation of $\Delta H_f^{^{\circ}}$ values for many substances to be used in the calculation of $\Delta$H_rxn for a wide variety of reactions as shown below.

Calculation of Heats of Reaction Utilizing Enthalpies of Reaction and Hess's Law

Utilizing Hess's law and tabulated $\Delta H_f^{^{\circ}}$ values, it is possible to calculate the $\Delta$H_rxn for any reaction using the following equation:

$\Delta H_{rxn}=\Sigma\Delta H_f^{^{\circ}}\left(products\right)-\Sigma\Delta H_f^{^{\circ}}\left(reactants\right)$

It is important to note that in order to utilize this method for calculating $\Delta$H_rxn, it is necessary to consult tabulated data as mentioned above. An example of this data can be accessed from Openstax. A sample of the pertinent data has been organized in the table below to show how to calculate the $\Delta$H_rxn for the following reaction:

4 NH₃ (g) + 5 O₂ (g)  $\longrightarrow$  4 NO (g) + 6 H₂O (g)

Table

Substance	$\Delta H^{^{\circ}}_f$ (kJ/mol)
NH3 (g)	-45.9
O2 (g)	0
NO (g)	90.3
H2O (g)	-241.8

$\Delta H_{rxn}=\Sigma\Delta H_f^{^{\circ}}\left(products\right)-\Sigma\Delta H_f^{^{\circ}}\left(reactants\right)$

$\Delta H_{rxn}=[(4\times90.3)+(6\times-241.8)]-[(4\times-45.9)+(5\times0)]=-906kJ$

Notice in the example above that not only were the $\Delta H_f^{^{\circ}}$ values for the reactants subtracted from those of the products, but each value was also multiplied by the coefficient from the balanced chemical equation that was provided.

You Try It!

In the following self-assessment activity, find $\Delta H_{rxn}.$ Click on the plus sign to check your answer!

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