Chapter U5, Problem C21.3RE

Interpretation Introduction

Interpretation: The heat of reaction for the following decomposition of rust to iron and oxygen gas needs to be determine and whether the reaction is endothermic or exothermic should be explained:

  ${\text{2Fe}}_{\text{2}}{\text{O}}_{\text{3}}\text{(s) }\to {\text{ 4Fe(s) + 3O}}_{\text{2}}\text{(g)}$

Concept Introduction: The change in enthalpy by formation of a compound in 1 mole from its constituent elements in their standard state is said to be standard heat of formation. The ${\text{ΔH}}_{\text{f}}^{\text{o}}$ for a chemical reaction can be calculated using formula:

  ${\text{ΔH}}_{\text{f}}^{\text{o}}{\text{ = ΣnH}}_{\text{f}}^{\text{o}}{\text{(products) - ΣmH}}_{\text{f}}^{\text{o}}\text{(reactants)}$

Where m and n are stoichiometric numbers.

Answer to Problem C21.3RE

The heat of reaction for the decomposition of rust to iron and oxygen gas is $\text{+1652 kJ/mol}$ and the reaction is endothermic.

Explanation of Solution

The given reaction is:

  ${\text{2Fe}}_{\text{2}}{\text{O}}_{\text{3}}\text{(s) }\to {\text{ 4Fe(s) + 3O}}_{\text{2}}\text{(g)}$

The value of heat of formation of all the species involved in the reaction is:

  $\begin{array}{l}{\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\text{(s)}=\text{ -826 kJ/mol}\\ \text{Fe(s) = 0 kJ/mol}\\ {\text{O}}_{\text{2}}\text{(g) = 0 kJ/mol}\end{array}$

The ${\text{ΔH}}_{\text{f}}^{\text{o}}$ for a chemical reaction is calculated as:

  ${\text{ΔH}}_{\text{f}}^{\text{o}}\text{ = }\left[\text{4}\Delta {\text{H}}_{\text{f}}^{\text{o}}\text{(Fe) + 3}\Delta {\text{H}}_{\text{f}}^{\text{o}}{\text{(O}}_{\text{2}}\text{)}\right]\text{ - 2}\Delta {\text{H}}_{\text{f}}^{\text{o}}{\text{(Fe}}_{\text{2}}{\text{O}}_3\text{)}$

Substituting the values:

  $\begin{array}{l}{\text{ΔH}}_{\text{f}}^{\text{o}}\text{ = }\left[\text{4(0 kJ/mol) + 3(0 kJ/mol)}\right]\text{ - 2}\Delta {\text{H}}_{\text{f}}^{\text{o}}\text{(- 826 kJ/mol)}\\ {\text{ΔH}}_{\text{f}}^{\text{o}}\text{ = +1652 kJ/mol}\end{array}$

Thus, the heat of reaction for the decomposition of rust to iron and oxygen gas is $\text{+1652 kJ/mol}$ .

Endothermic and exothermic processes are defined on the basis of energy involved. The addition of energy is endothermic whereas loss of energy is exothermic.

Since, in this process the reaction is added (indicated by positive sign of heat of reaction value) so, it is endothermic.