Chemistry

Steven S. Zumdahl, Susan A. Zumdahl

Chapter 6

Thermochemistry - all with Video Answers

Educators

Chapter Questions

Problem 1

Objects placed together eventually reach the same temperature. When you go into a room and touch a piece of metal in that room, it feels colder than a piece of plastic. Explain.

Jeffrey Aglow

Jeffrey Aglow

Numerade Educator

Problem 2

What is meant by the term lower in energy? Which is lower in energy, a mixture of hydrogen and oxygen gases or liquid water? How do you know? Which of the two is more stable? How do you know?

Jamie Huang

Numerade Educator

Problem 3

A fire is started in a fireplace by striking a match and lighting crumpled paper under some logs. Explain all the energy transfers in this scenario using the terms exothermic, endothermic, system, surroundings, potential energy, and kinefic energy in the discussion.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 4

Liquid water turns to ice. Is this process endothermic or exothermic? Explain what is occurring using the terms system, surroundings, heat, potential energy, and kinetic energy in the discussion.

Angela Deane

Numerade Educator

Problem 5

Consider the following statements: "Heat is a form of energy, and energy is conserved. The heat lost by a system must be equal to the amount of heat gained by the surroundings. Therefore, heat is conserved." Indicate everything you think is correct in these statements. Indicate everything you think is incorrect. Correct the incorrect statements and explain.

Jeffrey Aglow

Numerade Educator

Problem 6

Consider $5.5 \mathrm{~L}$ of a gas at a pressure of $3.0 \mathrm{~atm}$ in a cylinder with a movable piston. The external pressure is changed so that the volume changes to $10.5 \mathrm{~L}$.
a. Calculate the work done, and indicate the correct sign.
b. Use the preceding data but consider the process to occur in two steps. At the end of the first step, the volume is $7.0 \mathrm{~L}$. The second step results in a final volume of $10.5$ L. Calculate the work done, and indicate the correct sign.
c. Calculate the work done if after the first step the volume is $8.0 \mathrm{~L}$ and the second step leads to a volume of $10.5 \mathrm{~L}$. Does the work differ from that in part b? Explain.

Angela Deane

Numerade Educator

Problem 7

In Question 6 the work calculated for the different conditions in the various parts of the question was different even though the system had the same initial and final conditions. Based on this information, is work a state function?
a. Explain how you know that work is not a state function.
b. Why does the work increase with an increase in the number of steps?
c. Which two-step process resulted in more work, when the first step had the bigger change in volume or when the second step had the bigger change in volume? Explain.

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 8

Explain why oceanfront areas generally have smaller temperature fluctuations than inland areas.

Jamie Huang

Numerade Educator

Problem 9

Hess's law is really just another statement of the first law of thermodynamics. Explain.

Jeffrey Aglow

Numerade Educator

Problem 10

In the equation $w=-P \Delta V$, why is there a negative sign?

Angela Deane

Numerade Educator

Problem 11

Consider an airplane trip from Chicago, Illinois, to Denver, Colorado. List some path-dependent functions and some state functions for the plane trip.

Jeffrey Aglow

Numerade Educator

Problem 12

How is average bond strength related to relative potential energies of the reactants and the products?

Angela Deane

Numerade Educator

Problem 13

Assuming gasoline is pure $\mathrm{C}_{8} \mathrm{H}_{1 \mathrm{~s}}(l)$, predict the signs of $q$ and $w$ for the process of combusting gasoline into $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) .$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 14

What is the difference between $\Delta H$ and $\Delta E_{3}$ ?

Angela Deane

Numerade Educator

Problem 15

The enthalpy change for the reaction
$$
\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)
$$
is $-891 \mathrm{~kJ}$ for the reaction as written.
a. What quantity of heat is released for each mole of water formed?
b. What quantity of heat is released for each mole of oxygen reacted?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 16

For the reaction $\mathrm{HgO}(s) \rightarrow \mathrm{Hg}(l)+\frac{1}{2} \mathrm{O}_{2}(g), \Delta H=+90.7 \mathrm{~kJ}:$
a. What quantity of heat is required to produce $1 \mathrm{~mol}$ of mercury by this reaction?
b. What quantity of heat is required to produce $1 \mathrm{~mol}$ of oxygen gas by this reaction?
c. What quantity of heat would be released in the following reaction as written?
$$
2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{HgO}(s)
$$

Jamie Huang

Numerade Educator

Problem 17

The enthalpy of combustion of $\mathrm{CH}_{4}(\mathrm{~g})$ when $\mathrm{H}_{2} \mathrm{O}(l)$ is formed is $-891 \mathrm{~kJ} / \mathrm{mol}$ and the enthalpy of combustion of $\mathrm{CH}_{4}(\mathrm{~g})$ when $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ is formed is $-803 \mathrm{~kJ} / \mathrm{mol} .$ Use these data and Hess's law to determine the enthalpy of vaporization for water.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 18

The enthalpy change for a reaction is a state function and it is an extensive property. Explain.

Angela Deane

Numerade Educator

Problem 19

Standard enthalpies of formation are relative values. What are $\Delta H_{\mathrm{f}}^{\circ}$ values relative to?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 20

Why is it a good idea to rinse your thermos bottle with hot water before filling it with hot coffee?

Jeffrey Aglow

Numerade Educator

Problem 21

What is incomplete combustion of fossil fuels? Why can this be a problem?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 22

Explain the advantages and disadvantages of hydrogen as an alternative fuel.

Jamie Huang

Numerade Educator

Problem 23

Calculate the kinetic energy of a baseball (mass $=5.25 \mathrm{oz}$ ) with a velocity of $1.0 \times 10^{2} \mathrm{mi} / \mathrm{h}$.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 24

Calculate the kinetic energy of an object with a mass of $1.0 \times$ $10^{-5} \mathrm{~g}$ and a velocity of $2.0 \times 10^{5} \mathrm{~cm} / \mathrm{s}$

Anas Venkitta

Numerade Educator

Problem 25

Which has the greater kinetic energy, an object with a mass of 2.0 $\mathrm{kg}$ and a velocity of $1.0 \mathrm{~m} / \mathrm{s}$ or an object with a mass of $1.0 \mathrm{~kg}$ and a velocity of $2.0 \mathrm{~m} / \mathrm{s}$ ?

Jamie Huang

Numerade Educator

Problem 26

Consider the accompanying diagram. Ball $\mathrm{A}$ is allowed to fall and strike ball B. Assume that all of ball A's energy is transferred to ball $\mathrm{B}$, at point $\mathrm{I}$, and that there is no loss of energy to other sources. What is the kinetic energy and the potential energy of ball $\mathrm{B}$ at point $\mathrm{II}$ ? The potential energy is given by $\mathrm{PE}=m g z$, where $m$ is the mass in kilograms, $g$ is the gravitational constant $\left(9.81 \mathrm{~m} / \mathrm{s}^{2}\right)$, and $z$ is the distance in meters.

Jamie Huang

Numerade Educator

Problem 27

A gas absorbs $45 \mathrm{~kJ}$ of heat and does $29 \mathrm{~kJ}$ of work. Calculate $\Delta E$.

JD

Jasmine Dogu

Numerade Educator

Problem 28

A system releases $125 \mathrm{~kJ}$ of heat while $104 \mathrm{~kJ}$ of work is done
on it. Calculate $\Delta E$.

Jamie Huang

Numerade Educator

Problem 29

Calculate $\Delta E$ for each of the following.
a. $q=-47 \mathrm{~kJ}, w=+88 \mathrm{~kJ}$
b. $q=+82 \mathrm{~kJ}, w=-47 \mathrm{~kJ}$
c. $q=+47 \mathrm{~kJ}, w=0$
d. In which of these cases do the surroundings do work on the system?

Angela Deane

Numerade Educator

Problem 30

A system undergoes a process consisting of the following two steps:

Step 1: The system absorbs $72 \mathrm{~J}$ of heat while $35 \mathrm{~J}$ of work is done on it.

Step 2: The system absorbs $35 \mathrm{~J}$ of heat while performing $72 \mathrm{~J}$ of work.
Calculate $\Delta E$ for the overall process.

Jamie Huang

Numerade Educator

Problem 31

If the internal energy of a thermodynamic system is increased by $300 .$ J while $75 \mathrm{~J}$ of expansion work is done, how much heat was transferred and in which direction, to or from the system?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 32

Calculate the internal energy change for each of the following.
a. One hundred (100.) joules of work is required to compress a gas. At the same time, the gas releases $23 \mathrm{~J}$ of heat.
b. A piston is compressed from a volume of $8.30 \mathrm{~L}$ to $2.80 \mathrm{~L}$ against a constant pressure of $1.90 \mathrm{~atm} .$ In the process, there is a heat gain by the system of $350 . \mathrm{J}$.
c. A piston expands against $1.00 \mathrm{~atm}$ of pressure from $11.2 \mathrm{~L}$ to $29.1 \mathrm{~L}$. In the process, $1037 \mathrm{~J}$ of heat is absorbed.

Jamie Huang

Numerade Educator

Problem 33

A sample of an ideal gas at $15.0 \mathrm{~atm}$ and $10.0 \mathrm{~L}$ is allowed to expand against a constant external pressure of $2.00 \mathrm{~atm}$ at a constant temperature. Calculate the work in units of $\mathrm{kJ}$ for the gas expansion. (Hint: Boyle's law applies.)

Noah Barguez-Arias

Noah Barguez-Arias

Numerade Educator

Problem 34

A piston performs work of $210 . \mathrm{L} \cdot \mathrm{atm}$ on the surroundings, while the cylinder in which it is placed expands from $10 . \mathrm{L}$ to 25 L. At the same time, $45 \mathrm{~J}$ of heat is transferred from the surroundings to the system. Against what pressure was the piston working?

Osman Elomda

Numerade Educator

Problem 35

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is $40 . \mathrm{cm}^{3} .$ If the combustion of this mixture releases 950. J of energy, to what volume will the gases expand against a constant pressure of 650 . torr if all the energy of combustion is converted into work to push back the piston?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 36

As a system increases in volume, it absorbs $52.5 \mathrm{~J}$ of energy in the form of heat from the surroundings. The piston is working against a pressure of $0.500 \mathrm{~atm}$. The final volume of the system is $58.0 \mathrm{~L}$. What was the initial volume of the system if the internal energy of the system decreased by $102.5 \mathrm{~J}$ ?

Angela Deane

Numerade Educator

Problem 37

A balloon filled with $39.1$ mol helium has a volume of $876 \mathrm{~L}$ at $0.0^{\circ} \mathrm{C}$ and $1.00$ atm pressure. The temperature of the balloon is increased to $38.0^{\circ} \mathrm{C}$ as it expands to a volume of $998 \mathrm{~L}$, the pressure remaining constant. Calculate $q, w$, and $\Delta E$ for the helium in the balloon. (The molar heat capacity for helium gas is $20.8 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot$ mol. $)$

Shalini Tyagi

Numerade Educator

Problem 38

One mole of $\mathrm{H}_{2} \mathrm{O}(g)$ at $1.00 \mathrm{~atm}$ and $100 .^{\circ} \mathrm{C}$ occupies a volume of $30.6 \mathrm{~L}$. When one mole of $\mathrm{H}_{2} \mathrm{O}(g)$ is condensed to one mole of $\mathrm{H}_{2} \mathrm{O}(l)$ at $1.00 \mathrm{~atm}$ and $100 .{ }^{\circ} \mathrm{C}, 40.66 \mathrm{~kJ}$ of heat is released.
If the density of $\mathrm{H}_{2} \mathrm{O}(l)$ at this temperature and pressure is $0.996 \mathrm{~g} / \mathrm{cm}^{3}$, calculate $\Delta E$ for the condensation of one mole of water at $1.00 \mathrm{~atm}$ and $100 .{ }^{\circ} \mathrm{C}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 39

One of the components of polluted air is NO. It is formed in the high-temperature environment of internal combustion engines by the following reaction:
$$
\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) \quad \Delta H=180 \mathrm{~kJ}
$$
Why are high temperatures needed to convert $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ to NO?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 40

The reaction
$$
\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q)
$$
is the last step in the commercial production of sulfuric acid. The enthalpy change for this reaction is $-227 \mathrm{~kJ} .$ In designing a sulfuric acid plant, is it necessary to provide for heating or cooling of the reaction mixture? Explain.

Angela Deane

Numerade Educator

Problem 41

Are the following processes exothermic or endothermic?
a. When solid $\mathrm{KBr}$ is dissolved in water, the solution gets coldel
b. Natural gas $\left(\mathrm{CH}_{4}\right)$ is burned in a furnace.
c. When concentrated $\mathrm{H}_{2} \mathrm{SO}_{4}$ is added to water, the solution get very hot.
d. Water is boiled in a teakettle.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 42

Are the following processes exothermic or endothermic?
a. the combustion of gasoline in a car engine
b. water condensing on a cold pipe
c. $\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)$
d. $\mathrm{F}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{~F}(\mathrm{~g})$

Jamie Huang

Numerade Educator

Problem 43

The overall reaction in a commercial heat pack can be represented as
$$
4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1652 \mathrm{~kJ}
$$
a. How much heat is released when $4.00 \mathrm{~mol}$ iron is reacted with excess $\mathrm{O}_{2}$ ?
b. How much heat is released when $1.00 \mathrm{~mol} \mathrm{Fe}_{2} \mathrm{O}_{3}$ is produced?
c. How much heat is released when $1.00 \mathrm{~g}$ iron is reacted with excess $\mathrm{O}_{2} ?$
d. How much heat is released when $10.0 \mathrm{~g} \mathrm{Fe}$ and $2.00 \mathrm{~g} \mathrm{O}_{2}$ are reacted?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 44

Consider the following reaction:
$$
2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{~kJ}
$$
a. How much heat is evolved for the production of $1.00 \mathrm{~mol}$ $\mathrm{H}_{2} \mathrm{O}(l) ?$
b. How much heat is evolved when $4.03 \mathrm{~g}$ hydrogen is reacted with excess oxygen?
c. How much heat is evolved when $186 \mathrm{~g}$ oxygen is reacted with excess hydrogen?
d. The total volume of hydrogen gas needed to fill the Hindenburg was $2.0 \times 10^{8} \mathrm{~L}$ at $1.0 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$. How much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted?

Ronald Prasad

Numerade Educator

Problem 45

Consider the combustion of propane:
$\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-2221 \mathrm{~kJ}$
Assume that all the heat in Example $6.3$ comes from the combustion of propane. What mass of propane must be burned to furnish this amount of energy assuming the heat transfer process is $60 . \%$ efficient?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 46

Consider the following reaction:
$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-891 \mathrm{~kJ}$
Calculate the enthalpy change for each of the following cases:
a. $1.00 \mathrm{~g}$ methane is burned in excess oxygen.
b. $1.00 \times 10^{3} \mathrm{~L}$ methane gas at 740 . torr and $25^{\circ} \mathrm{C}$ is burned in excess oxygen.

Angela Deane

Numerade Educator

Problem 47

For the process $\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)$ at $298 \mathrm{~K}$ and $1.0 \mathrm{~atm}, \Delta H$
is more positive than $\Delta E$ by $2.5 \mathrm{~kJ} / \mathrm{mol}$. What does the $2.5 \mathrm{~kJ} / \mathrm{mol}$ ouantity renresent?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 48

For the following reactions at constant pressure, predict if $\Delta H>$ $\Delta E, \Delta H<\Delta E$, or $\Delta H=\Delta E$
a. $2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)$
b. $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$
c. $4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$

Angela Deane

Numerade Educator

Problem 49

Consider the substances in Table 6.1. Which substance requires the largest amount of energy to raise the temperature of $25.0 \mathrm{~g}$ of the substance from $15.0^{\circ} \mathrm{C}$ to $37.0^{\circ} \mathrm{C}$ ? Calculate the energy. Which substance in Table $6.1$ has the largest temperature change when $550 . \mathrm{g}$ of the substance absorbs $10.7 \mathrm{~kJ}$ of energy? Calculate the temperature change.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 50

The specific heat capacity of silver is $0.24 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$.
a. Calculate the energy required to raise the temperature of $150.0 \mathrm{~g}$ Ag from $273 \mathrm{~K}$ to $298 \mathrm{~K}$.
b. Calculate the energy required to raise the temperature of $1.0 \mathrm{~mol} \mathrm{Ag}$ by $1.0^{\circ} \mathrm{C}$ (called the molar heat capacity of silver).
c. It takes $1.25 \mathrm{~kJ}$ of energy to heat a sample of pure silver from $12.0^{\circ} \mathrm{C}$ to $15.2^{\circ} \mathrm{C}$. Calculate the mass of the sample of silver.

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 51

A $5.00-\mathrm{g}$ sample of one of the substances listed in Table $6.1$ was heated from $25.2^{\circ} \mathrm{C}$ to $55.1^{\circ} \mathrm{C}$, requiring $133 \mathrm{~J}$ to do so. What substance was it?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 52

It takes $585 \mathrm{~J}$ of energy to raise the temperature of $125.6 \mathrm{~g}$ mercury from $20.0^{\circ} \mathrm{C}$ to $53.5^{\circ} \mathrm{C}$. Calculate the specific heat capacity and the molar heat capacity of mercury.

Angela Deane

Numerade Educator

Problem 53

A $30.0-\mathrm{g}$ sample of water at $280 . \mathrm{K}$ is mixed with $50.0 \mathrm{~g}$ water at $330 . \mathrm{K}$. Calculate the final temperature of the mixture assuming no heat loss to the surroundings.

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 54

A sample of nickel is heated to $99.8^{\circ} \mathrm{C}$ and placed in a coffeecup calorimeter containing $150.0 \mathrm{~g}$ water at $23.5^{\circ} \mathrm{C}$. After the metal cools, the final temperature of metal and water mixture is $25.0^{\circ} \mathrm{C}$. If the specific heat capacity of nickel is $0.444 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$, what mass of nickel was originally heated? Assume no heat loss to the surroundings.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 55

A $5.00-\mathrm{g}$ sample of aluminum pellets (specific heat capacity $=$ $0.89 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ ) and a $10.00-\mathrm{g}$ sample of iron pellets (specific heat capacity $=0.45 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ ) are heated to $100.0^{\circ} \mathrm{C}$. The mixture of hot iron and aluminum is then dropped into $97.3 \mathrm{~g}$ water at $22.0^{\circ} \mathrm{C}$. Calculate the final temperature of the metal and water mixture, assuming no heat loss to the surroundings.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 56

Hydrogen gives off $120 . \mathrm{J} / \mathrm{g}$ of energy when burned in oxygen, and methane gives off $50 .$ J/g under the same circumstances. If a mixture of $5.0 \mathrm{~g}$ hydrogen and $10 . \mathrm{g}$ methane is burned, and the heat released is transferred to $50.0 \mathrm{~g}$ water at $25.0^{\circ} \mathrm{C}$, what final temperature will be reached by the water?

Angela Deane

Numerade Educator

Problem 57

A $150.0-\mathrm{g}$ sample of a metal at $75.0^{\circ} \mathrm{C}$ is added to $150.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}$
at $15.0^{\circ} \mathrm{C}$. The temperature of the water rises to $18.3^{\circ} \mathrm{C}$. Calculate the specific heat capacity of the metal, assuming that all the heat lost by the metal is gained by the water.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 58

A $110 .-\mathrm{g}$ sample of copper (specific heat capacity $=0.20 \mathrm{~J} /{ }^{\circ} \mathrm{C}$.
$\mathrm{g}$ ) is heated to $82.4^{\circ} \mathrm{C}$ and then placed in a container of water at $22.3^{\circ} \mathrm{C}$. The final temperature of the water and copper is $24.9^{\circ} \mathrm{C}$. What is the mass of the water in the container, assuming that all the heat lost by the copper is gained by the water?

Shalini Tyagi

Numerade Educator

Problem 59

In a coffee-cup calorimeter, $50.0 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{AgNO}_{3}$ and $50.0 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{HCl}$ are mixed to yield the following reaction:
$$
\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s)
$$
The two solutions were initially at $22.60^{\circ} \mathrm{C}$, and the final temperature is $23.40^{\circ} \mathrm{C}$. Calculate the heat that accompanies this reaction in $\mathrm{kJ} / \mathrm{mol}$ of $\mathrm{AgCl}$ formed. Assume that the combined solution has a mass of $100.0 \mathrm{~g}$ and a specific heat capacity of $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$.

Osman Elomda

Numerade Educator

Problem 60

In a coffee-cup calorimeter, $100.0 \mathrm{~mL}$ of $1.0 \mathrm{M} \mathrm{NaOH}$ and $100.0 \mathrm{~mL}$ of $1.0 \mathrm{M} \mathrm{HCl}$ are mixed. Both solutions were originally at $24.6^{\circ} \mathrm{C}$. After the reaction, the final temperature is $31.3^{\circ} \mathrm{C}$. Assuming that all the solutions have a density of $1.0 \mathrm{~g} / \mathrm{cm}^{3}$ and a specific heat capacity of $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$, calculate the enthalpy change for the neutralization of $\mathrm{HCl}$ by $\mathrm{NaOH}$. Assume that no heat is lost to the surroundings or to the calorimeter.

Osman Elomda

Numerade Educator

Problem 61

A coffee-cup calorimeter initially contains $125 \mathrm{~g}$ water at $24.2^{\circ} \mathrm{C}$. Potassium bromide $(10.5 \mathrm{~g})$, also at $24.2^{\circ} \mathrm{C}$, is added to the water, and after the KBr dissolves, the final temperature is $21.1^{\circ} \mathrm{C}$. Calculate the enthalpy change for dissolving the salt in $\mathrm{J} / \mathrm{g}$ and $\mathrm{kJ} / \mathrm{mol}$. Assume that the specific heat capacity of the solution is $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ and that no heat is transferred to the surroundings or to the calorimeter.

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 62

In a coffee-cup calorimeter, $1.60 \mathrm{~g} \mathrm{NH}_{4} \mathrm{NO}_{3}$ is mixed with $75.0 \mathrm{~g}$ water at an initial temperature of $25.00^{\circ} \mathrm{C}$. After dissolution of the salt, the final temperature of the calorimeter contents is $23.34^{\circ} \mathrm{C}$. Assuming the solution has a heat capacity of $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ and assuming no heat loss to the calorimeter, calculate the enthalpy change for the dissolution of $\mathrm{NH}_{4} \mathrm{NO}_{3}$ in units of $\mathrm{kJ} / \mathrm{mol}$.

Angela Deane

Numerade Educator

Problem 63

Consider the dissolution of $\mathrm{CaCl}_{2}$ :
$$
\mathrm{CaCl}_{2}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) \quad \Delta H=-81.5 \mathrm{~kJ}
$$
An $11.0-\mathrm{g}$ sample of $\mathrm{CaCl}_{2}$ is dissolved in $125 \mathrm{~g}$ water, with both substances at $25.0^{\circ} \mathrm{C}$. Calculate the final temperature of the solution assuming no heat loss to the surroundings and assuming the solution has a specific heat capacity of $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$.

Lizabeth Tumminello

Lizabeth Tumminello

Numerade Educator

Problem 64

Consider the reaction
$$
\begin{array}{r}
2 \mathrm{HCl}(a q)+\mathrm{Ba}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{BaCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \\
\Delta H=-118 \mathrm{~kJ}
\end{array}
$$
Calculate the heat when $100.0 \mathrm{~mL}$ of $0.500 \mathrm{M} \mathrm{HCl}$ is mixed with $300.0 \mathrm{~mL}$ of $0.100 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}$. Assuming that the temperature of both solutions was initially $25.0^{\circ} \mathrm{C}$ and that the final mixture has a mass of $400.0 \mathrm{~g}$ and a specific heat capacity of $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$, calculate the final temperature of the mixture.

Osman Elomda

Numerade Educator

Problem 65

The heat capacity of a bomb calorimeter was determined by burning $6.79 \mathrm{~g}$ methane (energy of combustion $=-802 \mathrm{~kJ} / \mathrm{mol} \mathrm{CH}_{4}$ ) in the bomb. The temperature changed by $10.8^{\circ} \mathrm{C}$.
a. What is the heat capacity of the bomb?
b. A $12.6-\mathrm{g}$ sample of acetylene, $\mathrm{C}_{2} \mathrm{H}_{2}$, produced a temperature increase of $16.9^{\circ} \mathrm{C}$ in the same calorimeter. What is the energy of combustion of acetylene (in $\mathrm{kJ} / \mathrm{mol}$ )?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 66

The combustion of $0.1584 \mathrm{~g}$ benzoic acid increases the temperature of a bomb calorimeter by $2.54^{\circ} \mathrm{C}$. Calculate the heat capacity of this calorimeter. (The energy released by combustion of benzoic acid is $26.42 \mathrm{~kJ} / \mathrm{g} .$ ) A $0.2130-\mathrm{g}$ sample of vanillin $\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right)$ is then burned in the same calorimeter, and the temperature increases by $3.25^{\circ} \mathrm{C}$. What is the energy of combustion per gram of vanillin? Per mole of vanillin?

Jamie Huang

Numerade Educator

Problem 67

The enthalpy of combustion of solid carbon to form carbon dioxide is $-393.7 \mathrm{~kJ} / \mathrm{mol}$ carbon, and the enthalpy of combustion of carbon monoxide to form carbon dioxide is $-283.3 \mathrm{~kJ} / \mathrm{mol}$ CO. Use these data to calculate $\Delta H$ for the reaction
$$
2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g)
$$

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 68

Combustion reactions involve reacting a substance with oxygen. When compounds containing carbon and hydrogen are combusted, carbon dioxide and water are the products. Using the enthalpies of combustion for $\mathrm{C}_{4} \mathrm{H}_{4}(-2341 \mathrm{~kJ} / \mathrm{mol}), \mathrm{C}_{4} \mathrm{H}_{8}(-2755 \mathrm{~kJ} / \mathrm{mol})$,
and $\mathrm{H}_{2}(-286 \mathrm{~kJ} / \mathrm{mol})$, calculate $\Delta H$ for the reaction
$$
\mathrm{C}_{4} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{4} \mathrm{H}_{8}(g)
$$

Angela Deane

Numerade Educator

Problem 69

Given the following data
$$
\begin{array}{ll}
\mathrm{NH}_{3}(g) \longrightarrow \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) & \Delta H=46 \mathrm{~kJ} \\
2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H=-484 \mathrm{~kJ}
\end{array}
$$
calculate $\Delta H$ for the reaction
$$
2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{O}_{2}(g)+4 \mathrm{NH}_{3}(g)
$$
On the basis of the enthalpy change, is this a useful reaction for the synthesis of ammonia?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 70

Given the following data
$$
\begin{aligned}
2 \mathrm{ClF}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{Cl}_{2} \mathrm{O}(g)+\mathrm{F}_{2} \mathrm{O}(g) & \Delta H &=167.4 \mathrm{~kJ} \\
2 \mathrm{ClF}_{3}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{Cl}_{2} \mathrm{O}(g)+3 \mathrm{~F}_{2} \mathrm{O}(g) & \Delta H &=341.4 \mathrm{~kJ} \\
2 \mathrm{~F}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{~F}_{2} \mathrm{O}(g) & \Delta H &=-43.4 \mathrm{~kJ}
\end{aligned}
$$
calculate $\Delta H$ for the reaction
$$
\mathrm{ClF}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{ClF}_{3}(g)
$$

Jamie Huang

Numerade Educator

Problem 71

$$
\begin{array}{l}
\text { Given the following data }\\
\begin{aligned}
2 \mathrm{O}_{3}(g) & \longrightarrow 3 \mathrm{O}_{2}(g) & \Delta H=-427 \mathrm{~kJ} \\
\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{O}(g) & \Delta H=+495 \mathrm{~kJ} \\
\mathrm{NO}(g)+\mathrm{O}_{3}(g) & \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) & \Delta H=-199 \mathrm{~kJ}
\end{aligned}
\end{array}
$$
calculate $\Delta H$ for the reaction
$$
\mathrm{NO}(g)+\mathrm{O}(g) \longrightarrow \mathrm{NO}_{2}(g)
$$

Catherine Lemar

Catherine Lemar

Numerade Educator

Problem 72

Calculate $\Delta H$ for the reaction
$$
\mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)
$$
given the following data:
$$
\begin{aligned}
2 \mathrm{NH}_{3}(g)+3 \mathrm{~N}_{2} \mathrm{O}(g) & \longrightarrow 4 \mathrm{~N}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H &=-1010 . \mathrm{kJ} \\
\mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2}(g) & \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) & \Delta H &=-317 \mathrm{~kJ} \\
2 \mathrm{NH}_{3}(g)+\frac{1}{2} \mathrm{O}_{2}(g) & \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{H}_{2} \mathrm{O}(l) & \Delta H &=-143 \mathrm{~kJ} \\
\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) & \Delta H &=-286 \mathrm{~kJ}
\end{aligned}
$$

Ronald Prasad

Numerade Educator

Problem 73

Given the following data
$$
\begin{aligned}
\mathrm{Ca}(s)+2 \mathrm{C}(\text { graphite }) & \longrightarrow \mathrm{CaC}_{2}(s) & \Delta H &=-62.8 \mathrm{~kJ} \\
\mathrm{Ca}(s)+\frac{1}{2} \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CaO}(s) & \Delta H &=-635.5 \mathrm{~kJ} \\
\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q) & \Delta H &=-653.1 \mathrm{~kJ} \\
\mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & \Delta H &=-1300 . \mathrm{kJ} \\
\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) & \Delta H &=-393.5 \mathrm{~kJ}
\end{aligned}
$$
calculate $\Delta H$ for the reaction
$$
\mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{C}_{2} \mathrm{H}_{2}(g)
$$

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 74

Given the following data
$$
\begin{aligned}
\mathrm{P}_{4}(s)+6 \mathrm{Cl}_{2}(g) & \longrightarrow 4 \mathrm{PCl}_{3}(g) & & \Delta H=-1225.6 \mathrm{~kJ} \\
\mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s) & & \Delta H=-2967.3 \mathrm{~kJ} \\
\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) & \longrightarrow \mathrm{PCl}_{5}(g) & & \Delta H=-84.2 \mathrm{~kJ} \\
\mathrm{PCl}_{3}(g)+\frac{1}{2} \mathrm{O}_{2}(g) & \mathrm{Cl}_{3} \mathrm{PO}(g) & & \Delta H=-285.7 \mathrm{~kJ}
\end{aligned}
$$
calculate $\Delta H$ for the reaction
$$
\mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{PCl}_{5}(g) \longrightarrow 10 \mathrm{Cl}_{3} \mathrm{PO}(g)
$$

Lottie Adams

Numerade Educator

Problem 75

Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of $\mathrm{NaCl}$, $\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$, and $\mathrm{PbSO}_{4}$ that have $\Delta H^{\circ}$ values equal to $\Delta H_{\mathrm{f}}^{\circ}$
for each compound.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 76

Write reactions for which the enthalpy change will be
a. $\Delta H_{\mathrm{f}}^{\circ}$ for solid aluminum oxide.
b. The standard enthalpy of combustion of liquid ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) .$
c. The standard enthalpy of neutralization of sodium hydroxide solution by hydrochloric acid.
d. $\Delta H_{\mathrm{f}}^{\circ}$ for gaseous vinyl chloride, $\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}(g)$.
e. The enthalpy of combustion of liquid benzene, $\mathrm{C}_{6} \mathrm{H}_{6}(l)$.
f. The enthalpy of solution of solid ammonium bromide.

Angela Deane

Numerade Educator

Problem 77

Use the values of $\Delta H_{f}^{\circ}$ in Appendix 4 to calculate $\Delta H^{\circ}$ for the following reactions.
a.
b. $\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+3 \mathrm{H}_{2} \mathrm{SO}_{4}(l) \longrightarrow 3 \mathrm{CaSO}_{4}(s)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(l)$
c. $\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$

Ronald Prasad

Numerade Educator

Problem 78

Use the values of $\Delta H_{\mathrm{f}}^{\circ}$ in Appendix 4 to calculate $\Delta H^{\circ}$ for the following reactions. (See Exercise 77.)
a.
b. $\mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(a q)$
c. $\mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)$

Jamie Huang

Numerade Educator

Problem 79

The Ostwald process for the commercial production of nitric acid from ammonia and oxygen involves the following steps:
$$
\begin{aligned}
4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \\
2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{NO}_{2}(g) \\
3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)
\end{aligned}
$$
a. Use the values of $\Delta H_{\mathrm{f}}^{\circ}$ in Appendix 4 to calculate the value of $\Delta H^{\circ}$ for each of the preceding reactions.
b. Write the overall equation for the production of nitric acid by the Ostwald process by combining the preceding equations. (Water is also a product.) Is the overall reaction exothermic or endothermic?

Lottie Adams

Numerade Educator

Problem 80

Calculate $\Delta H^{\circ}$ for each of the following reactions using the data in Appendix 4:
$$
\begin{array}{c}
4 \mathrm{Na}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Na}_{2} \mathrm{O}(s) \\
2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) \\
2 \mathrm{Na}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{O}(s)+\mathrm{CO}(\mathrm{g})
\end{array}
$$
Explain why a water or carbon dioxide fire extinguisher might not be effective in putting out a sodium fire.

Jamie Huang

Numerade Educator

Problem 81

The reusable booster rockets of the space shuttle use a mixture of aluminum and ammonium perchlorate as fuel. A possible reaction is
$3 \mathrm{Al}(s)+3 \mathrm{NH}_{4} \mathrm{ClO}_{4}(s) \longrightarrow$
$\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{AlCl}_{3}(s)+3 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
Calculate $\Delta H^{\circ}$ for this reaction.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 82

The space shuttle orbiter utilizes the oxidation of methylhydrazine by dinitrogen tetroxide for propulsion:
$4 \mathrm{~N}_{2} \mathrm{H}_{3} \mathrm{CH}_{3}(l)+5 \mathrm{~N}_{2} \mathrm{O}_{4}(l) \longrightarrow 12 \mathrm{H}_{2} \mathrm{O}(g)+9 \mathrm{~N}_{2}(g)+4 \mathrm{CO}_{2}(g)$
Calculate $\Delta H^{\circ}$ for this reaction.

Angela Deane

Numerade Educator

Problem 83

Consider the reaction
$2 \mathrm{ClF}_{3}(g)+2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{N}_{2}(g)+6 \mathrm{HF}(g)+\mathrm{Cl}_{2}(g)$
$\Delta H^{\circ}=-1196 \mathrm{~kJ}$
Calculate $\Delta H_{\mathrm{f}}^{\circ}$ for $\mathrm{ClF}_{3}(g)$.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 84

The standard enthalpy of combustion of ethene gas, $\mathrm{C}_{2} \mathrm{H}_{4}(g)$, is $-1411.1 \mathrm{~kJ} / \mathrm{mol}$ at $298 \mathrm{~K}$. Given the following enthalpies of formation, calculate $\Delta H_{\mathrm{f}}^{\circ}$ for $\mathrm{C}_{2} \mathrm{H}_{4}(g)$.
$$
\begin{array}{ll}
\mathrm{CO}_{2}(g) & -393.5 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{H}_{2} \mathrm{O}(l) & -285.8 \mathrm{~kJ} / \mathrm{mol}
\end{array}
$$

Angela Deane

Numerade Educator

Problem 85

Water gas is produced from the reaction of steam with coal:
$$
\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}(g)
$$
Assuming that coal is pure graphite, calculate $\Delta H^{\circ}$ for this reaction.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 86

Syngas can be burned directly or converted to methanol. Calculate $\Delta H^{\circ}$ for the reaction
$$
\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)
$$

Jamie Huang

Numerade Educator

Problem 87

Ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ has been proposed as an alternative fuel. Calculate the standard of enthalpy of combustion per gram of liquid ethanol.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 88

Methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ has also been proposed as an alternative fuel. Calculate the standard enthalpy of combustion per gram of liquid methanol and compare this answer to that for ethanol in Exercise 87 .

Jamie Huang

Numerade Educator

Problem 89

Some automobiles and buses have been equipped to burn propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) .$ Compare the amounts of energy that can be obtained per gram of $\mathrm{C}_{3} \mathrm{H}_{8}(g)$ and per gram of gasoline, assuming that gasoline is pure octane, $\mathrm{C}_{8} \mathrm{H}_{18}(l) .$ (See Example $6.11 .$ ) Look up the boiling point of propane. What disadvantages are there to using propane instead of gasoline as a fuel?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 90

Acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$ and butane $\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)$ are gaseous fuels with enthalpies of combustion of $-49.9 \mathrm{~kJ} / \mathrm{g}$ and $-49.5 \mathrm{~kJ} / \mathrm{g}$, respectively. Compare the energy available from the combustion of a given volume of acetylene to the combustion energy from the same volume of butane at the same temperature and pressure.

Angela Deane

Numerade Educator

Problem 91

Assume that $4.19 \times 10^{6} \mathrm{~kJ}$ of energy is needed to heat a home. If this energy is derived from the combustion of methane $\left(\mathrm{CH}_{4}\right)$, what volume of methane, measured at STP, must be burned? $\left(\Delta H_{\text {combustion }}^{\circ}\right.$ for $\mathrm{CH}_{4}=-891 \mathrm{~kJ} / \mathrm{mol}$ )

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 92

The complete combustion of acetylene, $\mathrm{C}_{2} \mathrm{H}_{2}(g)$, produces
1300. kJ of energy per mole of acetylene consumed. How many grams of acetylene must be burned to produce enough heat to raise the temperature of $1.00$ gal water by $10.0^{\circ} \mathrm{C}$ if the process is $80.0 \%$ efficient? Assume the density of water is $1.00 \mathrm{~g} / \mathrm{cm}^{3}$

Angela Deane

Numerade Educator

Problem 93

The equation for the fermentation of glucose to alcohol and carbon dioxide is
$$
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g)
$$
The enthalpy change for the reaction is $-67 \mathrm{~kJ}$. Is the reaction
exothermic or endothermic? Is energy, in the form of heat, absorbed or evolved as the reaction occurs?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 94

One way to lose weight is to exercise! Walking briskly at 4.0 miles per hour for an hour consumes about $400 \mathrm{kcal}$ of energy. How many hours would you have to walk at $4.0$ miles per hour to lose one pound of body fat? One gram of body fat is equivalent to $7.7 \mathrm{kcal}$ of energy. There are $454 \mathrm{~g}$ in $1 \mathrm{lb}$.

Angela Deane

Numerade Educator

Problem 95

It has been determined that the body can generate $5500 \mathrm{~kJ}$ of energy during one hour of strenuous exercise. Perspiration is the body's mechanism for eliminating this heat. What mass of water would have to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise? (The heat of vaporization of water is $40.6 \mathrm{~kJ} / \mathrm{mol}$.)

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 96

A biology experiment requires the preparation of a water bath at $37.0^{\circ} \mathrm{C}$ (body temperature). The temperature of the cold tap water is $22.0^{\circ} \mathrm{C}$, and the temperature of the hot tap water is $55.0^{\circ} \mathrm{C}$. If a student starts with $90.0 \mathrm{~g}$ cold water, what mass of hot water must be added to reach $37.0^{\circ} \mathrm{C} ?$

Nicole Basile

Numerade Educator

Problem 97

Quinone is an important type of molecule that is involved in photosynthesis. The transport of electrons mediated by quinone in certain enzymes allows plants to take water, carbon dioxide, and the energy of sunlight to create glucose. A $0.1964-\mathrm{g}$ sample of quinone $\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)$ is burned in a bomb calorimeter with a heat capacity of $1.56 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}$. The temperature of the calorimeter increases by $3.2^{\circ} \mathrm{C}$. Calculate the energy of combustion of quinone per gram and per mole.

Jamie Huang

Numerade Educator

Problem 98

Combustion of table sugar produces $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ When $1.46 \mathrm{~g}$ table sugar is combusted in a constant-volume (bomb) calorimeter, $24.00 \mathrm{~kJ}$ of heat is liberated.
a. Assuming that table sugar is pure sucrose, $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)$, write the balanced equation for the combustion reaction.
b. Calculate $\Delta E$ in $\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}$ for the combustion reaction of sucrose.
c. Calculate $\Delta I I$ in $\mathrm{kJ} / \mathrm{mol} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}$ for the combustion reaction of sucrose at $25^{\circ} \mathrm{C}$.

Crystal Wang

Numerade Educator

Problem 99

The bombardier beetle uses an explosive discharge as a defensive measure. The chemical reaction involved is the oxidation of hydroquinone by hydrogen peroxide to produce quinone and water:
$$
\mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)
$$
Calculate $\Delta H$ for this reaction from the following data:
$\mathrm{C}_{6} \mathrm{H}_{4}(\mathrm{OH})_{2}(a q) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}(a q)+\mathrm{H}_{2}(g)$
$$
\begin{aligned}
\Delta H &=+177.4 \mathrm{~kJ} \\
\mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}_{2}(a q) & \Delta H=-191.2 \mathrm{~kJ} \\
\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H=-241.8 \mathrm{~kJ} \\
\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) & \Delta H=-43.8 \mathrm{~kJ}
\end{aligned}
$$

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 100

Photosynthetic plants use the following reaction to produce glucose, cellulose, and so forth:
$$
6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \stackrel{\text { Sunlight }}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)
$$
How might extensive destruction of forests exacerbate the greenhouse effect?

Angela Deane

Numerade Educator

Problem 101

Three gas-phase reactions were run in a constant-pressure piston apparatus as shown in the following illustration. For each reaction, give the balanced reaction and predict the sign of $w$ (the work done) for the reaction.
If just the balanced reactions were given, how could you predict the sign of $w$ for a reaction?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 102

Consider the following changes:
a. $\mathrm{N}_{2}(g) \longrightarrow \mathrm{N}_{2}(l)$
b. $\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$
c. $\mathrm{Ca}_{3} \mathrm{P}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 3 \mathrm{Ca}(\mathrm{OH})_{2}(s)+2 \mathrm{PH}_{3}(g)$
d. $2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)$
e. $\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)$
At constant temperature and pressure, in which of these changes is work done by the system on the surroundings? By the surroundings on the system? In which of them is no work done?

Angela Deane

Numerade Educator

Problem 103

Consider the following cyclic process carried out in two steps
on a gas:
Step 1: $45 \mathrm{~J}$ of heat is added to the gas, and $10 . \mathrm{J}$ of expansion work is performed. Step 2: $60 . \mathrm{J}$ of heat is removed from the gas as the gas is compressed back to the initial state.
Calculate the work for the gas compression in step $2 .$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 104

Calculate $\Delta H^{\circ}$ for the reaction
$$
2 \mathrm{~K}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{KOH}(a q)+\mathrm{H}_{2}(g)
$$
A $5.00-\mathrm{g}$ chunk of potassium is dropped into $1.00 \mathrm{~kg}$ water at $24.0^{\circ} \mathrm{C}$. What is the final temperature of the water after the preceding reaction occurs? Assume that all the heat is used to raise the temperature of the water. (Never run this reaction. It is very dangerous; it bursts into flame!)

Jamie Huang

Numerade Educator

Problem 105

The enthalpy of neutralization for the reaction of a strong acid with a strong base is $-56 \mathrm{~kJ} / \mathrm{mol}$ water produced. How much energy will be released when $200.0 \mathrm{~mL}$ of $0.400 \mathrm{M} \mathrm{HCl}$ is mixed with $150.0 \mathrm{~mL}$ of $0.500 \mathrm{M} \mathrm{NaOH}$ ?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 106

When $1.00 \mathrm{~L}$ of $2.00 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}$ solution at $30.0^{\circ} \mathrm{C}$ is added to
$2.00 \mathrm{~L}$ of $0.750 \mathrm{M} \mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$ solution at $30.0^{\circ} \mathrm{C}$ in a calorimeter,
a white solid $\left(\mathrm{BaSO}_{4}\right)$ forms. The temperature of the mixture increases to $42.0^{\circ} \mathrm{C}$. Assuming that the specific heat capacity of the solution is $6.37 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ and that the density of the final solution is $2.00 \mathrm{~g} / \mathrm{mL}$, calculate the enthalpy change per mole of $\mathrm{BaSO}_{4}$ formed.

Angela Deane

Numerade Educator

Problem 107

If a student performs an endothermic reaction in a calorimeter, how does the calculated value of $\Delta H$ differ from the actual value if the heat exchanged with the calorimeter is not taken into account?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 108

In a bomb calorimeter, the reaction vessel is surrounded by water that must be added for each experiment. Since the amount of water is not constant from experiment to experiment, the mass of water must be measured in each case. The heat capacity of the calorimeter is broken down into two parts: the water and the calorimeter components. If a calorimeter contains $1.00 \mathrm{~kg}$ water and has a total heat capacity of $10.84 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}$, what is the heat capacity of the calorimeter components?

Jamie Huang

Numerade Educator

Problem 109

The bomb calorimeter in Exercise 108 is filled with $987 \mathrm{~g}$ water. The initial temperature of the calorimeter contents is $23.32^{\circ} \mathrm{C}$. A $1.056-\mathrm{g}$ sample of benzoic acid $\left(\Delta E_{\text {comb }}=-26.42 \mathrm{~kJ} / \mathrm{g}\right)$ is combusted in the calorimeter. What is the final temperature of the calorimeter contents?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 110

Consider the two space shuttle fuel reactions in Exercises 81 and 82. Which reaction produces more energy per kilogram of reactant mixture (stoichiometric amounts)?

Ronald Prasad

Numerade Educator

Problem 111

Consider the following equations:
$$
\begin{aligned}
3 \mathrm{~A}+6 \mathrm{~B} \longrightarrow & 3 \mathrm{D} & \Delta H &=-403 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{E}+2 \mathrm{~F} & \longrightarrow \mathrm{A} & \Delta H &=-105.2 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{C} & \longrightarrow \mathrm{E}+3 \mathrm{D} & \Delta H &=+64.8 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
Suppose the first equation is reversed and multiplied by $\frac{1}{6}$, the second and third equations are divided by 2, and the three adjusted equations are added. What is the net reaction and what is the overall heat of this reaction?

David Collins

Numerade Educator

Problem 112

Given the following data
$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-23 \mathrm{~kJ}$
$3 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-39 \mathrm{~kJ}$
$\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) \longrightarrow 3 \mathrm{FeO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=+18 \mathrm{~kJ}$
calculate $\Delta H^{\circ}$ for the reaction
$$
\mathrm{FeO}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)
$$

Osman Elomda

Numerade Educator

Problem 113

At $298 \mathrm{~K}$, the standard enthalpies of formation for $\mathrm{C}_{2} \mathrm{H}_{2}(g)$ and $\mathrm{C}_{6} \mathrm{H}_{6}(l)$ are $227 \mathrm{~kJ} / \mathrm{mol}$ and $49 \mathrm{~kJ} / \mathrm{mol}$, respectively.
a. Calculate $\Delta H^{\circ}$ for
$$
\mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g)
$$
b. Both acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$ and benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)$ can be used as fuels. Which compound would liberate more energy per gram when combusted in air?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 114

Using the following data, calculate the standard heat of formation of $\operatorname{ICl}(g)$ in $\mathrm{kJ} / \mathrm{mol}$ :
$$
\begin{aligned}
\mathrm{Cl}_{2}(g) & \longrightarrow 2 \mathrm{Cl}(g) & \Delta H^{\circ} &=242.3 \mathrm{~kJ} \\
\mathrm{I}_{2}(g) & \longrightarrow 2 \mathrm{I}(g) & \Delta H^{\circ} &=151.0 \mathrm{~kJ} \\
\mathrm{ICl}(g) & \longrightarrow \mathrm{I}(g)+\mathrm{Cl}(g) & \Delta H^{\circ} &=211.3 \mathrm{~kJ} \\
\mathrm{I}_{2}(s) & \Delta H^{\circ}=62.8 \mathrm{~kJ}
\end{aligned}
$$

Osman Elomda

Numerade Educator

Problem 115

Calculate $\Delta H^{\circ}$ for each of the following reactions, which occur in the atmosphere.
a. $\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{CHO}(g)+\mathrm{O}_{2}(g)$
b. $\mathrm{O}_{3}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$
c. $\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q)$
d. $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 116

Consider $2.00 \mathrm{~mol}$ of an ideal gas that is taken from state $A\left(P_{A}=\right.$ $\left.2.00 \mathrm{~atm}, V_{A}=10.0 \mathrm{~L}\right)$ to state $B\left(P_{B}=1.00 \mathrm{~atm}, V_{B}=30.0 \mathrm{~L}\right)$
by two different pathways:
Calculate the work (in units of J) associated with the two pathways. Is work a state function? Explain.

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 117

Calculate $w$ and $\Delta E$ when one mole of a liquid is vaporized at its boiling point $\left(80 .^{\circ} \mathrm{C}\right)$ and $1.00$ atm pressure. $\Delta H_{\mathrm{vap}}$ for the liquid is $30.7 \mathrm{~kJ} / \mathrm{mol}^{-1}$ at $80 .{ }^{\circ} \mathrm{C}$.

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 118

The sun supplies energy at a rate of about $1.0$ kilowatt per square meter of surface area ( 1 watt $=1 \mathrm{~J} / \mathrm{s}$ ). The plants in an agricultural field produce the equivalent of $20 . \mathrm{kg}$ sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ per hour per hectare ( $1 \mathrm{ha}=10,000 \mathrm{~m}^{2}$ ). Assuming that sucrose is produced by the reaction
$12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+12 \mathrm{O}_{2}(g)$
$\Delta H=5640 \mathrm{~kJ}$
calculate the percentage of sunlight used to produce the sucrosethat is, determine the efficiency of photosynthesis.

Jamie Huang

Numerade Educator

Problem 119

The best solar panels currently available are about $13 \%$ efficient in converting sunlight to electricity. A typical home will use about $40 . \mathrm{kWh}$ of electricity per day $(1 \mathrm{kWh}=1$ kilowatt hour; $1 \mathrm{~kW}=1000 \mathrm{~J} / \mathrm{s}$ ). Assuming $8.0$ hours of useful sunlight per day, calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity. (See Exercise 118 for the energy rate supplied by the sun.)

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 120

On Easter Sunday, April 3, 1983 , nitric acid spilled from a tank car near downtown Denver, Colorado. The spill was neutralized with sodium carbonate:
$2 \mathrm{HNO}_{3}(a q)+\mathrm{Na}_{2} \mathrm{CO}_{3}(s) \longrightarrow 2 \mathrm{NaNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)$
a. Calculate $\Delta H^{\circ}$ for this reaction. Approximately $2.0 \times 10^{4}$ gal nitric acid was spilled. Assume that the acid was an aqueous solution containing $70.0 \% \mathrm{HNO}_{3}$ by mass with a density of $1.42 \mathrm{~g} / \mathrm{cm}^{3}$. What mass of sodium carbonate was required for complete neutralization of the spill, and what quantity of heat was evolved? $\left(\Delta H_{\mathrm{f}}^{\circ}\right.$ for $\mathrm{NaNO}_{3}(a q)=-467 \mathrm{~kJ} / \mathrm{mol}$ )
b. According to The Denver Post for April 4, 1983 , authorities feared that dangerous air pollution might occur during the neutralization. Considering the magnitude of $\Delta H^{\circ}$, what was their major concern?

Ronald Prasad

Numerade Educator

Problem 121

A piece of chocolate cake contains about 400 Calories. A nutritional Calorie is equal to 1000 calories (thermochemical calories), which is equal to $4.184 \mathrm{~kJ} .$ How many 8 -in-high steps must a 180 -lb man climb to expend the 400 Cal from the piece of cake? See Exercise 26 for the formula for potential
energy.

Jamie Huang

Numerade Educator

Problem 122

The standard enthalpy of formation of $\mathrm{H}_{2} \mathrm{O}(l)$ at $298 \mathrm{~K}$ is $-285.8$ $\mathrm{kJ} / \mathrm{mol} .$ Calculate the change in internal energy for the following process at $298 \mathrm{~K}$ and 1 atm:
$$
\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta E^{\circ}=?
$$
(Hint: Using the ideal gas equation, derive an expression for work in terms of $n, R$, and $T$.)

Angela Deane

Numerade Educator

Problem 123

You have a $1.00$ -mol sample of water at $-30 .{ }^{\circ} \mathrm{C}$ and you heat it until you have gaseous water at $140 .^{\circ} \mathrm{C}$. Calculate $q$ for the entire process. Use the following data.
Specific heat capacity of ice $=2.03 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$
Specific heat capacity of water $=4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$
Specific heat capacity of steam $=2.02 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ $\begin{array}{lr}\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) & \Delta H_{\text {fusion }}=6.02 \mathrm{~kJ} / \mathrm{mol}\left(\text { at } 0^{\circ} \mathrm{C}\right) \\ \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H_{\text {vaporization }}=40.7 \mathrm{~kJ} / \mathrm{mol}\left(\text { at } 100 .{ }^{\circ} \mathrm{C}\right)\end{array}$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 124

A $500.0$ -g sample of an element at $195^{\circ} \mathrm{C}$ is dropped into an ice-water mixture; $109.5 \mathrm{~g}$ ice melts and an ice-water mixture remains. Calculate the specific heat of the element. See Exercise 123 for pertinent information.

Jamie Huang

Numerade Educator

Problem 125

The preparation of $\mathrm{NO}_{2}(g)$ from $\mathrm{N}_{2}(g)$ and $\mathrm{O}_{2}(g)$ is an endothermic reaction:
$$
\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) \text { (unbalanced) }
$$
The enthalpy change of reaction for the balanced equation (with lowest whole-number coefficients) is $\Delta H=67.7 \mathrm{~kJ}$. If $2.50 \times$ $10^{2} \mathrm{~mL} \mathrm{~N}_{2}(g)$ at $100 .{ }^{\circ} \mathrm{C}$ and $3.50$ atm and $4.50 \times 10^{2} \mathrm{~mL} \mathrm{O}_{2}(g)$
at $100 .{ }^{\circ} \mathrm{C}$ and $3.50 \mathrm{~atm}$ are mixed, what amount of heat is necessary to synthesize the maximum yield of $\mathrm{NO}_{2}(g)$ ?

Rebecca Wallace

Rebecca Wallace

Numerade Educator

Problem 126

Nitromethane, $\mathrm{CH}_{3} \mathrm{NO}_{2}$, can be used as a fuel. When the liquid is burned, the (unbalanced) reaction is mainly
$$
\mathrm{CH}_{3} \mathrm{NO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
a. The standard enthalpy change of reaction $\left(\Delta H_{\mathrm{rxn}}^{\circ}\right)$ for the balanced reaction (with lowest whole-number coefficients) is $-1288.5 \mathrm{~kJ} .$ Calculate the $\Delta H_{\mathrm{f}}^{\circ}$ for nitromethane.
b. A $15.0$ - $\mathrm{L}$ flask containing a sample of nitromethane is filled with $\mathrm{O}_{2}$ and the flask is heated to $100 .^{\circ} \mathrm{C}$. At this temperature, and after the reaction is complete, the total pressure of all the gases inside the flask is 950 . torr. If the mole fraction of nitrogen ( $\chi_{\text {nitrogen }}$ ) is $0.134$ after the reaction is complete, what mass of nitrogen was produced?

Angela Deane

Numerade Educator

Problem 127

A cubic piece of uranium metal (specific heat capacity $=0.117$ $\mathrm{J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ ) at $200.0^{\circ} \mathrm{C}$ is dropped into $1.00 \mathrm{~L}$ deuterium oxide
("heavy water," specific heat capacity $=4.211 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ ) at $25.5^{\circ} \mathrm{C}$. The final temperature of the uranium and deuterium oxide mixture is $28.5^{\circ} \mathrm{C}$. Given the densities of uranium $\left(19.05 \mathrm{~g} / \mathrm{cm}^{3}\right)$ and deuterium oxide (1.11 $\mathrm{g} / \mathrm{mL}$ ), what is the edge length of the cube of uranium?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 128

A sample consisting of $22.7 \mathrm{~g}$ of a nongaseous, unstable compound $\mathrm{X}$ is placed inside a metal cylinder with a radius of $8.00 \mathrm{~cm}$, and a piston is carefully placed on the surface of the compound so that, for all practical purposes, the distance between the bottom of the cylinder and the piston is zero. (A hole in the piston allows trapped air to escape as the piston is placed on the compound; then this hole is plugged so that nothing inside the cylinder can escape.) The piston-and-cylinder apparatus is carefully placed in $10.00 \mathrm{~kg}$ water at $25.00^{\circ} \mathrm{C}$. The barometric pressure is 778 torr.

When the compound spontaneously decomposes, the piston moves up, the temperature of the water reaches a maximum of $29.52^{\circ} \mathrm{C}$, and then it gradually decreases as the water loses heat to the surrounding air. The distance between the piston and the bottom of the cylinder, at the maximum temperature, is $59.8 \mathrm{~cm}$. Chemical analysis shows that the cylinder contains $0.300 \mathrm{~mol}$ carbon dioxide, $0.250$ mol liquid water, $0.025$ mol oxygen gas, and an undetermined amount of a gaseous element $\mathrm{A}$.

It is known that the enthalpy change for the decomposition of $X$, according to the reaction described above, is $-1893$ $\mathrm{kJ} / \mathrm{mol} \mathrm{X}$. The standard enthalpies of formation for gaseous carbon dioxide and liquid water are $-393.5 \mathrm{~kJ} / \mathrm{mol}$ and $-286 \mathrm{~kJ} / \mathrm{mol}$, respectively. The heat capacity for water is $4.184 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$. The conversion factor between $\mathrm{L} \cdot \mathrm{atm}$ and $\mathrm{J}$ can be determined from the two values for the gas constant $R$, namely, $0.08206 \mathrm{~L}$. $\mathrm{atm} / \mathrm{K} \cdot \mathrm{mol}$ and $8.3145 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$. The vapor pressure of water
at $29.5^{\circ} \mathrm{C}$ is 31 torr. Assume that the heat capacity of the pistonand-cylinder apparatus is negligible and that the piston has negligible mass. Given the preceding information, determine
a. The formula for $\mathrm{X}$.
b. The pressure-volume work (in $\mathrm{kJ}$ ) for the decomposition of the $22.7-\mathrm{g}$ sample of $\mathrm{X}$.
c. The molar change in internal energy for the decomposition of $X$ and the approximate standard enthalpy of formation for $X$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 129

A gaseous hydrocarbon reacts completely with oxygen gas to form carbon dioxide and water vapor. Given the following data, determine $\Delta H_{\mathrm{f}}^{\circ}$ for the hydrocarbon:
$$
\begin{aligned}
\Delta H_{\mathrm{rxn}}^{\circ} &=-2044.5 \mathrm{~kJ} / \mathrm{mol} \text { hydrocarbon } \\
\Delta H_{\mathrm{f}}^{\circ}\left(\mathrm{CO}_{2}\right) &=-393.5 \mathrm{~kJ} / \mathrm{mol} \\
\Delta H_{\mathrm{f}}^{\circ}\left(\mathrm{H}_{2} \mathrm{O}\right) &=-242 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
Density of $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ product mixture at $1.00 \mathrm{~atm}, 200 .{ }^{\circ} \mathrm{C}=$
$0.751 \mathrm{~g} / \mathrm{L}$
The density of the hydrocarbon is less than the density of $\mathrm{Kr}$ at the same conditions.

Ronald Prasad

Numerade Educator