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Chapter 16: Q16.9 CYL (page 900)

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?

Short Answer

Expert verified

The given reaction is non-spontaneous at higher temperatures and more spontaneous at lower temperatures.

Step by step solution

01

Define enthalpy of the reaction

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.

02

Determine the Gibbs free energy change using free energies of formation  

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.

03

Determine the Gibbs free energy change using entropies

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.

04

Determine the Gibbs free energy change using free energies of formation  

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

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.

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Most popular questions from this chapter

An important source of copper is from the copper ore, chalcocite, a form of copper(I) sulfide. When heated, the \({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{S}}\) decomposes to form copper and sulfur described by the following equation:

\({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{\;S(s)}} \to {\bf{Cu(s) + S(s)}}\)

(a) Determine \({\bf{\Delta G}}_{{\bf{298}}}^{\bf{^\circ }}\)for the decomposition of \({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{S(\;s)}}\).

(b) The reaction of sulfur with oxygen yields sulfur dioxide as the only product. Write an equation that describes this reaction, and determine\({\bf{\Delta G}}_{{\bf{298}}}^{\bf{^\circ }}\)for the process.

(c) The production of copper from chalcocite is performed by roasting the \({\bf{C}}{{\bf{u}}_{\bf{2}}}{\bf{S}}\) in air to produce the \({\bf{Cu}}\). By combining the equations from Parts (a) and (b), write the equation that describes the roasting of the chalcocite, and explain why coupling these reactions together makes for a more efficient process for the production of the copper.

What happens to \({\bf{\Delta G}}_{{\bf{298}}}^{\bf{^\circ }}\) (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) \({\bf{S(s) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{S}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

(b) \({\bf{2S}}{{\bf{O}}_{\bf{2}}}{\bf{(g) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{S}}{{\bf{O}}_{\bf{3}}}{\bf{(g)}}\)

(c) \({\bf{HgO(s)}} \to {\bf{Hg(l) + }}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\)

Calculate ΔG° using

(a) free energies of formation and

(b) enthalpies of formation and entropies(Appendix G). Do the results indicate the reaction to be spontaneous or nonspontaneous at 25 °C?

\({{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}{\bf{(g)}} \to {{\bf{H}}_{\bf{2}}}{\bf{(g) + }}{{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}{\bf{(g)}}\)

Use the thermodynamic data provided in Appendix G to calculate the equilibrium constant for the dissociation of dinitrogen tetraoxide at 25 °C.

Use the information in Appendix G to estimate the boiling point of CS2.
See all solutions

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