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

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

(a)  ${\mathbf{\text{2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{ S(g)+3O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{2H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(g)+2SO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

(b)  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{SO}}}_{\mathbf{\text{4}}}\mathbf{\text{(l)}}\mathbf{\rightleftharpoons }{\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O(l)+SO}}}_{\mathbf{\text{3}}}\mathbf{\text{(g)}}$

(c)  $\mathbf{\text{HCN(aq)+NaOH(aq)}}\mathbf{\rightleftharpoons }{\mathbf{\text{NaCN(aq)+H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(l)}}$

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

 (a)  data-custom-editor="chemistry" ${\mathbf{\text{MgCO}}}_{\mathbf{\text{3}}}\mathbf{\text{(s)}}\mathbf{\rightleftharpoons }{\mathbf{\text{Mg}}}^{\mathbf{\text{2+}}}{{\mathbf{\text{(aq)+CO}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{2-}}}\mathbf{\text{(aq)}}$

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

(c) ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{2}}}\mathbf{\text{(l)}}$

For the reaction ${\mathbf{\text{I}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g)+Cl}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }\mathbf{\text{2ICl(g)}}$, calculate K_p at ${\mathbf{\text{25}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}\mathbf{[}{\mathbf{\text{ΔG}}}_{\mathbf{\text{f}}}^{\mathbf{\text{°}}}$ of $\mathbf{\text{ICl(g)=-6.075 kJ/mol}}\mathbf{]}$.

The K_SP of PbCl₂ is $\mathbf{1}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}$ at ${\mathbf{25}}^{\mathbf{°}}\mathbf{\text{C}}$. What is $\mathit{\Delta }{\mathit{G}}^{\mathbf{°}}$? Is it possible to prepare a solution that contains ${\mathbf{\text{Pb}}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}$ and ${\mathbf{\text{Cl}}}^{\mathbf{-}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}$, at their standard-state concentrations?

According to advertisements, "a diamond is forever."

(a) Calculate $\mathit{\Delta }{\mathit{H}}^{\mathbf{°}}\mathbf{,}\mathit{\Delta }{\mathit{S}}^{\mathbf{°}}$ , and  $\mathit{\Delta }{\mathit{G}}^{\mathbf{°}}$ at 298k for the phase change Diamond $\to$graphite.

(b) Given the conditions under which diamond jewelry is normally kept, argue for and against the statement in the ad.

(c) Given the answers in part (a), what would need to be done to make synthetic diamonds from graphite?

(d) Assuming  $\mathit{\Delta }{\mathit{H}}^{\mathbf{°}}$ and  $\mathit{\Delta }{\mathit{S}}^{\mathbf{°}}$ do not change with temperature, can graphite be converted to diamond spontaneously at 1 atm?

Replace each question mark with the correct information:

Among the many complex ions of cobalt are the following: 

$\mathbf{\text{Co}}{{\mathbf{\left(}{\mathbf{\text{NH}}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{6}}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{3}\mathbf{\text{en}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{\text{Co}}{{\mathbf{\left(}\mathbf{\text{en}}\mathbf{\right)}}_{\mathbf{3}}}^{\mathbf{3}\mathbf{+}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{\text{NH}}}_{\mathbf{3}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}$ where "en" stands for ethylenediamine, ${\mathbf{\text{H}}}_{\mathbf{2}}{\mathbf{\text{NCH}}}_{\mathbf{2}}{\mathbf{\text{CH}}}_{\mathbf{2}}{\mathbf{\text{NH}}}_{\mathbf{2}}$. Six $\mathbf{\text{Co}}\mathbf{-}\mathbf{\text{N}}$ bonds are broken and six $\mathbf{\text{Co}}\mathbf{-}\mathbf{\text{N}}$ bonds are formed in this reaction, so $\mathit{\Delta }{\mathit{H}}_{\mathbf{\text{rxn}}}^{\mathbf{°}}\mathbf{\approx }\mathbf{0}$; yet $\mathit{K}\mathbf{>}\mathbf{1}$ . What are the signs of $\mathit{\Delta }{\mathit{S}}^{\mathbf{°}}$ and $\mathit{\Delta }{\mathit{G}}^{\mathbf{°}}$? What drives the reaction?

What is the change in entropy when 0.200ml of potassium freezes at $\mathbf{63}{\mathbf{.7}}^{\mathbf{°}}\mathbf{\text{C}}\mathbf{(}\mathbf{\Delta }{\mathbf{H}}_{\mathbf{\text{fus }}}\mathbf{=}\mathbf{2}\mathbf{.39}\mathbf{ }\mathbf{\text{kJ}}\mathbf{/}\mathbf{\text{mol}}\mathbf{)}$?

Is each statement true or false? If false, correct it.

(a) All spontaneous reactions occur quickly.

(b) The reverse of a spontaneous reaction is nonspontaneous.

(c) All spontaneous processes release heat.

(d) The boiling of water at ${\mathbf{100}}^{\mathbf{°}}\mathbf{\text{C}}$and 1 atm is spontaneous.

(e) If a process increases the freedom of motion of the particles of a system, the entropy of the system decreases.

(f) The energy of the universe is constant; the entropy of the universe decreases toward a minimum.

(g) All systems disperse their energy spontaneously.

(h) Both $\mathit{\Delta }{\mathit{S}}_{\mathbf{\text{sys }}}$and  $\mathit{\Delta }{\mathit{S}}_{\mathbf{\text{surr }}}$equal zero at equilibrium.

Hemoglobin carries O₂ from the lungs to tissue cells, where the O₂ is released. The protein is represented as Hb in its unoxygenated form and as Hb.O₂ in its oxygenated form. One reason CO is toxic is that it competes with O₂ in binding to Hb: 

$\mathbf{\text{Hb}}\mathbf{\cdot }{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{\text{CO}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{\text{Hb}}\mathbf{\cdot }\mathbf{\text{CO}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

(a) If $\mathit{\Delta }{\mathit{G}}^{\mathbf{°}}\mathbf{\approx }\mathbf{-}\mathbf{14}\mathbf{ }\mathbf{\text{kJ}}$ at ${\mathbf{37}}^{\mathbf{°}}\mathbf{\text{C}}$ (body temperature), what is the ratio of [Hb.CO] to [Hb.O₂] at ${\mathbf{37}}^{\mathbf{°}}\mathbf{\text{C}}$ with [O₂]=[CO]?

(b) How is Le Châtelier's principle used to treat CO poisoning?

An important ore of lithium is spodumene,  . To extract the metal, the  form of spodumene is first converted into the less dense  form in preparation for subsequent leaching and washing steps. Use the following data to calculate the lowest temperature at which the  conversion is feasible:

Use Appendix B to determine the ${\mathbf{\text{K}}}_{\mathbf{\text{sp}}}$ of ${\mathbf{\text{CaF}}}_{\mathbf{\text{2}}}$

Use Appendix B to determine the ${\mathbf{\text{K}}}_{\mathbf{\text{sp }}}$ of ${\mathbf{\text{Ag}}}_{\mathbf{\text{2}}}\mathbf{\text{S}}$.

The K_sp of ZnF₂ is $\mathbf{3}\mathbf{.0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}$ at ${\mathbf{25}}^{\mathbf{°}}\mathbf{\text{C}}$ . What is $\mathit{\Delta }{\mathit{G}}^{\mathbf{°}}$  ? Is it possible to prepare a solution that contains Zn²⁺(aq) and F^-(aq) at their standard-state concentrations?

To prepare nuclear fuel, U₃O₈  ("yellow cake") is converted to UO₂(NO₃)₂, which is then converted to UO₃ and finally UO₂. The fuel is enriched (the proportion of the ${}^{\mathbf{\text{235}}}\mathbf{\text{U}}$ is increased) by a two-step conversion of UO₂ into UF₆, a volatile solid, followed by a gaseous-diffusion separation of the ${}^{\mathbf{\text{235}}}{\mathbf{\text{U and }}}^{\mathbf{\text{238}}}\mathbf{\text{U }}$ isotopes: 

$\begin{array}{l}{\mathbf{\text{UO}}}_{\mathbf{\text{2}}}\mathbf{\text{(s) + 4HF(g) }}\mathbf{\to }{\mathbf{\text{UF}}}_{\mathbf{\text{4}}}{\mathbf{\text{(s) + 2H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}}\\ {\mathbf{\text{UF}}}_{\mathbf{\text{4}}}{\mathbf{\text{(s) + F}}}_{\mathbf{\text{2}}}\mathbf{\text{(g) }}\mathbf{\to }{\mathbf{\text{ UF}}}_{\mathbf{\text{6}}}\mathbf{\text{(s)}}\end{array}$

Calculate ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}$ for the overall process at ${\mathbf{\text{85}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$.

Methanol, a major industrial feedstock, is made by several catalyzed reactions, such as ${\mathbf{\text{CO(g) + 2H}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}\mathbf{\text{OH(l).}}$ 

a) Show that this reaction is thermodynamically feasible.

b) Is it favoured at low or at high temperatures?

c) One concern about using CH₃OH  as an auto fuel is its oxidation in air to yield formaldehyde, CH₂O(g), which poses a health hazard. Calculate${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}{\mathbf{\text{ at 100.}}}^{\mathbf{\text{°}}}$C for this oxidation.

a) Write a balanced equation for the gaseous reaction between N₂O₅ and F₂ to form NF₃ and O₂.

b) Determine ${\mathbf{\text{ΔG}}}_{\mathbf{\text{rxn}}}^{\mathbf{\text{°}}}\mathbf{\text{. }}$

c) Find ${\mathbf{\text{ΔG}}}_{\mathbf{\text{rxn}}}\mathbf{\text{ at 298 K}}$if ${\mathbf{\text{P}}}_{{\mathbf{\text{N}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{5}}}}{\mathbf{\text{= P}}}_{{\mathbf{\text{F}}}_{\mathbf{\text{2}}}}{\mathbf{\text{= 0.20 atm, P}}}_{{\mathbf{\text{NF}}}_{\mathbf{\text{3}}}}{\mathbf{\text{= 0.25 atm, and P}}}_{{\mathbf{\text{O}}}_{\mathbf{\text{2}}}}\mathbf{\text{= 0.50 atm.}}$

Magnesia (MgO) is used for fire brick, crucibles, and furnace linings because of its high melting point. It is produced by decomposing magnesite (MgCO₃) at around ${\mathbf{\text{1200}}}^{\mathbf{\text{°}}}\mathbf{\text{C}}$

a)  Write a balanced equation for magnesite decomposition. 

b) Use ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}{\mathbf{\text{ and S}}}^{\mathbf{\text{°}}}$ values to find ${\mathbf{\text{ΔG}}}^{\mathbf{\text{°}}}\mathbf{\text{ at 298 K.}}$ 

c)  Assuming ${\mathbf{\text{ΔH}}}^{\mathbf{\text{°}}}{\mathbf{\text{ and S}}}^{\mathbf{\text{°}}}$ do not change with temperature, find the minimum temperature at which the reaction is spontaneous. 

d) Calculate the equilibrium ${\mathbf{\text{P}}}_{{\mathbf{\text{CO}}}_{\mathbf{\text{2}}}}$above ${\mathbf{\text{ MgCO}}}_{\mathbf{\text{3}}}\mathbf{\text{ at 298 K.}}$

e) Calculate the equilibrium ${\mathbf{\text{P}}}_{\mathbf{\text{CO}}}$  above ${\mathbf{\text{MgCO}}}_{\mathbf{\text{3}}}\mathbf{\text{ at 1200 K.}}$

Propylene (propene;${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH = CH}}}_{\mathbf{\text{2}}}$  ) is used to produce polypropylene and many other chemicals. Although most is obtained from the cracking of petroleum, about $\mathbf{2}\mathbf{\%}$   is produced by catalytic dehydrogenation of propane ( ${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}$): 

 ${\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH}}}_{\mathbf{\text{2}}}\mathbf{\text{C}}{\mathbf{\text{H}}}_{\mathbf{\text{3}}}\stackrel{{\mathbf{\text{Pt/Al}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}{\mathbf{\to }}{\mathbf{\text{CH}}}_{\mathbf{\text{3}}}{\mathbf{\text{CH = CH}}}_{\mathbf{\text{2}}}{\mathbf{\text{ + H}}}_{\mathbf{\text{2}}}$

Because this reaction is endothermic, heaters are placed between the reactor vessels to maintain the required temperature. 

(a) If the molar entropy${\mathit{S}}^{\mathbf{°}}$,  , of propylene is$\mathbf{\text{267.1 J/molK}}$  , find its entropy of formation, ${\mathbf{\text{S}}}_{\mathbf{\text{f}}}^{\mathbf{\text{o}}}$ .

(b) Find  $\mathbf{∆}{\mathit{G}}_{\mathbf{f}}^{\mathbf{°}}$ of propylene ($\mathbf{∆}{\mathit{H}}_{\mathbf{f}}^{\mathbf{°}}$ for propylene$\mathbf{\text{ = 20.4 kJ/mol}}$ ).

(c) Calculate $\mathbf{∆}{\mathit{H}}_{\mathbf{r}\mathbf{x}\mathbf{n}}^{\mathbf{°}}$  and$\mathbf{∆}{\mathit{G}}_{\mathbf{r}\mathbf{x}\mathbf{n}}^{\mathbf{°}}$   for the dehydrogenation.

(d) What is the theoretical yield of propylene at $\mathbf{580}\mathbf{°}\mathit{C}$  if the initial pressure of propane is $\mathbf{1}\mathbf{.}\mathbf{00}\mathit{a}\mathit{t}\mathit{m}$ ? 

(e) Would the yield change if the reactor walls were permeable to${\mathit{H}}_{\mathbf{2}}$  ? Explain. 

(f) At what temperature is the dehydrogenation spontaneous, with all substances in the standard state?

The oxidation of $\mathbf{1}\mathit{m}\mathit{o}\mathit{l}$  of glucose supplies enough metabolic energy to form $\mathbf{36}\mathit{m}\mathit{o}\mathit{l}$  of ATP. Oxidation of $\mathbf{1}\mathit{m}\mathit{o}\mathit{l}$  of a typical dietary fat like tristearin  $\mathbf{\left(}{\mathit{C}}_{\mathbf{57}}{\mathit{H}}_{\mathbf{116}}{\mathit{O}}_{\mathbf{6}}\mathbf{\right)}$ yields enough energy to form  $\mathbf{458}\mathit{m}\mathit{o}\mathit{l}$ of ATP. 

(a) How many molecules of ATP can form per gram of glucose? 

(b) Per gram of tristearin?

Nonspontaneous processes like muscle contraction, protein building, and nerve conduction are coupled to the spontaneous hydrolysis of ATP to ADP. ATP is then regenerated by coupling its synthesis to other energy-yielding reactions such as 

$$\begin{gathered} \mathbf{\text{Creatine phosphate}}\mathbf{\to }\mathbf{\text{creatine + phosphate ∆G}}{}^{\mathbf{\text{o}}}\mathbf{\text{'=-43.1kJ/mol}} \\ \mathbf{\text{ADP + phosphate}}\mathbf{\to }\mathbf{\text{ATP ∆G}}{}^{\mathbf{\text{o}}}\mathbf{\text{'=+30.5kJ/mol}} \end{gathered}$$

Calculate  $\mathbf{∆}\mathit{G}{}^{\mathbf{\text{o}}}\mathbf{\text{'}}$ for the overall reaction that regenerates ATP.

Energy from ATP hydrolysis drives many nonspontaneous cell reactions: 

$$\begin{gathered} \mathit{A}\mathit{T}{\mathit{P}}^{\mathbf{4}\mathbf{-}}\left(aq\right)\mathbf{+}{\mathit{H}}_{\mathbf{2}}\mathit{O}\left(I\right)\mathbf{\rightleftharpoons } \\ \mathit{A}\mathit{D}{\mathit{P}}^{\mathbf{3}\mathbf{-}}\left(aq\right)\mathbf{+}\mathit{H}\mathit{P}{\mathit{O}}_{\mathbf{4}}^{\mathbf{2}\mathbf{-}}\left(aq\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{∆}{\mathit{G}}^{\mathbf{\text{o'}}}\mathbf{=}\mathbf{-}\mathbf{30}\mathbf{.}\mathbf{5}\mathit{k}\mathit{J} \end{gathered}$$

Energy for the reverse process comes ultimately from glucose metabolism: 

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

(a) Find K for the hydrolysis of ATP at ${\mathbf{37}}^{\mathbf{°}}\mathit{C}$. 

(b) Find$\mathbf{∆}{\mathit{G}}_{\mathbf{r}\mathbf{x}\mathbf{n}}^{\mathbf{\text{o'}}}$ for metabolism of $\mathbf{1}$mol of glucose.

(c) How many moles of ATP can be produced by metabolism of $\mathbf{1}$mol of glucose? 

(d) If $\mathbf{36}$ mol of ATP is formed, what is the actual yield?

A chemical reaction, such as HI forming from its elements, can reach equilibrium at many temperatures. In contrast, a phase change, such as ice melting, is in equilibrium at a given pressure only at the melting point. Each of the graphs below depicts ${\mathbf{G}}_{\mathbf{sys}}$ vs. extent of change.

(a) Which graph depicts how ${\mathbf{G}}_{\mathbf{sys}}$ changes for the formation of HI? Explain. 

(b) Which graph depicts how ${\mathbf{G}}_{\mathbf{sys}}$ changes as ice melts at $\mathbf{1}\mathbf{°}\mathbf{C}$ and 1 atm? Explain.

When heated, the DNA double helix separates into two random-coil single strands. When cooled, the random coils reform the double helix: double helix 2 random coils. 

(a) What is the sign of $\mathbf{∆}\mathbf{\text{s}}$ for the forward process? Why? 

(b) Energy must be added to overcome H bonds and dispersion forces between the strands. What is the sign of $\mathbf{∆}\mathit{G}$ for the forward process when $\mathbf{T\Delta S}$ is smaller than  $\mathbf{∆}\mathbf{\text{H}}$? 

(c) Write an expression that shows T in terms of $\mathbf{∆}\mathbf{\text{H}}$ and $\mathbf{∆}\mathbf{\text{s}}$ when the reaction is at equilibrium. (This temperature is called the melting temperature of the nucleic acid.)

In the process of respiration, glucose is oxidized completely. In fermentation, ${\mathbf{O}}_{\mathbf{2}}$ is absent and glucose is broken down to ethanol and ${\mathbf{CO}}_{\mathbf{2}}$. Ethanol is oxidized to ${\mathbf{CO}}_{\mathbf{2}}$ and ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$. 

Respiration: ${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{12}}{\mathbf{O}}_{\mathbf{6}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}$

Fermentation: ${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{12}}{\mathbf{O}}_{\mathbf{6}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{+}\mathbf{C}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

Ethanol oxidation: ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{l}\mathbf{\right)}$

1. Calculate ${\mathbf{\Delta G}}_{\mathbf{rxn}}^{\mathbf{o}}$ for respiration of $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{g}$ glucose.
2. Calculate ${\mathbf{\Delta G}}_{\mathbf{rxn}}^{\mathbf{o}}$ for fermentation of $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{g}$ glucose. 
3. Calculate ${\mathbf{\Delta G}}_{\mathbf{rxn}}^{\mathbf{o}}$ for oxidation of the ethanol from part (c).

Consider the formation of ammonia: ${\mathbf{N}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{2}{\mathbf{NH}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

(a) Assuming that $\mathbf{\Delta H}\mathbf{°}$ and $\mathbf{\Delta S}\mathbf{°}$are constant with temperature, find the temperature at which  ${\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}$ . 

(b) Find ${\mathbf{K}}_{\mathbf{p}}$at 400°C, a typical temperature for ${\mathbf{NH}}_{\mathbf{3}}$production. 

(c) Given the lower ${\mathbf{K}}_{\mathbf{p}}$ at the higher temperature, why are these conditions used industrially?

Write equations for the oxidation of Fe and of Al. Use $\mathbf{∆}{\mathit{G}}^{\mathbf{°}}$ to determine whether either process is spontaneous at ${\mathbf{25}}^{\mathbf{°}}\mathit{C}$.

The molecular scene depicts a gaseous equilibrium mixture at$\mathbf{460}\mathbf{°}\mathit{C}$  for the reaction of${\mathit{H}}_{\mathbf{2}}$  (blue) and  ${\mathit{I}}_{\mathbf{2}}$(purple) to form HI. Each molecule represents  $\mathbf{0}\mathbf{.}\mathbf{010}$mol and the container volume is $\mathbf{1}\mathbf{.}\mathbf{0}$L. 

(a) Is${\mathit{K}}_{\mathbf{c}}\mathbf{>}\mathbf{,}\mathbf{=}\mathbf{,}\mathbf{ }\mathit{o}\mathit{r}\mathbf{<}\mathbf{1}$ ? 

(b) Is${\mathit{K}}_{\mathbf{p}}\mathbf{>}\mathbf{,}\mathbf{=}\mathbf{,}\mathit{o}\mathit{r}\mathbf{<}{\mathit{K}}_{\mathbf{c}}$ ? 

(c) Calculate$\mathbf{∆}{\mathit{G}}_{\mathbf{r}\mathbf{x}\mathbf{n}}^{\mathbf{°}}$ . 

(d) How would the value of $\mathbf{∆}{\mathit{G}}_{\mathbf{r}\mathbf{x}\mathbf{n}}^{\mathbf{°}}$ change if the purple molecules represented ${\mathit{H}}_{\mathbf{2}}$and the blue${\mathit{I}}_{\mathbf{2}}$ ? Explain.