Equilibrium: The Extent of Chenmical Reactions

Phosgene $\mathbf{(}{\mathbf{\text{COCl}}}_{\mathbf{\text{2}}}\mathbf{\text{)}}$  is a toxic substance that forms readily from carbon monoxide and chlorine at elevated temperatures: 

${\mathbf{\text{CO(g)+Cl}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\rightleftharpoons }{\mathbf{\text{COCl}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

If  $\mathbf{\text{0.350 mol}}$ of each reactant is placed in a  $\mathbf{\text{0.500-L}}$ flask at $\mathbf{\text{600 K}}$, what are the concentrations of all three substances at equilibrium ( ${\mathbf{\text{K}}}_{\mathbf{\text{c}}}\mathbf{\text{=4.95}}$at this temperature)?

When $\mathbf{\text{0.100 mol}}$ of ${\mathbf{\text{CaCO}}}_{\mathbf{\text{3}}}\mathbf{\left(}\mathit{s}\mathbf{\right)}$ and $\mathbf{\text{0.100 mol}}$ mol of $\mathbf{\text{CaO(s)}}$  are placed in an evacuated sealed $\mathbf{\text{10.0-L}}$ container and heated to $\mathbf{\text{385 K}}$ , ${\mathbf{\text{P}}}_{{\mathbf{\text{CO}}}_{\mathbf{\text{2}}}}\mathbf{\text{=0.220 atm}}$ after equilibrium is established:

${\mathbf{\text{CaCO}}}_{\mathbf{\text{3}}}\mathbf{\text{(s)}}\mathbf{\rightleftharpoons }{\mathbf{\text{CaO(s)+CO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

An additional $\mathbf{\text{0.300 atm}}$ of  ${\mathbf{\text{CO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$is pumped in. What is the total mass (in  $\mathbf{g}$ ) of ${\mathbf{\text{CaCO}}}_{\mathbf{\text{3}}}$ after equilibrium is re-established?

Use each of the following reaction quotients to write the balanced equation:

(a) $\mathbf{Q}\mathbf{=}\frac{{\left[{\mathbf{CO}}_2\right]}^2{\left[{\mathbf{H}}_2\mathbf{O}\right]}^2}{\left[{\mathbf{C}}_2{\mathbf{H}}_4\right]{\left[{\mathbf{O}}_2\right]}^3}$

(b) $\mathbf{Q}\mathbf{=}\frac{{\left[{\mathbf{NH}}_3\right]}^4{\left[{\mathbf{O}}_2\right]}^7}{{\left[{\mathbf{NO}}_2\right]}^4{\left[{\mathbf{H}}_2\mathbf{O}\right]}^6}$

Hydrogenation of carbon-carbon $\mathbf{\pi }$ bonds is important in the petroleum and food industries. The conversion of acetylene to ethylene is a simple example of the process:

 ${\mathbf{\text{C}}}_{\mathbf{2}}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{\text{C}}}_{\mathbf{2}}{\mathbf{\text{H}}}_{\mathbf{4}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

The calculated ${\mathbf{K}}_{\mathbf{c}}$  at 2000K is $\mathbf{2}\mathbf{.9}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}$ . But the process is run at lower temperatures with the aid of a catalyst to prevent decomposition. Use  ${\mathbf{\Delta H}}_{\mathbf{\text{f}}}^{\mathbf{°}}$  values to calculate the ${\mathbf{K}}_{\mathbf{C}}$   at 300K.

A mixture of \(5.00\) volumes of ${\mathbf{N}}_{\mathbf{2}}$ and 1.00 volume of ${\mathbf{O}}_{\mathbf{2}}$ passes slowly through a heated furnace. Assuming it reaches equilibrium at $\mathbf{1850}\mathbf{K}$ and $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{ }\mathbf{atm}$, the reaction is

${\mathbf{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{2}\mathbf{NO}\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{47}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$

(a) What is the partial pressure of NO? 

(b) What is the concentration in micrograms per litre $\left(\mathrm{\mu g}/L\right)$ of $\mathbf{NO}$ in the mixture?

Isolation of Group $\mathbf{8}\mathbf{ }\mathbf{B}\left(10\right)$ elements, used as industrial catalysts, involves a series of steps. For nickel, the sulfide ore is roasted in air: ${\mathbf{Ni}}_{\mathbf{3}}{\mathbf{S}}_{\mathbf{2}}\left(s\right)\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{NiO}\left(s\right)\mathbf{+}{\mathbf{SO}}_{\mathbf{2}}\left(g\right)$. The metal oxide is reduced by the ${\mathbf{H}}_{\mathbf{2}}$ in water gas $\left(\mathrm{CO}+H_2\right)$ to impure $\mathbf{Ni}\mathbf{:}\mathbf{NiO}\left(s\right)\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{Ni}\left(s\right)\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(g\right)$. The CO in water gas then reacts with the metal in the Mond process to form gaseous nickel carbonyl, $\mathbf{Ni}\left(s\right)\mathbf{+}\mathbf{CO}\left(g\right)\mathbf{\to }\mathbf{Ni}{\left(\mathrm{CO}\right)}_{\mathbf{4}}\left(g\right)$, which is subsequently decomposed to the metal. 

(a) Balance each of the three steps, and obtain an overall balanced equation for the conversion of ${\mathbf{Ni}}_{\mathbf{3}}{\mathbf{S}}_{\mathbf{2}}$ to $\mathbf{Ni}{\left(\mathrm{CO}\right)}_{\mathbf{4}}$. 

(b) Show that the overall ${\mathbf{Q}}_{\mathbf{c}}$ is the product of the  ${\mathbf{Q}}_{\mathbf{c}}$'s for the individual reactions.

Consider the formation of ammonia in two experiments.

1.   To a $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{L}$ container at ${\mathbf{727}}^{\mathbf{o}}\mathbf{ }\mathbf{C}$ $\mathbf{1}\mathbf{.}\mathbf{30}\mathbf{ }\mathbf{mol}$ of ${\mathbf{N}}_{\mathbf{2}}$ and $\mathbf{1}\mathbf{.}\mathbf{65}\mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}$ are added. At equilibrium, $\mathbf{0}\mathbf{.}\mathbf{100}\mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{NH}}_{\mathbf{3}}$  is present. Calculate the equilibrium concentrations of ${\mathbf{N}}_{\mathbf{2}}\mathbf{ }\mathbf{and}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}$, and find ${\mathbf{K}}_{\mathbf{c}}$ for the reaction: $\mathbf{2}{\mathbf{NH}}_{\mathbf{3}}\left(g\right)\mathbf{\to }{\mathbf{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}\mathbf{3}{\mathbf{H}}_{\mathbf{2}}\left(g\right)$  
2.   In a different $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{-}\mathbf{L}$ container at the same temperature, equilibrium is established with $\mathbf{8}\mathbf{.}\mathbf{34}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}\mathbf{ }}\mathbf{mol}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{NH}}_{\mathbf{3}}\mathbf{,}\mathbf{1}\mathbf{.}\mathbf{50}\mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{,}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{25}\mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}$  present. Calculate ${\mathbf{K}}_{\mathbf{c}}$ for the reaction: ${\mathbf{NH}}_{\mathbf{3}}\left(g\right)\mathbf{\to }{\mathbf{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}\frac{\mathbf{3}}{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}\left(g\right)$ 
3.  (c) What is the relationship between the ${\mathbf{K}}_{\mathbf{c}}$  values in parts  $\left(a\right)$ and $\left(b\right)$ ? Why aren't these values the same?

An important industrial source of ethanol is the reaction, catalyzed by ${\mathbf{H}}_{\mathbf{3}}{\mathbf{PO}}_{\mathbf{4}}$ , of steam with ethylene derived from oil:

 ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{4}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{ }\mathbf{∆}{\mathbf{H}}_{\mathbf{rxn}}^{\mathbf{o}}\mathbf{=}\mathbf{-}\mathbf{47}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{kJ}\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{K}}_{\mathbf{c}}\mathbf{=}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathbf{at}\mathbf{ }\mathbf{600}\mathbf{K}$

1.   At equilibrium, ${\mathbf{P}}_{{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}}\mathbf{=}\mathbf{200}\mathbf{ }\mathbf{atm}\mathbf{ }\mathbf{and}\mathbf{ }{\mathbf{P}}_{{\mathbf{H}}_{\mathbf{2}}\mathbf{O}}\mathbf{=}\mathbf{400}\mathbf{ }\mathbf{atm}$ Calculate ${\mathbf{P}}_{{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{4}}}$ .
2.   Is the highest yield of ethanol obtained at high or low $\mathbf{P}\mathbf{?}$ High or low $\mathbf{T}\mathbf{?}$ 
3.   Calculate ${\mathbf{K}}_{\mathbf{c}}\mathbf{ }\mathbf{at}\mathbf{ }\mathbf{450}\mathbf{ }\mathbf{K}$.  
4.  In  manufacture, the yield is increased by condensing the ${\mathbf{NH}}_{\mathbf{3}}$ to a liquid and removing it. Would condensing the ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}$ have the same effect in ethanol production? Explain.

As an EPA scientist studying catalytic converters and urban smog, you want to find ${\mathbf{K}}_{\mathbf{c}}$ for the following reaction: 

$\mathbf{2}{\mathbf{NO}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}\mathbf{2}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{K}}_{\mathbf{c}}\mathbf{=}\mathbf{?}$

Use the following data to find the unknown :

$$\begin{gathered} \frac{\mathbf{1}}{\mathbf{2}}{\mathbf{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{NO}\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{K}}_{\mathbf{c}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{10}} \\ \mathbf{2}{\mathbf{NO}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{2}\mathbf{NO}\left(g\right)\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{K}}_{\mathbf{c}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}} \end{gathered}$$

An important industrial source of ethanol is the reaction, catalyzed by H₃PO₄, of steam with ethylene derived from oil:

$$\begin{gathered} {\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{4}}\left(g\right)\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(g\right)\mathbf{\rightleftharpoons }{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{5}}\mathbf{OH}\left(g\right) \\ {\mathbf{\Delta H}}_{\mathbf{r}\mathbf{\times }\mathbf{n}}^{\mathbf{0}}\mathbf{=}\mathbf{-}\mathbf{47}\mathbf{.}\mathbf{8}{\mathbf{KJK}}_{\mathbf{c}}\mathbf{=}\mathbf{9}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{at}\mathbf{ }\mathbf{600}\mathbf{.}\mathbf{k} \end{gathered}$$

Which of the following situations represent equilibrium?

(a) Migratory birds fly north in summer and south in winter.

(b) In a grocery store, some carts are kept inside and some outside. Customers bring carts out to their cars, while store clerks bring carts in to replace those taken out.

(c) In a tug o’ war, a ribbon tied to the center of the rope moves back and forth until one side loses, after which the ribbon goes all the way to the winner’s side.

(d) As a stew is cooking, water in the stew vaporizes, and the vapor condenses on the lid to droplets that drip into the stew.

An inorganic chemist places 1 mol of BrCl in container A and 0.5 mol of Br₂ and 0.5 mol of Cl₂ in container B. She seals the containers and heats them to 300⁰C. With time, both containers hold identical mixtures of BrCl, Br₂, and Cl₂.

(a) Write a balanced equation for the reaction in container A.

(b) Write the reaction quotient, Q, for this reaction.

(c) How do the values of Q in A and in B compare over time?

(d) Explain on the molecular level how it is possible for both containers to end up with identical mixtures.

An engineer examining the oxidation of SO₂ in the manufacture

of sulfuric acid determines that ${\mathbf{K}}_{\mathbf{C}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{7}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}$ at 600. K:

$\mathbf{2}{\mathbf{SO}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\rightleftharpoons }\mathbf{2}{\mathbf{SO}}_{\mathbf{3}}\left(g\right)$

(a) At equilibrium, ${\mathbf{P}}_{{\mathbf{SO}}_{\mathbf{3}}}\mathbf{=}\mathbf{300}\mathbf{.}\mathbf{atm}$ and ${\mathbf{P}}_{{\mathbf{O}}_2}\mathbf{=}1\mathbf{00}\mathbf{.}\mathbf{atm}$ .Calculate ${\mathbf{P}}_{{\mathbf{SO}}_{\mathbf{2}}}$

(b) The engineer places a mixture of 0.0040 mol of SO₂(g) and 0.0028 mol of O₂(g) in a 1.0-L container and raises the temperature to 1000 K. At equilibrium, 0.0020 mol of SO₃(g) is present. Calculate Kc and for this reaction at 1000. K.

Use each of the following reaction quotients to write the balanced equation:

For the reaction ${\mathbf{\text{M}}}_{\mathbf{2}}\mathbf{+}{\mathbf{\text{N}}}_{\mathbf{2}}\mathbf{\rightleftharpoons }\mathbf{2}\mathbf{\text{MN}}$ , scene A represents the mixture at equilibrium, with  $\mathbf{M}$black and  $\mathbf{N}$orange. If each molecule represents  $\mathbf{0}\mathbf{.10}\mathbf{ }\mathbf{\text{mol}}$ and the volume is $\mathbf{1}\mathbf{.0}\mathbf{ }\mathbf{\text{L}}$  , how many moles of each substance will be present in scene B when that mixture reaches equilibrium?

Highly toxic disulfurdecafluoride decomposes by a free radical process: ${\mathbf{\text{S}}}_{\mathbf{2}}\mathbf{ }{\mathbf{\text{F}}}_{\mathbf{10}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{\text{SF}}}_{\mathbf{4}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{\text{SF}}}_{\mathbf{6}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$  . In a study of the decomposition, ${\mathbf{\text{S}}}_{\mathbf{2}}\mathbf{ }{\mathbf{\text{F}}}_{\mathbf{10}}$  was placed in a $\mathbf{2}\mathbf{.}\mathbf{0}$ $\mathbf{L}$-  flask and heated to ${\mathbf{100}}^{\mathbf{°}}\mathbf{\text{C}}\mathbf{;}\mathbf{[}{\mathbf{\text{S}}}_{\mathbf{2}}\mathbf{ }{\mathbf{\text{F}}}_{\mathbf{10}}\mathbf{]}$ was  $\mathbf{0}\mathbf{.50}\mathbf{\text{M}}$ at equilibrium. More ${\mathbf{\text{S}}}_{\mathbf{2}}\mathbf{ }{\mathbf{\text{F}}}_{\mathbf{10}}$  was added, and when equilibrium was retained,  $\mathbf{[}{\mathbf{\text{S}}}_{\mathbf{2}}\mathbf{ }{\mathbf{\text{F}}}_{\mathbf{10}}\mathbf{]}$ was  $\mathbf{2}\mathbf{.5}\mathbf{\text{M}}$ . How did data-custom-editor="chemistry" $\mathbf{\left[}{\mathbf{\text{SF}}}_{\mathbf{4}}\mathbf{\right]}$and $\mathbf{\left[}{\mathbf{\text{SF}}}_{\mathbf{6}}\mathbf{\right]}$ change from the original to the new equilibrium position after the addition of more  data-custom-editor="chemistry" ${\mathbf{\text{S}}}_{\mathbf{2}}\mathbf{ }{\mathbf{\text{F}}}_{\mathbf{10}}$?

A study of the water-gas shift reaction (see Problem 17.37) was made in which equilibrium was reached with $\mathbf{\left[}\mathbf{\text{CO}}\mathbf{\right]}\mathbf{=}$$\mathbf{\left[}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\right]}\mathbf{=}\mathbf{\left[}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\right]}\mathbf{=}\mathbf{0}\mathbf{.10}\mathbf{\text{M}}$  and $\mathbf{\left[}{\mathbf{\text{CO}}}_{\mathbf{2}}\mathbf{\right]}\mathbf{=}\mathbf{0}\mathbf{.40}\mathbf{\text{M}}$ . After  data-custom-editor="chemistry" $\mathbf{0}\mathbf{.60}\mathbf{ }\mathbf{\text{mol}}$  of  data-custom-editor="chemistry" ${\mathbf{H}}_{\mathbf{2}}$  is added to the $\mathbf{2}\mathbf{.0}$ -$\mathbf{L}$ container and equilibrium is re-established, what are the new concentrations of all the components?

When ammonia is made industrially, the mixture of ${\mathbf{\text{N}}}_{\mathbf{2}}\mathbf{,}{\mathbf{\text{H}}}_{\mathbf{2}}$ , and data-custom-editor="chemistry" ${\mathbf{\text{NH}}}_{\mathbf{3}}$ that emerges from the reaction chamber is far from equilibrium. Why does the plant supervisor use reaction conditions that produce less than the maximum yield of ammonia?

A gaseous mixture of $\mathbf{10}\mathbf{.}\mathbf{0}$ volumes of   ${\mathbf{\text{CO}}}_{\mathbf{2}}\mathbf{,}\mathbf{1.00}$  volume of unreacted data-custom-editor="chemistry" ${\mathbf{O}}_{\mathbf{2}}$ , and $\mathbf{50}\mathbf{.}\mathbf{0}$ volumes of unreacted ${\mathbf{N}}_{\mathbf{2}}$  leaves an engine at $\mathbf{4}\mathbf{.0}\mathbf{ }\mathbf{\text{atm}}$ and 800K. Assuming that the mixture reaches equilibrium, what are

(a) the partial pressure and

(b) The concentration (in picograms per litre,$\mathbf{\text{pg}}\mathbf{/}\mathbf{\text{L}}$  ) of  data-custom-editor="chemistry" $\mathbf{\text{CO}}$ in this exhaust gas? data-custom-editor="chemistry" $\mathbf{2}{\mathbf{\text{CO}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{2}\mathbf{\text{CO}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}{\mathbf{K}}_{\mathbf{\text{p}}}\mathbf{=}\mathbf{1}\mathbf{.4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{28}}$ at  data-custom-editor="chemistry" $\mathbf{800}\mathbf{.}\mathbf{\text{\hspace{0.17em}K}}$ (The actual concentration of  data-custom-editor="chemistry" $\mathbf{CO}$ in exhaust gas is much higher because the gases do not reach equilibrium in the short transit time through the engine and exhaust system.)

Consider the following reaction:

 $\mathbf{3}\mathbf{\text{Fe}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }{\mathbf{\text{Fe}}}_{\mathbf{3}}{\mathbf{\text{O}}}_{\mathbf{4}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{4}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

(a) What is the apparent oxidation state of $\mathbf{\text{Fe}}$ in ${\mathbf{\text{Fe}}}_{\mathbf{3}}{\mathbf{\text{O}}}_{\mathbf{4}}$  ?

(b) Actually, Fe has two oxidation states in ${\mathbf{\text{Fe}}}_{\mathbf{3}}{\mathbf{\text{O}}}_{\mathbf{4}}$ . What are they?

(c) At  ${\mathbf{900}}^{\mathbf{°}}\mathbf{\text{C}}\mathbf{,}{\mathbf{K}}_{\mathbf{\text{c}}}$ for the reaction is $\mathbf{5}\mathbf{.1}$ . If   $\mathbf{0}\mathbf{.050}\mathbf{ }\mathbf{\text{mol}}$ of ${\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathbf{\text{g}}\mathbf{\right)}$   and  $\mathbf{0}\mathbf{.100}\mathbf{ }\mathbf{\text{mol}}$  of $\mathbf{\text{Fe}}\mathbf{\left(}\mathbf{\text{s}}\mathbf{\right)}$  are placed in a $\mathbf{1}\mathbf{.0}\mathbf{-}\mathbf{\text{L}}$   container at ${\mathbf{900}}^{\mathbf{°}}\mathbf{\text{C}}$  , how many grams of  ${\mathbf{\text{Fe}}}_{\mathbf{3}}{\mathbf{\text{O}}}_{\mathbf{4}}$  are present at equilibrium?

Note: The synthesis of ammonia is a major process throughout the industrialized world. Problems  $\mathbf{17}\mathbf{.99}$  to $\mathbf{17}\mathbf{.105}$  refer to various aspects of this all-important reaction:

 ${\mathbf{\text{N}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\rightleftharpoons }\mathbf{2}{\mathbf{\text{NH}}}_{\mathbf{3}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}{\mathbf{\Delta H}}_{\mathbf{\text{rxn}}}^{\mathbf{°}}\mathbf{=}\mathbf{-}\mathbf{91}\mathbf{.8}\mathbf{ }\mathbf{\text{kJ}}$

101 The methane used to obtain ${\text{H}}_2$  for  manufacture is impure and usually contains other hydrocarbons, such as propane, ${\text{C}}_3{\text{H}}_8$ . Imagine the reaction of propane occurring in two steps:

 $\begin{array}{l}{\text{C}}_3{\text{H}}_8\left(g\right)+3{\text{H}}_2\text{O}\left(g\right)\rightleftharpoons 3\text{CO}\left(g\right)+7{\text{H}}_2\left(g\right)\\ K_{\text{p}}=8.175\times {10}^{15}\text{ at }1200\text{K}\\ \\ \text{CO}\left(g\right)+{\text{H}}_2\text{O}\left(g\right)\rightleftharpoons {\text{CO}}_2\left(g\right)+{\text{H}}_2\left(g\right)\\ K_{\text{p}}=0.6944\text{ at }1200\text{K}\end{array}$

(a) Write the overall equation for the reaction of propane and steam to produce carbon dioxide and hydrogen.

(b) Calculate $K_{\text{p}}$ for the overall process at 1200K

(c) When $1.00$  volume of  ${\text{C}}_3{\text{H}}_8$ and  $4.00$ volumes of ${\text{H}}_2\text{O}$ , each at $1200.\text{K}$ and $5.0 \text{atm}$ , are mixed in a container, what is the final pressure? Assume the total volume remains constant, that the reaction is essentially complete, and that the gases behave ideally.

(d) What percentage of the  ${\text{C}}_3{\text{H}}_8$ remains unreacted?

Using ${\text{CH}}_4$ and steam as a source of ${\text{H}}_2$for ${\text{NH}}_3$ synthesis requires high temperatures. Rather than burning ${\text{CH}}_4$separately to heat the mixture, it is more efficient to inject some ${\text{O}}_2$ into the reaction mixture. All of the ${\text{H}}_2$ is thus released for the synthesis, and the heat of reaction for the combustion of ${\text{CH}}_4$ helps maintain the required temperature. Imagine the reaction occurring in two steps:

$\begin{array}{l}2{\text{CH}}_4\left(g\right)+{\text{O}}_2\left(g\right)\rightleftharpoons 2\text{CO}\left(g\right)+4{\text{H}}_2\left(g\right)\\ K_{\text{p}}=9.34\times {10}^{28}\text{ at }1000\text{K}\\ \\ \text{CO}\left(g\right)+{\text{H}}_2\text{O}\left(g\right)\rightleftharpoons {\text{CO}}_2\left(g\right)+{\text{H}}_2\left(g\right)\\ K_{\text{p}}=1.374\text{ at }1000\text{K}\end{array}$

(a) Write the overall equation for the reaction of methane, steam, and oxygen to form carbon dioxide and hydrogen.

(b) What is $K_{\text{p}}$  for the overall reaction?

(c) What is $K_{\text{c}}$  for the overall reaction?

(d) A mixture of $2.0 \text{mol}$ of ${\text{CH}}_4,1.0 \text{mol}$ of ,${\text{O}}_2$ and $2.0 \text{mol}$ of steam with a total pressure of 30atm reacts at 1000K at constant volume. Assuming that the reaction is complete and the ideal gas law is a valid approximation, what is the final pressure?

Mixture of  $3.00$ volumes of ${\text{H}}_2$ and $1.00$ volume of  ${\text{N}}_2$ reacts at  ${344}^{°}\text{C}$  to form ammonia. The equilibrium mixture at 110atm contains  $41.49\%{\text{NH}}_3$ by volume. Calculate  $K_{\text{p}}$ for the reaction, assuming that the gases behave ideally.

One mechanism for the synthesis of ammonia proposes that ${\text{N}}_2$ and ${\text{H}}_2$ molecules catalytically dissociate into atoms:

 $\begin{array}{l}{\text{N}}_2\left(g\right)\rightleftharpoons 2 \text{N}\left(g\right)log{K}_{\text{p}}=-43.10\\ {\text{H}}_2\left(g\right)\rightleftharpoons 2\text{H}\left(g\right)log{K}_{\text{p}}=-17.30\end{array}$

(a) Find the partial pressure of $\text{N}$ in ${\text{N}}_2$ at 1000 and  200atm.

(b) Find the partial pressure of  $\text{H}$ in ${\text{H}}_2$ at 1000 and 600atm.

(c) How many $\text{N}$ atoms and $\text{H}$ atoms are present per litre?

(d) Based on these answers, which of the following is a more reasonable step to continue the mechanism after the catalytic dissociation? Explain.

$\begin{array}{l}\text{N}\left(g\right)+\text{H}\left(g\right)\to \text{NH}\left(g\right)\\ {\text{N}}_2\left(g\right)+\text{H}\left(g\right)\text{NH}\left(g\right)+\text{N}\left(g\right)\end{array}$

Consider the following reaction: 

$\mathbf{3}\mathit{F}{\mathit{e}}_{\mathbf{\left(}\mathbf{s}\mathbf{\right)}}\mathbf{+}\mathbf{4}{\mathbf{H}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }\mathit{F}{\mathit{e}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{4}\mathbf{\left(}\mathbf{s}\mathbf{\right)}}\mathbf{+}\mathbf{4}{\mathbf{H}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}$

(a) What is the apparent oxidation state of Fe in ${\mathbf{Fe}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{4}}$? 

(b) Actually, Fe has two oxidation states in ${\mathbf{Fe}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{4}}$. What are they? 

(c) At $\mathbf{900}{\mathbf{ }}^{\mathbf{0}}\mathbf{C}$, Kc for the reaction is 5.1. If 0.050 mol of ${\mathbf{H}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}$ and 0.100 mol of Fe(s) are placed in a 1.0-L container at $\mathbf{900}{\mathbf{ }}^{\mathbf{0}}\mathbf{C}$, how many grams of ${\mathbf{Fe}}_{\mathbf{3}}{\mathbf{O}}_{\mathbf{4}}$are present at equilibrium?

When ammonia is made industrially, the mixture of ${}^{{\mathbf{N}}_{\mathbf{2}}}$ , ${}^{{\mathbf{H}}_{\mathbf{2}}}$ and ${}^{{\mathbf{NH}}_{\mathbf{3}}}$ that emerges from the reaction chamber is far from equilibrium. Why does the plant supervisor use reaction conditions that produce less than the maximum yield of ammonia?

The following reaction can be used to make ${\mathbf{H}}_{\mathbf{2}}$for the synthesis of ammonia from the greenhouse gases carbon dioxide and methane: 

                                 ${\mathbf{CH}}_{\mathbf{4}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}{\mathbf{CO}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }\mathbf{2}{\mathbf{CO}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}\mathbf{2}{\mathbf{H}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}$

(b) What is the percent yield of ${\mathbf{H}}_{\mathbf{2}}$ for this system at 1300. K, at which ${\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{626}\mathbf{\times }{\mathbf{10}}^7$?

 (c) Use the van’t Hoff equation to find $\mathbf{∆}{\mathbf{H}}_{\mathbf{rxn}}^{\mathbf{0}}$ .

 Using  ${\mathbf{CH}}_{\mathbf{4}}$and steam as a source of ${\mathbf{H}}_{\mathbf{2}}$ for ${\mathbf{NH}}_{\mathbf{3}}$synthesis requires high temperatures. Rather than burning ${\mathbf{CH}}_{\mathbf{4}}$ separately to heat the mixture, it is more efficient to inject some ${\mathbf{O}}_{\mathbf{2}}$ into the reaction mixture. All of the ${\mathbf{H}}_{\mathbf{2}}$ is thus released for the synthesis, and the heat of reaction for the combustion of ${\mathbf{CH}}_{\mathbf{4}}$  helps maintain the required temperature. Imagine the reaction occurring in two steps:

$$\begin{gathered} \mathbf{2}{\mathbf{CH}}_{\mathbf{4}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}{\mathbf{O}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }\mathbf{2}{\mathbf{CO}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}\mathbf{4}{\mathbf{H}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{ }}{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{34}\mathbf{\times }{\mathbf{10}}^{\mathbf{28}}\mathbf{at}\mathbf{1000}\mathbf{.}\mathbf{K} \\ {\mathbf{CO}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }{\mathbf{CO}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{+}{\mathbf{H}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{374}\mathbf{ }\mathbf{at}\mathbf{ }\mathbf{1000}\mathbf{.}\mathbf{K} \end{gathered}$$

 
 (a) Write the overall equation for the reaction of methane, steam, and oxygen to form carbon dioxide and hydrogen. 

(b) What is Kp for the overall reaction? 

(c) What is Kc for the overall reaction? 

(d) A mixture of 2.0 mol of ${\mathbf{CH}}_{\mathbf{4}}$ ,1.0 mol of ${\mathbf{O}}_{\mathbf{2}}$, and 2.0 mol of steam with a total pressure of 30. atm reacts at 1000. K at constant volume. Assuming that the reaction is complete and the ideal gas law is a valid approximation, what is the final pressure?

One mechanism for the synthesis of ammonia proposes that ${}^{{\mathbf{H}}_{\mathbf{2}}}$ molecules catalytically dissociate into atoms:

$$\begin{gathered} {\mathbf{N}}_{\mathbf{2}\left(g\right)}\mathbf{\rightleftharpoons }\mathbf{2}{\mathbf{N}}_{\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{log}\mathbf{ }{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{-}\mathbf{43}\mathbf{.}\mathbf{10} \\ {\mathbf{H}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }\mathbf{2}{\mathbf{H}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{log}\mathbf{ }{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\mathbf{17}\mathbf{.}\mathbf{30} \end{gathered}$$

(a) Find the partial pressure of N in${}^{{\mathbf{N}}_{\mathbf{2}}}$ at 1000. K and 200. atm.

(b) Find the partial pressure of H in${}^{{\mathbf{H}}_{\mathbf{2}}}$ at 1000. K and 600. atm.

(c) How many N atoms and H atoms are present per litre? 

(d) Based on these answers, which of the following is a more reasonable step to continue the mechanism after the catalytic dissociation? Explain

$$\begin{gathered} {\mathbf{N}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }{\mathbf{H}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }}\mathbf{\to }\mathbf{ }{\mathbf{NH}}_{\left(g\right)} \\ {\mathbf{H}}_{\mathbf{2}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{\rightleftharpoons }{\mathbf{H}}_{\mathbf{\left(}\mathbf{g}\mathbf{\right)}}\mathbf{ }\mathbf{\to }\mathbf{ }\mathbf{ }{\mathbf{NH}}_{\left(g\right)}\mathbf{+}\mathbf{N}\left(g\right) \end{gathered}$$

You are a member of a research team of chemists discussing the plans to operate an ammonia processing plant: ${\mathbf{N}}_{\mathbf{2}\left(g\right)}\mathbf{+}\mathbf{3}{\mathbf{H}}_{\mathbf{2}\left(g\right)}\mathbf{ }\mathbf{2}{\mathbf{NH}}_{\mathbf{3}\left(g\right)}$

 (a) The plant operates at close to 700 K, at which ${\mathbf{K}}_{\mathbf{p}}$is $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}$, and employs the stoichiometric 1/3 ratio of ${\mathbf{N}}_{\mathbf{2}}\mathbf{/}{\mathbf{H}}_{\mathbf{2}}$. At equilibrium, the partial pressure of ${\mathbf{NH}}_{\mathbf{3}}$is 50atm. Calculate the partial pressures of each reactant and ${\mathbf{P}}_{\mathbf{total}}$.

(b) One member of the team suggests the following: since the partial pressure of ${\mathbf{H}}_{\mathbf{2}}$is cubed in the reaction quotient, the plant could produce the same amount of ${\mathbf{NH}}_{\mathbf{3}}$if the reactants were in a 1/6 ratio of ${\mathbf{N}}_{\mathbf{2}}\mathbf{/}{\mathbf{H}}_{\mathbf{2}}$and could do so at a lower pressure, which would cut operating costs. Calculate the partial pressure of each reactant and ${\mathbf{P}}_{\mathbf{total}}$under these conditions, assuming an unchanged partial pressure of 50. atm for ${\mathbf{NH}}_{\mathbf{3}}$. Is the suggestion valid?

The oxidation of nitrogen monoxide is favoured at : $\text{457 K}$

${\text{2NO(g)+O}}_{\text{2}}\text{(g)}\rightleftharpoons {\text{2NO}}_{\text{2}}{\text{(g) K}}_{\text{p}}{\text{=1.3×10}}^{\text{4}}$

(a) Calculate ${\text{K}}_{\text{c}}$ at . $\text{457 K}$

(b) Find ${\text{ΔH}}_{\text{rxn}}^{\text{o}}$ from standard heats of formation. 

(c) At what temperature does ${\text{K}}_{\text{c}}{\text{=6.4×10}}^{\text{9}}$ ?

The kinetics and equilibrium of the decomposition of hydrogen iodide have been studied extensively:

$\text{2HI(g)}\rightleftharpoons {\text{H}}_{\text{2}}{\text{(g)+I}}_{\text{2}}\text{(g)}$

(a) At ${\text{298 K, K}}_{\text{c}}{\text{=1.26×10}}^{\text{-3}}$ for this reaction. Calculate ${\text{K}}_{\text{p}}$.

(b) Calculate ${\text{K}}_{\text{c}}$ for the formation of $\text{HI}$ at $\text{298 K}$.

(c)Calculate ${\text{ΔH}}_{\text{rxn}}^{\text{o}}$for $\text{HI}$ decomposition from ${\text{ΔH}}_{\text{f}}^{\text{o}}$values.

(d) At ${\text{729 K, K}}_{\text{c}}{\text{=2.0×10}}^{\text{-2}}$ for $\text{HI}$ decomposition. Calculate ${\text{ΔH}}_{\text{rxn}}$ for this reaction from the Vant-Hoff equation.

The molecular scenes below depict the reaction $\mathbf{\text{Y}}\mathbf{\rightleftharpoons }\mathbf{2}\mathbf{\text{Z}}$ at four different times, out of sequence, as it reaches equilibrium. Each sphere (Y is red and  Z is green) represents $\mathbf{0}\mathbf{.}\mathbf{025}\mathbf{ }\mathbf{\text{mol}}$ and the volume is $\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{ }\mathbf{\text{L}}$ . 

(a) Which scene represents equilibrium? 

(b) List the scenes in the correct sequence. 

(c) Calculate ${\mathit{K}}_{\mathbf{\text{c}}}$ .