Popular chemical hand warmers generate heat by the air-oxidation of iron:\({\bf{4Fe(s) + 3}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2F}}{{\bf{e}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}{\bf{(s)}}\).How does the spontaneity of this process depend upon temperature?

The change in Gibbs free energy is as follows:

\({\bf{\Delta G = \Delta H - T\Delta S}}\)

where,

\({\bf{\Delta G }}\) = the change in Gibbs free energy,

\({\bf{\Delta H}}\)= the change in enthalpy,

T = the absolute temperature in Kelvin and

\({\bf{\Delta S}}\)= the change in entropy.

The Gibbs free energy change is used to determine the spontaneity of a process. It is expressed in terms of the enthalpy and the entropy of a system.

The air-oxidation reaction of iron generates heat. The reaction is as follows:

\(4{\rm{Fe}}({\rm{s}}) + 3{{\rm{O}}_2}(\;{\rm{g}}) \to 2{\rm{F}}{{\rm{e}}_2}{{\rm{O}}_3}(\;{\rm{s}})\)

The spontaneity of a reaction is dependent upon the Gibbs free energy change, whereas free energy change depends on the temperature, change in enthalpy and change in entropy. According to Le Chatelier's Principle, when the temperature is increased in an exothermic reaction, the equilibrium moves in the backward direction, thereby resulting in less spontaneity in the forward direction. When the temperature is decreased, the equilibrium moves in the forward direction, and the reaction is also more spontaneous.

The reaction of air-oxidation of iron is as follows:

\(4{\rm{Fe}}({\rm{s}}) + 3{{\rm{O}}_2}(\;{\rm{g}}) \to 2{\rm{F}}{{\rm{e}}_2}{{\rm{O}}_3}(\;{\rm{s}})\)

Heat is released during the air-oxidation of iron; hence it is an exothermic reaction. For the exothermic reaction, the value of change in enthalpy is negative. For the reaction to be spontaneous, the value of change in free energy should also be negative.

\(\Delta {\rm{G}} = \Delta {\rm{H}} - {\rm{T}}\Delta {\rm{S}}\)

For spontaneous reaction,

\(\begin{array}{l}\Delta {\rm{G}} = {\rm{ negative }}\\\Delta {\rm{H}} = {\rm{ negative}}\end{array}\)

The value of change in free energy will be negative only when the value of \(T\)∆\(S\) is less than ∆\({\rm{H}}\). Hence, the given reaction is non-spontaneous at higher temperatures and more spontaneous at lower temperatures.