# CHEMISTRY: The Molecular Nature of Matter and Change 2016

## Educators

Problem 1

A change in reaction conditions increases the rate of a certain forward reaction more than that of the reverse reaction. What is the effect on the equilibrium constant and on the concentrations of reactants and products at equilibrium?

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Problem 2

When a chemical company employs a new reaction to manufacture a product, the chemists consider its rate (kinetics) and yield (equilibrium). How do each of these affect the usefulness of a manufacturing process?

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Problem 3

If there is no change in concentrations, why is the equilibrium state considered dynamic?

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Problem 4

Is K very large or very small for a reaction that goes essentially to completion? Explain.

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Problem 5

White phosphorus, $P_{4},$ is produced by the reduction of phosphate rock, $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$ . If exposed to oxygen, the waxy, white solid smokes, bursts into flames, and releases a large quantity of heat:
$$\mathrm{P}_{4}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(s)+\text { heat }$$
Does this reaction have a large or small equilibrium constant? Explain.

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Problem 6

For a given reaction at a given temperature, the value of $K$ is constant. Is the value of $Q$ also constant? Explain.

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Problem 7

In a study of the thermal decomposition of lithium peroxide,
$$2 \mathrm{Li}_{2} \mathrm{O}_{2}(s) \rightleftharpoons 2 \mathrm{Li}_{2} \mathrm{O}(s)+\mathrm{O}_{2}(g)$$
a chemist finds that, as long as some $\mathrm{Li}_{2} \mathrm{O}_{2}$ is present at the end of the experiment, the amount of $\mathrm{O}_{2}$ obtained in a given container at a given $T$ is the same. Explain.

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Problem 8

In a study of the formation of HI from its elements,
$$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)$$
equal amounts of $\mathrm{H}_{2}$ and $\mathrm{I}_{2}$ were placed in a container, which was then sealed and heated.
(a) On one set of axes, sketch concentration vs. time curves for $\mathrm{H}_{2}$ and HI, and explain how $Q$ changes as a function of time.
(b) Is the value of $Q$ different if $\left[\mathrm{I}_{2}\right]$ is plotted instead of $\left[\mathrm{H}_{2}\right] ?$

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Problem 9

Explain the difference between a heterogeneous and a homogeneous equilibrium. Give an example of each.

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Problem 10

Does Q for the formation of 1 mol of NO from its elements differ from Q for the decomposition of 1 mol of NO to its elements? Explain and give the relationship between the two Q’s.

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Problem 11

Does $Q$ for the formation of 1 $\mathrm{mol}$ of $\mathrm{NH}_{3}$ from $\mathrm{H}_{2}$ and $\mathrm{N}_{2}$ differ from $Q$ for the formation of $\mathrm{NH}_{3}$ from $\mathrm{H}_{2}$ and 1 $\mathrm{mol}$ of $\mathrm{N}_{2} ?$ Explain and give the relationship between the two $Q$ 's.

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Problem 12

Balance each reaction and write its reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{3}(g)$
(b) $\mathrm{S}_{6}(g)+\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2} \mathrm{F}_{2}(g)$
(c) $\mathrm{SCIF}_{5}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{S}_{2} \mathrm{F}_{10}(g)+\mathrm{HCl}(g)$

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Problem 13

Balance each reaction and write its reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(b) $\mathrm{CH}_{4}(g)+\mathrm{F}_{2}(g)=\mathrm{C} \mathrm{F}_{4}(g)+\mathrm{HF}(g)$
(c) $\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$

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Problem 14

Balance each reaction and write its reaction quotient, $Q_{\mathrm{c}}$
(a) $\mathrm{NOCI}(g) \Longrightarrow \mathrm{NO}_{2}(g)+\mathrm{Cl}_{2}(g)$
(b) $\mathrm{POCl}_{3}(g) \Longrightarrow \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g)$
(c) $\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$

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Problem 15

Balance each reaction and write its reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{O}_{2}(g) \Longrightarrow \mathrm{O}_{3}(g)$
(b) $\mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$
(c) $\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g)$

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Problem 16

At a particular temperature, $K_{\mathrm{c}}=1.6 \times 10^{-2}$ for
$$2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)$$
Calculate $K_{\mathrm{c}}$ for each of the following reactions:
(a) $\frac{1}{2} \mathrm{S}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{S}(g)$
(b) $5 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 5 \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{S}_{2}(g)$

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Problem 17

At a particular temperature, $K_{\mathrm{c}}=6.5 \times 10^{2}$ for
$$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$
Calculate $K_{c}$ for each of the following reactions:
(a) $\mathrm{NO}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(b) $2 \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{NO}(g)+4 \mathrm{H}_{2}(g)$

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Problem 18

Balance each of the following examples of heterogeneous equilibria and write each reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{Na}_{2} \mathrm{O}_{2}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{O}_{2}(g)$
(b) $\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$

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Problem 19

Balance each of the following examples of heterogeneous equilibria and write each reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{SO}_{4}(a q)$
(b) $\mathrm{KNO}_{3}(s) \rightleftharpoons \mathrm{KNO}_{2}(s)+\mathrm{O}_{2}(g)$
(c) $\mathrm{S}_{8}(s)+\mathrm{F}_{2}(g) \rightleftharpoons \mathrm{SF}_{6}(g)$

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Problem 20

Balance each of the following examples of heterogeneous equilibria and write each reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(b) $\mathrm{SnO}_{2}(s)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Sn}(s)+\mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{H}_{2} \mathrm{SO}_{4}(l)+\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{S}_{2} \mathrm{O}_{7}(l)$

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Problem 21

Balance each of the following examples of heterogeneous equilibria and write each reaction quotient, $Q_{\mathrm{c}} :$
(a) $\mathrm{Al}(s)+\mathrm{NaOH}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_{4}\right](a q)+\mathrm{H}_{2}(g)$
(b) $\mathrm{CO}_{2}(s) \rightleftharpoons \mathrm{CO}_{2}(g)$
(c) $\mathrm{N}_{2} \mathrm{O}_{5}(s) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$

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Problem 22

Write $Q_{\mathrm{c}}$ for each of the following:
(a) Hydrogen chloride gas reacts with oxygen gas to produce chlorine gas and water vapor.
(b) Solid diarsenic trioxide reacts with fluorine gas to produce liquid arsenic pentafluoride and oxygen gas.
(c) Gaseous sulfur tetrafluoride reacts with liquid water to produce gaseous sulfur dioxide and hydrogen fluoride gas.
(d) Solid molybdenum(VI) oxide reacts with gaseous xenon difluoride to form liquid molybdenum(VI) fluoride, xenon gas, and oxygen gas.

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Problem 23

The interhalogen $\mathrm{ClF}_{3}$ is prepared in a two-step fluorination of chlorine gas:
\begin{aligned} \mathrm{Cl}_{2}(g)+\mathrm{F}_{2}(g) & \rightleftharpoons \mathrm{ClF}(g) \\ \mathrm{ClF}(g)+\mathrm{F}_{2}(g) & \rightleftharpoons \mathrm{ClF}_{3}(g) \end{aligned}
(a) Balance each step and write the overall equation.
(b) Show that the overall $Q_{\mathrm{c}}$ equals the product of the $Q_{\mathrm{c}}$ 's for the individual steps.

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Problem 24

Guldberg and Waage proposed the definition of the equilibrium constant as a certain ratio of concentrations. What relationship allows us to use a particular ratio of partial pressures (for a gaseous reaction) to express an equilibrium constant? Explain.

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Problem 25

When are $K_{\mathrm{c}}$ and $K_{\mathrm{p}}$ equal, and when are they not?

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Problem 26

A certain reaction at equilibrium has more moles of gaseous products than of gaseous reactants.
(a) Is $K_{\mathrm{c}}$ larger or smaller than $K_{\mathrm{p}} ?$
(b) Write a statement about the relative sizes of $K_{\mathrm{c}}$ and $K_{\mathrm{p}}$ for any gaseous equilibrium.

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Problem 27

Determine $\Delta n_{\mathrm{gas}}$ for each of the following reactions:
(a) $2 \mathrm{KClO}_{3}(s) \rightleftharpoons 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$
(b) $2 \mathrm{PbO}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{PbO}_{2}(s)$
(c) $\mathrm{I}_{2}(s)+3 \mathrm{XeF}_{2}(s) \rightleftharpoons 2 \mathrm{IF}_{3}(s)+3 \mathrm{Xe}(g)$

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Problem 28

Determine $\Delta n_{\text { gas }}$ for each of the following reactions:
(a) $\mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{MgO}(s)+\mathrm{CO}_{2}(g)$
(b) $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)$
(c) $\mathrm{HNO}_{3}(l)+\mathrm{ClF}(g) \rightleftharpoons \mathrm{ClONO}_{2}(g)+\mathrm{HF}(g)$

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Problem 29

Calculate $K_{\mathrm{c}}$ for each of the following equilibria:
(a) $\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) ; K_{\mathrm{p}}=3.9 \times 10^{-2}$ at $1000 . \mathrm{K}$
(b) $\mathrm{S}_{2}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CS}_{2}(g) ; K_{\mathrm{p}}=28.5$ at $500 . \mathrm{K}$

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Problem 30

Calculate $K_{\mathrm{c}}$ for each of the following equilibria:
(a) $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)=2 \mathrm{HI}(g) ; K_{\mathrm{p}}=49$ at $730 . \mathrm{K}$
(b) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) ; K_{\mathrm{p}}=2.5 \times 10^{10} \mathrm{at} 500 . \mathrm{K}$

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Problem 31

Calculate $K_{\mathrm{p}}$ for each of the following equilibria:
(a) $\mathrm{N}_{2} \mathrm{O}_{4}(g) \Longrightarrow 2 \mathrm{NO}_{2}(g) ; K_{\mathrm{c}}=6.1 \times 10^{-3}$ at 298 $\mathrm{K}$
(b) $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) ; K_{\mathrm{c}}=2.4 \times 10^{-3}$ at $1000 . \mathrm{K}$

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Problem 32

Calculate $K_{\mathrm{p}}$ for each of the following equilibria:
(a) $\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) ; K_{\mathrm{c}}=0.77$ at $1020 . \mathrm{K}$
(b) $3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g) ; K_{\mathrm{c}}=1.8 \times 10^{-56} \mathrm{at} 570 . \mathrm{K}$

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Problem 33

When the numerical value of Q is less than K, in which direction does the reaction proceed to reach equilibrium? Explain.

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Problem 34

The following molecular scenes depict the aqueous reaction $2 \mathrm{D} \rightleftharpoons \mathrm{E},$ with $\mathrm{D}$ red and $\mathrm{E}$ blue. Each sphere represents 0.0100 $\mathrm{mol}$ , but the volume is 1.00 $\mathrm{L}$ in scene $\mathrm{A},$ whereas in scenes $\mathrm{B}$ and $\mathrm{C},$ it is 0.500 $\mathrm{L}$
(a) If the reaction in scene $\mathrm{A}$ is at equilibrium, calculate $K_{\mathrm{c}} .$
(b) Are the reactions in scenes $\mathrm{B}$ and $\mathrm{C}$ at equilibrium? Which, if either, is not, and in which direction will it proceed?

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Problem 35

At $425^{\circ} \mathrm{C}, K_{\mathrm{p}}=4.18 \times 10^{-9}$ for the reaction
$$2 \mathrm{HBr}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)$$
In one experiment, 0.20 atm of $\mathrm{HBr}(g), 0.010$ atm of $\mathrm{H}_{2}(g),$ and 0.010 $\mathrm{atm}$ of $\mathrm{Br}_{2}(g)$ are introduced into a container. Is the reaction at equilibrium? If not, in which direction will it proceed?

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Problem 36

At $100^{\circ} \mathrm{C}, K_{\mathrm{p}}=60.6$ for the reaction
$$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$
In a given experiment, 0.10 atm of each component is placed in a container. Is the system at equilibrium? If not, in which direction will the reaction proceed?

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Problem 37

The water-gas shift reaction plays a central role in the chemical methods for obtaining cleaner fuels from coal:
$$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$$
At a given temperature, $K_{\mathrm{p}}=2.7 .$ If 0.13 mol of $\mathrm{CO}, 0.56 \mathrm{mol}$ of $\mathrm{H}_{2} \mathrm{O}, 0.62 \mathrm{mol}$ of $\mathrm{CO}_{2},$ and 0.43 $\mathrm{mol}$ of $\mathrm{H}_{2}$ are put in a $2.0-\mathrm{L}$ flask, in which direction does the reaction proceed?

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Problem 38

In the 1980 s, $\mathrm{CFC}-11$ was one of the most heavily produced chlorofluorocarbons. The last step in its formation is
$$\mathrm{CCl}_{4}(g)+\mathrm{HF}(g) \rightleftharpoons \mathrm{CFCl}_{3}(g)+\mathrm{HCl}(g)$$
If you start the reaction with equal concentrations of $\mathrm{CCl}_{4}$ and $\mathrm{HF}$ , you obtain equal concentrations of $\mathrm{CFCl}_{3}$ and $\mathrm{HCl}$ at equilibrium. Are the final concentrations of $\mathrm{CFCl}_{3}$ and HCl equal if you start with unequal concentrations of $\mathrm{CCl}_{4}$ and $\mathrm{HF}$ ? Explain.

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Problem 39

For a problem involving the catalyzed reaction of methane and steam, the following reaction table was prepared:
Explain the entries in the “Change” and “Equilibrium” rows.

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Problem 40

a) What is the basis of the approximation that avoids using the quadratic formula to find an equilibrium concentration?
(b) When should this approximation not be made?

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Problem 41

In an experiment to study the formation of HI(g),
$$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)$$
$\mathrm{H}_{2}(g)$ and $\mathrm{I}_{2}(g)$ were placed in a sealed container at a certain temperature. At equilibrium, $\left[\mathrm{H}_{2}\right]=6.50 \times 10^{-5} \mathrm{M},\left[\mathrm{I}_{2}\right]=$ $1.06 \times 10^{-3} \mathrm{M},$ and $[\mathrm{HI}]=1.87 \times 10^{-3} \mathrm{M} .$ Calculate $K_{\mathrm{c}}$ for the reaction at this temperature.

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Problem 42

Gaseous ammonia was introduced into a sealed container and heated to a certain temperature:
$$2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$$
At equilibrium, $\left[\mathrm{NH}_{3}\right]=0.0225 M,\left[\mathrm{N}_{2}\right]=0.114 M,$ and $\left[\mathrm{H}_{2}\right]=$ 0.342 $\mathrm{M} .$ Calculate $K_{\mathrm{c}}$ for the reaction at this temperature.

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Problem 43

Gaseous $\mathrm{PCl}_{5}$ decomposes according to the reaction
$$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$
In one experiment, 0.15 mol of $\mathrm{PCl}_{5}(g)$ was introduced into a 2.0 -L container. Construct the reaction table for this process.

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Problem 44

Hydrogen fluoride, HF, can be made from the reaction
$$\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)$$
In one experiment, 0.10 mol of $\mathrm{H}_{2}(g)$ and 0.050 mol of $\mathrm{F}_{2}(g)$ are added to a 0.50 -L flask. Write a reaction table for this process.

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Problem 45

For the following reaction, $K_{\mathrm{p}}=6.5 \times 10^{4}$ at $308 \mathrm{K} :$
$$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)$$
At equilibrium, $P_{\mathrm{NO}}=0.35$ atm and $P_{\mathrm{Cl}_{2}}=0.10$ atm. What is the equilibrium partial pressure of $\mathrm{NOCl}(g)$ )?

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Problem 46

For the following reaction, $K_{\mathrm{p}}=0.262$ at $1000^{\circ} \mathrm{C} :$
$$\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)$$
At equilibrium, $P_{\mathrm{H}_{2}}$ is 1.22 $\mathrm{atm} .$ What is the equilibrium partial pressure of $\mathrm{CH}_{4}(g) ?$

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Problem 47

Ammonium hydrogen sulfide decomposes according to the following reaction, for which $K_{\mathrm{p}}=0.11$ at $250^{\circ} \mathrm{C} :$
$$\mathrm{NH}_{4} \mathrm{HS}(s) \rightleftharpoons \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{NH}_{3}(g)$$
If 55.0 g of $\mathrm{NH}_{4} \mathrm{HS}(s)$ is placed in a sealed 5.0 -L container, what is the partial pressure of $\mathrm{NH}_{3}(g)$ at equilibrium?

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Problem 48

Hydrogen sulfide decomposes according to the following reaction, for which $K_{c}=9.30 \times 10^{-8}$ at $700^{\circ} \mathrm{C} :$
$$2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)$$
If 0.45 $\mathrm{mol}$ of $\mathrm{H}_{2} \mathrm{S}$ is placed in a $3.0-\mathrm{L}$ container, what is the equilibrium concentration of $\mathrm{H}_{2}(g)$ at $700^{\circ} \mathrm{C} ?$

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Problem 49

Even at high T, the formation of NO is not favored:
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad K_{\mathrm{c}}=4.10 \times 10^{-4} at 2000^{\circ} \mathrm{C}$$
What is [NO] when a mixture of 0.20 $\mathrm{mol}$ of $\mathrm{N}_{2}(g)$ and 0.15 $\mathrm{mol}$ of $\mathrm{O}_{2}(g)$ reach equilibrium in a 1.0 $\mathrm{-L}$ container at $2000^{\circ} \mathrm{C} ?$

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Problem 50

Nitrogen dioxide decomposes according to the reaction
$$2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$
where $K_{\mathrm{p}}=4.48 \times 10^{-13}$ at a certain temperature. If 0.75 atm of $\mathrm{NO}_{2}$ is added to a container and allowed to come to equilibrium, what are the equilibrium partial pressures of $\mathrm{NO}(g)$ and $\mathrm{O}_{2}(g) ?$

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Problem 51

Hydrogen iodide decomposes according to the reaction
$$2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)$$
A sealed $1.50-\mathrm{L}$ container initially holds 0.00623 $\mathrm{mol}$ of $\mathrm{H}_{2}, 0.00414 \mathrm{mol}$ of $\mathrm{I}_{2},$ and 0.0244 $\mathrm{mol}$ of $\mathrm{HI}$ at 703 $\mathrm{K}$ . When equilibrium is reached, the concentration of $\mathrm{H}_{2}(g)$ is 0.00467 $\mathrm{M}$ . What are the concentrations of $\mathrm{HI}(g)$ and $\mathrm{I}_{2}(g) ?$

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Problem 52

Compound A decomposes according to the equation
$$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{B}(g)+\mathrm{C}(g)$$
A sealed $1.00-\mathrm{L}$ container initially contains $1.75 \times 10^{-3} \mathrm{mol}$ of $\mathrm{A}(g), 1.25 \times 10^{-3} \mathrm{mol}$ of $\mathrm{B}(g),$ and $6.50 \times 10^{-4} \mathrm{mol}$ of $\mathrm{C}(g)$ at $100^{\circ} \mathrm{C} .$ At equilibrium, [A] is $2.15 \times 10^{-3}$ M. Find $[\mathrm{B}]$ and $[\mathrm{C}] .$

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Problem 53

In an analysis of interhalogen reactivity, 0.500 mol of ICl was placed in a 5.00-L flask, where it decomposed at a high T:
$2 \mathrm{ICl}(g) \Longrightarrow \mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g) .$ Calculate the equilibrium concentrations of $\mathrm{I}_{2}, \mathrm{Cl}_{2},$ and $\mathrm{ICl}\left(K_{\mathrm{c}}=0.110 \text { at this temperature). }\right.$

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Problem 54

A toxicologist studying mustard gas, $S\left(\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\right)_{2},$ a blistering agent, prepares a mixture of 0.675$M \mathrm{SCl}_{2}$ and 0.973 $\mathrm{M}$ $\mathrm{C}_{2} \mathrm{H}_{4}$ and allows it to react at room temperature $\left(20.0^{\circ} \mathrm{C}\right)$ :
$$\mathrm{SCl}_{2}(g)+2 \mathrm{C}_{2} \mathrm{H}_{4}(g) \rightleftharpoons \mathrm{S}\left(\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\right)_{2}(g)$$
At equilibrium, $\left[\mathrm{S}\left(\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\right)_{2}\right]=0.350$ M. Calculate $K_{\mathrm{p}}$

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Problem 55

The first step in HNO $_{3}$ production is the catalyzed oxidation of $\mathrm{NH}_{3}$ . Without a catalyst, a different reaction predominates:
$$4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$
When 0.0150 mol of $\mathrm{NH}_{3}(g)$ and 0.0150 $\mathrm{mol}$ of $\mathrm{O}_{2}(g)$ are placed in a $1.00-\mathrm{L}$ container at a certain temperature, the $\mathrm{N}_{2}$ concentration at equilibrium is $1.96 \times 10^{-3} \mathrm{M} .$ Calculate $K_{\mathrm{c}} .$

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Problem 56

A key step in the extraction of iron from its ore is
$$\mathrm{FeO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) \quad K_{\mathrm{p}}=0.403 at 1000^{\circ} \mathrm{C}$$
This step occurs in the $700^{\circ} \mathrm{C}$ to $1200^{\circ} \mathrm{C}$ zone within a blast furnace. What are the equilibrium partial pressures of $\mathrm{CO}(g)$ and $\mathrm{CO}_{2}(g)$ when 1.00 atm of $\mathrm{CO}(g)$ and excess FeO(s) react in a sealed container at $1000^{\circ} \mathrm{C} ?$

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Problem 57

What does “disturbance” mean in Le Chatelier’s principle?

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Problem 58

What is the difference between the equilibrium position and the equilibrium constant of a reaction? Which changes as a result of a change in reactant concentration?

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Problem 59

Scenes A, B, and C below depict the following reaction at three temperatures:
$$\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \quad \Delta H_{\mathrm{mn}}^{\circ}=176 \mathrm{kJ}$$
(a) Which best represents the reaction mixture at the highest temperature? Explain. (b) Which best represents the reaction mixture at the lowest temperature? Explain.

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Problem 60

What is implied by the word “constant” in the term equilibrium constant? Give two reaction parameters that can be changed without changing the value of an equilibrium constant.

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Problem 61

Le Chatelier’s principle is related ultimately to the rates of the forward and reverse steps in a reaction. Explain (a) why an increase in reactant concentration shifts the equilibrium position to the right but does not change K; (b) why a decrease in V shifts the equilibrium position toward fewer moles of gas but does not change K; (c) why a rise in T shifts the equilibrium position of an exothermic reaction toward reactants and also changes K; and (d) why a rise in temperature of an endothermic reaction from $T_{1}$ to $T_{2}$ results in $K_{2}$ being larger than $K_{1}$ .

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Problem 62

An equilibrium mixture of two solids and a gas, in the reaction $\mathrm{XY}(s) \rightleftharpoons$ $\mathrm{X}(g)+\mathrm{Y}(s),$ is depicted at right $(\mathrm{X} \text { is }$ green and $\mathrm{Y}$ is black). Does scene A, B, or C best represent the system at equilibrium after two formula units of $\mathrm{Y}(s)$ is added? Explain.

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Problem 63

Consider this equilibrium system:
$$\mathrm{CO}(g)+\mathrm{Fe}_{3} \mathrm{O}_{4}(s) \rightleftharpoons \mathrm{CO}_{2}(g)+3 \mathrm{FeO}(s)$$
How does the equilibrium position shift as a result of each of the following disturbances? (a) $\mathrm{CO}$ is added. (b) $\mathrm{CO}_{2}$ is removed by adding solid NaOH. (c) Additional Fe_ $_{3} \mathrm{O}_{4}(s)$ is added to the system. (d) Dry ice is added at constant temperature.

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Problem 64

Sodium bicarbonate undergoes thermal decomposition according to the reaction
$$2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$
How does the equilibrium position shift as a result of each of the following disturbances? (a) 0.20 atm of argon gas is added. (b) $\mathrm{NaHCO}_{3}(s)$ is added. (c) $\mathrm{Mg}\left(\mathrm{ClO}_{4}\right)_{2}(s)$ is added as a drying agent to remove $\mathrm{H}_{2} \mathrm{O} .$ (d) Dry ice is added at constant $T$

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Problem 65

Predict the effect of increasing the container volume on the amounts of each reactant and product in the following reactions:
(a) $\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{F}(g)$
(b) $2 \mathrm{CH}_{4}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)$

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Problem 66

Predict the effect of increasing the container volume on the amounts of each reactant and product in the following reactions:Predict the effect of increasing the container volume on the amounts of each reactant and product in the following reactions:
(a) $\mathrm{CH}_{3} \mathrm{OH}(l) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)$
(b) $\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{HCN}(g)+3 \mathrm{H}_{2}(g)$

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Problem 67

Predict the effect of decreasing the container volume on the amounts of each reactant and product in the following reactions:
(a) $\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)$
(b) $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)$

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Problem 68

Predict the effect of decreasing the container volume on the amounts of each reactant and product in the following reactions:
(a) $\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$
(b) $4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$

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Problem 69

How would you adjust the volume of the container in order to maximize product yield in each of the following reactions?
(a) $\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{H}_{2}(g) \rightleftharpoons 3 \mathrm{Fe}(s)+4 \mathrm{H}_{2} \mathrm{O}(g)$
(b) $2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$

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Problem 70

How would you adjust the volume of the container in order to maximize product yield in each of the following reactions?
(a) $\mathrm{Na}_{2} \mathrm{O}_{2}(s) \rightleftharpoons 2 \mathrm{Na}(l)+\mathrm{O}_{2}(g)$
(b) $\mathrm{C}_{2} \mathrm{H}_{2}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g)$

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Problem 71

redict the effect of increasing the temperature on the amounts of products in the following reactions:
(a) $\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-90.7 \mathrm{kJ}$
(b) $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=131 \mathrm{kJ}$
(c) $2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$ (endothermic)
(d) $2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$ (exothermic)

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Problem 72

Predict the effect of decreasing the temperature on the amounts of reactants in the following reactions:
(a) $\mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CHO}(g) \quad \Delta H_{\mathrm{xn}}^{\circ}=-151 \mathrm{kJ}$
(b) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(l)+\mathrm{H}_{2} \mathrm{O}(g)$ $\Delta H_{\mathrm{rxn}}^{\circ}=-451 \mathrm{kJ}$
(c) $2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CH}_{3} \mathrm{CHO}(g)$ (exothermic)
(d) $\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$ (endothermic)

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Problem 73

The molecule $\mathrm{D}_{2}$ (where $D,$ deuterium, is $^{2} \mathrm{H} )$ undergoes a reaction with ordinary $\mathrm{H}_{2}$ that leads to isotopic equilibrium:
$$\mathrm{D}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{DH}(g) \quad K_{\mathrm{p}}=1.80 \mathrm{at} 298 \mathrm{K}$$
If $\Delta H_{\mathrm{rxn}}^{\circ}$ is 0.32 $\mathrm{kJ} / \mathrm{mol} \mathrm{DH}$ , calculate $K_{\mathrm{p}}$ at $500 . \mathrm{K}$

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Problem 74

The formation of methanol is important to the processing of new fuels. At $298 \mathrm{K}, K_{\mathrm{p}}=2.25 \times 10^{4}$ for the reaction
$$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(l)$$
If $\Delta H_{\mathrm{rxn}}^{\circ}=-128 \mathrm{kJ} / \mathrm{mol} \mathrm{CH}_{3} \mathrm{OH},$ calculate $K_{\mathrm{p}}$ at $0^{\circ} \mathrm{C}$

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Problem 75

The minerals hematite $\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)$ and magnetite $\left(\mathrm{Fe}_{3} \mathrm{O}_{4}\right)$ exist in equilibrium with atmospheric oxygen:
$$4 \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 6 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad K_{\mathrm{p}}=2.5 \times 10^{87} at 298 \mathrm{K}$$
(a) Determine $P_{\mathrm{O}_{2}}$ at equilibrium. (b) Given that $P_{\mathrm{O}_{2}}$ in air is $0.21 \mathrm{atm},$ in which direction will the reaction proceed to reach equilibrium? (c) Calculate $K_{\mathrm{c}}$ at 298 $\mathrm{K}$

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Problem 76

The oxidation of $\mathrm{SO}_{2}$ is the key step in $\mathrm{H}_{2} \mathrm{SO}_{4}$ production:
$\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g) \qquad \Delta H_{\mathrm{rxn}}^{\circ}=-99.2 \mathrm{kJ}$
(a) What qualitative combination of $T$ and $P$ maximizes $\mathrm{SO}_{3}$ yield?
(b) How does addition of $\mathrm{O}_{2}$ affect $Q$ ? $K$ ?
(c) Why is catalysis used for this reaction?

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Problem 77

A mixture of 3.00 volumes of $\mathrm{H}_{2}$ and 1.00 volume of $\mathrm{N}_{2}$ reacts at $344^{\circ} \mathrm{C}$ to form ammonia. The equilibrium mixture at 110 . atm contains 41.49$\% \mathrm{NH}_{3}$ by volume. Calculate $K_{\mathrm{p}}$ for the reaction, assuming that the gases behave ideally.

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Problem 78

You are a member of a research team of chemists discussing plans for a plant to produce ammonia:
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$
(a) The plant will operate at close to $700 \mathrm{K},$ at which $K_{\mathrm{p}}$ is $1.00 \times 10^{-4},$ and employs the stoichiometric 1$/ 3$ ratio of $\mathrm{N}_{2} / \mathrm{H}_{2} .$ At equilibrium, the partial pressure of $\mathrm{NH}_{3}$ is 50 . atm. Calculate the partial pressures of each reactant and $P_{\text { total. }}$
(b) One member of the team suggests the following: since the partial pressure of $\mathrm{H}_{2}$ is cubed in the reaction quotient, the plant could produce the same amount of $\mathrm{NH}_{3}$ if the reactants were in $\mathrm{a} 1 / 6$ ratio of $\mathrm{N}_{2} / \mathrm{H}_{2}$ and could do so at a lower pressure, which would cut operating costs. Calculate the partial pressure of each reactant and $P_{\text { total }}$ under these conditions, assuming an unchanged partial pressure of $50 .$ atm for $\mathrm{NH}_{3} .$ Is the suggestion valid?

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Problem 79

For the following equilibrium system, which of the changes will form more $\mathrm{CaCO}_{3} ?$
$\mathrm{CO}_{2}(g)+\mathrm{Ca}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \Delta H^{\circ}=-113 \mathrm{kJ}$
(a) Decrease temperature at constant pressure (no phase change)
(b) Increase volume at constant temperature
(c) Increase partial pressure of $\mathrm{CO}_{2}$
(d) Remove one-half of the initial $\mathrm{CaCO}_{3}$

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Problem 80

The “filmstrip” represents five molecular scenes of a gaseous mixture as it reaches equilibrium over time:
$\mathrm{X}$ is purple and $\mathrm{Y}$ is orange: $\mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \rightleftharpoons 2 \mathrm{XY}(g)$
(a) Write the reaction quotient, $Q,$ for this reaction.
(b) If each particle represents $0.1 \mathrm{mol},$ find $Q$ for each scene.
(c) If $K>1,$ is time progressing to the right or to the left? Explain.
(d) Calculate $K$ at this temperature.
(e) If $\Delta H_{\mathrm{rxn}}^{\circ}<0,$ which scene, if any, best represents the mixture at a higher temperature? Explain.
(f) Which scene, if any, best represents the mixture at a higher pressure (lower volume)? Explain.

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Problem 81

Ammonium carbamate $\left(\mathrm{NH}_{2} \mathrm{COONH}_{4}\right)$ is a salt of carbamic acid that is found in the blood and urine of mammals. At 250. $\mathrm{C},$ $K_{\mathrm{c}}=1.58 \times 10^{-8}$ for the following equilibrium:
$$\mathrm{NH}_{2} \mathrm{COONH}_{4}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)$$
If 7.80 $\mathrm{g}$ of $\mathrm{NH}_{2} \mathrm{COONH}_{4}$ is put into a 0.500 -L evacuated container, what is the total pressure at equilibrium?

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Problem 82

Isolation of Group 8B(10) elements, used as industrial catalysts, involves a series of steps. For nickel, the sulfide ore is roasted in air: $\mathrm{Ni}_{3} \mathrm{S}_{2}(s)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NiO}(s)+\mathrm{SO}_{2}(g) .$ The metal oxide is reduced by the $\mathrm{H}_{2}$ in water gas $\left(\mathrm{CO}+\mathrm{H}_{2}\right)$ to impure $\mathrm{Ni} : \mathrm{NiO}(s)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g) .$ The $\mathrm{CO}$ in water gas then reacts with the metal in the Mond process to form gaseous nickel carbonyl, Ni(s) $+\mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g),$ which is subsequently decomposed to the metal. a) Balance each of the three steps, and obtain an overall balanced equation for the conversion of $\mathrm{Ni}_{3} \mathrm{S}_{2}$ to $\mathrm{Ni}(\mathrm{CO})_{4} \cdot(\mathrm{b})$ Show that the overall $Q_{\mathrm{c}}$ is the product of the $Q_{\mathrm{c}}^{\prime}$ s for the individual reactions.

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Problem 83

Consider the formation of ammonia in two experiments.
(a) To a $1.00-\mathrm{L}$ container at $727^{\circ} \mathrm{C}, 1.30 \mathrm{mol}$ of $\mathrm{N}_{2}$ and 1.65 $\mathrm{mol}$ of $\mathrm{H}_{2}$ are added. At equilibrium, 0.100 $\mathrm{mol}$ of $\mathrm{NH}_{3}$ is present. Calculate the equilibrium concentrations of $\mathrm{N}_{2}$ and $\mathrm{H}_{2},$ and find $K_{\mathrm{c}}$ for the reaction: $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$
(b) In a different $1.00-\mathrm{L}$ container at the same temperature, equilibrium is established with $8.34 \times 10^{-2} \mathrm{mol}$ of $\mathrm{NH}_{3}, 1.50 \mathrm{mol}$ of $\mathrm{N}_{2},$ and 1.25 $\mathrm{mol}$ of $\mathrm{H}_{2}$ present. Calculate $K_{\mathrm{c}}$ for the reaction:
$$\mathrm{NH}_{3}(g) \rightleftharpoons \frac{1}{2} \mathrm{N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g)$$
(c) What is the relationship between the $K_{\mathrm{c}}$ values in parts (a) and
(b)? Why aren't these values the same?

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Problem 84

17.84 An important industrial source of ethanol is the reaction, catalyzed by $\mathrm{H}_{3} \mathrm{PO}_{4},$ of steam with ethylene derived from oil:
$$\begin{array}{c}{\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)} \\ {\Delta H_{\mathrm{ran}}^{\circ}=-47.8 \mathrm{kJ} \quad K_{\mathrm{c}}=9 \times 10^{3} \mathrm{at} 600 . \mathrm{K}}\end{array}$$
(a) At equilibrium, $P_{\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}}=200 .$ atm and $P_{\mathrm{H}_{2} \mathrm{O}}=400 . \mathrm{atm}$ Calculate $P_{\mathrm{C}, \mathrm{H}_{4}} \cdot(\mathrm{b})$ Is the highest yield of ethanol obtained at high or low $P ?$ High or low $T ?(\mathrm{c})$ Calculate $K_{\mathrm{c}}$ at $450 . \mathrm{K}$ . (d) In $\mathrm{NH}_{3}$ manufacture, the yield is increased by condensing the $\mathrm{NH}_{3}$ to a liquid and removing it. Would condensing the $\mathrm{C}_{2} \mathrm{H}_{5}$ OH have the same effect in ethanol production? Explain.

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Problem 85

An industrial chemist introduces 2.0 atm of $\mathrm{H}_{2}$ and 2.0 $\mathrm{atm}$ of $\mathrm{CO}_{2}$ into a $1.00-\mathrm{L}$ container at $25.0^{\circ} \mathrm{C}$ and then raises the temperature to $700 \cdot \mathrm{C},$ at which $K_{\mathrm{c}}=0.534$ :
$$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$$
How many grams of $\mathrm{H}_{2}$ are present at equilibrium?

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Problem 86

As an EPA scientist studying catalytic converters and urban smog, you want to find $K_{\mathrm{c}}$ for the following reaction:
$$2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \quad K_{\mathrm{c}}=?$$
Use the following data to find the unknown $K_{\mathrm{c}}$
$\frac{1}{2} \mathrm{N}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NO}(g) \quad\quad\quad\quad K_{\mathrm{c}}=4.8 \times 10^{-10} \\ \quad\quad\quad 2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad K_{\mathrm{c}}=1.1 \times 10^{-5}$

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Problem 87

An engineer examining the oxidation of $\mathrm{SO}_{2}$ in the manufacture of sulfuric acid determines that $K_{\mathrm{c}}=1.7 \times 10^{8}$ at $600 . \mathrm{K}$ :
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$
(a) At equilibrium, $P_{\mathrm{SO}_{3}}=300 .$ atm and $P_{\mathrm{O}_{2}}=100 .$ atm. Calculate $P_{\mathrm{SO}_{2}} \cdot(\mathrm{b})$ The engineer places a mixture of 0.0040 $\mathrm{mol}$ of $\mathrm{SO}_{2}(g)$ and 0.0028 $\mathrm{mol}$ of $\mathrm{O}_{2}(g)$ in a $1.0-\mathrm{L}$ container and raises the temperature to 1000 $\mathrm{K}$ . At equilibrium, 0.0020 mol of $\mathrm{SO}_{3}(g)$ is present. Calculate $K_{\mathrm{c}}$ and $P_{\mathrm{SO}_{2}}$ for this reaction at $1000 . \mathrm{K} .$

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Problem 88

Phosgene $\left(\mathrm{COCl}_{2}\right)$ is a toxic substance that forms readily from carbon monoxide and chlorine at elevated temperatures:
$$\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)$$
If 0.350 mol of each reactant is placed in a $0.500-\mathrm{L}$ flask at $600 \mathrm{K},$ what are the concentrations of all three substances at equilibrium $\left(K_{\mathrm{c}}=4.95 \text { at this temperature)? }\right.$

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Problem 89

When 0.100 mol of $\mathrm{CaCO}_{3}(s)$ and 0.100 $\mathrm{mol}$ of $\mathrm{CaO}(s)$ are placed in an evacuated sealed $10.0-\mathrm{L}$ container and heated to $385 \mathrm{K}, P_{\mathrm{CO}_{2}}=0.220$ atm after equilibrium is established:
$$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$
An additional 0.300 atm of $\mathrm{CO}_{2}(g)$ is pumped in. What is the total mass (in $\mathrm{g}$ ) of $\mathrm{CaCO}_{3}$ after equilibrium is re-established?

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Problem 90

Use each of the following reaction quotients to write the balanced equation:
(a) $Q=\frac{\left[\mathrm{CO}_{2}\right]^{2}\left[\mathrm{H}_{2} \mathrm{O}\right]^{2}}{\left[\mathrm{C} \mathrm{O}_{4}\right]\left[\mathrm{O}_{2}\right]^{3}} \qquad$ (b) $Q=\frac{\left[\mathrm{NH}_{3}\right]^{4}\left[\mathrm{O}_{2}\right]^{7}}{\left[\mathrm{NO}_{2}\right]^{4}\left[\mathrm{H}_{2} \mathrm{O}\right]^{6}}$

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Problem 91

Hydrogenation of carbon-carbon $\pi$ bonds is important in the petroleum and food industries. The conversion of acetylene to ethylene is a simple example of the process:
$$\mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(g)$$
The calculated $K_{\mathrm{c}}$ at $2000 . \mathrm{K}$ is 2.9 $\times 10^{8} .$ But the process is run at lower temperatures with the aid of a catalyst to prevent decomposition. Use $\Delta H^{\circ}$ values to calculate $K_{\mathrm{c}}$ at $300 . \mathrm{K} .$

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Problem 92

For the reaction $\mathrm{M}_{2}+\mathrm{N}_{2} \rightleftharpoons 2 \mathrm{MN}$ , scene A represents the mixture at equilibrium, with M black and N orange. If each molecule represents 0.10 mol and the volume is 1.0 $\mathrm{L}$ , how many moles of each substance will be present in scene $\mathrm{B}$ when that mixture reaches equilibrium?

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Problem 93

Highly toxic disulfur decafluoride decomposes by a free-radical process: $\mathrm{S}_{2} \mathrm{F}_{10}(g) \rightleftharpoons \mathrm{SF}_{4}(g)+\mathrm{SF}_{6}(g) .$ In a study of the decomposition, $\mathrm{S}_{2} \mathrm{F}_{10}$ was placed in a 2.0 $\mathrm{L}$ flask and heated to $100^{\circ} \mathrm{C} ;\left[\mathrm{S}_{2} \mathrm{F}_{10}\right]$ was 0.50$M$ at equilibrium. More $\mathrm{S}_{2} \mathrm{F}_{10}$ was added and when equilibrium was reattained, $\left[\mathrm{S}_{2} \mathrm{F}_{10}\right]$ was 2.5 $\mathrm{M} .$ How did $\left[\mathrm{SF}_{4}\right]$ and $\left[\mathrm{SF}_{6}\right]$ change from the original to the new equilibrium position after the addition of more $\mathrm{S}_{2} \mathrm{F}_{10} ?$

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Problem 94

A study of the water-gas shift reaction (see Problem 17.37$)$ was made in which equilibrium was reached with $[\mathrm{CO}]=\left[\mathrm{H}_{2} \mathrm{O}\right]=$ $\left[\mathrm{H}_{2}\right]=0.10 M$ and $\left[\mathrm{CO}_{2}\right]=0.40 M .$ After 0.60 $\mathrm{mol}$ of $\mathrm{H}_{2}$ is added to the $2.0-\mathrm{L}$ container and equilibrium is re-established, what are the new concentrations of all the components?

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Problem 95

A gaseous mixture of 10.0 volumes of $\mathrm{CO}_{2}, 1.00$ volume of unreacted $\mathrm{O}_{2},$ and 50.0 volumes of unreacted $\mathrm{N}_{2}$ leaves an engine at 4.0 $\mathrm{atm}$ and $800 . \mathrm{K}$ . Assuming that the mixture reaches equilibrium, what are (a) the partial pressure and (b) the concentration (in picograms per liter, pg/L) of $\mathrm{CO}$ in this exhaust gas?
$$2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \qquad K_{\mathrm{p}}=1.4 \times 10^{-28} at 800 . \mathrm{K}$$
(The actual concentration of $\mathrm{CO}$ in exhaust gas is much higher because the gases do not reach equilibrium in the short transit time through the engine and exhaust system.)

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Problem 96

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

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Problem 97

The following reaction can be used to make $\mathrm{H}_{2}$ for the syn- thesis of ammonia from the greenhouse gases carbon dioxide and methane:
$$\mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$
(a) What is the percent yield of $\mathrm{H}_{2}$ when an equimolar mixture of $\mathrm{CH}_{4}$ and $\mathrm{CO}_{2}$ with a total pressure of 20.0 atm reaches equilibrium at $11200 . \mathrm{K},$ at which $K_{\mathrm{p}}=3.548 \times 10^{6} ?$
(b) What is the percent yield of $\mathrm{H}_{2}$ for this system at $1300 . \mathrm{K},$ at which $K_{\mathrm{p}}=2.626 \times 10^{7} ?$
(c) Use the van't Hoff equation to find $\Delta H_{\mathrm{rxn}}^{\circ}$

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Problem 98

The methane used to obtain $\mathrm{H}_{2}$ for $\mathrm{NH}_{3}$ manufacture is impure and usually contains other hydrocarbons, such as propane, $\mathrm{C}_{3} \mathrm{H}_{8} .$ Imagine the reaction of propane occurring in two steps:
$\mathrm{C}_{3} \mathrm{H}_{8}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 3 \mathrm{CO}(g)+7 \mathrm{H}_{2}(g) \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad K_{\mathrm{p}}=8.175 \times 10^{15} \mathrm{at} 1200 . \mathrm{K}$
$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad K_{\mathrm{p}}=0.6944 \text { at } 1200 . \mathrm{K}$
(a) Write the overall equation for the reaction of propane and steam to produce carbon dioxide and hydrogen.
(b) Calculate $K_{\mathrm{p}}$ for the overall process at $1200 . \mathrm{K}$ .
(c) When 1.00 volume of $\mathrm{C}_{3} \mathrm{H}_{8}$ and 4.00 volumes of $\mathrm{H}_{2} \mathrm{O},$ each at $1200 . \mathrm{K}$ and 5.0 $\mathrm{atm}$ , are mixed in a container, what is the final pressure? Assume the total volume remains constant, that the reaction is essentially complete, and that the gases behave ideally.
(d) What percentage of the $\mathrm{C}_{3} \mathrm{H}_{8}$ remains unreacted?

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Problem 99

Using $\mathrm{CH}_{4}$ and steam as a source of $\mathrm{H}_{2}$ for $\mathrm{NH}_{3}$ synthesis requires high temperatures. Rather than burning $\mathrm{CH}_{4}$ separately to heat the mixture, it is more efficient to inject some $\mathrm{O}_{2}$ into the reaction mixture. All of the $\mathrm{H}_{2}$ is thus released for the synthesis, and the heat of reaction for the combustion of $\mathrm{CH}_{4}$ helps maintain the required temperature. Imagine the reaction occurring in two steps:
$2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+4 \mathrm{H}_{2}(g) \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad K_{\mathrm{p}}=9.34 \times 10^{28} \text { at } 1000 . \mathrm{K}$
$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad K_{\mathrm{p}}=1.374 \text { at } 1000 . \mathrm{K}$
(a) Write the overall equation for the reaction of methane, steam, and oxygen to form carbon dioxide and hydrogen.
(b) What is $K_{\mathrm{p}}$ for the overall reaction?
(c) What is $K_{\mathrm{c}}$ for the overall reaction?
(d) A mixture of 2.0 $\mathrm{mol}$ of $\mathrm{CH}_{4}, 1.0 \mathrm{mol}$ of $\mathrm{O}_{2},$ and 2.0 $\mathrm{mol}$ of steam with a total pressure of $30 .$ atm reacts at $1000 . \mathrm{K}$ at constant volume. Assuming that the reaction is complete and the ideal gas law is a valid approximation, what is the final pressure?

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Problem 100

One mechanism for the synthesis of ammonia proposes that $\mathrm{N}_{2}$ and $\mathrm{H}_{2}$ molecules catalytically dissociate into atoms:
$$\begin{array}{ll}{\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{N}(g)} & {\log K_{\mathrm{p}}=-43.10} \\ {\mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{H}(g)} & {\log K_{\mathrm{p}}=-17.30}\end{array}$$
(a) Find the partial pressure of $\mathrm{N}$ in $\mathrm{N}_{2}$ at $1000 . \mathrm{K}$ and 200 . atm.
(b) Find the partial pressure of $\mathrm{H}$ in $\mathrm{H}_{2}$ at $1000 . \mathrm{K}$ and 600 . atm.
(c) How many $\mathrm{N}$ atoms and $\mathrm{H}$ atoms are present per liter?
(d) Based on these answers, which of the following is a more reasonable step to continue the mechanism after the catalytic dissociation? Explain.
\begin{aligned} \mathrm{N}(g)+\mathrm{H}(g) & \longrightarrow \mathrm{NH}(g) \\ \mathrm{N}_{2}(g)+\mathrm{H}(g) & \longrightarrow \mathrm{NH}(g)+\mathrm{N}(g) \end{aligned}

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Problem 101

The molecular scenes below depict the reaction $\mathrm{Y} \Longrightarrow 2 \mathrm{Z}$ at four different times, out of sequence, as it reaches equilibrium. Each sphere (Y is red and $Z$ is green) represents 0.025 mol, and the volume is 0.40 $\mathrm{L}$ . (a) Which scene(s) represent(s) equilibrium? (b) List the scenes in the correct sequence. (c) Calculate $K_{\mathrm{c}}$ .

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Problem 102

For the equilibrium
$$\mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \quad K_{\mathrm{c}}=9.0 \times 10^{-8} \mathrm{at} 700^{\circ} \mathrm{C}$$
the initial concentrations of the three gases are 0.300$M \mathrm{H}_{2} \mathrm{S}$ , $0.300 \mathrm{M} \mathrm{H}_{2},$ and 0.150 $\mathrm{M} \mathrm{S}_{2}$ . Determine the equilibrium concentrations of the gases.

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Problem 103

The two most abundant atmospheric gases react to a tiny extent at 298 K in the presence of a catalyst:
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad K_{\mathrm{p}}=4.35 \times 10^{-31}$$
(a) What are the equilibrium pressures of the three gases when the atmospheric partial pressures of $\mathrm{O}_{2}(0.210 \mathrm{atm})$ and of $\mathrm{N}_{2}$ $(0.780 \mathrm{atm})$ are put into an evacuated $1.00-\mathrm{L}$ flask at 298 $\mathrm{K}$ with the catalyst? (b) What is $P_{\text { total }}$ in the container? (c) Find $K_{\mathrm{c}}$ at 298 $\mathrm{K}$ .

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Problem 104

The oxidation of nitrogen monoxide is favored at 457 K:
$$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad K_{\mathrm{p}}=1.3 \times 10^{4}$$
(a) Calculate $K_{c}$ at 457 $\mathrm{K}$ . (b) Find $\Delta H_{\mathrm{rom}}^{\circ}$ from standard heats of formation. ( $\mathrm{c} )$ At what temperature does $K_{\mathrm{c}}=6.4 \times 10^{9} ?$

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Problem 105

The kinetics and equilibrium of the decomposition of hydrogen iodide have been studied extensively:
$$2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)$$
(a) At $298 \mathrm{K}, K_{\mathrm{c}}=1.26 \times 10^{-3}$ for this reaction. Calculate $K_{\mathrm{p}}$ .
(b) Calculate $K_{\mathrm{c}}$ for the formation of HI at 298 $\mathrm{K} .$
(c) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for HI decomposition from $\Delta H_{\mathrm{f}}^{\circ}$ values.
(d) At $729 \mathrm{K}, K_{\mathrm{c}}=2.0 \times 10^{-2}$ for HI decomposition. Calculate $\Delta H_{\mathrm{rxn}}$ for this reaction from the van't Hoff equation.

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Problem 106

Isopentyl alcohol reacts with pure acetic acid to form isopentyl acetate, the essence of banana oil:
$$\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{OH}+\mathrm{CH}_{3} \mathrm{COOH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COOC}_{5} \mathrm{H}_{11}+\mathrm{H}_{2} \mathrm{O}$$
A student adds a drying agent to remove $\mathrm{H}_{2} \mathrm{O}$ and thus increase the yield of banana oil. Is this approach reasonable? Explain.

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Problem 107

Isomers Q (blue) and R (yellow) interconvert. They are depicted in an equilibrium mixture in scene A. Scene B represents the mixture after addition of more Q. How many molecules of each isomer are present when the mixture in scene B attains equilibrium again?

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Problem 108

Glauber's salt, $\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O},$ was used by J. R. Glauber in the $17^{\mathrm{th}}$ century as a medicinal agent. At $25^{\circ} \mathrm{C}, K_{\mathrm{p}}=4.08 \times 10^{-25}$ for the loss of waters of hydration from Glauber's salt:
$$\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot^{-10 \mathrm{H}_{2} \mathrm{O}(s)} \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{4}(s)+10 \mathrm{H}_{2} \mathrm{O}(g)$$
(a) What is the vapor pressure of water at $25^{\circ} \mathrm{C}$ in a closed container holding a sample of $\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(s) ?$
(b) How do the following changes affect the ratio (higher, lower, same) of hydrated form to anhydrous form for the system above?
(1) Add more $\mathrm{Na}_{2} \mathrm{SO}_{4}(s)$
(2) Reduce the container volume
(4) Add $\mathrm{N}_{2}$ gas

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Problem 109

In a study of synthetic fuels, 0.100 $\mathrm{mol}$ of $\mathrm{CO}$ and 0.100 $\mathrm{mol}$ of water vapor are added to a $20.00-\mathrm{L}$ container at $900 .^{\circ} \mathrm{C},$ and they react to form $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} .$ At equilibrium, $[\mathrm{CO}]$ is $2.24 \times 10^{-3} \mathrm{M} .$ (a) Calculate $K_{\mathrm{c}}$ at this temperature. (b) Calculate $P_{\text { total }}$ in the flask at equilibrium. (c) How many moles of $\mathrm{CO}$ must be added to double this pressure? (d) After $P_{\text { total }}$ is doubled and the system reattains equilibrium, what is $[\mathrm{CO}]_{\mathrm{eq}}$ ?

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Problem 110

Synthetic diamonds are made under conditions of high temperature (2000 K) and high pressure $\left(10^{10} \mathrm{Pa} ; 10^{5} \mathrm{atm}\right)$ in the presence of catalysts. Carbon's phase diagram is useful for finding the conditions for formation of natural and synthetic diamonds. Along the diamond-graphite line, the two allotropes are in equilibrium. (a) At point A, what is the sign of $\Delta H$ for the formation of diamond from graphite? Explain. (b) Which allotrope is denser? Explain.

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