Chemistry

Julia Burdge

Chapter 15

Chemical Equilibrium - all with Video Answers

Educators

Chapter Questions

Problem 1

Define equilibrium. Give two examples of a dynamic equilibrium.

Kevin Zaborsky

Kevin Zaborsky

Numerade Educator

Problem 2

Which of the following statements is correct about a reacting system at equilibrium: (a) the concentrations of reactants are equal to the concentrations of products, (b) the rate of the forward reaction is equal to the rate of the reverse reaction.

Kevin Zaborsky

Numerade Educator

Problem 3

Consider the reversible reaction $A$ $\rightleftarrows B .$ Explain how equilibrium can be reached by starting with only $\mathrm{A}$, only $\mathrm{B}$, or a mixture of $\mathrm{A}$ and $\mathrm{B}$.

Kevin Zaborsky

Numerade Educator

Problem 4

What is the law of mass action?

Kevin Zaborsky

Numerade Educator

Problem 5

Briefly describe the importance of equilibrium in the study of chemical reactions.

Kevin Zaborsky

Numerade Educator

Problem 6

Define reaction quotient. How does it differ from the equilibrium constant?

Kevin Zaborsky

Numerade Educator

Problem 7

Write reaction quotients for the following reactions: (a) $2 \mathrm{NO}(g)$ $+\mathrm{O}_{2}(g) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(g),(\mathrm{b}) \mathrm{S}(s)+3 \mathrm{F}_{2}(g) \rightleftharpoons \mathrm{SF}_{6}(g)$ (c) $\operatorname{Co}^{3+}(a q)+6 \mathrm{NH}_{3}(a q) \rightleftarrows \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}$
(d) $\mathrm{HCOOH}(a q) \rightleftharpoons \mathrm{HCOO}^{-}(a q)+\mathrm{H}^{+}(a q)$

Kevin Zaborsky

Numerade Educator

Problem 8

Write the equation for the reaction that corresponds to each of the following reaction quotients;
(a) $Q_{c}=$ $\frac{\left[\mathrm{H}_{2}\right]^{2}\left[\mathrm{S}_{2}\right]}{\left[\mathrm{H}_{2} \mathrm{S}\right]^{2}}$
(b) $Q_{c}=$ $\frac{\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{Cl}_{2}\right]}{\left[\mathrm{NClO}_{2}\right]^{2}}$
(c) $Q_{c}=$ $\frac{\left[\mathrm{HgI}_{4}^{2}\right]}{\left[\mathrm{Hg}^{2+}\right]\left[\mathrm{I}^{-}\right]^{4}}$
(d) $Q_{c}=$ $\frac{[\mathrm{NO}]^{2}\left[\mathrm{Br}_{2}\right]}{[\mathrm{NOBr}]^{2}}$

Kevin Zaborsky

Numerade Educator

Problem 9

Consider the reaction
$$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftarrows \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$
At a certain temperature, the equilibrium concentrations are $[\mathrm{NO}]=0.31 M,\left[\mathrm{H}_{2}\right]=0.16 M,\left[\mathrm{N}_{2}\right]=0.082 M,$ and $\left[\mathrm{H}_{2} \mathrm{O}\right]=$
4.64 M. (a) Write the equilibrium expression for the reaction.
(b) Determine the value of the equilibrium constant.

Kevin Zaborsky

Numerade Educator

Problem 10

The equilibrium constant for the reaction
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{SO}_{3}(g)$$
is $2.8 \times 10^{2}$ at a certain temperature. If $\left[\mathrm{SO}_{2}\right]=0.0124 \mathrm{M}$ and $\left[\mathrm{O}_{2}\right]=0.031 \mathrm{M},$ what is $\left[\mathrm{SO}_{3}\right] ?$

Kevin Zaborsky

Numerade Educator

Problem 11

Consider the following equilibrium process at $700^{\circ} \mathrm{C}$ :
$$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftarrows 2 \mathrm{H}_{2} \mathrm{S}(g)$$
Analysis shows that there are 2.50 moles of $\mathrm{H}_{2}, 1.35 \times 10^{-5}$ mole of $S_{2},$ and 8.70 moles of $\mathrm{H}_{2} \mathrm{S}$ present in a 12.0 -L flask. Calculate the equilibrium constant $K_{c}$ for the reaction.

Kevin Zaborsky

Numerade Educator

Problem 12

The equilibrium constant for the reaction
$$2 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}(g)$$
is $1.6 \times 10^{-2}$ at a certain temperature. If there are $1.17 \times 10^{-2}$ mole of $\mathrm{H}_{2}$ and $3.46 \times 10^{-3}$ mole of $\mathrm{CH}_{3} \mathrm{OH}$ at equilibrium in a 5.60-L flask, what is the concentration of CO?

Kevin Zaborsky

Numerade Educator

Problem 13

Define homogeneous equilibrium and heterogeneous equilibrium. Give two examples of each.

Kevin Zaborsky

Numerade Educator

Problem 14

What do the symbols $K_{c}$ and $K_{P}$ represent?

Kevin Zaborsky

Numerade Educator

Problem 15

Write the expressions for the equilibrium constants $K_{P}$ of the following thermal decomposition reactions:
(a) $2 \mathrm{NaHCO}_{3}(s) \rightleftarrows \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(b) $2 \mathrm{CaSO}_{4}(s) \rightleftharpoons 2 \mathrm{CaO}(s)+2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$

Kevin Zaborsky

Numerade Educator

Problem 16

Write equilibrium constant expressions for $K_{\mathrm{c}},$ and for $K_{P},$ if applicable, for the following processes:
(a) $2 \mathrm{CO}_{2}(g) \rightleftarrows 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)$
(b) $3 \mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{O}_{3}(g)$
(c) $\operatorname{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \operatorname{COCl}_{2}(g)$
(d) $\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)$
(e) $\mathrm{HCOOH}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HCOO}^{-}(a q)$
(f) $2 \mathrm{HgO}(s) \rightleftarrows 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)$

Kevin Zaborsky

Numerade Educator

Problem 17

Write the equilibrium constant expressions for $K_{c}$ and for $K_{P}$, if applicable, for the following reactions:
(a) $2 \mathrm{NO}_{2}(g)+7 \mathrm{H}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$
(b) $2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g)$
(c) $\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftarrows 2 \mathrm{CO}(g)$
(d) $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}(a q) \rightleftarrows \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(a q)+\mathrm{H}^{+}(a q)$

Kevin Zaborsky

Numerade Educator

Problem 18

Write the equation relating $K_{\mathrm{c}}$ to $K_{P},$ and define all the terms.

Kevin Zaborsky

Numerade Educator

Problem 19

What is the rule for writing the equilibrium constant for the overall reaction that is the sum of two or more reactions?

Kevin Zaborsky

Numerade Educator

Problem 20

Give an example of a multiple equilibria reaction.

Natalie Almond

Numerade Educator

Problem 21

The equilibrium constant for the reaction $\mathrm{A} \rightleftarrows \mathrm{B}$ is $K_{\mathrm{c}}=$ 10 at a certain temperature. (1) Starting with only reactant A, which of the diagrams shown here best represents the system at equilibrium? (2) Which of the diagrams best represents the system at equilibrium if $K_{c}=0.10 ?$ Explain why you can calculate $K_{\mathrm{c}}$ in each case without knowing the volume of the container. The grey spheres represent the A molecules, and the green spheres represent the B molecules.

Kevin Zaborsky

Numerade Educator

Problem 22

The following diagrams represent the equilibrium state for three different reactions of the type
$$
\mathrm{A}+\mathrm{X} \rightleftarrows \mathrm{AX}(\mathrm{X}=\mathrm{B}, \mathrm{C}, \text { or } \mathrm{D})
$$(a) Which reaction has the largest equilibrium constant?
(b) Which reaction has the smallest equilibrium constant?

Kevin Zaborsky

Numerade Educator

Problem 23

The equilibrium constant $\left(K_{c}\right)$ for the reaction
$$
2 \mathrm{HCl}(g) \rightleftarrows \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)
$$
is $4.17 \times 10^{-34}$ at $25^{\circ} \mathrm{C}$. What is the equilibrium constant for the reaction
$$
\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows 2 \mathrm{HCl}(g)
$$
at the same temperature?

Kevin Zaborsky

Numerade Educator

Problem 24

What is $K_{P}$ at $1273^{\circ} \mathrm{C}$ for the reaction
$$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{CO}_{2}(g)$$
if $K_{c}$ is $2.24 \times 10^{22}$ at the same temperature?

Kevin Zaborsky

Numerade Educator

Problem 25

The equilibrium constant $K_{P}$ for the reaction
$$2 \mathrm{SO}_{3}(g) \rightleftarrows 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$
is $1.8 \times 10^{-5}$ at $350^{\circ} \mathrm{C}$. What is $K_{\mathrm{c}}$ for this reaction?

Kevin Zaborsky

Numerade Educator

Problem 26

Consider the reaction
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)$$
If the equilibrium partial pressures of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and $\mathrm{NO}$ are 0.15 $0.33,$ and 0.050 atm, respectively, at $2200^{\circ} \mathrm{C},$ what is $K_{P} ?$

Kevin Zaborsky

Numerade Educator

Problem 27

A reaction vessel contains $\mathrm{NH}_{3}, \mathrm{N}_{2},$ and $\mathrm{H}_{2}$ at equilibrium at a certain temperature. The equilibrium concentrations are $\left[\mathrm{NH}_{3}\right]=0.25 M,\left[\mathrm{N}_{2}\right]=0.11 M,$ and $\left[\mathrm{H}_{2}\right]=1.91 M .$ Calculate
the equilibrium constant $K_{\mathrm{c}}$ for the synthesis of ammonia if the reaction is represented as
(a) $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g)$
(b) $\frac{1}{2} \mathrm{N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftarrows \mathrm{NH}_{3}(g)$

Kevin Zaborsky

Numerade Educator

Problem 28

The equilibrium constant $K_{\mathrm{c}}$ for the reaction
$$\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g)$$
is $3.8 \times 10^{-5}$ at $727^{\circ} \mathrm{C}$. Calculate $K_{\mathrm{c}}$ and $K_{P}$ for the equilibrium
$$2 \mathrm{I}(g) \rightleftarrows \mathrm{I}_{2}(g)$$
at the same temperature.

Kevin Zaborsky

Numerade Educator

Problem 29

At equilibrium, the pressure of the reacting mixture
$$\mathrm{CaCO}_{3}(s) \rightleftarrows \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$
is 0.105 atm at $350^{\circ} \mathrm{C}$. Calculate $K_{P}$ and $K_{\mathrm{c}}$ for this reaction.

Kevin Zaborsky

Numerade Educator

Problem 30

The equilibrium constant $K_{P}$ for the reaction
$$\mathrm{PCl}_{5}(g) \rightleftarrows \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$
is 1.05 at $250^{\circ} \mathrm{C}$. The reaction starts with a mixture of $\mathrm{PCl}_{5}, \mathrm{PCl}_{3}$ and $\mathrm{Cl}_{2}$ at pressures of $0.177,0.223,$ and 0.111 atm, respectively, at $250^{\circ} \mathrm{C}$. When the mixture comes to equilibrium at that temperature, which pressures will have decreased and which will have increased? Explain why.

Kevin Zaborsky

Numerade Educator

Problem 31

Ammonium carbamate $\left(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\right)$ decomposes as follows:
$$\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s) \rightleftarrows 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)$$
Starting with only the solid, it is found that when the system reaches equilibrium at $40^{\circ} \mathrm{C},$ the total gas pressure $\left(\mathrm{NH}_{3}$ and \right. $\mathrm{CO}_{2}$ ) is 0.363 atm. Calculate the equilibrium constant $K_{P}$

Kevin Zaborsky

Numerade Educator

Problem 32

Pure phosgene gas (COCl $_{2}$ ), $3.00 \times 10^{-2}$ mol, was placed in a $1.50-\mathrm{L}$ container. It was heated to $800 \mathrm{K}$, and at equilibrium the pressure of CO was found to be 0.497 atm. Calculate the equilibrium constant $K_{P}$ for the reaction
$$\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{COCl}_{2}(g)$$

Kevin Zaborsky

Numerade Educator

Problem 33

Consider the equilibrium
$$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$
If nitrosyl bromide (NOBr) is 34 percent dissociated at 25 ^ C and the total pressure is 0.25 atm, calculate $K_{P}$ and $K_{c}$ for the dissociation at this temperature.

Daniel Gosser

Numerade Educator

Problem 34

The following equilibrium constants have been determined for hydrosulfuric acid at $25^{\circ} \mathrm{C}$ :
$$\begin{aligned}&\mathrm{H}_{2} \mathrm{S}(a q) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{HS}^{-}(a q) \quad K_{c}^{\prime}=9.5 \times 10^{-8}\\&\mathrm{HS}^{-}(a q) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{S}^{2-}(a q) \quad K_{\mathrm{c}}^{\prime \prime}=1.0 \times 10^{-19}\end{aligned}$$
Calculate the equilibrium constant for the following reaction at the same temperature:
$$\mathrm{H}_{2} \mathrm{S}(a q) \rightleftarrows 2 \mathrm{H}^{+}(a q)+\mathrm{S}^{2-}(a q)$$

Kevin Zaborsky

Numerade Educator

Problem 35

The following equilibrium constants have been determined for oxalic acid at $25^{\circ} \mathrm{C}$ :
$$\begin{aligned}&\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q) \quad K_{c}^{\prime}=6.5 \times 10^{-2}\\
&\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q) \rightleftarrows \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \quad K_{\mathrm{c}}^{\prime \prime}=6.1 \times 10^{-5}
\end{aligned}$$
Calculate the equilibrium constant for the following reaction at the same temperature:
$$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftarrows 2 \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q)$$

Kevin Zaborsky

Numerade Educator

Problem 36

The following equilibrium constants were determined at $1123 \mathrm{K}$ :
Write the equilibrium constant expression $K_{P}$, and calculate the equilibrium constant at $1123 \mathrm{K}$ for
$$\mathrm{C}(s)+\mathrm{CO}_{2}(g)+2 \mathrm{Cl}_{2}(g) \rightleftarrows 2 \mathrm{COCl}_{2}(g)$$

Kevin Zaborsky

Numerade Educator

Problem 37

At a certain temperature, the following reactions have the constants shown:
$$
\begin{aligned}
\mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightleftarrows & \mathrm{SO}_{2}(g) & K_{\mathrm{c}}^{\prime}=4.2 \times 10^{52} \\
2 \mathrm{S}(s)+3 \mathrm{O}_{2}(g) & \rightleftarrows & 2 \mathrm{SO}_{3}(g) & K_{\mathrm{c}}^{\prime \prime}=9.8 \times 10^{128}
\end{aligned}
$$Calculate the equilibrium constant $K_{c}$ for the following reaction at that temperature:$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{SO}_{3}(g)$$

Kevin Zaborsky

Numerade Educator

Problem 38

Outline the steps for calculating the concentrations of reacting species in an equilibrium reaction.

Kevin Zaborsky

Numerade Educator

Problem 39

The equilibrium constant $K_{P}$ for the reaction
$$
2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{SO}_{3}(g)
$$
is $5.60 \times 10^{4}$ at $350^{\circ} \mathrm{C}$. The initial pressures of $\mathrm{SO}_{2}, \mathrm{O}_{2},$ and $\mathrm{SO}_{3}$ in a mixture are $0.350,0.762,$ and 0 atm, respectively, at $350^{\circ} \mathrm{C}$. When the mixture reaches equilibrium, is the total pressure less than or greater than the sum of the initial pressures?

Kevin Zaborsky

Numerade Educator

Problem 40

For the synthesis of ammonia
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g)$$
the equilibrium constant $K_{\mathrm{c}}$ at $375^{\circ} \mathrm{C}$ is $1.2 .$ Starting with $\left[\mathrm{H}_{2}\right]_{0}=$ $0.76 M,\left[\mathrm{N}_{2}\right]_{0}=0.60 \mathrm{M},$ and $\left[\mathrm{NH}_{3}\right]_{0}=0.48 \mathrm{M},$ which gases will
have increased in concentration and which will have decreased in concentration when the mixture comes to equilibrium?

Kevin Zaborsky

Numerade Educator

Problem 41

For the reaction
$$
\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)
$$
at $700^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.534 .$ Calculate the number of moles of $\mathrm{H}_{2}$ that are present at equilibrium if a mixture of 0.300 mole of $\mathrm{CO}$ and 0.300 mole of $\mathrm{H}_{2} \mathrm{O}$ is heated to $700^{\circ} \mathrm{C}$ in a 10.0 -L container.

Kevin Zaborsky

Numerade Educator

Problem 42

At $1000 \mathrm{K},$ a sample of pure $\mathrm{NO}_{2}$ gas decomposes:
$$
2 \mathrm{NO}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)
$$
The equilibrium constant $K_{P}$ is $158 .$ Analysis shows that the partial pressure of $\mathrm{O}_{2}$ is 0.25 atm at equilibrium. Calculate the pressure of $\mathrm{NO}$ and $\mathrm{NO}_{2}$ in the mixture.

Kevin Zaborsky

Numerade Educator

Problem 43

The equilibrium constant $K_{\mathrm{c}}$ for the reaction
$$
\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftarrows 2 \mathrm{HBr}(g)
$$
is $2.18 \times 10^{6}$ at $730^{\circ} \mathrm{C}$. Starting with 3.20 moles of $\mathrm{HBr}$ in a 12.0-L reaction vessel, calculate the concentrations of $\mathrm{H}_{2}, \mathrm{Br}_{2}$ and HBr at equilibrium.

Kevin Zaborsky

Numerade Educator

Problem 44

The dissociation of molecular iodine into iodine atoms is represented as
$$
\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g)
$$
At $1000 \mathrm{K}$, the equilibrium constant $K_{\mathrm{c}}$ for the reaction is $3.80 \times$ $10^{-5} .$ Suppose you start with 0.0456 mole of $I_{2}$ in a 2.30 -L flask at 1000 K. What are the concentrations of the gases at equilibrium?

Kevin Zaborsky

Numerade Educator

Problem 45

The equilibrium constant $K_{c}$ for the decomposition of phosgene $\left(\mathrm{COCl}_{2}\right)$ is $4.63 \times 10^{-3}$ at $527^{\circ} \mathrm{C}:$
$$
\mathrm{COCl}_{2}(g) \rightleftarrows \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)
$$
Calculate the equilibrium partial pressures of all the components, starting with pure phosgene at 0.760 atm.

Kevin Zaborsky

Numerade Educator

Problem 46

Consider the following equilibrium process at $686^{\circ} \mathrm{C}$ :
$$
\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftarrows \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
The equilibrium concentrations of the reacting species are $[\mathrm{CO}]=0.050 M,\left[\mathrm{H}_{2}\right]=0.045 \mathrm{M},\left[\mathrm{CO}_{2}\right]=0.086 \mathrm{M},$ and
$\left[\mathrm{H}_{2} \mathrm{O}\right]=0.040 \mathrm{M} .$ (a) Calculate $K_{\mathrm{c}}$ for the reaction at $686^{\circ} \mathrm{C}$
(b) If we add $\mathrm{CO}_{2}$ to increase its concentration to $0.50 \mathrm{mol} / \mathrm{L}$ what will the concentrations of all the gases be when equilibrium is reestablished?

Kevin Zaborsky

Numerade Educator

Problem 47

Consider the heterogeneous equilibrium process:
$$
\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftarrows 2 \mathrm{CO}(g)
$$
At $700^{\circ} \mathrm{C},$ the total pressure of the system is found to be 4.50 atm. If the equilibrium constant $K_{p}$ is $1.52,$ calculate the equilibrium partial pressures of $\mathrm{CO}_{2}$ and $\mathrm{CO}$

Kevin Zaborsky

Numerade Educator

Problem 48

The equilibrium constant $K_{\mathrm{c}}$ for the reaction
$$
\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)
$$
is 4.2 at $1650^{\circ} \mathrm{C}$. Initially $0.80 \mathrm{mol} \mathrm{H}_{2}$ and $0.80 \mathrm{mol} \mathrm{CO}_{2}$ are
injected into a 5.0 -L flask. Calculate the concentration of each species at equilibrium.

Kevin Zaborsky

Numerade Educator

Problem 49

The aqueous reaction L-glutamate $+$ pyruvate $\rightleftarrows \alpha$ -ketoglutarate $+$ L-alanine
is catalyzed by the enzyme L-glutamate-pyruvate aminotransferase. At $300 \mathrm{K}$, the equilibrium constant for the reaction is 1.11. Predict whether the forward reaction will occur if the concentrations of the reactants and products are [L-glutamate] $\left.=3.0 \times 10^{-5} \mathrm{M}, \text { [pyruvate }\right]=3.3 \times 10^{-4} \mathrm{M}$ $[\alpha \text { -ketoglutarate }]=1.6 \times 10^{-2} M,$ and $[\mathrm{L} \text { -alanine }]=6.25 \times$$10^{-3} M$

Kevin Zaborsky

Numerade Educator

Problem 50

Explain Le Châtelier's principle. How does this principle enable us to maximize the yields of desirable reactions and minimize the effect of undesirable ones?

Kevin Zaborsky

Numerade Educator

Problem 51

Use Le Châtelier's principle to explain why the equilibrium vapor pressure of a liquid increases with increasing temperature.

Kevin Zaborsky

Numerade Educator

Problem 52

List four factors that can shift the position of an equilibrium. Only one of these factors can alter the value of the equilibrium constant. Which one is it?

Kevin Zaborsky

Numerade Educator

Problem 53

Does the addition of a catalyst have any effects on the position of an equilibrium?

Kevin Zaborsky

Numerade Educator

Problem 54

Consider the following equilibrium system involving $\mathrm{SO}_{2}, \mathrm{Cl}_{2}$ and $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ (sulfuryl dichloride):
$$
\mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{SO}_{2} \mathrm{Cl}_{2}(g)
$$
Predict how the equilibrium position would change if (a) $\mathrm{Cl}_{2}$ gas were added to the system, (b) $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ were removed from the system, (c) $\mathrm{SO}_{2}$ were removed from the system. The temperature remains constant in each case.

Kevin Zaborsky

Numerade Educator

Problem 55

Heating solid sodium bicarbonate in a closed vessel establishes the following equilibrium:
$$2 \mathrm{NaHCO}_{3}(s) \rightleftarrows \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g)$$
What would happen to the equilibrium position if (a) some of the $\mathrm{CO}_{2}$ were removed from the system, (b) some solid $\mathrm{Na}_{2} \mathrm{CO}_{3}$ were added to the system, (c) some of the solid $\mathrm{NaHCO}_{3}$ were removed from the system? The temperature remains constant.

Kevin Zaborsky

Numerade Educator

Problem 56

Consider the following equilibrium systems:
$\begin{array}{ll}\text { (a) } \mathrm{A} \rightleftarrows 2 \mathrm{B} \quad & \Delta H^{\circ}=20.0 \mathrm{kJ} / \mathrm{mol}\end{array}$
(b) $\mathrm{A}+\mathrm{B} \rightleftarrows \mathrm{C} \quad \Delta H^{\circ}=-5.4 \mathrm{kJ} / \mathrm{mol}$
(c) $\mathrm{A} \rightleftarrows \mathrm{B} \quad \Delta H^{\circ}=0.0 \mathrm{kJ} / \mathrm{mol}$
Predict the change in the equilibrium constant $K_{\mathrm{c}}$ that would occur in each case if the temperature of the reacting system were raised.

Kevin Zaborsky

Numerade Educator

Problem 57

What effect does an increase in pressure have on each of the following systems at equilibrium? The temperature is kept constant, and, in each case, the reactants are in a cylinder fitted with a movable piston.
(a) $\mathrm{A}(s) \rightleftharpoons 2 \mathrm{B}(s)$
(b) $2 \mathrm{A}(l) \rightleftarrows \mathrm{B}(l)$
(c) $\mathrm{A}(s) \rightleftharpoons \mathrm{B}(g)$
(d) $\mathrm{A}(g) \rightleftarrows \mathrm{B}(g)$
(e) $\mathrm{A}(g) \rightleftarrows 2 \mathrm{B}(g)$

Kevin Zaborsky

Numerade Educator

Problem 58

Consider the equilibrium
$$2 \mathrm{I}(g) \rightleftarrows \mathrm{I}_{2}(g)$$
What would be the effect on the position of equilibrium of
(a) increasing the total pressure on the system by decreasing its volume, (b) adding $I_{2}$ to the reaction mixture, and (c) decreasing the temperature?

Kevin Zaborsky

Numerade Educator

Problem 59

Consider the following equilibrium process:
$$\mathrm{PCl}_{5}(g) \rightleftarrows \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \quad \quad \Delta H^{\circ}=92.5 \mathrm{kJ} / \mathrm{mol}$$
Predict the direction of the shift in equilibrium when (a) the temperature is raised, (b) more chlorine gas is added to the reaction mixture, (c) some $\mathrm{PCl}_{3}$ is removed from the mixture,
(d) the pressure on the gases is increased, (e) a catalyst is added to the reaction mixture.

Kevin Zaborsky

Numerade Educator

Problem 60

Consider the reaction
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{SO}_{3}(g) \quad \quad\Delta H^{\circ}=-198.2 \mathrm{kJ} / \mathrm{mol}$$
Comment on the changes in the concentrations of $\mathrm{SO}_{2}, \mathrm{O}_{2},$ and $\mathrm{SO}_{3}$ at equilibrium if we were to (a) increase the temperature,
(b) increase the pressure, (c) increase $\mathrm{SO}_{2},$ (d) add a catalyst,
(e) add helium at constant volume.

Kevin Zaborsky

Numerade Educator

Problem 61

In the uncatalyzed reaction
$$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftarrows 2 \mathrm{NO}_{2}(g)$$
the pressure of the gases at equilibrium are $P_{\mathrm{N}_{2} \mathrm{O}_{4}}=0.377 \mathrm{atm}$ and $P_{\mathrm{NO}_{2}}=1.56 \mathrm{atm}$ at $100^{\circ} \mathrm{C} .$ What would happen to these pressures if a catalyst were added to the mixture?

Kevin Zaborsky

Numerade Educator

Problem 62

Consider the gas-phase reaction
$$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{CO}_{2}(g)$$
Predict the shift in the equilibrium position when helium gas is added to the equilibrium mixture (a) at constant pressure and
(b) at constant volume.

David Collins

Numerade Educator

Problem 63

Consider the following equilibrium reaction in a closed container:
$$\mathrm{CaCO}_{3}(s) \rightleftarrows \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$
What will happen if (a) the volume is increased, (b) some $\mathrm{CaO}$ is added to the mixture, (c) some $\mathrm{CaCO}_{3}$ is removed, (d) some $\mathrm{CO}_{2}$ is added to the mixture, (e) a few drops of an $\mathrm{NaOH}$ solution are added to the mixture, (f) a few drops of an HCl solution are added to the mixture (ignore the reaction between $\mathrm{CO}_{2}$ and water), (g) temperature is increased?

Kevin Zaborsky

Numerade Educator

Problem 64

The following diagrams show the reaction $\mathrm{A}+\mathrm{B} \rightleftarrows \mathrm{AB}$ at two different temperatures. Is the forward reaction endothermic or exothermic?

Kevin Zaborsky

Numerade Educator

Problem 65

The following diagrams show an equilibrium mixture of $\mathrm{O}_{2}$ and
$\mathrm{O}_{3}$ at temperatures $T_{1}$ and $T_{2}\left(T_{2}>T_{1}\right) .$ (a) Write an equilibrium equation showing the forward reaction to be exothermic.
(b) Predict how the number of $\mathrm{O}_{2}$ and $\mathrm{O}_{3}$ molecules would change if the volume were decreased at constant temperature.

Kevin Zaborsky

Numerade Educator

Problem 66

Consider the statement: "The equilibrium constant of a reacting mixture of solid $\mathrm{NH}_{4} \mathrm{Cl}$ and gaseous $\mathrm{NH}_{3}$ and $\mathrm{HCl}$ is 0.316 ." List three important pieces of information that are missing from this statement.

Zubair Abdulla

Numerade Educator

Problem 67

Pure nitrosyl chloride (NOCl) gas was heated to $240^{\circ} \mathrm{C}$ in a 1.00-L container. At equilibrium, the total pressure was 1.00 atm and the NOCl pressure was 0.64 atm.
$$2 \mathrm{NOCl}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$
(a) Calculate the partial pressures of $\mathrm{NO}$ and $\mathrm{Cl}_{2}$ in the system.
(b) Calculate the equilibrium constant $K_{P}$

Kevin Zaborsky

Numerade Educator

Problem 68

The equilibrium constant $\left(K_{P}\right)$ for the formation of the air pollutant nitric oxide (NO) in an automobile engine at $530^{\circ} \mathrm{C}$ is $2.9 \times 10^{-11}$
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)$$
(a) Calculate the partial pressure of NO under these conditions if the partial pressures of nitrogen and oxygen are 3.0 and 0.012 atm, respectively. (b) Repeat the calculation for atmospheric conditions where the partial pressures of nitrogen and oxygen are 0.78 and 0.21 atm and the temperature is $25^{\circ} \mathrm{C}$. (The $K_{P}$ for the reaction is $4.0 \times 10^{-31}$ at this temperature.)
(c) Is the formation of NO endothermic or exothermic? (d) What natural phenomenon promotes the formation of NO? Why?

David Collins

Numerade Educator

Problem 69

Baking soda (sodium bicarbonate) undergoes thermal decomposition as follows:
$$2 \mathrm{NaHCO}_{3}(s) \rightleftarrows \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$
Would we obtain more $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ by adding extra baking soda to the reaction mixture in (a) a closed vessel or (b) an open vessel?

Natalie Almond

Numerade Educator

Problem 70

Consider the following reaction at equilibrium:
$$\mathrm{A}(g) \rightleftarrows 2 \mathrm{B}(g)$$
From the data shown here, calculate the equilibrium constant (both $K_{P}$ and $K_{c}$ ) at each temperature. Is the reaction endothermic or exothermic?

Kevin Zaborsky

Numerade Educator

Problem 71

The equilibrium constant $K_{P}$ for the reaction
$$2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$$
is $2 \times 10^{-42}$ at $25^{\circ} \mathrm{C}$. (a) What is $K_{c}$ for the reaction at the same temperature? (b) The very small value of $K_{P}$ (and $K_{\mathrm{c}}$ ) indicates that the reaction overwhelmingly favors the formation of water molecules. Explain why, despite this fact, a mixture of hydrogen and oxygen gases can be kept at room temperature without any change.

Kevin Zaborsky

Numerade Educator

Problem 72

Consider the following reacting system:
$$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows 2 \mathrm{NOCl}(g)$$
What combination of temperature and pressure would maximize the yield of nitrosyl chloride (NOCl)? [Hint: $\Delta H_{\mathrm{f}}^{\circ}(\mathrm{NOCl})=$ 51.7 kJ/mol.]

Kevin Zaborsky

Numerade Educator

Problem 73

At a certain temperature and a total pressure of 1.2 atm, the partial pressures of an equilibrium mixture
$$2 \mathrm{A}(g) \rightleftarrows \mathrm{B}(g)$$
are $P_{\mathrm{A}}=0.60 \mathrm{atm}$ and $P_{\mathrm{B}}=0.60$ atm. (a) Calculate the $K_{P}$ for the reaction at this temperature. (b) If the total pressure were increased to 1.5 atm, what would be the partial pressures of $A$ and $\mathrm{B}$ at equilibrium?

Kevin Zaborsky

Numerade Educator

Problem 74

The decomposition of ammonium hydrogen sulfide
$$
\mathrm{NH}_{4} \mathrm{HS}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g)
$$
is an endothermic process. A 6.1589 -g sample of the solid is placed in an evacuated 4.000-L vessel at exactly 24 ^ C. After equilibrium has been established, the total pressure inside is 0.709 atm. Some solid $\mathrm{NH}_{4} \mathrm{HS}$ remains in the vessel. (a) What is the $K_{P}$ for the reaction? (b) What percentage of the solid has decomposed? (c) If the volume of the vessel were doubled at constant temperature, what would happen to the amount of solid in the vessel?

Kevin Zaborsky

Numerade Educator

Problem 75

Consider the reaction
$$
2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)
$$
At $430^{\circ} \mathrm{C},$ an equilibrium mixture consists of 0.020 mole of $\mathrm{O}_{2}$ 0.040 mole of $\mathrm{NO},$ and $0.96 \mathrm{mole}$ of $\mathrm{NO}_{2} .$ Calculate $K_{P}$ for the reaction, given that the total pressure is 0.20 atm.

Kevin Zaborsky

Numerade Educator

Problem 76

When heated, ammonium carbamate decomposes as follows:
$$\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)$$
At a certain temperature, the equilibrium pressure of the system is 0.318 atm. Calculate $K_{P}$ for the reaction.

Kevin Zaborsky

Numerade Educator

Problem 77

A mixture of 0.47 mole of $\mathrm{H}_{2}$ and 3.59 moles of $\mathrm{HCl}$ is heated to $2800^{\circ} \mathrm{C} .$ Calculate the equilibrium partial pressures of $\mathrm{H}_{2}, \mathrm{Cl}_{2}$ and HCl if the total pressure is 2.00 atm. For the reaction
$$
\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows 2 \mathrm{HCl}(g)
$$
$K_{P}$ is 193 at $2800^{\circ} \mathrm{C}$

Natalie Almond

Numerade Educator

Problem 78

When heated at high temperatures, iodine vapor dissociates as follows:
$$
\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{I}(g)
$$
In one experiment, a chemist finds that when 0.054 mole of $I_{2}$ was placed in a flask of volume $0.48 \mathrm{L}$ at $587 \mathrm{K}$, the degree of dissociation (that is, the fraction of $I_{2}$ dissociated) was 0.0252 . Calculate $K_{c}$ and $K_{P}$ for the reaction at this temperature.

Kevin Zaborsky

Numerade Educator

Problem 79

One mole of $\mathrm{N}_{2}$ and three moles of $\mathrm{H}_{2}$ are placed in a flask at $375^{\circ} \mathrm{C} .$ Calculate the total pressure of the system at equilibrium if the mole fraction of $\mathrm{NH}_{3}$ is $0.21 .$ The $K_{P}$ for the reaction is $4.31 \times 10^{-4}$

Natalie Almond

Numerade Educator

Problem 80

At $1130^{\circ} \mathrm{C}$, the equilibrium constant $\left(K_{c}\right)$ for the reaction
$$2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)$$
is $2.25 \times 10^{-4} .$ If $\left[\mathrm{H}_{2} \mathrm{S}\right]=4.84 \times 10^{-3} \mathrm{M}$ and $\left[\mathrm{H}_{2}\right]=1.50 \times$
$10^{-3} M,$ calculate $\left[\mathrm{S}_{2}\right]$

Kevin Zaborsky

Numerade Educator

Problem 81

A quantity of $6.75 \mathrm{g}$ of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ was placed in a 2.00 -L flask. At $648 \mathrm{K},$ there is 0.0345 mole of $\mathrm{SO}_{2}$ present. Calculate $K_{c}$ for the reaction
$$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$

Kevin Zaborsky

Numerade Educator

Problem 82

The following diagram represents a gas-phase equilibrium mixture for the reaction $\mathrm{AB} \rightleftharpoons \mathrm{A}+\mathrm{B}$ at a certain temperature. Describe what would happen to the system after each of the following changes: (a) the temperature is decreased,
(b) the volume is increased, (c) He atoms are added to the mixture at constant volume, (d) a catalyst is added to the mixture.

Luke Monroe

Numerade Educator

Problem 83

The formation of $\mathrm{SO}_{3}$ from $\mathrm{SO}_{2}$ and $\mathrm{O}_{2}$ is an intermediate step in the manufacture of sulfuric acid, and it is also responsible for the acid rain phenomenon. The equilibrium constant $K_{P}$ for the reaction
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$
is 0.13 at $830^{\circ} \mathrm{C}$. In one experiment, $2.00 \mathrm{mol} \mathrm{SO}_{2}$ and $2.00 \mathrm{mol}$
$\mathrm{O}_{2}$ were initially present in a flask. What must the total pressure at equilibrium be in order to have an 80.0 percent yield of $\mathrm{SO}_{3}$ ?

Kevin Zaborsky

Numerade Educator

Problem 84

Consider the following reaction at $1600^{\circ} \mathrm{C}$ :
$$\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)$$
A $1.00-\mathrm{g}$ sample of $\mathrm{I}_{2}$ is heated to $1200^{\circ} \mathrm{C}$ in a $500-\mathrm{mL}$. flask. At equilibrium, the total pressure is 1.51 atm. Calculate $K_{p}$ for the reaction at this temperature.

Kevin Zaborsky

Numerade Educator

Problem 85

Consider the following reaction at $1600^{\circ} \mathrm{C}$ :
$$\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)$$
When 1.05 moles of $\mathrm{Br}_{2}$ are put in a $0.980-\mathrm{L}$ flask, 1.20 percent of the $\mathrm{Br}_{2}$ undergoes dissociation. Calculate the equilibrium constant $K_{c}$ for the reaction.

Kevin Zaborsky

Numerade Educator

Problem 86

Eggshells are composed mostly of calcium carbonate (CaCO $_{3}$ ) formed by the reaction
$$
\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{CaCO}_{3}(s)
$$
The carbonate ions are supplied by carbon dioxide produced as a result of metabolism. Explain why eggshells are thinner in the summer when the rate of panting by chickens is greater. Suggest a remedy for this situation.

David Collins

Numerade Educator

Problem 87

The equilibrium constant $K_{p}$ for the following reaction is $4.31 \times$ $10^{-4}$ at $375^{\circ} \mathrm{C}:$
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$
In a certain experiment a student starts with 0.862 atm of $\mathrm{N}_{2}$ and 0.373 atm of $\mathrm{H}_{2}$ in a constant-volume vessel at $375^{\circ} \mathrm{C}$. Calculate the partial pressures of all species when equilibrium is reached.

Kevin Zaborsky

Numerade Educator

Problem 88

A quantity of 0.20 mole of carbon dioxide was heated to a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached:
$$
\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)
$$
Under these conditions, the average molar mass of the gases was $35 \mathrm{g} / \mathrm{mol} .$ (a) Calculate the mole fractions of $\mathrm{CO}$ and $\mathrm{CO}_{2}$
(b) What is $K_{p}$ if the total pressure is 11 atm? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas and its molar mass.)

David Collins

Numerade Educator

Problem 89

When dissolved in water, glucose (corn sugar) and fructose (fruit sugar) exist in equilibrium as follows:
fructose $\rightleftharpoons$ glucose
A chemist prepared a $0.244 \mathrm{M}$ fructose solution at $25^{\circ} \mathrm{C}$. At equilibrium, it was found that its concentration had decreased to $0.113 M .$ (a) Calculate the equilibrium constant for the reaction.
(b) At equilibrium, what percentage of fructose was converted to glucose?

Kevin Zaborsky

Numerade Educator

Problem 90

At room temperature, solid iodine is in equilibrium with its vapor through sublimation and deposition. Describe how you would use radioactive iodine, in either solid or vapor form, to show that there is a dynamic equilibrium between these two phases.

Zubair Abdulla

Numerade Educator

Problem 91

At $1024^{\circ} \mathrm{C}$, the pressure of oxygen gas from the decomposition of copper(II) oxide (CuO) is 0.49 atm:
$$
4 \mathrm{CuO}(s) \rightleftharpoons 2 \mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{O}_{2}(g)
$$
(a) What is $K_{P}$ for the reaction? (b) Calculate the fraction of $\mathrm{CuO}$ that will decompose if 0.16 mole of it is placed in a 2.0 -L flask at $1024^{\circ} \mathrm{C}$. (c) What would the fraction be if a 1.0 -mole sample of CuO were used? (d) What is the smallest amount of $\mathrm{CuO}$ (in moles) that would establish the equilibrium?

Kevin Zaborsky

Numerade Educator

Problem 92

A mixture containing 3.9 moles of $\mathrm{NO}$ and 0.88 mole of $\mathrm{CO}_{2}$ was allowed to react in a flask at a certain temperature according to the equation
$$
\mathrm{NO}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{CO}(g)
$$
At equilibrium, 0.11 mole of $\mathrm{CO}_{2}$ was present. Calculate the equilibrium constant $K_{\mathrm{c}}$ of this reaction.

Kevin Zaborsky

Numerade Educator

Problem 93

The equilibrium constant $K_{\mathrm{c}}$ for the reaction
$$
\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)
$$
is 54.3 at $430^{\circ} \mathrm{C}$. At the start of the reaction, there are 0.714 mole of $\mathrm{H}_{2}, 0.984$ mole of $\mathrm{I}_{2},$ and 0.886 mole of $\mathrm{HI}$ in a 2.40 -L reaction chamber. Calculate the concentrations of the gases at equilibrium.

Kevin Zaborsky

Numerade Educator

Problem 94

When heated, a gaseous compound A dissociates as follows:
$$
\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)+\mathrm{C}(g)
$$
In an experiment, A was heated at a certain temperature until its equilibrium pressure reached $0.14 P$, where $P$ is the total pressure. Calculate the equilibrium constant $K_{P}$ of this reaction.

David Collins

Numerade Educator

Problem 95

When a gas was heated under atmospheric conditions, its color deepened. Heating above $150^{\circ} \mathrm{C}$ caused the color to fade, and at $550^{\circ} \mathrm{C}$ the color was barely detectable. However, at $550^{\circ} \mathrm{C}$ the color was partially restored by increasing the pressure of the system. Which of the following best fits the preceding description:
(a) a mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine has a reddish color, and nitrogen dioxide is a brown gas. The other gases are colorless.) Justify your choice.

Zubair Abdulla

Numerade Educator

Problem 96

Both $\mathrm{Mg}^{2+}$ and $\mathrm{Ca}^{2+}$ are important biological ions. One of their functions is to bind to the phosphate group of ATP molecules or amino acids of proteins. For Group 2 A metals in general, the equilibrium constant for binding to the anions increases in the order $\mathrm{Ba}^{2+}<\mathrm{Sr}^{2+}<\mathrm{Ca}^{2+}<\mathrm{Mg}^{2+}$. What property of the Group
2 A metal cations might account for this trend?

Luke Monroe

Numerade Educator

Problem 97

The equilibrium constant $K_{c}$ for the following reaction is 1.2 at $375^{\circ} \mathrm{C}$
$$
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)
$$
(a) What is the value of $K_{P}$ for this reaction? (b) What is the value of the equilibrium constant $K_{\mathrm{c}}$ for $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) ?$
(c) What is $K_{c}$ for $\underline{1} \mathrm{N}_{2}(g)+\underline{3} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g) ?$ (d) What are the values of $K_{P}$ for the reactions described in parts (b) and (c)?

Kevin Zaborsky

Numerade Educator

Problem 98

In this chapter we learned that a catalyst has no effect on the position of an equilibrium because it speeds up both the forward and reverse rates to the same extent. To test this statement, consider a situation in which an equilibrium of the type
$$
2 \mathrm{A}(g) \rightleftarrows \mathrm{B}(\mathrm{g})
$$
is established inside a cylinder fitted with a weightless piston. The piston is attached by a string to the cover of a box containing a catalyst. When the piston moves upward (expanding against atmospheric pressure), the cover is lifted and the catalyst is exposed to the gases. When the piston moves downward, the box is closed. Assume that the catalyst speeds up the forward reaction $(2 \mathrm{A} \longrightarrow \mathrm{B})$ but does not affect the reverse process $(\mathrm{B} \longrightarrow 2 \mathrm{A})$
Suppose the catalyst is suddenly exposed to the equilibrium system as shown here. Describe what would happen subsequently. How does this "thought experiment" convince you that no such catalyst can exist?

David Collins

Numerade Educator

Problem 99

A sealed glass bulb contains a mixture of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ gases. Describe what happens to the following properties of the gases when the bulb is heated from $20^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}:$ (a) color,
(b) pressure, (c) average molar mass, (d) degree of dissociation (from $\mathrm{N}_{2} \mathrm{O}_{4}$ to $\mathrm{NO}_{2}$ ), (e) density. Assume that volume remains constant. (Hint: $\mathrm{NO}_{2}$ is a brown gas; $\mathrm{N}_{2} \mathrm{O}_{4}$ is colorless.)

David Collins

Numerade Educator

Problem 100

At $20^{\circ} \mathrm{C}$, the vapor pressure of water is 0.0231 atm. Calculate $K_{P}$ and $K_{c}$ for the process
$$
\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)
$$

Kevin Zaborsky

Numerade Educator

Problem 101

Industrially, sodium metal is obtained by electrolyzing molten sodium chloride. The reaction at the cathode is $\mathrm{Na}^{+}+e^{-} \longrightarrow$ Na. We might expect that potassium metal would also be prepared by electrolyzing molten potassium chloride. However, potassium metal is soluble in molten potassium chloride and therefore is hard to recover. Furthermore, potassium vaporizes readily at the operating temperature, creating hazardous conditions. Instead, potassium is prepared by the distillation of molten potassium chloride in the presence of sodium vapor at $892^{\circ} \mathrm{C}$ :
$$
\mathrm{Na}(g)+\mathrm{KCl}(l) \rightleftharpoons \mathrm{NaCl}(l)+\mathrm{K}(g)
$$
In view of the fact that potassium is a stronger reducing agent than sodium, explain why this approach works. (The boiling points of sodium and potassium are $892^{\circ} \mathrm{C}$ and $770^{\circ} \mathrm{C}$ respectively.)

David Collins

Numerade Educator

Problem 102

In the gas phase, nitrogen dioxide is actually a mixture of nitrogen dioxide $\left(\mathrm{NO}_{2}\right)$ and dinitrogen tetroxide $\left(\mathrm{N}_{2} \mathrm{O}_{4}\right) .$ If the density of such a mixture is $2.3 \mathrm{g} / \mathrm{L}$ at $74^{\circ} \mathrm{C}$ and $1.3 \mathrm{atm}$ calculate the partial pressures of the gases and $K_{p}$ for the dissociation of $\mathrm{N}_{2} \mathrm{O}_{4}$

Kevin Zaborsky

Numerade Educator

Problem 103

A 2.50 -mole sample of NOCl was initially in a 1.50 -L. reaction chamber at $400^{\circ} \mathrm{C}$. After equilibrium was established, it was found that 28.0 percent of the NOCI had dissociated:
$$
2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)
$$
Calculate the equilibrium constant $K_{c}$ for the reaction.

Kevin Zaborsky

Numerade Educator

Problem 104

About 75 percent of hydrogen for industrial use is produced by the steam-reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at $800^{\circ} \mathrm{C}$ to give hydrogen and carbon monoxide:
$$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=206 \mathrm{kJ} / \mathrm{mol}$$
The secondary stage is carried out at about $1000^{\circ} \mathrm{C}$, in the presence of air, to convert the remaining methane to hydrogen:
$$\mathrm{CH}_{4}(g)+\underline{1} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=35.7 \mathrm{kJ} / \mathrm{mol}$$
(a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stages? (b) The equilibrium constant $K_{c}$ for the primary stage is 18 at $800^{\circ} \mathrm{C}$. (i) Calculate $K_{P}$ for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?

Zubair Abdulla

Numerade Educator

Problem 105

Photosynthesis can be represented by
$$\begin{aligned}&6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)\\&\Delta H^{\circ}=2801 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$
Explain how the equilibrium would be affected by the following changes: (a) partial pressure of $\mathrm{CO}_{2}$ is increased, (b) $\mathrm{O}_{2}$ is removed from the mixture, (c) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ (glucose) is removed from the mixture, (d) more water is added, (e) a catalyst is added,
(f) temperature is decreased.

Kevin Zaborsky

Numerade Educator

Problem 106

Consider the decomposition of ammonium chloride at a certain temperature:
$$
\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)
$$
Calculate the equilibrium constant $K_{p}$ if the total pressure is
2.2 atm at that temperature.

Kevin Zaborsky

Numerade Educator

Problem 107

Water is a very weak electrolyte that undergoes the following ionization (called autoionization):
(a) If $k_{1}=2.4 \times 10^{-5} \mathrm{s}^{-1}$ and $k_{-1}=1.3 \times 10^{11} / M \cdot$ s, calculate the
equilibrium constant $K$ where $K=\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{O}\right] .$ (b) Calculate the product $\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right],\left[\mathrm{H}^{+}\right],$ and $\left[\mathrm{OH}^{-}\right] .$ Hint: Calculate the concentration of liquid water using its density, $1.0 \mathrm{g} / \mathrm{mL} .)$

Kevin Zaborsky

Numerade Educator

Problem 108

Consider the following reaction, which takes place in a single elementary step:
$$2 \mathrm{A}+\mathrm{B} \stackrel{k_{1}}{\Longleftarrow} \mathrm{A}_{2} \mathrm{B}$$
If the equilibrium constant $K_{\mathrm{c}}$ is 12.6 at a certain temperature and
if $k_{1}=5.1 \times 10^{-2} \mathrm{s}^{-1},$ calculate the value of $k_{-1}$

Kevin Zaborsky

Numerade Educator

Problem 109

At $25^{\circ} \mathrm{C}$, the equilibrium partial pressures of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ are 0.15 atm and 0.20 atm, respectively. If the volume is doubled at constant temperature, calculate the partial pressures of the gases when a new equilibrium is established.

Natalie Almond

Numerade Educator

Problem 110

In 1899 the German chemist Ludwig Mond developed a process for purifying nickel by converting it to the volatile nickel tetracarbonyl $\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]$ (b.p. $=42.2^{\circ} \mathrm{C}$ ):
$$
\mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftarrows \mathrm{Ni}(\mathrm{CO})_{4}(g)
$$
(a) Describe how you can separate nickel and its solid impurities.
(b) How would you recover nickel?

Zubair Abdulla

Numerade Educator

Problem 111

Consider the equilibrium reaction described in Problem $15.30 .$ A quantity of $2.50 \mathrm{g}$ of $\mathrm{PCl}_{5}$ is placed in an evacuated 0.500-L flask and heated to $250^{\circ} \mathrm{C}$. (a) Calculate the pressure of $\mathrm{PCl}_{5}$, assuming it does not dissociate. (b) Calculate the partial pressure of $\mathrm{PCl}_{5}$ at equilibrium. (c) What is the total pressure at equilibrium? (d) What is the degree of dissociation of $\mathrm{PCl}_{5}$ ? (The degree of dissociation is given by the fraction of $\mathrm{PCl}_{5}$ that has undergone dissociation.)

Kevin Zaborsky

Numerade Educator

Problem 112

Consider the equilibrium system $3 \mathrm{A} \rightleftarrows \mathrm{B} .$ Sketch the changes in the concentrations of $\mathrm{A}$ and $\mathrm{B}$ over time for the following situations: (a) initially only A is present, (b) initially only $\mathrm{B}$ is present, (c) initially both $\mathrm{A}$ and $\mathrm{B}$ are present (with $\mathrm{A}$ in higher concentration). In each case, assume that the concentration of $\mathrm{B}$ is higher than that of $\mathrm{A}$ at equilibrium.

David Collins

Numerade Educator

Problem 113

The vapor pressure of mercury is $0.0020 \mathrm{mmHg}$ at $26^{\circ} \mathrm{C}$. (a) Calculate $K_{\mathrm{c}}$ and $K_{P}$ for the process $\mathrm{Hg}(l) \rightleftarrows \mathrm{Hg}(g) .$ (b) $\mathrm{A}$ chemist breaks a thermometer and spills mercury onto the floor of a laboratory measuring $6.1 \mathrm{m}$ long, $5.3 \mathrm{m}$ wide, and $3.1 \mathrm{m}$ high. Calculate the mass of mercury (in grams) vaporized at equilibrium and the concentration of mercury vapor (in $\mathrm{mg} / \mathrm{m}^{3}$ ). Does this concentration exceed the safety limit of $0.05 \mathrm{mg} / \mathrm{m}^{3} ?$ (Ignore the volume of furniture and other objects in the laboratory.)

Kevin Zaborsky

Numerade Educator

Problem 114

At $25^{\circ} \mathrm{C},$ a mixture of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ gases are in equilibrium in a cylinder fitted with a movable piston. The concentrations are $\left[\mathrm{NO}_{2}\right]=0.0475 \mathrm{M}$ and $\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.487 \mathrm{M} .$ The volume of the
gas mixture is halved by pushing down on the piston at constant temperature. Calculate the concentrations of the gases when equilibrium is reestablished. Will the color become darker or lighter after the change?

Zubair Abdulla

Numerade Educator

Problem 115

A student placed a few ice cubes in a drinking glass with water.
A few minutes later she noticed that some of the ice cubes were fused together. Explain what happened.

Natalie Almond

Numerade Educator

Problem 116

Consider the potential energy diagrams for two types of reactions $A \rightleftarrows B .$ In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant?
(d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture.

Zubair Abdulla

Numerade Educator

Problem 117

The equilibrium constant $K_{\mathrm{c}}$ for the reaction
$$
2 \mathrm{NH}_{3}(g) \rightleftarrows \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)
$$
is 0.83 at $375^{\circ} \mathrm{C}$. A $14.6-\mathrm{g}$ sample of ammonia is placed in a 4.00-L flask and heated to $375^{\circ} \mathrm{C}$. Calculate the concentrations of all the gases when equilibrium is reached.

Kevin Zaborsky

Numerade Educator

Problem 118

The dependence of the equilibrium constant of a reaction on temperature is given by the van't Hoff equation:
$$\ln K=\frac{-\Delta H^{\circ}}{R T}+C$$
where $C$ is a constant. The following table gives the equilibrium constant $\left(K_{P}\right)$ for the reaction at various temperatures.
$$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}_{2}(g)$$
$$\begin{array}{l|rrrrr}K_{P} & 138 & 5.12 & 0.436 & 0.0626 & 0.0130 \\\hline T(\mathrm{K}) & 600 & 700 &800 & 900 & 1000\end{array}$$
Determine graphically the $\Delta H^{\circ}$ for the reaction.

Zubair Abdulla

Numerade Educator

Problem 119

Consider the reaction between $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ in a closed container:
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftarrows 2 \mathrm{NO}_{2}(g)
$$
Initially, 1 mole of $\mathrm{N}_{2} \mathrm{O}_{4}$ is present. At equilibrium, $x$ mole of $\mathrm{N}_{2} \mathrm{O}_{4}$ has dissociated to form $\mathrm{NO}_{2}$. (a) Derive an expression for $K_{P}$ in terms of $x$ and $P$, the total pressure. (b) How does the expression in part (a) help you predict the shift in equilibrium due to an increase in $P ?$ Does your prediction agree with Le Châtelier's principle?

Kevin Zaborsky

Numerade Educator

Problem 120

(a) Use the van't Hoff equation in Problem 15.118 to derive the following expression, which relates the equilibrium constants at two different temperatures:
$$
\ln \frac{K_{1}}{K_{2}}=\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right)
$$
How does this equation support the prediction based on Le Châtelier's principle about the shift in equilibrium with temperature? (b) The vapor pressures of water are $31.82 \mathrm{mmHg}$ at $30^{\circ} \mathrm{C}$ and $92.51 \mathrm{mm} \mathrm{Hg}$ at $50^{\circ} \mathrm{C}$. Calculate the molar heat of vaporization of water.

David Collins

Numerade Educator

Problem 121

The $K_{P}$ for the reaction
$$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$
is 2.05 at $648 \mathrm{K}$. A sample of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is placed in a container and heated to $648 \mathrm{K},$ while the total pressure is kept constant at $9.00 \mathrm{atm} .$ Calculate the partial pressures of the gases at equilibrium.

Natalie Almond

Numerade Educator

Problem 122

The "boat" form and the "chair" form of cyclohexane (C $_{6} \mathrm{H}_{12}$ ) interconvert as shown here:
In this representation, the $\mathrm{H}$ atoms are omitted and a $\mathrm{C}$ atom is assumed to be at each intersection of two lines (bonds). The conversion is first order in each direction. The activation energy for the chair $\longrightarrow$ boat conversion is $41 \mathrm{kJ} / \mathrm{mol}$. If the frequency factor is $1.0 \times 10^{12} \mathrm{s}^{-1},$ what is $k_{1}$ at $298 \mathrm{K} ?$ The equilibrium constant $K_{\mathrm{c}}$ for the reaction is $9.83 \times 10^{3}$ at $298 \mathrm{K}$

Zubair Abdulla

Numerade Educator

Problem 123

Consider the following reaction at a certain temperature
$$
\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}
$$
The mixing of 1 mole of $\mathrm{A}_{2}$ with 3 moles of $\mathrm{B}_{2}$ gives rise to $x$ mole of $\mathrm{AB}$ at equilibrium. The addition of 2 more moles of $\mathrm{A}_{2}$ produces another $x$ mole of AB. What is the equilibrium constant for the reaction?

Kevin Zaborsky

Numerade Educator

Problem 124

Iodine is sparingly soluble in water but much more so in carbon tetrachloride (CCl_). The equilibrium constant, also called the partition coefficient, for the distribution of $I_{2}$ between these two phases
$$\mathrm{I}_{2}(a q) \rightleftarrows \mathrm{I}_{2}\left(\mathrm{CCl}_{4}\right)$$
is 83 at $20^{\circ} \mathrm{C}$. (a) $\mathrm{A}$ student adds $0.030 \mathrm{L}$ of $\mathrm{CC} 1_{4}$ to $0.200 \mathrm{L}$ of an aqueous solution containing $0.032 \mathrm{g}$ of $\mathrm{I}_{2}$. The mixture at $20^{\circ} \mathrm{C}$ is shaken, and the two phases are then allowed to separate. Calculate the fraction of $\mathrm{I}_{2}$ remaining in the aqueous phase.
(b) The student now repeats the extraction of $I_{2}$ with another $0.030 \mathrm{L}$ of $\mathrm{CC} 1_{4} .$ Calculate the fraction of the $\mathrm{I}_{2}$ from the original solution that remains in the aqueous phase. (c) Compare the result in part (b) with a single extraction using $0.060 \mathrm{L}$ of $\mathrm{CC} 1_{4}$ Comment on the difference.

Zubair Abdulla

Numerade Educator