Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions

Calculate ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ for each reaction using ${\mathbf{\text{ΔG}}}_{\mathbf{\text{f}}}^{\mathbf{\text{°}}}$ values:

(a)  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+I}}}_{\mathbf{\text{2}}}\mathbf{\text{(s)}}\mathbf{\to }\mathbf{\text{2HI(g)}}$

(b)  ${\mathbf{\text{MnO}}}_{\mathbf{\text{2}}}\mathbf{\text{(s)+2CO(g)}}\mathbf{\to }{\mathbf{\text{Mn(s)+2CO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

(c)${\mathbf{\text{NH}}}_{\mathbf{\text{4}}}\mathbf{\text{Cl(s)}}\mathbf{\to }{\mathbf{\text{NH}}}_{\mathbf{\text{3}}}\mathbf{\text{(g)+HCl(g)}}$

State qualitatively the relationship between entropy and freedom of particle motion. Use this idea to explain why you will probably never 

(a) be suffocated because all the air near you has moved to the other side of the room; 

(b) see half the water in your cup of tea freeze while the other half boils.

Why is $∆{\text{S}}_{\text{vap}}$of a substance always larger than $∆{\text{S}}_{\text{fus}}$.

How does the entropy of the surroundings change during an exothermic reaction? An endothermic reaction? Other than the examples in text, describe a spontaneous endothermic process.

(a) What is the entropy of a perfect crystal at $\text{0 K}$?

(b) Does entropy increase or decrease as the temperature rises?  

(c) Why is ${\text{∆H}}_{\text{f}}^{\text{o}}\text{ = 0}$ but ${\text{S}}^{\text{o}}\text{ > 0}$ for an element?  

(d)  Why does Appendix B list $∆{\text{H}}_{\text{f}}^{\text{o}}$ values but not $∆{\text{S}}_{\text{f}}^{\text{o}}$ values? 

Which of the following processes are spontaneous? 

(a) Methane burns in air. 

(b) A teaspoonful of sugar dissolves in a cup of hot coffee. 

(c) A soft-boiled egg becomes raw.

Distinguish between the terms spontaneous and instantaneous. Give an example of a process that is spontaneous but very slow, and one that is very fast but not spontaneous.

Distinguish between the terms spontaneous and nonspontaneous. Can a nonspontaneous process occur? Explain.

State the first law of thermodynamics in terms of 

(a) the energy of the universe. 

(b) the creation or destruction of energy; 

(c) the energy change of system and surroundings. Does the first law reveal the direction of spontaneous change? Explain.

Without consulting Appendix B, arrange each group in order of decreasing standard molar entropy (S°). Explain.

 (a)   $\mathbf{Cl}{{\mathbf{O}}_{\mathbf{4}}}^{\mathbf{-}}$(aq), $\mathbf{Cl}{{\mathbf{O}}_{\mathbf{2}}}^{\mathbf{-}}$(aq), $\mathbf{Cl}{{\mathbf{O}}_{\mathbf{3}}}^{\mathbf{-}}$(aq)

(b)   ${\mathbf{NO}}_{\mathbf{2}}$(g),  $\mathbf{NO}$(g), ${\mathbf{N}}_{\mathbf{2}}$(g)

(c)   ${\mathbf{Fe}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}$(s),  ${\mathbf{Al}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}$(s),  ${\mathbf{Fe}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{4}}$(s).

Without consulting Appendix B, arrange each group in order of decreasing standard molar entropy (S°). Explain. 

(a) Mg metal, Ca metal, Ba metal 

(b) Hexane $\mathbf{\left(}{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{14}}\mathbf{\right)}$, benzene $\mathbf{\left(}{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{6}}\mathbf{\right)}$, cyclohexane $\mathbf{\left(}{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{12}}\mathbf{\right)}$ 

(c) ${\mathbf{PF}}_{\mathbf{2}}{\mathbf{Cl}}_{\mathbf{3}}$(g), ${\mathbf{PF}}_{\mathbf{5}}$(g), ${\mathbf{PF}}_{\mathbf{3}}$(g).

For the reaction depicted in the molecular scenes, X is red and Y is green. 

1. Write a balanced equation. 
2. Determine the sign of ΔS. 
3. Which species has the highest molar entropy?

Describe the equilibrium condition in terms of the entropy changes of a system and its surroundings. What does this description mean about the entropy change of the universe?

For the reaction  ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{C}{\mathbf{l}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathbf{HClO}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$, you know ${\mathbf{\Delta S}}_{\mathbf{rxn}}^{\mathbf{o}}$ and  ${\mathbf{S}}^{\mathbf{o}}$of HClO(g) and of  ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$(g). Write an expression that can be used to determine  ${\mathbf{S}}^{\mathbf{o}}$ of ${\mathbf{\text{Cl}}}_{\mathbf{2}}\mathbf{O}$(g).

For each reaction, predict the sign and find the value of  ${\mathbf{\Delta S}}^{\mathbf{o}}$:

$\begin{array}{c}\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{3}\mathbf{NO}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{N}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{F}{\mathbf{e}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathbf{Fe}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}{\mathbf{P}}_{\mathbf{4}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }{\mathbf{P}}_{\mathbf{4}}{\mathbf{O}}_{\mathbf{10}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\end{array}$

For each reaction, predict the sign and find the value of  ${\mathbf{\Delta S}}^{\mathbf{o}}$:

data-custom-editor="chemistry" $\begin{array}{c}\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{3}\mathbf{N}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{HNO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{+}\mathbf{NO}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}{\mathbf{N}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{F}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{NF}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}{\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{12}}{\mathbf{O}}_{\mathbf{6}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{6}{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\end{array}$

Find ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the combustion of ethane $\mathbf{\left(}{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}\mathbf{\right)}$to carbon dioxide and gaseous water. Is the sign of ${\mathbf{\Delta S}}^{\mathbf{o}}$ as expected?

Find  ${\mathbf{\Delta S}}^{\mathbf{o}}$for the combustion of methane to carbon dioxide and liquid water. Is the sign of  ${\mathbf{\Delta S}}^{\mathbf{o}}$as expected?

Find ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the reaction of nitrogen monoxide with hydrogen to form ammonia and water vapor. Is the sign of  ${\mathbf{\Delta S}}^{\mathbf{o}}$ as expected?

Find ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the combustion of ammonia to nitrogen dioxide and water vapor. Is the sign of  ${\mathbf{\Delta S}}^{\mathbf{o}}$ as expected?

Find ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the formation of  ${\mathbf{\text{CU}}}_{\mathbf{2}}\mathbf{\text{O}}$(s) from its elements.

: Find  ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the formation of HI(g) from its elements.

Find  ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the formation of  ${\mathbf{CH}}_{\mathbf{3}}\mathbf{OH}$(l) from its elements.

Find ${\mathbf{\Delta S}}^{\mathbf{o}}$  for the formation of   (g) from its elements.

Sulfur dioxide is released in the combustion of coal. Scrubbers use aqueous slurries of calcium hydroxide to remove the ${\mathbf{SO}}_{\mathbf{2}}$ from flue gases. Write a balanced equation for this reaction and calculate ${\mathbf{\Delta S}}^{\mathbf{o}}$ at 298 K [ ${\mathbf{S}}^{\mathbf{o}}$of  ${\mathbf{CaSO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{=}\mathbf{101}\mathbf{.}\mathbf{4}$J/mol K].

Oxyacetylene welding is used to repair metal structures, including bridges, buildings, and even the Statue of Liberty. Calculate ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the combustion of $\mathbf{1}$ mole of acetylene ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}$.

What is the advantage of calculating free energy changes rather than entropy changes to determine reaction spontaneity?

Given that ${\mathbf{\Delta G}}_{\mathbf{sys}}\mathbf{ }\mathbf{=}\mathbf{-}{\mathbf{T\Delta S}}_{\mathbf{univ}}$, explain how the sign of ${\mathbf{\Delta G}}_{\mathbf{sys}}$ correlates with reaction spontaneity.

(a) Is an endothermic reaction more likely to be spontaneous at higher temperatures or lower temperatures? Explain.

(b) The change depicted below occurs at constant pressure. Explain your answers to each of the following: 

(1) What is the sign of  $\mathbf{\Delta H}$? 

(2) What is the sign of  $\mathbf{\Delta S}$? 

(3) What is the sign of  ${\mathbf{\Delta S}}_{\mathbf{surr}}$? 

(4) How does the sign of $\mathbf{\Delta G}$ vary with temperature?

Calculate K at $\mathbf{\text{298 K}}$  for each reaction:

(a)  $\mathbf{\text{NO(g)+}}\frac{\mathbf{\text{1}}}{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{NO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

(b)  $\mathbf{\text{2HCl(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+Cl}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

(c)${\mathbf{\text{2C(graphite)+O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }\mathbf{\text{2CO(g)}}$

The scenes and the graph relate to the reaction of  ${\mathbf{\text{X}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$ (black) with  ${\mathbf{\text{Y}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$ (orange) to form $\mathbf{\text{XY(g)}}$.

(a) If reactants and products are in their standard states, what quantity is represented on the graph by x?

(b) Which scene represents point 1? Explain. 

(c) Which scene represents point 2? Explain.

As a fuel, ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{( g)}}$ produces only nonpolluting   ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}}$when it burns. Moreover, it combines with  ${\mathbf{\text{O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$in a fuel cell (Chapter 21) to provide electrical energy.

(a) Calculate ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}{\mathbf{\text{, ΔS}}}^{\mathbf{\text{°}}}$ , and ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ per mole of  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$at 298 K.

(b) Is the spontaneity of this reaction dependent on T? Explain.

(c) At what temperature does the reaction become spontaneous?

A reaction that occurs in the internal combustion engine is

 ${\mathbf{\text{N}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }\mathbf{\text{2NO(g)}}$

 (a) Determine ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$ and ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$  for the reaction at  $\mathbf{\text{298 K}}$.

(b) Assuming that these values are relatively independent of temperature, calculate  ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$at  ${\mathbf{\text{100.}}}^{\mathbf{\text{°}}}{\mathbf{\text{C, 2560.}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$, and  ${\mathbf{\text{3540.}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$.

(c) What is the significance of the different values of ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ ?

One reaction used to produce small quantities of pure ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$ is

 ${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{OH(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{CO(g)+2H}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

 (a) Determine ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$ and ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$ for the reaction at $\mathbf{\text{298 K}}$ .

(b) Assuming that these values are relatively independent of temperature, calculate  ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$at${\mathbf{\text{28}}}^{\mathbf{\text{°}}}{\mathbf{\text{C,128}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$ , and ${\mathbf{\text{228}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$.

(c) What is the significance of the different values of   ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$?

Consider the combustion of butane gas:

 ${\mathbf{\text{C}}}_{\mathbf{\text{4}}}{\mathbf{\text{H}}}_{\mathbf{\text{10}}}\mathbf{\text{(g)+}}\frac{\mathbf{\text{13}}}{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{4CO}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+5H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}}$

 (a) Predict the signs of  ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}{\mathbf{\text{ and ΔH}}}^{\mathbf{\text{°}}}$. Explain.

(b) Calculate ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ by two different methods.

Consider the oxidation of carbon monoxide:

 $\mathbf{\text{CO(g)+}}\frac{\mathbf{\text{1}}}{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{CO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

(a) Predict the signs of ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$ and ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$ . Explain.

(b) Calculate ${\text{ΔG}}^{\text{°}}$ by two different methods

What is the difference between ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ and $\mathbf{\text{ΔG}}$ ? Under what circumstances does  ${\mathbf{\text{ΔG=ΔG}}}^{\mathbf{\text{°}}}$?

How is the free energy change of a process related to the work that can be obtained from the process? Is this quantity of work obtainable in practice? Explain.

(a) If K<<1 for a reaction, what do you know about the sign and magnitude of ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ ? 

(b) If ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}\mathbf{\text{<<0}}$ for a reaction, what do you know about the magnitude of K? Of Q?

Use  ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$and  ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$values to find the temperature at which these sulfur allotropes reach equilibrium at  $\mathbf{\text{1 atm}}$:

 $\mathbf{\text{S(rhombic)}}\mathbf{\rightleftharpoons }\mathbf{\text{S(monoclinic)}}$

Use  ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$and ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$  values for the following process at $\mathbf{\text{1 atm}}$ to find the normal boiling point of ${\mathbf{\text{Br}}}_{\mathbf{\text{2}}}$  :

 ${\mathbf{\text{Br}}}_{\mathbf{\text{2}}}\mathbf{\text{(l)}}\mathbf{\rightleftharpoons }{\mathbf{\text{Br}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

For the gaseous reaction of carbon monoxide and chlorine to form phosgene  $\mathbf{\left(}{\mathbf{\text{COCl}}}_{\mathbf{\text{2}}}\mathbf{\right)}$ :

(a) Calculate ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$ at  $\mathbf{\text{298 K}}\mathbf{(}{\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}\mathbf{\text{=-220.kJ/mol}}$and  ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}\mathbf{\text{=-206 kJ/mol)}}$.

(b) Assuming that ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$ and ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$ change little with temperature, calculate ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ at  $\text{450.K}$.

For the gaseous reaction of xenon and fluorine to form xenon hexafluoride:

(a) Calculate ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$ at  $\mathbf{\text{298 K}}\mathbf{(}{\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}\mathbf{\text{=-402 kJ/mol}}$ and  ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}\mathbf{\text{=-280.kJ/mol}}$ ).

(b) Assuming that ${\mathbf{\text{ΔS}}}^{\mathbf{\text{°}}}$ and  ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}$change little with temperature, calculate   ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$at 500. K.

With its components in their standard states, a certain reaction is spontaneous only at high $\mathbf{T}$. What do you know about the signs of  ${\mathbf{\Delta H}}^{\mathbf{o}}$ and ${\mathbf{\Delta S}}^{\mathbf{o}}$? Describe a process for which this is true.

How can ${\mathbf{\Delta S}}^{\mathbf{o}}$ be relatively independent of $\mathbf{T}$ if  ${\mathbf{S}}^{\mathbf{o}}$ of each reactant and product increases with $\mathbf{T}$?

Calculate ${\mathbf{\Delta G}}^{\mathbf{\circ }}$for each reaction using  ${\mathbf{\Delta G}}_{\mathbf{f}}^{\mathbf{\circ }}$values:

(a)  $\mathbf{2}\mathbf{Mg}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathbf{MgO}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$

(b)  $\mathbf{2}{\mathbf{CH}}_{\mathbf{3}}\mathbf{OH}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

(c)  $\mathbf{BaO}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{C}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }{\mathbf{BaCO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}$

Find ${\mathbf{\Delta G}}^{\mathbf{\circ }}$  for the reactions in Problem 20.50 using  ${\mathbf{\Delta H}}_{\mathbf{f}}^{\mathbf{\circ }}$ and ${\mathbf{S}}^{\mathbf{\circ }}$ values.

The U.S. government requires automobile fuels to contain a renewable component. Fermentation of glucose from corn yields ethanol, which is added to gasoline to fulfil this requirement:

 ${\mathbf{\text{C}}}_{\mathbf{\text{6}}}{\mathbf{\text{H}}}_{\mathbf{\text{12}}}{\mathbf{\text{O}}}_{\mathbf{\text{6}}}\mathbf{\text{(s)}}\mathbf{\to }{\mathbf{\text{2C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{5}}}{\mathbf{\text{OH(l)+2CO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

Calculate ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}{\mathbf{\text{,ΔS}}}^{\mathbf{\text{°}}}$, and ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ for the reaction at ${\mathbf{\text{25}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$ . Is the spontaneity of this reaction dependent on T? Explain

Find  ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$for the reactions in Problem 20.51 using  ${\mathbf{\text{ΔH}}}_{\mathbf{\text{f}}}^{\mathbf{\text{°}}}$ and  S values.

Calculate K at $\mathbf{\text{298 K}}$ for each reaction:

(a)  ${\mathbf{\text{SrSO}}}_{\mathbf{\text{4}}}\mathbf{\text{(s)}}\mathbf{\rightleftharpoons }{\mathbf{\text{Sr}}}^{\mathbf{\text{2+}}}{{\mathbf{\text{(aq)+SO}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{2-}}}\mathbf{\text{(aq)}}$

(b)  ${\mathbf{\text{2NO(g)+Cl}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }\mathbf{\text{2NOCl(g)}}$

(c)${\mathbf{\text{Cu}}}_{\mathbf{\text{2}}}{\mathbf{\text{ S(s)+O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{2Cu(s)+SO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$