Chapter 15, Chemical equilibrium Video Solutions, Chemistry $^{3}$ : Introducing inorganic, organic and physical chemistry

Chapter Questions

Problem 1

Write the expressions for the thermodynamic equilibrium constant $K$ for the following reactions. (Section 15.1)
(a) $4 \mathrm{NH}_{3}(\mathrm{~g})+7 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 4 \mathrm{NO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$
(b) $\mathrm{HCN}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{O}) \rightleftharpoons \mathrm{CN}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})$
(c) $\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})$
(d) $3 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{O}_{3}(\mathrm{~g})$
(e) $2 \mathrm{H}_{2} \mathrm{O}(0) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{\circ}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})$
(f) $3 \mathrm{Zn}(\mathrm{s})+2 \mathrm{~F}_{\mathrm{e}}^{3+}(\mathrm{aq}) \rightleftharpoons 2 \mathrm{~F}_{\theta}(\mathrm{s})+3 \mathrm{Zn}^{2+}(\mathrm{aq})$

Ayushi S.

Numerade Educator

Problem 2

The solubility of silver chloride in water at $25^{\circ} \mathrm{C}$ is $1.27 \times 10^{-5} \mathrm{~mol} \mathrm{dm}^{-3}$. Calculate
(a) the solubility product of $\mathrm{AgCl}$
(b) the solubility of $\mathrm{AgCl}$ in $0.01 \mathrm{~mol} \mathrm{dm}^{-3}$ aqueous sodium chloride solution. (Section 15.1)\}

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02:33

Problem 3

The equilibrium constants for two gas phase reactions at $1000^{\circ} \mathrm{C}$ are shown.
$$
\begin{array}{ll}
\mathrm{CO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) & K_{1}=9.1 \times 10^{-12} \\
\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) & K_{2}=7.1 \times 10^{-12}
\end{array}
$$
Use these data to find the equilibrium constant at the same temperature for the reaction:
$$
\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})
$$
(Section 15.1)

Ayushi S.

Numerade Educator

01:56

Problem 4

The equilibrium constant for the following reaction is $K=1.5 \times 10^{4}$
$$
\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{~g})
$$
In a reaction vessel, the partial pressures of the reaction mixture are:
$\mathrm{COCl}_{2} 0.050$ bar, CO $0.0010$ bar, and $\mathrm{Cl}_{2} 0.0001 \mathrm{bar}$. (a) Calculate the value for the reaction quotient, $Q$, for this mixture.
(b) What will happen to the composition of the reaction mixture as it moves to equilibrium? (Section 15.2)

Ayushi S.

Numerade Educator

Problem 5

An important reaction in the formation of smog is:
$$
\mathrm{O}_{3}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \rightleftharpoons \mathrm{O}_{2}(\mathrm{~g})+\mathrm{NO}_{2}(\mathrm{~g})
$$
Under certain conditions, the equilibrium constant for this
11 reaction is $K=6.0 \times 10^{34}$. If the partial pressures of each gas in the air over your home town were $1.0 \times 10^{-6} \mathrm{bar} \mathrm{O}_{3}$. $1.0 \times 10^{-5}$ bar $\mathrm{NO}, 2.5 \times 10^{-4}$ bar $\mathrm{NO}_{2}$, and $8.2 \times 10^{-3} \mathrm{bar} \mathrm{O}_{2}$ what could you say about the course of the reaction as it moves to equilibrium? (Section 15.2)
12

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00:48

Problem 6

Calculate the equilibrium constant, $K$, at $298 \mathrm{~K}$ for the reaction
$$
\mathrm{H}_{2} \mathrm{O}(\mathrm{D}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})
$$
The standard Gibbs energy change of formation of $\mathrm{H}_{2} \mathrm{O}(\mathrm{l})$ at $298 \mathrm{~K}$ is - $237.1 \mathrm{~kJ} \mathrm{~mol}^{-1}$. (Section 15.3)

Ayushi S.

Numerade Educator

00:36

Problem 7

Use the data below to calculate the standard Gibbs energy change and the equilibrium constant, $K$, at $298 \mathrm{~K}$ for the reaction
$$
\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})
$$
(Section 15.3) $$
\begin{aligned}
&\begin{array}{lcc}
\hline & \Delta_{1} H_{299}^{\circ} / \mathrm{kJ} \mathrm{mol}^{-1} & \mathrm{~S}_{289}^{\circ} / \mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1} \\
\hline \mathrm{CO}(\mathrm{g}) & -110.5 & 197.7 \\
\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & -241.8 & 188.8 \\
\mathrm{CO}_{2}(\mathrm{~g}) & -393.5 & 213.7 \\
\mathrm{H}_{2}(\mathrm{~g}) & 0 & 130.7 \\
\hline
\end{array}\\
&14
\end{aligned}
$$

Ayushi S.

Numerade Educator

Problem 8

A vessel initially contains graphite and partial pressures of $\mathrm{O}_{2}(\mathrm{~g})$ and $\mathrm{CO}_{2}(\mathrm{~g})$ of $0.02 \mathrm{bar}$ and $0.001 \mathrm{bar}$, respectively, at $298 \mathrm{~K}$. The reaction that occurs is
$$
\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})
$$
In what direction will the reaction proceed? (The standard Gibbs energy change of formation of $\mathrm{CO}_{2}(\mathrm{~g})$ is $-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at 298\textrmK.) (Section 15.3)

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Problem 9

$2.0$ mol of carbon disulfide and $4.0 \mathrm{~mol}$ of chlorine react at constant temperature according to this equation
$$
\mathrm{CS}_{2}(\mathrm{~g})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{S}_{2} \mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{CCl}_{4}(\mathrm{~g})
$$
At equilibrium, $0.30$ mol of tetrachioromethane are formed. How much of each of the other components is present in this equilibrium mixture? (Section 15.4)

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Problem 10

Nitrosyl chloride (NOCl) decomposes to nitric oxide and chlorine when heated
$$
2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})
$$
In a mixture of all three gases at $600 \mathrm{~K}$, the partial pressure of NOCl is $0.88 \mathrm{bar}$, that of NO is $0.06$ bar, and the partial pressure of chlorine is $0.03$ bar. At $600 \mathrm{~K}$, the equilibrium constant, $K$, is $0.060$. (Section $15.2$ and several others) (a) What is the value of the reaction quotient for this mixture? Is the mixture at equilibrium?
(b) In which direction will the system move to reach equlibrium?
(c) What will happen if an additional amount of $\mathrm{NOCl}(\mathrm{g})$ is injected into the reaction?

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00:03

Problem 11

The following reaction is exothermic
$$
\mathrm{T}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{TiCl}_{4}(\mathrm{~g})
$$
How could the yield of $\mathrm{TICl}_{4}$ be increased? (Section 15.5)

Ayushi S.

Numerade Educator

Problem 12

The following gas phase reaction is exothermic
$$
\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})
$$
What will be the effect of (a) increasing the pressure,
(b) increasing the temperature, and (c) adding a catalyst on (i) the equilibrium constant, $K$, and (i) the yield of $\mathrm{CO}_{2}$ ?
(Section 15.5)

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Problem 13

For the gas phase reaction
$$
\mathrm{COCl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})
$$
at $100^{\circ} \mathrm{C}$ and 2 bar pressure, the fraction, $\alpha$, of phosgene $\left(\mathrm{COCl}_{2}\right)$ that reacts is $6.3 \times 10^{-5} .$ Calculate the equilibrium constant, $K$, for the reaction. (Section 15.4)

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01:22

Problem 14

Bromine and chlorine react to produce bromine monochloride according to the equation
$$
\mathrm{Br}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{BrCl}(\mathrm{g})
$$
$0.2 \mathrm{~mol}$ of bromine gas and $0.2 \mathrm{~mol}$ of chlorine gas are introduced into a sealed flask with a volume of $5.0 \mathrm{dm}^{3}$. Under the conditions of the experiment, $K=36.0$. How much BrCl will be present at equilibrium? (Section 15.4)

Ayushi S.

Numerade Educator

Problem 15

When ammonia dissolves in water, the following equilibrium is established
$$
\left.\mathrm{NH}_{3}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O} \mathrm{O}\right) \rightleftharpoons \mathrm{NH}_{4}{ }^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})
$$
Calculate the hydroxide ion concentration in the solution formed when $0.10$ mol of ammonia are dissolved in sufficient water to make $500 \mathrm{~cm}^{3}$ of solution. (At the temperature of the reaction, $\left.K=1.8 \times 10^{-5}\right)$ (Section 15.4)

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Problem 16

The standard Gibbs energy change for the gas phase isomerization of cis-2-pentene to trans-2-pentene is $-3.67 \mathrm{~kJ} \mathrm{~mol}^{-1}$. (Section $\left.15.4\right)$
(a) Calculate the equilibrium constant for the reaction.
(b) What are the equilibrium mole fractions of the cis and trans isomers at $298 \mathrm{~K}$ ?

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03:02

Problem 17

What is the standard enthalpy change for a reaction in which the equilibrium constant doubles when the temperature increases from $298 \mathrm{~K}$ to $308 \mathrm{~K}$ ? (Section $15.5$ )

Ayushi S.

Numerade Educator

Problem 18

${ }^{+} \mathrm{CO}_{2}$ decomposes into $\mathrm{CO}$ and $\mathrm{O}_{2}$ over a platinum catalyst
$$
2 \mathrm{CO}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g})
$$ At 1 bar pressure, the fraction, $\alpha$, of $\mathrm{CO}_{2}$ that reacts is $0.014$ at $1395 \mathrm{~K}, 0.025$ at $1443 \mathrm{~K}$, and $0.047$ at $1498 \mathrm{~K}$. (Section 15.5)
(a) Calculate the equilibrium constant at $1443 \mathrm{~K}$.
(b) Calculate $\Delta_{r} H^{\ominus}$ and $\Delta_{R} S^{\oplus}$ for the reaction.

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01:18

Problem 19

For a general reaction
$$
\alpha A+\beta B \rightleftharpoons \gamma C+\delta D
$$
derive the relationship between the Gibbs energy change of the reaction and the reaction quotient. Use the relationship to show that $\Delta_{t} G^{\ominus}=-R T \ln K$. (Section 15.3)

Ayushi S.

Numerade Educator

Problem 20

Silver carbonate decomposes on heating. Calculate the equilibrium constant at $383 \mathrm{~K}$ for the reaction. Would it be appropriate to dry a sample of silver carbonate in an oven at $383 \mathrm{~K} ?$ (Section 15.3)$$
\begin{array}{lccc}
\hline & \mathrm{Ag}_{2} \mathrm{CO}_{3}(\mathrm{~s}) & \mathrm{Ag}_{2} \mathrm{O}(\mathrm{s}) & \mathrm{CO}_{2}(\mathrm{~g}) \\
\hline \Delta_{1} H_{296}^{\theta} / \mathrm{kJ} \mathrm{mol}^{-1} & -501.4 & -31.1 & -393.5 \\
S_{298}^{\theta} / \mathrm{JK}^{-1} \mathrm{~mol}^{-1} & 167.3 & 121.3 & 213.7 \\
C_{\rho} / \mathrm{K}^{-1} \mathrm{~mol}^{-1} & 109.6 & 65.9 & 37.1 \\
\hline
\end{array}
$$

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Problem 21

"For the following esterification reaction
$$
\mathrm{C}_{2} \mathrm{H}_{0} \mathrm{OH}(\mathrm{D})+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{D}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{\mathrm{s}}\left(\mathrm{D}+\mathrm{H}_{2} \mathrm{O}(\mathrm{D})\right.
$$
the equilibrium constant at $298 \mathrm{~K}$ is $3.8$. A mixture containing $0.5 \mathrm{~mol} \mathrm{dm}^{-3}$ each of ethanol and ethanoic acid was reacted in a sealed flask at $298 \mathrm{~K}$. After a certain time, the concentrations of each had changed to $0.39 \mathrm{~mol} \mathrm{dm}^{-3}$. (Section 15.3)
(a) Had the reaction reached equilibrium?
(b) If not, what would the concentration of $\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}$ (aq) be at equilibrium?
(c) In practice, the reaction is carried out so as to remove the water as it forms. Explain why this is done.

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Problem 22

The equilibrium constant for the reaction
$$
\mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})
$$
has been measured as $0.157$ at $900 \mathrm{~K}$ and $0.513$ at $1000 \mathrm{~K}$. Assuming the values of $\Delta H$ and $\Delta S$ are constant over this temperature range, calculate the standard enthalpy change and the standard entropy change for the reaction. (Section 15.5)

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Problem 23

An equilibrium constant, $K$, is five times larger when a reaction is performed at $200 \mathrm{~K}$ than at $150 \mathrm{~K}$. Assuming the enthalpy change is constant over this temperature range, calculate $\Delta_{1} H^{\ominus}$ for the reaction. (Section 15.5)

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Problem 24

If the following reaction was at equilibrium in a closed vessel at a controlled temperature, what would be the effect of adding more $\mathrm{H}_{2}$ to the reaction vessel and permitting the reaction to approach equilibrium again? (Section $15.5$ )
$$
\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})
$$

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Problem 25

The folding and unfolding of proteins have important biological effects (see Chapter 14, p.673). Studies have been carried out on protein G which shows a reversible transition from a folded to an unfolded form as the temperature is raised.
protein $\mathrm{G}$ (folded) $\rightleftharpoons$ protein G (unfolded)
For the unfolding of protein $\mathrm{G}$ at the normal cell temperature of $37^{\circ} \mathrm{C}(310 \mathrm{~K}), \Delta H^{\ominus}=+210.9 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $\Delta S^{\Theta}=+616.7 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$. (Section $\left.15.5\right)$
(a) Write an expression for $K$ for this equilibrium.
(b) What is the value of $K$ at the temperature when the protein is half-folded and half-unfolded?
(c) What is the value of $\Delta G^{\circ}$ at this temperature?
(d) Calculate $\Delta G^{\theta}$ for the unfolding process at $310 \mathrm{~K}$.
(e) Calculate $\mathrm{K}$ at $310 \mathrm{~K}$ and comment on the value you ohtain.
(f) Calculate a value for $K$ at $69^{\circ} \mathrm{C}(342 \mathrm{~K})$ and comment on the value you obtain.

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Problem 26

For the reaction,
$$
\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})
$$ $$
\begin{array}{lcll}
\hline & \Delta_{1} H_{29 B}^{\ominus} / \mathrm{k} \mathrm{J} \mathrm{mol}^{-1} & \mathrm{~S}_{2}^{\ominus} / \mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1} & \mathrm{C}_{\rho} / \mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1} \\
\hline \mathrm{CO}(\mathrm{g}) & -110.5 & 197.7 & 29.1 \\
\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & -241.8 & 188.8 & 33.6 \\
\mathrm{CO}_{2}(\mathrm{~g}) & -393.5 & 213.7 & 37.1 \\
\mathrm{H}_{2}(\mathrm{~g}) & 0 & 130.7 & 28.8 \\
\hline
\end{array}
$$ (Section 15.6)
(a) Use the data to calculate the Gibbs energy change and the equilibrium constant at $798 \mathrm{~K}$.
(b) $1 \mathrm{~mol}$ of $\mathrm{CO}(\mathrm{g})$ and $1 \mathrm{~mol}$ of $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ are introduced into a container at $798 \mathrm{~K}$ and allowed to come to equilibrium at a total pressure of $0.1$ bar. Write an expression to relate the equilibrium constant, $K$, to the number of moles of each component in the equilibrium mixture and calculate the number of moles of $\mathrm{H}_{2}$ gas present at equilibrium.

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Problem 27

Calculate the maximum quantity (in mol) of $\mathrm{KIO}_{3}$ that can be added to $250 \mathrm{~cm}^{3}$ of a solution containing $1.00 \times 10^{-3} \mathrm{~mol} \mathrm{~d} \mathrm{~m}^{-3}$ of $\mathrm{Cu}^{2+}(\mathrm{aq})$ without precipitating $\mathrm{Cu}(\mathrm{IO} 3)_{2}$ (s). $K_{\mathrm{sp}}=1.4 \times 10^{-7}$ for $\mathrm{Cu}\left(\mathrm{IO}_{3}\right)_{2}(\mathrm{~s})$.

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Problem 28

For the reaction, $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~s}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}), \Delta_{r} \mathrm{G}^{\Theta}=3.40 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298.15 \mathrm{~K}$.
(a) Calculate the equilibrium constant.
(b) Does the reaction favour the products or reactants?
(c) If additional $\mathrm{H}_{2}(g)$ was added to the equilibrium mixture at the same temperature, predict what would happen to the position of equilibrium.

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Problem 29

Use data in Appendix 7 to answer the following for the reaction.
$$
2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})
$$
(a) Calculate the enthalpy change and the entropy change for the reaction at $25^{\circ} \mathrm{C}$. Is the reaction spontaneous at this temperature?
(b) Find the equilibrium constant under these conditions?

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Problem 30

A student was investigating the following equilibrium reaction which has an equilibrium constant of $0.220$ at $800^{\circ} \mathrm{C}$.
$$
\mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})
$$
and did four experiments.
(a) $0.2 \mathrm{~g}$ of $\mathrm{CaCO}_{3}(\mathrm{~s})$ was heated to $800^{\circ} \mathrm{C}$ in a $1.0 \mathrm{dm}^{3}$ container
(b) $2.0 \mathrm{~g}$ of $\mathrm{CaCO}_{3}(\mathrm{~s})$ was heated to $800^{\circ} \mathrm{C}$ in a $1.0 \mathrm{dm}^{3}$ container
(c) $0.2 \mathrm{~g}$ of $\mathrm{CaCO}_{3}$ (s) was heated to $800^{\circ} \mathrm{C}$ in a $500 \mathrm{~cm}^{3}$ container
(d) $2.0 \mathrm{~g}$ of $\mathrm{CaCO}_{3}(\mathrm{~s})$ was heated to $800^{\circ} \mathrm{C}$ in a $500 \mathrm{~cm}^{3}$ container
The pressure of $\mathrm{CO}_{2}(\mathrm{~g})$ measured in each case was $(i) 0.18 \mathrm{bar}$, (ii) $0.22$ bar, (iit) $0.22$ bar, (iv) $0.22$ bar. Explain these observations.

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Problem 31

The equilibrium constants for the gas-phase dissociation of molecular iodine,
$$
\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{I}(\mathrm{g})
$$
have been measured at the following temperatures: $$
\begin{array}{lllll}
\hline T / K & 872 & 973 & 1073 & 1173 \\
K_{p} & 1.8 \times 10^{-4} & 1.8 \times 10^{-3} & 1.08 \times 10^{-2} & 4.8 \times 10^{-2} \\
\hline
\end{array}
$$ (a) Use a graphical method to determine $\Delta_{1} H^{\ominus}$ and $\Delta_{r} S^{\ominus}$ for this reaction.
(b) Determine $\Delta, G^{\circ}$ at $1000 \mathrm{~K}$.
(c) What would be the effect on the position of equilibrium of increasing the temperature?

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