General Chemistry

Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly

Chapter 19

Chemical Equilibrium - all with Video Answers

Educators

Chapter Questions

Problem 1

Antimony pentachloride decomposes according to the equation
$$
\mathrm{SbCl}_{5}(g) \leftrightharpoons \mathrm{SbCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
Suppose that the initial concentrations are $\left[\mathrm{SbCl}_{5}\right]_{0}=$ $0.165 \mathrm{M},\left[\mathrm{SbCl}_{5}\right]_{0}=0.0955 \mathrm{M}$, and $\left[\mathrm{Cl}_{2}\right]_{0}=0.210 \mathrm{M}$
If it is determined that $\left[\mathrm{SbCl}_{5}\right]=0.135 \mathrm{M}$ at equilibrium, calculate the equilibrium values of $\left[\mathrm{SbCl}_{3}\right]$ and $\left[\mathrm{Cl}_{2}\right] .$

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Problem 2

Sulfur trioxide decomposes according to the equation
$$
2 \mathrm{SO}_{3}(g) \leftrightharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)
$$
Suppose that the initial concentrations are $\left[\mathrm{SO}_{5}\right]_{0}=$ $0.176 \mathrm{M},\left[\mathrm{SO}_{2}\right]_{0}=0.625 \mathrm{M}$, and $\left[\mathrm{O}_{2}\right]_{0}=0.436 \mathrm{M}$. If it is determined that $\left[\mathrm{O}_{2}\right]=0.387 \mathrm{M}$ at equilibrium, calculate the equilibrium values of $\left[\mathrm{SO}_{3}\right]$ and $\left[\mathrm{SO}_{2}\right]$

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Problem 3

Write the equilibrium-constant expression $\left(K_{c}\right)$ for the following equations:
(a) $\mathrm{ZnO}(s)+\mathrm{CO}(g) \leftrightharpoons \operatorname{Zn}(l)+\mathrm{CO}_{2}(g)$
(b) $2 \mathrm{C}_{3} \mathrm{H}_{6}(g) \leftrightharpoons \mathrm{C}_{10} \mathrm{H}_{12}(g)$
(c) $2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{soln}) \leftrightharpoons 4 \mathrm{NO}_{2}(\mathrm{soln})+\mathrm{O}_{2}(g)$
What are the units of $K_{c}$ in each case?

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Problem 4

Write the equilibrium-constant expression $\left(K_{c}\right)$ for the following equations:
(a) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \leftrightharpoons 2 \mathrm{SO}_{3}(g)$
(b) $2 \mathrm{NaHCO}_{3}(s) \leftrightharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{4}(g)$

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Problem 5

Write the equilibrium-constant expression ( $K_{c}$ ) for each of the following equations:
(a) $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \leftrightharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$
(b) $2 \mathrm{H}_{2} \mathrm{O}_{2}(g) \leftrightharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$
(c) $2 \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons 2 \mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}(s)$
What are the units of $K_{c}$ in each case?

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Problem 6

Write the equilibrium-constant expression $\left(K_{c}\right)$ for each of the following equations:
(a) $\mathrm{NH}_{2} \mathrm{COONH}_{4}(s) \leftrightharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)$
(b) $2 \mathrm{HgO}(s) \leftrightharpoons 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)$
(c) $\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \leftrightharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)$
What are the units of $K_{c}$ in each case?

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Problem 7

Write $K_{\mathrm{p}}$ expressions for the chemical equations in Problem $19-5 .$ What are the units of $K_{\mathrm{p}}$ in each case? Express pressures in bar.

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Problem 8

Write $K_{\mathrm{p}}$ expressions for the chemical equations in Problem $19-6 .$ What are the units of $K_{\mathrm{p}}$ in each case? Express pressures in bar.

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Problem 9

Consider the chemical equation
$$
\mathrm{CuSO}_{4} \cdot 4 \mathrm{NH}_{3}(s) \leftrightharpoons \mathrm{CuSO}_{4} \cdot 2 \mathrm{NH}_{3}(s)+2 \mathrm{NH}_{3}(g)
$$
At $20^{\circ} \mathrm{C}$, the equilibrium pressure of $\mathrm{NH}_{5}(g)$ is 62 Torr. Calculate the value of $K_{\mathrm{p}}$ for this equation and include the corresponding units.

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Problem 10

At $1000^{\circ} \mathrm{C}$, methane and water react according to the chemical equation
$$
\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)
$$
At equilibrium, it was found that $P_{\mathrm{cH}_{4}}=0.31$ bar, $P_{\mathrm{H}_{2} \mathrm{O}}=0.84$ bar, $P_{C O}=0.58 \mathrm{bar}$, and $P_{\mathrm{H}_{2}}=2.29 \mathrm{bar}$ Calculate the value of $K_{\mathrm{p}}$ for this equation and state the corresponding units.

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Problem 11

Phosgene, $\mathrm{COCl}_{2}(g)$, a toxic gas used in the synthesis of a variety of organic compounds, decomposes according to
$$
\mathrm{COCl}_{2}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)
$$
A sample of phosgene gas at an initial concentration of $0.500 \mathrm{M}$ is heated at $527^{\circ} \mathrm{C}$ in a reaction vessel. At equilibrium, the concentration of $\mathrm{CO}(g)$ was found to be $0.046 \mathrm{M}$. Calculate the equilibrium constant for the reaction equation at $527^{\circ} \mathrm{C}$.

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Problem 12

The decomposition of phosphorus pentachloride is described by
$$
\mathrm{PCl}_{5}(g) \leftrightharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
A sample of $\mathrm{PCl}_{5}(g)$ at an initial concentration of $1.10 \mathrm{M}$ is placed in a reaction vessel held at $250^{\circ} \mathrm{C}$. When equilibrium is attained, the concentration of $\mathrm{PCl}_{5}(g)$ is $0.33 \mathrm{M}$. Calculate the value of $K_{c}$ for the reaction equation.

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Problem 13

A mixture of $1.00$ mole of $\mathrm{H}_{2}(g)$ and $1.00$ mole of $\mathrm{I}_{2}(g)$ is placed in a 2.00-liter container held at a constant temperature. After equilibrium is attained, $1.56$ moles of $\mathrm{HI}(g)$ are found. Calculate the value of $K_{c}$ for the chemical equation
$$
\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \leftrightharpoons 2 \mathrm{HI}(g)
$$
and include the corresponding units.

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Problem 14

Nitrogen dioxide decomposes at high temperatures according to the equation
$$
2 \mathrm{NO}_{2}(g) \leftrightharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)
$$
Suppose initially we have pure $\mathrm{NO}_{2}(g)$ at $1000 \mathrm{~K}$ and $0.500$ bar. If the total pressure is $0.732$ bar when equilibrium is reached, what is the value of $K_{\mathrm{p}}$ ? What are its units?

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Problem 15

Nitrosyl chloride decomposes according to the chemical equation
$$
2 \mathrm{NOCl}(g) \leftrightharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)
$$
Suppose initially we have pure $\operatorname{NOCl}(g)$ at $400 \mathrm{~K}$ and $2.75$ bar. If the total pressure is $3.58$ bar when equilibrium is reached, what is the value of $K_{\mathrm{p}}$ ? What are the corresponding units?

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Problem 16

Hydrogen sulfide decomposes at $1400 \mathrm{~K}$ according to the chemical equation
$$
2 \mathrm{H}_{2} \mathrm{~S}(g) \leftrightharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)
$$
Suppose initially we have pure $\mathrm{H}_{2} \mathrm{~S}(g)$ at a pressure of $0.956$ bar. If the total pressure is $1.26$ bar when equilibrium is reached, what is the value of $K_{\mathrm{p}}$ and its corresponding units?

Susan Hallstrom

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Problem 17

Given that $\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]=0.85 \mathrm{M}$ at equilibrium for the equation
$$
\mathrm{Ni}(s)+4 \mathrm{CO}(g) \leftrightharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g) \quad K_{c}=5.0 \times 10^{4} \mathrm{M}^{-3}
$$
calculate the concentration of $\mathrm{CO}(g)$ at equilibrium.

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Problem 18

The equilibrium constant for the chemical equation
$$
\mathrm{C}(s)+\mathrm{CO}_{2}(g) \leftrightharpoons 2 \mathrm{CO}(g)
$$
at $1000 \mathrm{~K}$ is $1.90$ bar. If the equilibrium pressure of $\mathrm{CO}(g)$ is $1.50$ bar, what is the equilibrium pressure of $\mathrm{CO}_{2}(g) ?$

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Problem 19

Phosphorus pentachloride decomposes according to the chemical equation
$$
\mathrm{PCl}_{5}(g) \leftrightharpoons \mathrm{PCl}_{5}(g)+\mathrm{Cl}_{2}(g) \quad K_{c}=1.8 \mathrm{M} \text { at } 250^{\circ} \mathrm{C}
$$
A $0.50$ -mole sample of $\mathrm{PCl}_{5}(g)$ is injected into an empty $2.0$ -liter reaction vessel held at $250^{\circ} \mathrm{C}$. Calculate the concentrations of $\mathrm{PCl}_{5}(g)$ and $\mathrm{PCl}_{3}(g)$ at equilibrium.

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Problem 20

Carbon disulfide is prepared by heating sulfur and charcoal. The chemical equation is
$$
\mathrm{S}_{2}(g)+\mathrm{C}(s) \leftrightharpoons \mathrm{CS}_{2}(g) \quad K_{c}=9.40 \text { at } 900 \mathrm{~K}
$$
How many grams of $\mathrm{CS}_{2}(g)$ can be prepared by heating $10.0$ moles of $\mathrm{S}_{2}(g)$ with excess carbon in a $5.00$ liter reaction vessel held at $900 \mathrm{~K}$ until equilibrium is attained?

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Problem 21

At $1200^{\circ} \mathrm{C}, K_{c}=2.5 \times 10^{4}$ for the equation
$$
\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \leftrightharpoons 2 \mathrm{HCl}(g)
$$
If $0.50$ moles of $\mathrm{H}_{2}(g)$ and $0.50$ moles of $\mathrm{Cl}_{2}(g)$ are introduced initially into a reaction vessel, how many moles of $\mathrm{HCl}(g)$ are there at equilibrium?

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Problem 22

At $1000^{\circ} \mathrm{C}, K_{\mathrm{p}}=0.263 \mathrm{bar}^{-1}$ for the equation
$$
\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{4}(g)
$$
Calculate the equilibrium pressure of $\mathrm{CH}_{4}(g)$ in bars if $0.250$ moles of $\mathrm{CH}_{4}(g)$ is placed in a $4.00$ -liter container at $1000^{\circ} \mathrm{C}$.

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Problem 23

Ammonium hydrogen sulfide decomposes according to the chemical equation
$$
\mathrm{NH}_{4} \mathrm{HS}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)
$$
The equilibrium constant, $K_{c}$, is $1.81 \times 10^{-4} \mathrm{M}^{2}$ at $25^{\circ} \mathrm{C}$. If $\mathrm{NH}_{4} \mathrm{HS}(s)$ is placed in an evacuated reaction vessel at $25^{\circ} \mathrm{C}$, what is the total gas pressure (in bars) in the vessel when equilibrium is attained?

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Problem 24

Sodium hydrogen carbonate, commonly called sodium bicarbonate, is used in baking soda and in fire extinguishers as a source of $\mathrm{CO}_{2}(g) .$ It decomposes according to the equation
$$
2 \mathrm{NaHCO}_{3}(s) \leftrightharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
Given that $K_{\mathrm{p}}=0.26 \mathrm{bar}^{2}$ at $125^{\circ} \mathrm{C}$, calculate the partial pressures of $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$ in units of bars at equilibrium when $\mathrm{NaHCO}_{3}(s)$ is heated to $125^{\circ} \mathrm{C}$ in a closed vessel.

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Problem 25

The equilibrium constant for the equation
$$
2 \mathrm{ICl}(g) \leftrightharpoons \mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g)
$$
is $K_{c}=0.11 .$ Calculate the equilibrium concentrations of $\mathrm{ICl}(g), \mathrm{I}_{2}(g)$, and $\mathrm{Cl}_{2}(g)$ when $0.65$ moles of $\mathrm{I}_{2}(g)$ and $0.33$ moles of $\mathrm{Cl}_{2}(g)$ are mixed in a $1.5$ -liter reaction vessel.

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Problem 26

Suppose that $5.00$ moles of $\mathrm{CO}(g)$ are mixed with $2.50$ moles of $\mathrm{Cl}_{2}(g)$ in a $10.0$ -liter reaction vessel and the reaction attains equilibrium according to the equation $$
\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \leftrightharpoons \mathrm{COCl}_{2}(g)
$$
Given that $K_{c}=4.00 \mathrm{M}^{-1}$, calculate the equilibrium values of $[\mathrm{CO}],\left[\mathrm{Cl}_{2}\right]$, and $\left[\mathrm{COCl}_{2}\right]$

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Problem 27

Suppose that $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ and $\mathrm{NO}_{2}(g)$ are mixed together in a reaction vessel and that the total pressure at equilibrium is $1.45$ atm. Calculate $P_{\mathrm{N}_{2} \mathrm{o}_{4}}$ and $P_{\mathrm{NO}_{2}}$ at equilibrium when the value of $K_{\mathrm{p}}$ is $4.90 \mathrm{~atm}$ for the equation
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \leftrightharpoons 2 \mathrm{NO}_{2}(g)
$$

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Problem 28

Given that $\mathrm{H}_{2}(g)$ reacts with $\mathrm{I}_{2}(s)$ according to the chemical equation
$$
\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \leftrightharpoons 2 \mathrm{HI}(g) \quad K_{\mathrm{p}}=8.6 \text { bar }
$$
and that at equilibrium the total pressure in the reaction vessel is $4.5$ bar, calculate $P_{\mathrm{H} 1}$ and $P_{\mathrm{H}_{2}}$ at equilibrium. Neglect the vapor pressure of $\mathrm{I}_{2}(s)$.

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Problem 29

Zinc metal is produced by the reaction of its oxide with carbon monoxide at high temperature. The equilibrium constant for the equation
$$
\mathrm{ZnO}(s)+\mathrm{CO}(g) \leftrightharpoons \mathrm{Zn}(s)+\mathrm{CO}_{2}(g)
$$
is $K_{\mathrm{p}}=6.00 \times 10^{2}$. At equilibrium the total pressure in the reaction vessel is $1.80$ bar. Calculate $P_{\mathrm{co}_{2}}$ and $P_{\mathrm{Co}}$ at equilibrium.

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Problem 30

At equilibrium, the total pressure in the reaction vessel for the reaction between carbon and hydrogen described by the chemical equation,
$$
\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{4}(g)
$$
is $2.11$ bar. Given that $K_{\mathrm{p}}=0.263 \mathrm{bar}^{-1}$ at $1000^{\circ} \mathrm{C}$, calculate $P_{\mathrm{H}_{2}}$ and $P_{\mathrm{CH}_{4}}$ at equilibrium.

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Problem 31

Given that
(1) $\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$
$K_{\mathrm{P}_{1}}=1.44$
(2) $\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$
$K_{\mathrm{P}_{2}}=25.6 \mathrm{~atm}^{2}$
calculate the value of $K_{p}$ for the equation (3) $\mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}(g)$

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Problem 32

Given that
(1) $\mathrm{C}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2}(g)$
$K_{\mathrm{P}_{1}}=3.85$ bar
(2) $\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \leftrightharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$
$K_{\mathrm{P}_{2}}=0.71$
calculate the value of $K_{\mathrm{p}}$ for the equation
(3) $\mathrm{C}(s)+\mathrm{CO}_{2}(g) \leftrightharpoons 2 \mathrm{CO}(g)$

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Problem 33

Given that at $973 \mathrm{~K}$
(1) $2 \mathrm{MgCl}_{2}(s)+\mathrm{O}_{2}(g) \leftrightharpoons 2 \mathrm{MgO}(s)+2 \mathrm{Cl}_{2}(g)$
$K_{\mathrm{P}_{1}}=8.70 \mathrm{bar}$
(2) $\mathrm{MgCl}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{MgO}(s)+2 \mathrm{HCl}(g)$
$K_{\mathrm{P}_{2}}=8.40 \mathrm{bar}$ determine the equilibrium constant at $973 \mathrm{~K}$ for the equation
(3) $2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons 4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g)$

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Problem 34

Given the equilibrium constants at $1000 \mathrm{~K}$ for the following equations
(1) $\mathrm{CaCO}_{3}(s) \leftrightharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$
$K_{\mathrm{P}_{1}}=0.040 \mathrm{bar}$
(2) $\mathrm{C}(s)+\mathrm{CO}_{2}(g) \leftrightharpoons 2 \mathrm{CO}(g)$
$K_{\mathrm{P}_{2}}=1.9 \mathrm{bar}$
determine the equilibrium constant, $K_{\mathrm{p}}$, at $1000 \mathrm{~K}$ for the equation
(3) $\mathrm{CaCO}_{3}(s)+\mathrm{C}(s) \leftrightharpoons \mathrm{CaO}(s)+2 \mathrm{CO}(g)$

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Problem 35

Consider the chemical equilibrium described by the equation
$$
\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \leftrightharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)
$$
Use Le Châtelier's principle to predict the effect on the equilibrium pressure of $\mathrm{CO}_{2}(g)$ and of $\mathrm{CO}(g)$ resulting from
(a) an increase in the pressure of $\mathrm{H}_{2} \mathrm{O}(g)$
(b) an increase in the reaction volume

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Problem 36

Consider the chemical equilibrium described by the equation
$$
2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \leftrightharpoons 2 \mathrm{NOBr}(g)
$$
Use Le Châtelier's principle to predict the effect on the equilibrium concentration of $\operatorname{NOBr}(g)$ and of $\mathrm{NO}(g)$ resulting from
(a) an increase in the concentration of $\mathrm{Br}_{2}(g)$
(b) a twofold decrease in the reaction volume

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Problem 37

Consider the chemical equilibrium described by the equation
$$
\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{4}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-74.6 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}
$$
Predict the way in which the equilibrium will shift in response to each of the following changes in conditions (if the equilibrium is unaffected by the change, then write no change):
(a) decrease in temperature
(b) decrease in reaction volume
(c) decrease in $\bar{P}_{\mathrm{H}_{2}}$
(d) increase in $\bar{P}_{\mathrm{CH}_{4}}$
(e) addition of $\mathrm{C}(s)$

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Problem 38

For the chemical equilibrium described by the equation
$$
\mathrm{N}_{2}(a q) \leftrightharpoons \mathrm{N}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}>0
$$
in which direction will the equilibrium shiftin response to the following changes in conditions?
(a) increase in temperature
(b) increase in volume over the solution
(c) addition of $\mathrm{H}_{2} \mathrm{O}(l)$
(d) addition of $\mathrm{N}_{2}(g)$

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Problem 39

For the exothermic dissolution reaction of hydrofluoric acid described by
$$
\mathrm{HF}(a q) \leftrightharpoons \mathrm{H}^{*}(a q)+\mathrm{F}^{-}(a q)
$$
in which direction will the equilibrium shiftin response to the following changes?
(a) decrease in temperature
(b) addition of $\mathrm{H}_{2} \mathrm{O}(l)$
(c) addition of $\mathrm{KF}(s)$
(d) addition of $\mathrm{NaOH}(s)$ (Hint: What will this strong base react with in solution?)

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Problem 40

For the chemical equilibrium described by the equation
$$
\mathrm{PbCl}_{2}(s) \leftrightharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q)
$$
in which direction will the equilibrium shiftin response to the following changes?
(a) addition of $\mathrm{PbCl}_{2}(s)$
(b) addition of $\mathrm{NaCl}(s)$
(c) addition of $\mathrm{H}_{2} \mathrm{O}(l)$
(d) addition of $\mathrm{AgNO}_{3}(s)($ Hint $:$ What is the solubility of silver chloride?)

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Problem 41

Several key reactions in coal gasification are
(1) the synthesis gas reaction, (2) the water-gas-shift reaction, and (3) the catalytic methanation reaction as described, respectively, by the following three chemical equations:
(1) $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)$
$\Delta H_{\mathrm{rm}}^{\circ}=+131.3 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$
(2) $\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$
$\Delta H_{\mathrm{rxn}}^{0}=-41.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$
(3) $\mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CH}_{4}(g)$
$\Delta H_{\mathrm{rxn}}^{\circ}=-205.9 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$
(a) Write the equilibrium-constant expressions in terms of concentrations, $K_{c}$, for each of these three equations.
(b) Predict the direction in which each equilibrium shifts in response to an increase in temperature or a decrease in reaction volume.

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Problem 42

An important modern chemical problem is the liquefaction of coal because coal is still relatively abundant whereas oil is a dwindling resource (Interchapter $\mathrm{L}$ ). The first step is heating the coal with steam to produce synthesis gas, as described by the equation
(1) $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)$
$$
\Delta H_{\mathrm{rsn}}^{\circ}=+131.3 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}
$$
Carbon monoxide can be hydrogenated to form the important chemical methanol, $\mathrm{CH}_{3} \mathrm{OH}(g)$, according to
(2) $\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(g)$
$$
\Delta H_{\mathrm{rsin}}^{\circ}=-90.5 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}
$$

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Problem 43

At $320 \mathrm{~K}$ an equilibrium mixture of $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ and $\mathrm{NO}_{2}(g)$ has partial pressures of 292 Torr and 393 Torr, respectively. Aquantity of $\mathrm{NO}_{2}(g)$ is injected into the mixture, and the total pressure jumps to 812 Torr. Calculate the new partial pressures after equilibrium is reestablished. The appropriate chemical equation is
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \leftrightharpoons 2 \mathrm{NO}_{2}(g)
$$

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Problem 44

An equilibrium mixture of $\mathrm{PCl}_{5}(g), \mathrm{PCl}_{3}(g)$, and $\mathrm{Cl}_{2}(g)$ has partial pressures of 217 Torr, $13.2$ Torr, and $13.2$ Torr, respectively. A quantity of $\mathrm{Cl}_{2}(g)$ is injected into the mixture, and the total pressure jumps to 263 Torr. Calculate the new partial pressures after equilibrium is reestablished. The appropriate chemical equation is
$$
\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \leftrightharpoons \mathrm{PCl}_{5}(g)
$$

Adriano Chikande

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Problem 45

Ammonium hydrogen sulfide decomposes according to
$$
\mathrm{NH}_{4} \mathrm{HS}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)
$$
In a certain experiment, $\mathrm{NH}_{4} \mathrm{HS}(s)$ is placed in a sealed $1.00$ -liter container at $25^{\circ} \mathrm{C}$ and the total equilibrium pressure is observed to be $0.664$ bar, with a small amount of $\mathrm{NH}_{4} \mathrm{HS}(s)$ remaining. A quantity of $\mathrm{NH}_{3}(g)$ is injected into the container and the total pressure jumps to $0.906$ bar. Calculate the total pressure after equilibrium is reestablished.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 46

Dinitrogen tetroxide decomposes according to
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \leftrightharpoons 2 \mathrm{NO}_{2}(g)
$$
In a certain experiment, $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ at an initial pressure of $0.554$ bar is introduced into an empty reaction container; after equilibrium is established, the total pressure is $0.770$ bar. A quantity of $\mathrm{NO}_{2}(g)$ is injected into the container and the total pressure jumps to $0.906$ bar. Calculate the total pressure after equilibrium is reestablished.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 47

Consider the reaction described by
$$
\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
An equilibrium mixture of these gases has the partial pressures $P_{\mathrm{co}}=512$ Torr, $P_{\mathrm{H}_{2} \mathrm{O}}=77$ Torr, $P_{\mathrm{H}_{2}}=192$
Torr, and $P_{C O_{2}}=384$ Torr. If the volume of the reaction container is doubled, what will the new values of the partial pressures be?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 48

Ammonium bromide decomposes according to
$$
\mathrm{NH}_{4} \mathrm{Br}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{HBr}(g)
$$
Some $\mathrm{NH}_{4} \mathrm{Br}(s)$ is introduced into an empty reaction container; after equilibrium is established, the total pressure is $26.4$ Torr. Calculate the total pressure if the volume of the reaction container is halved.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 49

At $900 \mathrm{~K}$ the equilibrium constant for the equation
$$
2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \leftrightharpoons 2 \mathrm{SO}_{3}(g)
$$
is $13 \mathrm{M}^{-1} .$ If we mix the following concentrations of the three gases, predict in which direction the reaction will proceed toward equilibrium:

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 50

Suppose that $\mathrm{H}_{2}(g)$ and $\mathrm{CH}_{4}(g)$ are brought into contact with $\mathrm{C}(s)$ at $500^{\circ} \mathrm{C}$ with $P_{\mathrm{H}_{2}}=0.20$ bar and $P_{\mathrm{CH}_{4}}=3.0$ bar. Is the reaction described by the equation
$$
\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{4}(g) \quad K_{\mathrm{p}}=2.69 \times 10^{3} \mathrm{bar}^{-1}
$$
at equilibrium under these conditions? If not, in what direction will the reaction proceed to attain equilibrium?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 51

Suppose we have a mixture of the gases $\mathrm{H}_{2}(g)$, $\mathrm{CO}_{2}(g), \mathrm{CO}(g)$, and $\mathrm{H}_{2} \mathrm{O}(g)$ at $1260 \mathrm{~K}$, with $P_{\mathrm{H}_{2}}=$
$0.55$ bar, $P_{\mathrm{CO}_{2}}=0.20$ bar, $P_{\infty O}=1.25$ bar, and $P_{\mathrm{H}_{2} \mathrm{O}}=$
$0.10$ bar. Is the reaction described by the equation
$$
\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \quad K_{\mathrm{p}}=1.59
$$
at equilibrium under these conditions? If not, in what direction will the reaction proceed to attain equilibrium?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 52

Given that $K_{\mathrm{p}}=2.25 \times 10^{4} \mathrm{~atm}^{-2}$ at $25^{\circ} \mathrm{C}$ for the
equation
$$
2 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(g)
$$
predict the direction in which a reaction mixture for which $P_{\mathrm{CH}_{3} \mathrm{OH}}=10.0 \mathrm{~atm}, P_{\mathrm{H}_{2}}=0.010 \mathrm{~atm}$, and $P_{\mathrm{co}}=$ $0.0050$ atm proceeds to attain equilibrium.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 53

If the concentrations of the products and reactants are constant at equilibrium, why is an equilibrium state said to be dynamic?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 54

Explain the difference between an equilibrium constant and an equilibrium state. For a specific reaction equation at a given temperature, is it possible to have more than one equilibrium constant? Is it possible to have more than one equilibrium state?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 55

What does the magnitude of the equilibrium constant tell you about a reaction?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 56

A problem gives the equilibrium constant for the reaction equation
$$
2 \mathrm{ICl}(g) \leftrightharpoons \mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g)
$$
as $K=0.11$. Is this the value of $K_{\mathrm{p}}$ or $K_{c}$ ? Explain.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 57

Prior to learning about equilibrium states, we solved stoichiometric problems using the concept of "limiting reactants." Under what conditions does the method of limiting reactants apply?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 58

What is the difference between the equilibrium constant, $K_{e}$, and the reaction quotient, $Q_{c} ?$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 59

How is the value of the ratio of the reaction quotient to the equilibrium constant, $Q_{c} / K_{c}$, related to Le Châtelier's principle?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 60

Iodine crystals have a significant vapor pressure at room temperature and form a rich purple vapor when allowed to stand in a sealed container (Figure 15.22). A sealed container is filled with $10.0$ grams of solid iodine crystals and allowed to reach equilibrium between its solid and vapor phases at $25^{\circ} \mathrm{C}$. How will the vapor color change if
(a) the container is heated to $90^{\circ} \mathrm{C} ?$
(b) the container is cooled to $-5^{\circ} \mathrm{C} ?$
(c) an additional $10.0$ grams of iodine crystals are added to the container?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 61

Is a reaction with a large value of $K_{c}$ faster than a different reaction with a smaller value of $K_{c} ?$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 62

A student answering a question about equilibrium writes, "As a reaction approaches equilibrium from the left, the concentration of reactants decreases and the concentration of products increases until the two are equal. At this point a balance is reached and the reaction stops in a state of equilibrium." Rewrite the response, correcting the student's mistakes.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 63

Does the addition of a catalyst affect the value of the equilibrium constant? Explain your answer in terms of the forward and reverse reaction kinetics.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 64

(a) When the volume of a gas-phase reaction is increased (at constant pressure), in what direction does the equilibrium shift?
(b) Under what conditions does increasing the volume of a gas-phase reaction have no effect on the equilibrium state? (c) What is the equivalent to increasing the volume of a gasphase reaction for a reaction that occurs in solution?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 65

The value of $K_{\mathrm{p}}$ for the chemical equation
$$
\mathrm{CuSO}_{4} \cdot 4 \mathrm{NH}_{5}(s) \leftrightharpoons \mathrm{CuSO}_{4} \cdot 2 \mathrm{NH}_{3}(s)+2 \mathrm{NH}_{3}(g)
$$
is $6.66 \times 10^{-3} \mathrm{~atm}^{2}$ at $20^{\circ} \mathrm{C}$. Calculate the equilibrium pressure of ammonia at $20^{\circ} \mathrm{C}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 66

The equilibrium constant for the chemical equation
$$
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{NH}_{3}(g)
$$
is $K_{\mathrm{p}}=0.099 \mathrm{bar}^{-2}$ at $227^{\circ} \mathrm{C} .$ Calculate the value of $K_{c}$ for the reaction at $227^{\circ} \mathrm{C}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 67

At $500^{\circ} \mathrm{C}$ hydrogen iodide decomposes according to
$$
2 \mathrm{HI}(g) \leftrightharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)
$$
For $\mathrm{HI}(g)$ heated to $500^{\circ} \mathrm{C}$ in a $1.00$ -liter reaction vessel, chemical analysis gave the following concentrations at equilibrium: $\left[\mathrm{H}_{2}\right]=0.42 \mathrm{M},\left[\mathrm{I}_{2}\right]=0.42 \mathrm{M}$,
and $[\mathrm{HI}]=3.52 \mathrm{M}$. If an additional mole of $\mathrm{HI}(\mathrm{g})$ is introduced into the reaction vessel, what are the equi-

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 68

The equilibrium constant for the methanol synthesis equation
$$
2 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(g)
$$
is $K_{\mathrm{p}}=2.19 \times 10^{4} \mathrm{bar}^{-2}$ at $25^{\circ} \mathrm{C}$. (a) Calculate the value of $P_{\mathrm{CH}_{s} \mathrm{OH}}$ at equilibrium when $P_{\mathrm{H}_{2}}=0.020 \mathrm{bar}$ and
$P_{\mathrm{CO}}=0.010$ bar. (b) Given that at equilibrium $P_{\text {botal }}=$ $10.0$ bar and $P_{\mathrm{H}_{2}}=0.020$ bar, calculate $P_{\mathrm{co}}$ and $P_{\mathrm{CH}_{3} \mathrm{OH}}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 69

Given the reaction equation
$$
\begin{gathered}
\mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \leftrightharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g) \\
\Delta H_{r \mathrm{xn}}^{\circ}=-40.8 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}
\end{gathered}
$$
Predict the effect of the following changes on the item listed:

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 70

According to Table 19.1, $K_{c}=0.20 \mathrm{M}$ at $100^{\circ} \mathrm{C}$ for the chemical equation
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \leftrightharpoons 2 \mathrm{NO}_{2}(g)
$$
Calculate $K_{\mathrm{p}}$ at the same temperature in units of bars.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 71

Tin can be prepared by heating $\mathrm{SnO}_{2}(s)$ ore with hydrogen gas, according to:
$$
\mathrm{SnO}_{2}(s)+2 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{Sn}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)
$$
When the reactants are heated to $500^{\circ} \mathrm{C}$ in a closed vessel, $\left[\mathrm{H}_{2} \mathrm{O}\right]=\left[\mathrm{H}_{2}\right]=0.25 \mathrm{M}$ at equilibrium. If more hydrogen is added so that its new initial concentration is $0.50 \mathrm{M}$, what are the concentrations of $\mathrm{H}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$ when equilibrium is restored?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 72

The equilibrium constant for the chemical equation
$$
\mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \leftrightharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g)
$$
is 3.0. Calculate the number of moles of $\mathrm{NO}_{2}(g)$ that must be added to $2.4$ moles of $\mathrm{SO}_{2}(g)$ in order to form $1.2$ moles of $\mathrm{SO}_{3}(g)$ at equilibrium.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 73

Diatomic chlorine dissociates to chlorine atoms at elevated temperatures according to
$$
\mathrm{Cl}_{2}(g) \leftrightharpoons 2 \mathrm{Cl}(g)
$$
For example, $K_{\mathrm{p}}=0.578$ bar at $2000^{\circ} \mathrm{C} .$ Calculate the fraction of chlorine molecules that are dissociated at $2000^{\circ} \mathrm{C}$ if the initial concentration of $\mathrm{Cl}_{2}(g)$ is $0.050 \mathrm{M}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 74

The value of the equilibrium constant for the equation
$$
\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \leftrightharpoons 2 \mathrm{HI}(g)
$$
is $K_{\mathrm{p}}=85$ at $553 \mathrm{~K}$. (a) Is it possible at $553 \mathrm{~K}$ to have an equilibrium reaction mixture for which $P_{\mathrm{H} 1}=P_{\mathrm{H}_{2}}=P_{1_{2}} ?$
(b) Suppose a $5.0$ -gram sample of $\mathrm{HI}(g)$ is heated to $553 \mathrm{~K}$ in a $2.00$ -liter vessel. Calculate the composition of the equilibrium reaction mixture.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 75

The value of the equilibrium constant for the chemical equation
$$
\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \leftrightharpoons 2 \mathrm{HI}(g)
$$
is $K_{\mathrm{p}}=85$ at $280^{\circ} \mathrm{C}$. Calculate the value of $K_{\mathrm{p}}$ at $280^{\circ} \mathrm{C}$ for the equation
$$
\mathrm{HI}(g) \leftrightharpoons \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{I}_{2}(g)
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 76

The equilibrium constant at $823 \mathrm{~K}$ for the chemical equation
$$
\mathrm{MgCl}_{2}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \leftrightharpoons \mathrm{Mg} \mathrm{O}(s)+\mathrm{Cl}_{2}(g)
$$
is $K_{\mathrm{p}}=1.75 \mathrm{~atm}^{1 / 2}$. Suppose that $50.0$ grams of $\mathrm{MgCl}_{2}(s)$ is placed in a reaction vessel with $2.00$ liters of oxygen at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ and that the reaction vessel is sealed and heated to $823 \mathrm{~K}$ until equilibrium is attained. Calculate $P_{\mathrm{Cl}_{2}}$ and $P_{\mathrm{O}_{2}}$ at equilibrium in atm.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 77

Consider the reaction equilibrium described by the equation
$$
\mathrm{COCl}_{2}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)
$$
If $2.00$ moles of $\operatorname{COCl}_{2}(g)$ is introduced into a $10.0$ liter flask at $1000^{\circ} \mathrm{C}$, calculate the equilibrium concentrations of all species at this temperature. At $1000^{\circ} \mathrm{C}, K_{c}=0.329 \mathrm{M}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 78

Osmium dioxide occurs either as a black powder or as brown crystals. The density of the black powder form is $7.7 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ and the density of the brown crystalline form is $11.4 \mathrm{~g} \cdot \mathrm{cm}^{-3}$. Which is the more stable form at high pressure?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 79

Ammonia, $\mathrm{NH}_{3}(g)$, and hydrogen chloride, $\mathrm{HCl}(g)$, with ammonia in excess, are injected into a reaction vessel maintained at $300^{\circ} \mathrm{C}$. A white powder of ammonium chloride, $\mathrm{NH}_{4} \mathrm{Cl}(s)$, is observed to form according to
$$
\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \leftrightharpoons \mathrm{NH}_{4} \mathrm{Cl}(s)
$$
with $K_{\mathrm{p}}=17.1 \mathrm{bar}^{-2}$ at $300^{\circ} \mathrm{C}$. When the system comes to equilibrium, the total pressure is $2.776$ bar. Calculate the partial pressure of each gas at equilibrium.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 80

Phosphorus pentachloride decomposes according to the chemical equation
$$
\mathrm{PCl}_{5}(g) \leftrightharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
with $K_{\mathrm{p}}=1.78$ atm at $250^{\circ} \mathrm{C}$. How many moles of $\mathrm{PCl}_{5}(g)$ must be added to a 1.00-liter container at $250^{\circ} \mathrm{C}$ to obtain a concentration of $1.00 \mathrm{M}$ of $\mathrm{PCl}_{3}(g)$ ?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 81

An equilibrium mixture of $\mathrm{CO}(g), \mathrm{Cl}_{2}(g)$, and $\mathrm{COCl}_{2}(g)$ has partial pressures $P_{\mathrm{co}}=P_{\mathrm{Cl}_{2}}=1.09 \mathrm{bar}$
and $P_{\mathrm{Cocl}_{2}}=0.144$ bar. A quantity of $\mathrm{CO}(g)$ is suddenly injected into the reaction vessel and the total pressure jumps to $3.31$ bar. Calculate the total pressure after equilibrium is reestablished. The relevant chemical equation is
$$
\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \leftrightharpoons \operatorname{COCl}_{2}(g)
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 82

For the reaction described by
$$
\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \leftrightharpoons 2 \mathrm{HI}(g)
$$
the value of $K_{\mathrm{p}}$ is $54.4$ at $355^{\circ} \mathrm{C}$. What percentage of $\mathrm{I}_{2}(g)$ will be converted to $\mathrm{HI}(g)$ if $0.200$ moles each of $\mathrm{H}_{2}(g)$ and $\mathrm{I}_{2}(g)$ are mixed and allowed to come to equilibrium at $355^{\circ} \mathrm{C}$ in a $1.00$ -liter container?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 83

Antimony pentachloride, $\mathrm{SbCl}_{5}(s)$, decomposes to antimony trichloride, $\mathrm{SbCl}_{3}(s)$, and chlorine, $\mathrm{Cl}_{2}(g)$, according to
$$
\mathrm{SbCl}_{5}(s) \leftrightharpoons \mathrm{SbCl}_{s}(s)+\mathrm{Cl}_{2}(g)
$$
A $0.50$ -mole sample of $\mathrm{SbCl}_{3}(s)$ is put into a closed 1.00-liter container and heated to $250^{\circ} \mathrm{C}$. At equilibrium the mole fraction of $\mathrm{Cl}_{2}(g)$ is found to be $0.428$. Calculate the value of $K_{\mathrm{p}}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 84

Calculate the partial pressures in the equilibrium gas mixture that results when $26.1$ Torr of $\mathrm{CO}_{2}(g)$ and $26.1$ Torr of $\mathrm{H}_{2}(g)$ are mixed at $1000^{\circ} \mathrm{C} .$
The relevant chemical equation is
$$
\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \quad K_{\mathrm{p}}=0.719
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 85

Calculate the equilibrium partial pressures in the previous problem if the volume of the reaction container is doubled.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 86

Ammonium chloride decomposes according to the equation
$$
\mathrm{NH}_{4} \mathrm{Cl}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)
$$
with $K_{\mathrm{p}}=5.82 \times 10^{-2} \mathrm{bar}^{2}$ at $300^{\circ} \mathrm{C} .$ Calculate the equilibrium partial pressure of each gas and the number of grams of $\mathrm{NH}_{4} \mathrm{Cl}(s)$ produced if equal molar quantities of $\mathrm{NH}_{3}(g)$ and $\mathrm{HCl}(g)$ at an initial total pressure of $8.87$ bar are injected into a $2.00$ -liter container at $300^{\circ} \mathrm{C}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 87

Sulfuryl chloride, $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)$, decomposes to $\mathrm{SO}_{2}(g)$ and $\mathrm{Cl}_{2}(g)$ at $100^{\circ} \mathrm{C}$ according to
$$
\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \leftrightharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)
$$
A $6.175$ -gram sample of $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)$ is placed in an evacuated 1.00-liter container at $100^{\circ} \mathrm{C}$, and the total pressure at equilibrium is found to be $2.41$ bar. Calculate the partial pressures of $\mathrm{SO}_{2} \mathrm{Cl}_{2}(g), \mathrm{SO}_{2}(g)$, and $\mathrm{Cl}_{2}(g)$
and the value of $K_{\mathrm{p}}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 88

An equilibrium mixture contains $0.20$ moles of hydrogen gas, $0.80$ moles of carbon dioxide, $0.10$ moles of carbon monoxide, and $0.40$ moles of water vapor in a 1.00-liter container. How many moles of carbon dioxide would have to be added at constant temperature and volume to increase the amount of carbon monoxide to $0.20$ moles? The equation for the reaction is
$$
\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \leftrightharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 89

The decomposition of ammonium hydrogen sulfide is an endothermic reaction. The equation for the reaction is
$$
\mathrm{NH}_{4} \mathrm{HS}(s) \leftrightharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)
$$
A $5.260$ -gram sample of solid ammonium hydrogen sulfide is placed in an evacuated $9.00$ -liter container at $25^{\circ} \mathrm{C}$. After equilibrium is established, the total pressure inside the vessel is $0.659 \mathrm{~atm}$. Some solid ammonium hydrogen sulfide remains in the flask.
(a) What is the value of the equilibrium constant, $K_{\mathrm{p}} ?$
(b) What percentage of the solid placed in the flask has reacted?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 90

Prove that the relationship between $K_{\mathrm{p}}$ referenced to units of bars and $K_{\mathrm{p}}$ referenced to units of atmospheres is,
$$
K_{\mathrm{P}_{\mathrm{tar}}}=K_{\mathrm{P}_{\text {atin }}}\left(1.01325 \mathrm{bar} \cdot \mathrm{atm}^{-1}\right)^{\omega_{\mathrm{kan}}}
$$
where $\Delta v_{g a}$ is the difference between the sum of the stoichiometric coefficients of the products and that of the reactants for the gas-phase species in a given reaction equation.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 91

Given:
(1) $2 \mathrm{BrCl}(g) \leftrightharpoons \mathrm{Cl}_{2}(g)+\mathrm{Br}_{2}(g) \quad K_{\mathrm{P}_{1}}=0.45$
(2) $2 \operatorname{IBr}(g) \leftrightharpoons \mathrm{Br}_{2}(g)+\mathrm{I}_{2}(g) \quad K_{\mathrm{P}_{2}}=21.0$
Determine the value of $K_{\mathrm{p}}$ for the reaction equation
$$
\mathrm{BrCl}(g)+\frac{1}{2} \mathrm{I}_{2}(g) \leftrightharpoons \operatorname{IBr}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g)
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 92

Acetic acid in the vapor phase is in equilibrium with its dimer as described by
$$
\begin{array}{r}
2 \mathrm{CH}_{3} \mathrm{COOH}(g) \leftrightharpoons\left(\mathrm{CH}_{3} \mathrm{COOH}\right)_{2}(g) \\
K_{\mathrm{p}}=3.67 \mathrm{bar}^{-1} \text { at } 100^{\circ} \mathrm{C}
\end{array}
$$
If the total pressure is $1.50$ bar, calculate the partial pressure of the dimer.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 93

Dinitrogen tetraoxide decomposes according to
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \leftrightharpoons 2 \mathrm{NO}_{2}(g)
$$
Pure $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ was placed in an empty container at $127^{\circ} \mathrm{C}$ at a pressure of $0.0488 \mathrm{~atm} .$ After the system reached equilibrium, the total pressure was $0.0743$ atm. Calculate the value of $K_{\mathrm{p}}$ for this equation.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 94

The decomposition of ammonium carbamate, $\mathrm{NH}_{2} \mathrm{COONH}_{4}(s)$, takes place according to the chemical equation
$$
\mathrm{NH}_{2} \mathrm{COONH}_{4}(s) \leftrightharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)
$$
Show that if all the $\mathrm{NH}_{3}(g)$ and $\mathrm{CO}_{2}(g)$ result from the decomposition of ammonium carbamate, then $K_{\mathrm{p}}=$ $(4 / 27) P^{5}$, where $P$ is the total pressure at equilibrium.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 95

The equilibrium constant for the chemical equation
$$
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \leftrightharpoons 2 \mathrm{NH}_{3}(g)
$$
is $K_{\mathrm{p}}=0.097 \mathrm{bar}^{-2}$ at $227^{\circ} \mathrm{C} .$ (a) Given that at equilibrium $P_{\mathrm{N}_{2}}=1.00$ bar and $P_{\mathrm{H}_{2}}=9.00$ bar, calculate $P_{\mathrm{NH}_{3}}$ at equilibrium. (b) Given that at equilibrium the total pressure is $2.00$ bar and also that the mole fraction of $\mathrm{H}_{2}(g), x_{\mathrm{H}_{2}}$, is $0.20$, calculate $x_{\mathrm{NH}_{3}}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 96

Consider the methanation reaction described by the chemical equation
$$
\mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
It was found that $0.618$ moles of $\mathrm{CO}(g), 0.387$ moles of $\mathrm{H}_{2}(\mathrm{~g}), 0.387 \mathrm{moles}$ of $\mathrm{CH}_{4}(g)$, and $0.387$ moles of
$\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ were present in an equilibrium mixture in a 1.00-liter container. All the water vapor was removed and the system allowed to come to equilibrium again. Calculate the concentration of all gases in the new equilibrium system. (You must solve the resulting equation by trial and error.)

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 97

Referring to Problem $19-73$, show that the fraction of chlorine molecules $(x)$ that dissociate is given by
$$
\frac{x^{2}}{1-x}=\frac{K_{c}}{4\left[\mathrm{Cl}_{2}\right]_{0}}
$$
for any initial concentration of $\mathrm{Cl}_{2}(g)$.

Adriano Chikande

Adriano Chikande

Numerade Educator