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Chapter 16: Q16.4-67E (page 913)

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

Short Answer

Expert verified
  1. As the partial pressure of oxygen is increased the ratio of pressures decreases which would in effect decrease the value of \(\Delta G\) and make it more negative.
  2. As the partial pressure of oxygen is increased the ratio of pressures decreases which would in effect decrease the value of \(\Delta G\) and make it more negative.
  3. As the partial pressure of oxygen is increased the value of \(\ln \left( {{{\rm{P}}_{{\rm{O}}2}}} \right)\) will also increase which would in effect increase the value of \(\Delta G\) and make it more positive.

Step by step solution

01

Define free energy change

The free energy change is related to the partial pressures of the reactants and products through the following equation:

\(\Delta {\rm{G}} = \Delta {{\rm{G}}^0} + {\rm{RTln}}\left[ {\frac{{{\rm{ Partial pressure of products }}}}{{{\rm{ partial pressure of reactants }}}}} \right] - - - (1)\)

\(\Delta {{\rm{G}}^0} = \)standard free energy change

\({\rm{R}} = \) gas constant and \({\rm{T}} = \) temperature

02

a) Determine the decomposition reaction.

The given reaction is:

\({\rm{S}}({\rm{s}}) + {{\rm{O}}_2}(\;{\rm{g}}) \to {\rm{S}}{{\rm{O}}_2}(\;{\rm{g}})\)

Based on equation (1)

\(\Delta {\rm{G}} = \Delta {{\rm{G}}^0} + {\rm{RT}}\ln \left[ {\frac{{{{\rm{P}}_{{\rm{S}}{{\rm{O}}_2}}}}}{{{{\rm{P}}_{{{\rm{O}}_2}}}}}} \right]\)

As the partial pressure of oxygen is increased the ratio of pressures decreases which would in effect decrease the value of \(\Delta G\) and make it more negative.

03

b) Determine the free energy of the decomposition reaction.

The given reaction is:

\(2{\rm{S}}{{\rm{O}}_2}(\;{\rm{g}}) + {{\rm{O}}_2}(\;{\rm{g}}) \to 2{\rm{S}}{{\rm{O}}_3}(\;{\rm{g}})\)

Based on equation (1)

\(\Delta {\rm{G}} = \Delta {{\rm{G}}^0} + {\rm{RTln}}\left[ {\frac{{{\rm{P}}_{{\rm{S}}{{\rm{O}}_3}}^2}}{{{\rm{P}}_{{\rm{S}}{{\rm{O}}_2}}^2{{\rm{P}}_{{{\rm{O}}_2}}}}}} \right]\)

As the partial pressure of oxygen is increased the ratio of pressures decreases which would in effect decrease the value of \(\Delta G\) and make it more negative.

04

Determine the value of standard Gibbs free energy change

The given reaction is:

\({\rm{HgO}}({\rm{s}}) \to {\rm{Hg}}({\rm{l}}) + {{\rm{O}}_2}(\;{\rm{g}})\)

Based on equation (1)

\(\Delta {\rm{G}} = \Delta {{\rm{G}}^0} + {\rm{RTln}}\left[ {{{\rm{P}}_{{{\rm{O}}_2}}}} \right]\)

As the partial pressure of oxygen is increased the value of \(\ln \left( {{{\rm{P}}_{{\rm{O}}2}}} \right)\) will also increase which would in effect increase the value of \(\Delta G\) and make it more positive.

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Most popular questions from this chapter

Without doing a numerical calculation, determine which of the following will reduce the free energy change for the reaction, that is, make it less positive or more negative, when the temperature is increased. Explain.

(a) \({{\bf{N}}_{\bf{2}}}{\bf{(g) + 3}}{{\bf{H}}_{\bf{2}}}{\bf{(g)}} \to {\bf{2N}}{{\bf{H}}_{\bf{3}}}{\bf{(g)}}\)

(b) \({\bf{HCl(g) + N}}{{\bf{H}}_{\bf{3}}}{\bf{(g)}} \to {\bf{N}}{{\bf{H}}_{\bf{4}}}{\bf{Cl(s)}}\)

(c) \({\left( {{\bf{N}}{{\bf{H}}_{\bf{4}}}} \right)_{\bf{2}}}{\bf{C}}{{\bf{r}}_{\bf{2}}}{{\bf{O}}_{\bf{7}}}{\bf{(s)}} \to {\bf{C}}{{\bf{r}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}{\bf{(s) + 4}}{{\bf{H}}_{\bf{2}}}{\bf{O(g) + }}{{\bf{N}}_{\bf{2}}}{\bf{(g)}}\)

(d) \({\bf{2Fe(s) + 3}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}} \to {\bf{F}}{{\bf{e}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}{\bf{(s)}}\)

"Thermite" reactions have been used for welding metal parts such as railway rails and in metal refining. One such thermite reaction is \({\bf{F}}{{\bf{e}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}{\bf{(s) + 2Al(s)}} \to {\bf{A}}{{\bf{l}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}{\bf{(s) + 2Fe(s)}}\). Is the reaction spontaneous at room temperature under standard conditions? During the reaction, the surroundings absorb \({\bf{851}}{\bf{.8\;kJ/mol}}\)of heat.

Describe how matter and/or energy is redistributed when you empty a canister of compressed air into a room.

Consider the system shown in Figure 16.9. What is the change in entropy for the process where all the energy is transferred from the hot object (AB) to the cold object (CD)

Under what conditions is \({{\bf{N}}_{\bf{2}}}{{\bf{O}}_{\bf{3}}}{\bf{(g)}} \to {\bf{NO(g) + N}}{{\bf{O}}_{\bf{2}}}{\bf{(g)}}\) spontaneous?
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