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Chemical Principle

Steven S. Zumdahl, Donald J. DeCoste

Chapter 6

Chemical Equilibrium - all with Video Answers

Educators

Chapter Questions

06:53

Problem 1

Consider an equilibrium mixture of four chemicals $(\mathrm{A}, \mathrm{B}$ C, and D, all gases) reacting in a closed flask according to the equation
$$
A+B \rightleftharpoons C+D
$$
a. You add more A to the flask. How does the concentration of each chemical compare with its original concentration after equilibrium is reestablished? Justify your answer.
b. You have the original setup at equilibrium, and add more $D$ to the flask. How does the concentration of each chemical compare with its original concentration after equilibrium is reestablished? Justify your answer.

Carina Carlos
Carina Carlos
Numerade Educator
01:20

Problem 2

The boxes shown below represent a set of initial conditions for the reaction:
(FIGURE CAN'T COPY)
Draw a quantitative molecular picture that shows what this system looks like after the reactants are mixed in one of the boxes and the system reaches equilibrium. Support your answer with calculations.

David Collins
David Collins
Numerade Educator
01:48

Problem 3

For the reaction $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g),$ consider two
possibilities using the same-sized, rigid container: (a) you add 0.5 mole of each reactant, allow the system to come
to equilibrium, then add another mole of $\mathrm{H}_{2},$ and allow the system to reach equilibrium again, or (b) you add
1.5 moles of $\mathrm{H}_{2}$ and 0.5 mole of $\mathrm{I}_{2}$ and allow the system to come to equilibrium. Will the final equilibrium mixture be different for the two procedures? Explain.

Ronald Prasad
Ronald Prasad
Numerade Educator
14:03

Problem 4

Given the reaction $\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g),$ con-
sider the following situations:
i. You have $1.3 \mathrm{M} \mathrm{A}$ and $0.8 \mathrm{M} \mathrm{B}$ initially.
ii. You have $1.3 \mathrm{M} \mathrm{A}, 0.8 \mathrm{M} \mathrm{B},$ and $0.2 \mathrm{M}$ C initially.
iii. You have $2.0 \mathrm{M} \mathrm{A}$ and $0.8 \mathrm{M} \mathrm{B}$ initially. After equilibrium has been reached, order i-iii in terms of increasing equilibrium concentrations of D. Explain your sequence. Then give the order in terms of increasing equilibrium concentration of $\mathrm{B}$ and explain.

Carina Carlos
Carina Carlos
Numerade Educator
05:34

Problem 5

Consider the reaction $\mathrm{A}(g)+2 \mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g)$ in
a 1.0 - $L$ rigid flask. Answer the following questions for each situation (a-d):
i. Estimate a range (as small as possible) for the requested substance. For example, [A] could be between $95 \mathrm{M}$ and $100 \mathrm{M}$
ii. Explain how you decided on the limits for the estimated range.
iii. Indicate what other information would enable you to narrow your estimated range.
iv. Compare the estimated concentrations for a through
d, and explain any differences.
a. If at equilibrium $[\mathrm{A}]=1 M$, and then 1 mole of $\mathrm{C}$ is added, estimate the value for [A] once equilibrium is reestablished.
b. If at equilibrium $[\mathrm{B}]=1 M$, and then 1 mole of $\mathrm{C}$ is added, estimate the value for [B] once equilibrium is reestablished.
c. If at equilibrium $[\mathrm{C}]=1 \mathrm{M},$ and then 1 mole of $\mathrm{C}$ is added, estimate the value for $[\mathrm{C}]$ once equilibrium is reestablished.
d. If at equilibrium $[\mathrm{D}]=1 M,$ and then 1 mole of $\mathrm{C}$ is added, estimate the value for [D] once equilibrium is reestablished.

David Collins
David Collins
Numerade Educator
02:41

Problem 6

Consider the reaction $\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g) .$ A
friend asks the following: "I know we have been told that if a mixture of $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D}$ is at equilibrium and more of $\mathrm{A}$ is added, more $\mathrm{C}$ and $\mathrm{D}$ will form. But how can more C and D form if we do not add more B?" What do you tell your friend?

Teesta Dasgupta
Teesta Dasgupta
University of Pittsburgh - Main Campus
16:04

Problem 7

Consider the following statements: "Consider the reaction $\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g),$ at equilibrium in a $1-\mathrm{L}$ con-
tainer, with $[\mathrm{A}]=2 M,[\mathrm{B}]=1 M,$ and $[\mathrm{C}]=4 M .$ To this 1-L container you add 3 moles of B. A possible new equilibrium condition is $[\mathrm{A}]=1 M,[\mathrm{B}]=3 M,$ and $[\mathrm{C}]=6 \mathrm{M}$
because in both cases $K=2 . "$ Indicate everything you think is correct in these statements and everything that is incorrect. Correct the incorrect statements, and explain.

Carina Carlos
Carina Carlos
Numerade Educator
03:28

Problem 8

Consider a solution prepared by mixing equal moles of a weak acid HA, HCl, and NaA. Which of the following best describes what happens?
a. The $H^{+}$ from the HCl reacts completely with the $A^{-}$ from the NaA. Then the HA dissociates to some extent.
b. The $\mathrm{H}^{+}$ from the HCl reacts with the $\mathrm{A}^{-}$ from the NaA to make HA, whereas the HA is dissociating. Eventually you have equal amounts of everything.
c. The $\mathrm{H}^{+}$ from the HCl reacts with the $\mathrm{A}^{-}$ from the NaA to make HA, whereas the HA is dissociating. Eventually all the reactions have equal rates.
d. The $\mathrm{H}^{+}$ from the HCl reacts completely with the $\mathrm{A}^{-}$ from the NaA. Then the HA dissociates until "too much" $\mathrm{H}^{+}$ and $\mathrm{A}^{-}$ are formed, so the $\mathrm{H}^{+}$ and $\mathrm{A}^{-}$ react to form HA, and so on. Eventually equilibrium is reached.
Justify the best choice. For those you did not choose, explain why they are incorrect.

Anish Wadhwa
Anish Wadhwa
Numerade Educator
05:53

Problem 9

The value of the equilibrium constant $K$ depends on which of the following (there may be more than one answer)?
a. the initial concentrations of the reactants
b. the initial concentrations of the products
c. the temperature of the system
d. the nature of the reactants and products
Explain.

Carina Carlos
Carina Carlos
Numerade Educator
02:31

Problem 10

Consider an initial mixture of $\mathrm{N}_{2}$ and $\mathrm{H}_{2}$ gases that can be represented as follows.
(FIGURE CAN'T COPY)
The gases react to form ammonia gas $\left(\mathrm{NH}_{3}\right)$ as represented by the following concentration profile.
(FIGURE CAN'T COPY)
a. Label each plot on the graph as $\mathrm{N}_{2}, \mathrm{H}_{2},$ or $\mathrm{NH}_{3}$ and explain your answers.
b. Explain the relative shapes of the plots.
c. When is equilibrium reached? How do you know?

Ronald Prasad
Ronald Prasad
Numerade Educator
06:47

Problem 11

Consider the following reactions at some temperature:
$$
\begin{aligned}
2 \mathrm{NOCl}(g) & \Longrightarrow 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) & & K=1.6 \times 10^{-5} \\
2 \mathrm{NO}(g) & \Longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & & K=1 \times 10^{31}
\end{aligned}
$$
For each reaction some quantities of the reactants were placed in separate containers and allowed to come to equilibrium. Describe the relative amounts of reactants and products that are present at equilibrium. At equilibrium, which is faster, the forward or reverse reaction in each case?

Carina Carlos
Carina Carlos
Numerade Educator
05:25

Problem 12

Consider the following reaction:
$$
\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)
$$
Amounts of $\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},$ and $\mathrm{CO}_{2}$ are put into a flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive $^{14} \mathrm{C},$ will $^{14} \mathrm{C}$ be found only in $\mathrm{CO}$ molecules for an indefinite period of time? Why or why not?

Carina Carlos
Carina Carlos
Numerade Educator
08:42

Problem 13

Consider the same reaction as in Exercise $12 .$ In a particular experiment 1.0 mole of $\mathrm{H}_{2} \mathrm{O}(g)$ and 1.0 mole of $\mathrm{CO}(g)$ are put into a flask and heated to $350^{\circ} \mathrm{C}$. In another experiment 1.0 mole of $\mathrm{H}_{2}(g)$ and 1.0 mole of $\mathrm{CO}_{2}(g)$ are put into a different flask with the same volume as the first. This mixture is also heated to $350^{\circ} \mathrm{C} .$ After equilibrium is reached, will there be any difference in the composition of the mixtures in the two flasks?

Carina Carlos
Carina Carlos
Numerade Educator
01:27

Problem 14

Consider the following reaction at some temperature:
$$
\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \quad K=2.0
$$
Some molecules of $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{CO}$ are placed in a $1.0-\mathrm{L}$ container as shown below.
When equilibrium is reached, how many molecules of $\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},$ and $\mathrm{CO}_{2}$ are present? Do this problem by
trial and error-that is, if two molecules of CO react, is this equilibrium; if three molecules of CO react, is this equilibrium; and so on.
(FIGURE CAN'T COPY)

Ronald Prasad
Ronald Prasad
Numerade Educator
01:44

Problem 15

Consider the following generic reaction:
$$
2 \mathrm{A}_{2} \mathrm{B}(g) \rightleftharpoons 2 \mathrm{A}_{2}(g)+\mathrm{B}_{2}(g)
$$
Some molecules of $\mathrm{A}_{2} \mathrm{B}$ are placed in a 1.0 - $\mathrm{L}$ container. As time passes, several snapshots of the reaction mixture are taken as illustrated below.Which illustration is the first to represent an equilibrium mixture? Explain. How many molecules of $\mathrm{A}_{2} \mathrm{B}$ were initially placed in the container?
(FIGURE CAN'T COPY)

Ronald Prasad
Ronald Prasad
Numerade Educator
01:12

Problem 16

There is only one value of the equilibrium constant for a particular system at a particular temperature, but there are an infinite number of equilibrium positions. Explain.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:28

Problem 17

Explain the difference between $K, K_{\mathrm{p}},$ and $Q$

Ronald Prasad
Ronald Prasad
Numerade Educator
06:03

Problem 18

What are homogeneous equilibria? Heterogeneous equilibria? What is the difference in writing $K$ expressions for homogeneous versus heterogeneous reactions? Summarize which species are included in $K$ expressions and which species are not included.

Carina Carlos
Carina Carlos
Numerade Educator
01:36

Problem 19

Write expressions for $K$ and $K_{\mathrm{p}}$ for the following reactions.
a. $2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{CH}_{4} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(g)$
b. $2 \mathrm{NBr}_{3}(s) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{Br}_{2}(g)$
c. $2 \mathrm{KClO}_{3}(s) \rightleftharpoons 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$
d. $\mathrm{CuO}(s)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Cu}(l)+\mathrm{H}_{2} \mathrm{O}(g)$

Ronald Prasad
Ronald Prasad
Numerade Educator
06:47

Problem 20

For which reactions in Exercise 19 is $K_{\mathrm{p}}$ equal to $K ?$

Carina Carlos
Carina Carlos
Numerade Educator
02:16

Problem 21

At a particular temperature, a 3.0 - $L$ flask contains 2.4 moles of $\mathrm{Cl}_{2}, 1.0$ mole of $\mathrm{NOCl},$ and $4.5 \times 10^{-3}$ mole of $\mathrm{NO}$ Calculate $K$ at this temperature for the following reaction.
$$
2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)
$$

Ronald Prasad
Ronald Prasad
Numerade Educator
01:09

Problem 22

At $1100 \mathrm{K}, K_{\mathrm{p}}=0.25$ for the reaction
$$
2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)
$$
What is the value of $K$ at this temperature?

Ronald Prasad
Ronald Prasad
Numerade Educator
02:18

Problem 23

At $327^{\circ} \mathrm{C},$ the equilibrium concentrations are $\left[\mathrm{CH}_{3} \mathrm{OH}\right]=$ $0.15 \mathrm{M},[\mathrm{CO}]=0.24 \mathrm{M},$ and $\left[\mathrm{H}_{2}\right]=1.1 \mathrm{M}$ for the
reaction
$$
\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)
$$
Calculate $K_{\mathrm{p}}$ at this temperature.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:51

Problem 24

For the reaction
$\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)$
$K_{\mathrm{p}}=3.5 \times 10^{4}$ at $1495 \mathrm{K} .$ What is the value of $K_{\mathrm{p}}$ for the following reactions at $1495 \mathrm{K} ?$
a. $\mathrm{HBr}(g) \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)$
b. $2 \mathrm{HBr}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)$
c. $\frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Br}_{2}(g) \rightleftharpoons \mathrm{HBr}(g)$

Ronald Prasad
Ronald Prasad
Numerade Educator
03:18

Problem 25

At a particular temperature, a $2.00-\mathrm{L}$ flask at equilibrium contains $2.80 \times 10^{-4}$ mole of $\mathrm{N}_{2}, 2.50 \times 10^{-5}$ mole of $\mathrm{O}_{2},$ and $2.00 \times 10^{-2}$ mole of $\mathrm{N}_{2} \mathrm{O} .$ Calculate $K$ at this temperature for the reaction
$$
2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{N}_{2} \mathrm{O}(g)
$$
If $\left[\mathrm{N}_{2}\right]=2.00 \times 10^{-4} \mathrm{M},\left[\mathrm{N}_{2} \mathrm{O}\right]=0.200 \mathrm{M},$ and $\left[\mathrm{O}_{2}\right]=$
$0.00245 M,$ does this represent a system at equilibrium?

Ronald Prasad
Ronald Prasad
Numerade Educator
01:28

Problem 26

The following equilibrium pressures were observed at a certain temperature for the reaction
$$
\begin{array}{c}
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \\
P_{\mathrm{NH}_{3}}=3.1 \times 10^{-2} \mathrm{atm} \\
P_{\mathrm{N}_{2}}=8.5 \times 10^{-1} \mathrm{atm} \\
P_{\mathrm{H}_{2}}=3.1 \times 10^{-3} \mathrm{atm}
\end{array}
$$
Calculate the value for the equilibrium constant $K_{\mathrm{p}}$ at this temperature. If $P_{\mathrm{N}_{2}}=0.525 \mathrm{atm}, P_{\mathrm{NH}_{3}}=0.0167 \mathrm{atm}$
and $P_{\mathrm{H}_{2}}=0.00761 \mathrm{atm},$ does this represent a system at equilibrium?

Teesta Dasgupta
Teesta Dasgupta
University of Pittsburgh - Main Campus
01:20

Problem 27

For the reaction
$$
2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)
$$
$K=2.4 \times 10^{-3}$ at a given temperature. At equilibrium in a 2.0 - $L$ container, it is found that $\left[\mathrm{H}_{2} \mathrm{O}(g)\right]=1.1 \times$ $10^{-1} M$ and $\left[\mathrm{H}_{2}(g)\right]=1.9 \times 10^{-2} \mathrm{M} .$ Calculate the moles
of $\mathrm{O}_{2}(g)$ present under these conditions.

Ronald Prasad
Ronald Prasad
Numerade Educator
00:41

Problem 28

The reaction
$$
2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)
$$
as $K_{\mathrm{p}}=109$ at $25^{\circ} \mathrm{C} .$ If the equilibrium partial pressure of Br $_{2}$ is 0.0159 atm and the equilibrium partial pressure of NOBr is 0.0768 atm, calculate the partial pressure of NO at equilibrium.

Ronald Prasad
Ronald Prasad
Numerade Educator
05:30

Problem 29

In a study of the reaction
$$
3 \mathrm{Fe}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{H}_{2}(g)
$$
at $1200 \mathrm{K},$ it was observed that when the equilibrium partial pressure of water vapor is 15.0 torr, the total pressure at equilibrium is 36.3 torr. Calculate $K_{\mathrm{p}}$ for this reaction at $1200 \mathrm{K}$

Carina Carlos
Carina Carlos
Numerade Educator
02:49

Problem 30

Nitrogen gas $\left(\mathrm{N}_{2}\right)$ reacts with hydrogen gas $\left(\mathrm{H}_{2}\right)$ to form ammonia (NH $_{3}$ ). At $200^{\circ} \mathrm{C}$ in a closed container, $1.00 \mathrm{atm}$ of nitrogen gas is mixed with 2.00 atm of hydrogen gas. At equilibrium, the total pressure is 2.00 atm. Calculate the partial pressure of hydrogen gas at equilibrium, and calculate the value of $K_{\mathrm{p}}$ for this reaction.

Ronald Prasad
Ronald Prasad
Numerade Educator
08:22

Problem 31

A sample of gaseous $\mathrm{PCl}_{5}$ was introduced into an evacuated flask so that the pressure of pure $\mathrm{PCl}_{5}$ would be 0.50 atm at $523 \mathrm{K} .$ However, $\mathrm{PCl}_{5}$ decomposes to gaseous $\mathrm{PCl}_{3}$ and $\mathrm{Cl}_{2},$ and the actual pressure in the flask was found to be 0.84 atm. Calculate $K_{\mathrm{p}}$ for the decomposition reaction
$$
\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
at $523 \mathrm{K}$. Also calculate $K$ at this temperature.

Carina Carlos
Carina Carlos
Numerade Educator
01:31

Problem 32

A sample of $S_{8}(g)$ is placed in an otherwise empty, rigid container at $1325 \mathrm{K}$ at an initial pressure of $1.00 \mathrm{atm}$ where it decomposes to $\mathrm{S}_{2}(g)$ by the reaction
$$
\mathrm{S}_{8}(g) \rightleftharpoons 4 \mathrm{S}_{2}(g)
$$
At equilibrium, the partial pressure of $\mathrm{S}_{8}$ is 0.25 atm. Calculate $K_{\mathrm{p}}$ for this reaction at $1325 \mathrm{K}$

Ronald Prasad
Ronald Prasad
Numerade Educator
View

Problem 33

At a particular temperature, 12.0 moles of $\mathrm{SO}_{3}$ is placed into a 3.0 -L rigid container, and the $\mathrm{SO}_{3}$ dissociates by the reaction
$$
2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)
$$
At equilibrium, 3.0 moles of $\mathrm{SO}_{2}$ is present. Calculate $K$ for this reaction.

Ronald Prasad
Ronald Prasad
Numerade Educator
06:30

Problem 34

At a particular temperature, 8.0 moles of $\mathrm{NO}_{2}$ is placed into a 1.0 - $L$ container and the $\mathrm{NO}_{2}$ dissociates by the reaction
$$
2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)
$$
At equilibrium the concentration of $\mathrm{NO}(g)$ is $2.0 \mathrm{M} .$ Cal-
culate $K$ for this reaction.

Carina Carlos
Carina Carlos
Numerade Educator
10:43

Problem 35

The equilibrium constant is 0.0900 at $25^{\circ} \mathrm{C}$ for the reaction
$$
\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)
$$
For which of the following sets of conditions is the system at equilibrium? For those which are not at equilibrium, in which direction will the system shift?
a. A $1.0-\mathrm{L}$ flask contains 1.0 mole of $\mathrm{HOCl}, 0.10$ mole of $\mathrm{Cl}_{2} \mathrm{O},$ and 0.10 mole of $\mathrm{H}_{2} \mathrm{O}$
b. A 2.0 - $L$ flask contains 0.084 mole of $\mathrm{HOCl}$ 0.080 mole of $\mathrm{Cl}_{2} \mathrm{O},$ and 0.98 mole of $\mathrm{H}_{2} \mathrm{O}$
c. A 3.0 - $L$ flask contains 0.25 mole of $\mathrm{HOCl}$ 0.0010 mole of $\mathrm{Cl}_{2} \mathrm{O},$ and 0.56 mole of $\mathrm{H}_{2} \mathrm{O}$

Carina Carlos
Carina Carlos
Numerade Educator
09:59

Problem 36

The equilibrium constant is 0.0900 at $25^{\circ} \mathrm{C}$ for the reaction
$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)$
For which of the following sets of conditions is the system at equilibrium? For those which are not at equilibrium, in which direction will the system shift?
a. $P_{\mathrm{H}_{2} \mathrm{O}}=1.00 \mathrm{atm}, P_{\mathrm{C}_{2} \mathrm{O}}=1.00 \mathrm{atm}, P_{\mathrm{HOC}}=1.00 \mathrm{atm}$
b. $P_{\mathrm{H}_{2} \mathrm{O}}=200 .$ torr, $P_{\mathrm{C}_{2} \mathrm{O}}=49.8$ torr, $P_{\mathrm{HOCl}}=21.0$ torr
c. $P_{\mathrm{H}_{2} \mathrm{O}}=296$ torr, $P_{\mathrm{C}_{2} \mathrm{O}}=15.0$ torr, $P_{\mathrm{HOC}}=20.0$ torr

Carina Carlos
Carina Carlos
Numerade Educator
13:36

Problem 37

At $900 .^{\circ} \mathrm{C}, K_{\mathrm{p}}=1.04$ for the reaction
$$
\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)
$$
At a low temperature dry ice (solid $\mathrm{CO}_{2}$ ), calcium oxide, and calcium carbonate are introduced into a 50.0 - $\mathrm{L}$ reaction chamber. The temperature is raised to $900 .^{\circ} \mathrm{C} .$ For the following mixtures, will the initial amount of calcium oxide increase, decrease, or remain the same as the system moves toward equilibrium?
a. $655 \mathrm{g}$ of $\mathrm{CaCO}_{3}, 95.0 \mathrm{g}$ of $\mathrm{CaO}, 58.4 \mathrm{g}$ of $\mathrm{CO}_{2}$
b. $780 \mathrm{g}$ of $\mathrm{CaCO}_{3}, 1.00 \mathrm{g}$ of $\mathrm{CaO}, 23.76 \mathrm{g}$ of $\mathrm{CO}_{2}$
c. $0.14 \mathrm{g}$ of $\mathrm{CaCO}_{3}, 5000 \mathrm{g}$ of $\mathrm{CaO}, 23.76 \mathrm{g}$ of $\mathrm{CO}_{2}$
d. $715 \mathrm{g}$ of $\mathrm{CaCO}_{3}, 813 \mathrm{g}$ of $\mathrm{CaO}, 4.82 \mathrm{g}$ of $\mathrm{CO}_{2}$

Carina Carlos
Carina Carlos
Numerade Educator
03:27

Problem 38

At a particular temperature, $K=3.75$ for the reaction
$$
\mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)+\mathrm{NO}(g)
$$
If all four gases had initial concentrations of $0.800 \mathrm{M}$ calculate the equilibrium concentrations of the gases.

Ronald Prasad
Ronald Prasad
Numerade Educator
18:00

Problem 39

At $25^{\circ} \mathrm{C}, K=0.090$ for the reaction
$$
\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g)
$$
Calculate the concentrations of all species at equilibrium for each of the following cases.
a. $1.0 \mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$ and $2.0 \mathrm{g}$ of $\mathrm{Cl}_{2} \mathrm{O}$ are mixed in a $1.0-\mathrm{L}$
flask.
b. 1.0 mole of pure HOCl is placed in a 2.0 - $\mathrm{L}$ flask.

Carina Carlos
Carina Carlos
Numerade Educator
17:05

Problem 40

For the reaction below at a certain temperature, it is found that the equilibrium concentrations in a $5.00-\mathrm{L}$ rigid container are $\left[\mathrm{H}_{2}\right]=0.0500 \mathrm{M},\left[\mathrm{F}_{2}\right]=0.0100 \mathrm{M},$ and
$[\mathrm{HF}]=0.400 \mathrm{M}$
$$
\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)
$$
If 0.200 mole of $\mathrm{F}_{2}$ is added to this equilibrium mixture, calculate the concentrations of all gases once equilibrium is reestablished.

Carina Carlos
Carina Carlos
Numerade Educator
06:48

Problem 41

At $1100 \mathrm{K}, K_{\mathrm{p}}=0.25$ for the following reaction:
$$
2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)
$$
Calculate the equilibrium partial pressures of $\mathrm{SO}_{2}, \mathrm{O}_{2}$ and $\mathrm{SO}_{3}$ produced from an initial mixture in which $P_{\mathrm{SO}_{2}}=$ $P_{\mathrm{O}_{2}}=0.50 \mathrm{atm}$ and $P_{\mathrm{SO}_{3}}=0$

Carina Carlos
Carina Carlos
Numerade Educator
05:24

Problem 42

At $2200^{\circ} \mathrm{C}, K=0.050$ for the reaction
$$
\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)
$$
What is the partial pressure of NO at equilibrium assuming the $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ had initial pressures of 0.80 atm and 0.20 atm, respectively?

Carina Carlos
Carina Carlos
Numerade Educator
09:06

Problem 43

A type of reaction we will study is that having a very small $K$ value $(K<<1) .$ Solving for equilibrium concentrations in an equilibrium problem usually requires many mathematical operations to be performed. However, the math involved in solving equilibrium problems for reactions having small $K$ values $(K<<1)$ is simplified. What assumption is made when solving equilibrium concentrations for reactions having small $K$ values? Whenever assumptions are made, they must be checked for validity. In general, the "5\% rule" is used to check the validity of assuming that $x$ (or $2 x, 3 x,$ and so on) is very small compared to some number. When $x$ (or $2 x, 3 x,$ and so on) is less than $5 \%$ of the number the assumption was made against, then the assumption is said to be valid. If the $5 \%$ rule fails, what do you do to solve for the equilibrium concentrations?

Carina Carlos
Carina Carlos
Numerade Educator
35:54

Problem 44

At $35^{\circ} \mathrm{C}, K=1.6 \times 10^{-5}$ for the reaction
$$
2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)
$$
Calculate the concentrations of all species at equilibrium for each of the following original mixtures.
a. 2.0 moles of pure $\mathrm{NOCl}$ in a $2.0-\mathrm{L}$ flask
b. 2.0 moles of $\mathrm{NO}$ and 1.0 mole of $\mathrm{Cl}_{2}$ in a 1.0 - $\mathrm{L}$ flask
c. 1.0 mole of $\mathrm{NOCl}$ and 1.0 mole of $\mathrm{NO}$ in a 1.0 - $\mathrm{L}$ flask
d. 3.0 moles of $\mathrm{NO}$ and 1.0 mole of $\mathrm{Cl}_{2}$ in a 1.0 - $\mathrm{L}$ flask
e. 2.0 moles of $\mathrm{NOCl}, 2.0$ moles of $\mathrm{NO},$ and 1.0 mole of $\mathrm{Cl}_{2}$ in a 1.0 - $\mathrm{L}$ flask
f. $1.00 \mathrm{mol} / \mathrm{L}$ concentration of all three gases

Carina Carlos
Carina Carlos
Numerade Educator
02:18

Problem 45

At a particular temperature, $K=2.0 \times 10^{-6}$ for the reaction
$$
2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)
$$If 2.0 moles of $\mathrm{CO}_{2}$ is initially placed into a $5.0-\mathrm{L}$ vessel, calculate the equilibrium concentrations of all species.

Ronald Prasad
Ronald Prasad
Numerade Educator
17:12

Problem 46

At a particular temperature, $K_{\mathrm{p}}=0.25$ for the reaction
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)
$$
a. A flask containing only $\mathrm{N}_{2} \mathrm{O}_{4}$ at an initial pressure of 4.5 atm is allowed to reach equilibrium. Calculate the equilibrium partial pressures of the gases.
b. A flask containing only $\mathrm{NO}_{2}$ at an initial pressure of 9.0 atm is allowed to reach equilibrium. Calculate the equilibrium partial pressures of the gases.
c. From your answers to parts a and b, does it matter from which direction an equilibrium position is reached?
d. The volume of the container in part a is decreased to one-half the original volume. Calculate the new equilibrium partial pressures.

Carina Carlos
Carina Carlos
Numerade Educator
01:30

Problem 47

For the reaction below, $K_{\mathrm{p}}=1.16$ at $800 .^{\circ} \mathrm{C}$
$$
\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)
$$
If a 20.0 -g sample of $\mathrm{CaCO}_{3}$ is put into a 10.0 - $\mathrm{L}$ container and heated to $800 .^{\circ} \mathrm{C},$ what percentage by mass of the $\mathrm{CaCO}_{3}$ will react to reach equilibrium?

Teesta Dasgupta
Teesta Dasgupta
University of Pittsburgh - Main Campus
01:59

Problem 48

At $25^{\circ} \mathrm{C}, K_{\mathrm{p}}=2.9 \times 10^{-3}$ for the reaction
$$
\mathrm{NH}_{4} \mathrm{OCONH}_{2}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)
$$
In an experiment carried out at $25^{\circ} \mathrm{C},$ a certain amount of $\mathrm{NH}_{4} \mathrm{OCONH}_{2}$ is placed in an evacuated rigid container and allowed to come to equilibrium. Calculate the total pressure in the container at equilibrium.

Ronald Prasad
Ronald Prasad
Numerade Educator
15:59

Problem 49

Lexan is a plastic used to make compact discs, eyeglass lenses, and bullet-proof glass. One of the compounds used to make Lexan is phosgene $\left(\mathrm{COCl}_{2}\right),$ a poisonous gas. Phosgene is produced by the reaction
$$
\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)
$$
for which $K=4.5 \times 10^{9}$ at $100 .^{\circ} \mathrm{C}$
a. Calculate $K_{\mathrm{p}}$ at $100^{\circ} \mathrm{C}$
b. Equal moles of $\mathrm{CO}$ and $\mathrm{Cl}_{2}$ are reacted at $100 .^{\circ} \mathrm{C} .$ If the total pressure at equilibrium is 5.0 atm, calculate the equilibrium partial pressures of all the gases.

Carina Carlos
Carina Carlos
Numerade Educator
03:03

Problem 50

At a certain temperature, $K=1.1 \times 10^{3}$ for the reaction
$$
\mathrm{Fe}^{3+}(a q)+\mathrm{SCN}^{-}(a q) \rightleftharpoons \mathrm{FeSCN}^{2+}(a q)
$$

Calculate the concentrations of $\mathrm{Fe}^{3+}, \mathrm{SCN}^{-},$ and $\mathrm{FeSCN}^{2+}$ at equilibrium if 0.020 mole of $\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}$ is added to $1.0 \mathrm{L}$ of $0.10 \mathrm{M} \mathrm{KSCN} .$ (Neglect any volume change.)

Ronald Prasad
Ronald Prasad
Numerade Educator
03:09

Problem 51

Which of the following statements is(are) true? Correct the false statement(s).
a. When a reactant is added to a system at equilibrium at a given temperature, the reaction will shift right to reestablish equilibrium.
b. When a product is added to a system at equilibrium at
a given temperature, the value of $K$ for the reaction will increase when equilibrium is reestablished.
c. When temperature is increased for a reaction at equilibrium, the value of $K$ for the reaction will increase.
d. Addition of a catalyst (a substance that increases the speed of the reaction) has no effect on the equilibrium position.

Teesta Dasgupta
Teesta Dasgupta
University of Pittsburgh - Main Campus
10:48

Problem 52

How will the equilibrium position of a gas-phase reaction be affected if the volume of the reaction vessel changes? Are there reactions that will not have their equilibria shifted by a change in volume? Explain. Why does changing the pressure in a rigid container by adding an inert gas not shift the equilibrium position for a gas-phase reaction?

Carina Carlos
Carina Carlos
Numerade Educator
06:34

Problem 53

Suppose the reaction system
$$
\mathrm{UO}_{2}(s)+4 \mathrm{HF}(g) \rightleftharpoons \mathrm{UF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)
$$
has already reached equilibrium. Predict the effect that each of the following changes will have on the equilibrium position. Tell whether the equilibrium will shift to the right, will shift to the left, or will not be affected.
a. More $\mathrm{UO}_{2}(s)$ is added to the system.
b. The reaction is performed in a glass reaction vessel; $\mathrm{HF}(g)$ attacks and reacts with glass.
c. Water vapor is removed.

Carina Carlos
Carina Carlos
Numerade Educator
09:20

Problem 54

Consider the reaction
$$
\mathrm{Fe}^{3+}(a q)+\mathrm{SCN}^{-}(a q) \rightleftharpoons \mathrm{FeSCN}^{2+}(a q)
$$
How will the equilibrium position shift if
a. water is added, doubling the volume?
b. $A g N O_{3}(a q)$ is added? (AgSCN is insoluble.)
c. $\mathrm{NaOH}(a q)$ is added? $\left[\mathrm{Fe}(\mathrm{OH})_{3} \text { is insoluble. }\right]$
d. $\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q)$ is added?

Carina Carlos
Carina Carlos
Numerade Educator
09:56

Problem 55

Chromium(VI) forms two different oxyanions, the orange dichromate ion $\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right),$ and the yellow chromate ion $\left(\mathrm{CrO}_{4}^{2-}\right) .$ (See the photos below.) The equilibrium reaction between the two ions is
$$
\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons 2 \mathrm{CrO}_{4}^{2-}(a q)+2 \mathrm{H}^{+}(a q)
$$
Explain why orange dichromate solutions turn yellow when sodium hydroxide is added.
(FIGURE CAN'T COPY)

Carina Carlos
Carina Carlos
Numerade Educator
01:40

Problem 56

What will happen to the number of moles of $\mathrm{SO}_{3}$ in equilibrium with $\mathrm{SO}_{2}$ and $\mathrm{O}_{2}$ in the reaction
$$
2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)
$$
in each of the following cases?
a. Oxygen gas is added.
b. The pressure is increased by decreasing the volume of the reaction container.
c. In a rigid reaction container, the pressure is increased by adding argon gas.
d. The temperature is decreased (the reaction is endothermic).
e. Gaseous sulfur dioxide is removed.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:16

Problem 57

An important reaction in the commercial production of hydrogen is
$$
\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)
$$
How will this system at equilibrium shift in each of the five following cases?
a. Gaseous carbon dioxide is removed.
b. Water vapor is added.
c. In a rigid reaction container, the pressure is increased by adding helium gas.
d. The temperature is increased (the reaction is exothermic).
e. The pressure is increased by decreasing the volume of the reaction container.

Ronald Prasad
Ronald Prasad
Numerade Educator
08:38

Problem 58

Hydrogen for use in ammonia production is produced by the reaction
$$
\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \frac{\text { Ni catalyst }}{750^{\circ} \mathrm{C}} \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)
$$
What will happen to a reaction mixture at equilibrium if
a. $\mathrm{H}_{2} \mathrm{O}(g)$ is removed?
b. the temperature is increased (the reaction is endothermic)?
c. an inert gas is added to a rigid reaction container?
d. $\mathrm{CO}(g)$ is removed?
e. the volume of the container is tripled?

Carina Carlos
Carina Carlos
Numerade Educator
01:56

Problem 59

In which direction will the position of the equilibrium
$$
2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)
$$
be shifted for each of the following changes?
a. $\mathrm{H}_{2}(g)$ is added.
b. $\mathrm{I}_{2}(g)$ is removed.
c. $\mathrm{HI}(g)$ is removed.
d. In a rigid reaction container, some $\operatorname{Ar}(g)$ is added.
e. The volume of the container is doubled.
f. The temperature is decreased (the reaction is exothermic).

Ronald Prasad
Ronald Prasad
Numerade Educator
03:12

Problem 60

Predict the shift in the equilibrium position that will occur for each of the following reactions when the volume of the reaction container is increased.
a. $\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})$
b. $\operatorname{PCl}_{5}(g) \rightleftharpoons \operatorname{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$
c. $\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)$
d. $\operatorname{COCl}_{2}(g) \rightleftharpoons \operatorname{CO}(g)+\mathrm{Cl}_{2}(g)$
e. $\operatorname{CaCO}_{3}(s) \rightleftharpoons \operatorname{CaO}(s)+\operatorname{CO}_{2}(g)$

Ronald Prasad
Ronald Prasad
Numerade Educator
01:06

Problem 61

Old-fashioned "smelling salts" consist of ammonium carbonate $\left[\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\right] .$ The reaction for the decomposition of ammonium carbonate
$$
\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
is endothermic. Would the smell of ammonia increase or decrease as the temperature is increased?

Ronald Prasad
Ronald Prasad
Numerade Educator
09:29

Problem 62

Ammonia is produced by the Haber process, in which nitrogen and hydrogen are reacted directly using an iron mesh impregnated with oxides as a catalyst. For the reaction
$$
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)
$$equilibrium constants as a function of temperature are
$$
\begin{array}{l}
300^{\circ} \mathrm{C}, 4.34 \times 10^{-3} \\
500^{\circ} \mathrm{C}, 1.45 \times 10^{-5} \\
600^{\circ} \mathrm{C}, 2.25 \times 10^{-6}
\end{array}
$$
Is the reaction exothermic or endothermic? Explain.

Carina Carlos
Carina Carlos
Numerade Educator
03:42

Problem 63

At $25^{\circ} \mathrm{C}, K_{\mathrm{p}} \approx 1 \times 10^{-31}$ for the reaction
$$
\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)
$$
a. Calculate the concentration of NO (in molecules/cm') that can exist in equilibrium in air at $25^{\circ} \mathrm{C} .$ In air $P_{\mathrm{N}_{2}}=0.8 \mathrm{atm}$ and $P_{\mathrm{O}_{2}}=0.2 \mathrm{atm}$
b. Typical concentrations of NO in relatively pristine environments range from $10^{8}$ molecules/cm $^{3}$ to $10^{10}$ molecules $/ \mathrm{cm}^{3} .$ Why is there a discrepancy between these values and your answer to part a?

Ronald Prasad
Ronald Prasad
Numerade Educator
16:32

Problem 64

Given the following equilibrium constants at $427^{\circ} \mathrm{C}$
$\mathrm{Na}_{2} \mathrm{O}(s) \rightleftharpoons 2 \mathrm{Na}(l)+\frac{1}{2} \mathrm{O}_{2}(g) \quad K_{1}=2 \times 10^{-25}$
$\mathrm{NaO}(g) \rightleftharpoons \mathrm{Na}(l)+\frac{1}{2} \mathrm{O}_{2}(g) \quad K_{2}=2 \times 10^{-5}$
$\mathrm{Na}_{2} \mathrm{O}_{2}(s) \rightleftharpoons 2 \mathrm{Na}(l)+\mathrm{O}_{2}(g) \quad K_{3}=5 \times 10^{-29}$
$\mathrm{NaO}_{2}(s) \rightleftharpoons \mathrm{Na}(l)+\mathrm{O}_{2}(g) \quad K_{4}=3 \times 10^{-14}$
determine the values for the equilibrium constants for the following reactions.
a. $\mathrm{Na}_{2} \mathrm{O}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{Na}_{2} \mathrm{O}_{2}(s)$
b. $\mathrm{NaO}(g)+\mathrm{Na}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{O}_{2}(s)+\mathrm{Na}(l)$
c. $2 \mathrm{NaO}(g) \rightleftharpoons \mathrm{Na}_{2} \mathrm{O}_{2}(s)$
(Hint: When reaction equations are added, the equilibrium expressions are multiplied.)

Carina Carlos
Carina Carlos
Numerade Educator
07:13

Problem 65

Calculate a value for the equilibrium constant for the reaction
$$
\mathrm{O}_{2}(g)+\mathrm{O}(g) \rightleftharpoons \mathrm{O}_{3}(g)
$$
given that
$$
\mathrm{NO}_{2}(g) \stackrel{\text { bv }}{=} \mathrm{NO}(g)+\mathrm{O}(g) \quad K=6.8 \times 10^{-49}
$$
$\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \quad K=5.8 \times 10^{-34}$

Carina Carlos
Carina Carlos
Numerade Educator
06:43

Problem 66

Given $K=3.50$ at $45^{\circ} \mathrm{C}$ for the reaction
$$
\mathrm{A}(g)+\mathrm{B}(g) \leftrightharpoons \mathrm{C}(g)
$$
and $K=7.10$ at $45^{\circ} \mathrm{C}$ for the reaction
$$
2 \mathrm{A}(g)+\mathrm{D}(g) \leftrightharpoons \mathrm{C}(g)
$$
what is the value of $K$ at the same temperature for the reaction
$$
\mathrm{C}(g)+\mathrm{D}(g) \leftrightharpoons 2 \mathrm{B}(g)
$$
What is the value of $K_{\mathrm{p}}$ at $45^{\circ} \mathrm{C}$ for the reaction? Starting with 1.50 atm partial pressures of both $\mathrm{C}$ and $\mathrm{D},$ what is the mole fraction of $\mathrm{B}$ once equilibrium is reached?

Ronald Prasad
Ronald Prasad
Numerade Educator
08:33

Problem 67

An initial mixture of nitrogen gas and hydrogen gas is reacted in a rigid container at a certain temperature as follows:
$$
3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)
$$
At equilibrium, the concentrations are $\left[\mathrm{H}_{2}\right]=5.0 \mathrm{M}$ $\left[\mathrm{N}_{2}\right]=8.0 \mathrm{M},$ and $\left[\mathrm{NH}_{3}\right]=4.0 \mathrm{M} .$ What were the con-
centrations of nitrogen gas and hydrogen gas that were reacted initially?

Carina Carlos
Carina Carlos
Numerade Educator
02:07

Problem 68

At $25^{\circ} \mathrm{C}, K_{\mathrm{p}}=5.3 \times 10^{5}$ for the reaction
$$
\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)
$$
When a certain partial pressure of $\mathrm{NH}_{3}(g)$ is put into an otherwise empty rigid vessel at $25^{\circ} \mathrm{C},$ equilibrium is reached when $50.0 \%$ of the original ammonia has decomposed. What was the original partial pressure of ammonia before any decomposition occurred?

Ronald Prasad
Ronald Prasad
Numerade Educator
21:01

Problem 69

A $2.4156-\mathrm{g}$ sample of $\mathrm{PCl}_{5}$ was placed in an empty $2.000-\mathrm{L}$ flask and allowed to decompose to $\mathrm{PCl}_{3}$ and $\mathrm{Cl}_{2}$ at $250.0^{\circ} \mathrm{C}$
$$
\operatorname{PCl}_{5}(g) \rightleftharpoons \operatorname{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
At equilibrium the total pressure inside the flask was observed to be 358.7 torr.
a. Calculate the partial pressure of each gas at equilibrium and the value of $K_{\mathrm{p}}$ at $250.0^{\circ} \mathrm{C}$
b. What are the new equilibrium pressures if 0.250 mole of $\mathrm{Cl}_{2}$ gas is added to the flask?

Carina Carlos
Carina Carlos
Numerade Educator
02:38

Problem 70

At $25^{\circ} \mathrm{C},$ gaseous $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ decomposes to $\mathrm{SO}_{2}(g)$ and $\mathrm{Cl}_{2}(g)$
to the extent that $12.5 \%$ of the original $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ (by moles) has decomposed to reach equilibrium. The total pressure (at equilibrium) is 0.900 atm. Calculate the value of $K_{\mathrm{p}}$ for this system.

Ronald Prasad
Ronald Prasad
Numerade Educator
03:46

Problem 71

The partial pressures of an equilibrium mixture of $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ and $\mathrm{NO}_{2}(g)$ are $P_{\mathrm{N}_{2} \mathrm{O}_{4}}=0.34$ atm and $P_{\mathrm{NO}_{2}}=1.20 \mathrm{atm}$ at
a certain temperature. The volume of the container is doubled. Calculate the partial pressures of the two gases when a new equilibrium is established.

Ronald Prasad
Ronald Prasad
Numerade Educator
15:53

Problem 72

For the reaction
$$
\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
at $600 . \mathrm{K},$ the equilibrium constant is $11.5 .$ Suppose that $2.450 \mathrm{g}$ of $\mathrm{PCl}_{5}$ is placed in an evacuated $500 .-\mathrm{mL}$ bulb, which is then heated to $600 . \mathrm{K}$
a. What would the pressure of $\mathrm{PCl}_{5}$ be if it did not dissociate?
b. What is the partial pressure of $\mathrm{PCl}_{5}$ at equilibrium?
c. What is the total pressure in the bulb at equilibrium?
d. What is the degree of dissociation of $\mathrm{PCl}_{5}$ at equilibrium?

Carina Carlos
Carina Carlos
Numerade Educator
19:48

Problem 73

At $125^{\circ} \mathrm{C}, K_{\mathrm{p}}=0.25$ for the reaction
$$
2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
A $1.00-$ L flask containing $10.0 \mathrm{g}$ of $\mathrm{NaHCO}_{3}$ is evacuated and heated to $125^{\circ} \mathrm{C}$
a. Calculate the partial pressures of $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ after equilibrium is established.
b. Calculate the masses of $\mathrm{NaHCO}_{3}$ and $\mathrm{Na}_{2} \mathrm{CO}_{3}$ present at equilibrium.
c. Calculate the minimum container volume necessary for all the $\mathrm{NaHCO}_{3}$ to decompose.

Carina Carlos
Carina Carlos
Numerade Educator
07:42

Problem 74

The gas arsine $\left(\mathrm{AsH}_{3}\right)$ decomposes as follows:
$$
2 \mathrm{AsH}_{3}(g) \rightleftharpoons 2 \mathrm{As}(s)+3 \mathrm{H}_{2}(g)
$$
In an experiment pure $\mathrm{AsH}_{3}(g)$ was placed in an empty, rigid, sealed flask at a pressure of 392.0 torr. After $48 \mathrm{h}$ the pressure in the flask was observed to be constant at 488.0 torr.
a. Calculate the equilibrium pressure of $\mathrm{H}_{2}(g)$
b. Calculate $K_{\mathrm{p}}$ for this reaction.

Carina Carlos
Carina Carlos
Numerade Educator
04:46

Problem 75

For the reaction
$$
\mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{HS}(s)
$$
$K=400 .$ at $35.0^{\circ} \mathrm{C} .$ If 2.00 moles each of $\mathrm{NH}_{3}, \mathrm{H}_{2} \mathrm{S},$ and
NH $_{4}$ HS are placed in a $5.00-$ L vessel, what mass of NH,HS will be present at equilibrium? What is the pressure of $\mathrm{H}_{2} \mathrm{S}$ at equilibrium?

Ronald Prasad
Ronald Prasad
Numerade Educator
05:41

Problem 76

The hydrocarbon naphthalene was frequently used in mothballs until recently, when it was discovered that human inhalation of naphthalene vapors can lead to hemolytic anemia. Naphthalene is $93.71 \%$ carbon by mass, and a 0.256 -mole sample of naphthalene has a mass of 32.8 g. What is the molecular formula of naphthalene? This compound works as a pesticide in mothballs by sublimation of the solid so that it fumigates enclosed spaces with its vapors according to the equation
Naphthalene(s) $\leftrightharpoons$ naphthalene(g)
$$
K=4.29 \times 10^{-6}(\text {at } 298 \mathrm{K})
$$
If $3.00 \mathrm{g}$ of solid naphthalene is placed in an enclosed space with a volume of $5.00 \mathrm{L}$ at $25^{\circ} \mathrm{C},$ what percentage of the naphthalene will have sublimed once equilibrium has been established?

Ronald Prasad
Ronald Prasad
Numerade Educator
14:41

Problem 77

Consider the decomposition of the compound $\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}$ as follows:
$$
\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+3 \mathrm{CO}(g)
$$
When a 5.63 -g sample of pure $\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}_{3}(g)$ was sealed in an otherwise empty $2.50-\mathrm{L}$ flask and heated to $200 .^{\circ} \mathrm{C},$ the pressure in the flask gradually rose to 1.63 atm and remained at that value. Calculate $K$ for this reaction.

Carina Carlos
Carina Carlos
Numerade Educator
05:45

Problem 78

A sample of $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ is placed in an empty cylinder at $25^{\circ} \mathrm{C} .$ After equilibrium is reached, the total pressure is
1.5 atm, and $16 \%$ (by moles) of the original $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ has dissociated to NO $_{2}(g)$
a. Calculate the value of $K_{\mathrm{p}}$ for this dissociation reaction at $25^{\circ} \mathrm{C}$
b. If the volume of the cylinder is increased until the total pressure is 1.0 atm (the temperature of the system remains constant), calculate the equilibrium pressure of $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ and $\mathrm{NO}_{2}(g)$
c. What percentage (by moles) of the original $\mathrm{N}_{2} \mathrm{O}_{4}(g)$ is dissociated at the new equilibrium position (total pressure $=1.00 \mathrm{atm}) ?$

Ronald Prasad
Ronald Prasad
Numerade Educator
08:08

Problem 79

Nitric oxide and bromine at initial partial pressures of 98.4 torr and 41.3 torr, respectively, were allowed to react at $300 .$ K. At equilibrium the total pressure was 110.5 torr. The reaction is
$$
2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)
$$
a. Calculate the value of $K_{\mathrm{p}}$
b. What would be the partial pressures of all species if $\mathrm{NO}$ and $\mathrm{Br}_{2},$ both at an initial partial pressure of 0.30 atm, were allowed to come to equilibrium at this temperature?

Ronald Prasad
Ronald Prasad
Numerade Educator
06:21

Problem 80

Consider the decomposition equilibrium for dinitrogen pentoxide:
$$
2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightleftharpoons 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)
$$
At a certain temperature and a total pressure of $1.00 \mathrm{atm}$ the $\mathrm{N}_{2} \mathrm{O}_{5}$ is $0.50 \%$ decomposed (by moles) at equilibrium.
a. If the volume is increased by a factor of $10.0,$ will the mole percent of $\mathrm{N}_{2} \mathrm{O}_{5}$ decomposed at equilibrium be greater than, less than, or equal to $0.50 \% ?$ Explain your answer.
b. Calculate the mole percent of $\mathrm{N}_{2} \mathrm{O}_{5}$ that will be decomposed at equilibrium if the volume is increased by a factor of 10.0

Ronald Prasad
Ronald Prasad
Numerade Educator
04:45

Problem 81

Consider the reaction
$$
\mathrm{P}_{4}(g) \longrightarrow 2 \mathrm{P}_{2}(g)
$$
where $K_{p}=1.00 \times 10^{-1}$ at $1325 \mathrm{K} .$ In an experiment where $P_{4}(g)$ was placed in a container at $1325 \mathrm{K},$ the equilibrium mixture of $\mathrm{P}_{4}(g)$ and $\mathrm{P}_{2}(g)$ has a total pressure of 1.00 atm. Calculate the equilibrium pressures of $P_{4}(g)$ and $\mathrm{P}_{2}(g) .$ Calculate the fraction (by moles) of $\mathrm{P}_{4}(g)$ that has dissociated to reach equilibrium.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:46

Problem 82

Suppose 1.50 atm of $\mathrm{CH}_{4}(g), 2.50$ atm of $\mathrm{C}_{2} \mathrm{H}_{6}(g),$ and 15.00 atm of $\mathrm{O}_{2}(g)$ are placed in a flask at a given temperature. The reactions are
$$
\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \quad K_{\mathrm{p}}=1.0 \times 10^{4}
$$
$2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \rightleftharpoons 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
$$
K_{\mathrm{p}}=1.0 \times 10^{8}
$$
Calculate the equilibrium pressures of all gases.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:45

Problem 83

Consider the reaction
$$
3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g)
$$
At $175^{\circ} \mathrm{C}$ and a pressure of 128 torr, an equilibrium mixture of $\mathrm{O}_{2}$ and $\mathrm{O}_{3}$ has a density of $0.168 \mathrm{g} / \mathrm{L} .$ Calculate $K_{\mathrm{p}}$ for the above reaction at $175^{\circ} \mathrm{C}$

Amy Jiang
Amy Jiang
Numerade Educator
04:41

Problem 84

A mixture of $\mathrm{N}_{2}, \mathrm{H}_{2}$ and $\mathrm{NH}_{3}$ is at equilibrium according to the equation $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$ as depicted below.
(FIGURE CAN'T COPY)
The volume is suddenly decreased (by increasing the external pressure), and a new equilibrium is established as depicted below.
a. If the volume of the final equilibrium mixture is $1.00 \mathrm{L},$ determine the value of the equilibrium constant $K$ for the reaction. Assume temperature is constant.
b. Determine the volume of the initial equilibrium mixture assuming a final equilibrium volume of $1.00 \mathrm{L}$ and assuming a constant temperature.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:46

Problem 85

A 4.72 -g sample of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ was placed in an otherwise empty $1.00-\mathrm{L}$ flask and heated to $250 .^{\circ} \mathrm{C}$ to vaporize the methanol. Over time the methanol vapor decomposed by the following reaction:
$$
\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)
$$
After the system has reached equilibrium, a tiny hole is drilled in the side of the flask allowing gaseous compounds to effuse out of the flask. Measurements of the effusing gas show that it contains 33.0 times as much $\mathrm{H}_{2}(g)$ as $\mathrm{CH}_{3} \mathrm{OH}(g) .$ Calculate $K$ for this reaction at $250 .^{\circ} \mathrm{C}$

Teesta Dasgupta
Teesta Dasgupta
University of Pittsburgh - Main Campus
27:04

Problem 86

The compound $\mathrm{SbCl}_{5}(g)$ decomposes at high temperatures to gaseous antimony trichloride and chlorine gas. When $89.7 \mathrm{g}$ of $\mathrm{SbCl}_{5}(g)$ is placed in a 15.0 - L container at $180^{\circ} \mathrm{C}$ the $\operatorname{SbCl}_{5}(g)$ is $29.2 \%$ decomposed (by moles) after the system has reached equilibrium.
a. Calculate the value of $K$ for this reaction at $180^{\circ} \mathrm{C}$
b. Determine the number of moles of chlorine gas that must be injected into the flask to make the new equilibrium pressure of antimony trichloride half that of the original equilibrium pressure of antimony trichloride in the original experiment.

Carina Carlos
Carina Carlos
Numerade Educator
16:59

Problem 87

At $207^{\circ} \mathrm{C}, K_{\mathrm{p}}=0.267$ for the reaction
$$
\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)
$$
a. If 0.100 mole of $\mathrm{PCl}_{5}(g)$ is placed in an otherwise empty 12.0 -I. vessel at $207^{\circ} \mathrm{C},$ calculate the partial pressures of $\mathrm{PCl}_{5}(g), \mathrm{PCl}_{3}(g),$ and $\mathrm{Cl}_{2}(g)$ at
equilibrium.
b. In another experiment the total pressure of an equilibrium mixture is 2.00 atm at $207^{\circ} \mathrm{C} .$ What mass of PCl $_{5}$ was introduced into a $5.00-$ L vessel to reach this equilibrium position?

Carina Carlos
Carina Carlos
Numerade Educator
05:25

Problem 88

A 1.604 -g sample of methane $\left(\mathrm{CH}_{4}\right)$ gas and $6.400 \mathrm{g}$ of oxygen gas are sealed in a $2.50-\mathrm{L}$ vessel at $411^{\circ} \mathrm{C}$ and are allowed to reach equilibrium. Methane can react with oxygen to form gaseous carbon dioxide and water vapor, or methane can react with oxygen to form gaseous carbon monoxide and water vapor. At equilibrium the pressure of oxygen is 0.326 atm, and the pressure of water vapor is 4.45 atm. Calculate the pressures of carbon monoxide and carbon dioxide present at equilibrium.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:46

Problem 89

At $1000 \mathrm{K}$ the $\mathrm{N}_{2}(g)$ and $\mathrm{O}_{2}(g)$ in air $\left(78 \% \mathrm{N}_{2}, 21 \% \mathrm{O}_{2}\right.$
by moles) react to form a mixture of $\mathrm{NO}(g)$ and $\mathrm{NO}_{2}(g)$ The values of the equilibrium constants are $1.5 \times 10^{-4}$ and $1.0 \times 10^{-5}$ for the formation of $\mathrm{NO}(g)$ and $\mathrm{NO}_{2}(g)$ respectively. At what total pressure will the partial pressures of $\mathrm{NO}(g)$ and $\mathrm{NO}_{2}(g)$ be equal in an equilibrium mixture of $\mathrm{N}_{2}(g), \mathrm{O}_{2}(g), \mathrm{NO}(g),$ and $\mathrm{NO}_{2}(g) ?$

Adriano Chikande
Adriano Chikande
Numerade Educator
03:30

Problem 90

The equilibrium constant $K_{\mathrm{p}}$ for the reaction
$$
\mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g)
$$
at $700^{\circ} \mathrm{C}$ is $0.76 .$ Determine the initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 atm at $700^{\circ} \mathrm{C}$

Ronald Prasad
Ronald Prasad
Numerade Educator
03:46

Problem 91

An 8.00 -g sample of $\mathrm{SO}_{3}$ was placed in an evacuated container, where it decomposed at $600 .^{\circ} \mathrm{C}$ according to the following reaction:
$$
\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)
$$
At equilibrium the total pressure and the density of the gaseous mixture were 1.80 atm and $1.60 \mathrm{g} / \mathrm{L},$ respectively. Calculate $K_{\mathrm{p}}$ for this reaction.

Ronald Prasad
Ronald Prasad
Numerade Educator
03:46

Problem 92

An 8.00 -g sample of $\mathrm{SO}_{3}$ was placed in an evacuated container, where it decomposed at $600 .^{\circ} \mathrm{C}$ according to the following reaction:
$$
\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)
$$
At equilibrium the total pressure and the density of the gaseous mixture were 1.80 atm and $1.60 \mathrm{g} / \mathrm{L},$ respectively. Calculate $K_{\mathrm{p}}$ for this reaction.

Ronald Prasad
Ronald Prasad
Numerade Educator
02:20

Problem 93

At $450^{\circ} \mathrm{C}, K_{\mathrm{p}}=6.5 \times 10^{-3}$ for the ammonia synthesis reaction. Assume that a reaction vessel with a movable piston initially contains 3.0 moles of $\mathrm{H}_{2}(g)$ and 1.0 mole of $\mathrm{N}_{2}(g) .$ Make a plot to show how the partial pressure of $\mathrm{NH}_{3}(g)$ present at equilibrium varies for the total pressures of $1.0 \mathrm{atm}, 10.0 \mathrm{atm}, 100 .$ atm, and $1000 .$ atm (assuming that $K_{\mathrm{p}}$ remains constant). [Note: Assume these total pressures represent the initial total pressure of $\mathrm{H}_{2}(g)$ plus $\left.\mathrm{N}_{2}(g), \text { where } P_{\mathrm{NH}_{3}}=0 .\right]$

Stephen Ho
Stephen Ho
Numerade Educator
07:44

Problem 94

A sample of gaseous nitrosyl bromide (NOBr) was placed in a container fitted with a frictionless, massless piston, where it decomposed at $25^{\circ} \mathrm{C}$ according to the following equation:
$$
2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)
$$The initial density of the system was recorded as $4.495 \mathrm{g} / \mathrm{L}$ After equilibrium was reached, the density was noted to be $4.086 \mathrm{g} / \mathrm{L}$
a. Determine the value of the equilibrium constant $K$ for the reaction.
b. If $\operatorname{Ar}(g)$ is added to the system at equilibrium at constant temperature, what will happen to the equilibrium position? What happens to the value of $K ?$ Explain each answer.

Ronald Prasad
Ronald Prasad
Numerade Educator
06:11

Problem 95

A gaseous material $\mathrm{XY}(g)$ dissociates to some extent to produce $\mathrm{X}(g)$ and $\mathrm{Y}(g):$
$$
\mathrm{XY}(g) \rightleftharpoons \mathrm{X}(g)+\mathrm{Y}(g)
$$
A 2.00 -g sample of $\mathrm{XY}$ (molar mass $=165 \mathrm{g} / \mathrm{mol}$ ) is placed in a container with a movable piston at $25^{\circ} \mathrm{C} .$ The pressure is held constant at 0.967 atm. As XY begins to dissociate, the piston moves until 35.0 mole percent of the original XY has dissociated and then remains at a constant position. Assuming ideal behavior, calculate the density of the gas in the container after the piston has stopped moving, and determine the value of $K$ for this reaction at $25^{\circ} \mathrm{C}$

Ronald Prasad
Ronald Prasad
Numerade Educator
View

Problem 96

Consider the reaction
$$
\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)
$$
for which $K=1.30 \times 10^{2} .$ Assume that 0.406 mole of $\mathrm{C}(g)$ is placed in the cylinder represented here. The temperature is $300.0 \mathrm{K},$ and the barometric pressure on the piston (which is assumed to be massless and frictionless) is
constant at 1.00 atm. The original volume [before the $0.406 \text { mole of } \mathrm{C}(g) \text { begins to decompose }]$ is $10.00 \mathrm{L} .$ What is the volume in the cylinder at equilibrium?

Susan Hallstrom
Susan Hallstrom
Numerade Educator