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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 6

Thermochemistry: Energy Flow and Chemical Change

Educators


Problem 1

Why do heat (q) and work (w) have positive values when entering a system and negative values when leaving?

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Problem 2

If you feel warm after exercising, have you increased the internal energy of your body? Explain.

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Problem 3

An adiabatic process is one that involves no heat transfer. What is the relationship between work and the change in internal energy in an adiabatic process?

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Problem 4

State two ways that you increase the internal energy of your body and two ways that you decrease it.

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Problem 5

Name a common device used to accomplish each change:
(a) Electrical energy to thermal energy
(b) Electrical energy to sound energy
(c) Electrical energy to light energy
(d) Mechanical energy to electrical energy
(e) Chemical energy to electrical energy

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Problem 6

In winter, an electric heater uses a certain amount of electrical energy to heat a room to $20^{\circ} \mathrm{C}$ . In summer, an air conditioner uses the same amount of electrical energy to cool the room to $20^{\circ} \mathrm{C} .$ Is the change in internal energy of the heater larger, smaller, or the same as that of the air conditioner? Explain.

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Problem 7

You lift your textbook and drop it onto a desk. Describe the energy transformations (from one form to another) that occur, moving backward in time from a moment after impact.

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Problem 8

A system receives 425 J of heat from and delivers 425 J of work to its surroundings. What is the change in internal energy of the system (in J)?

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Problem 9

A system releases 255 cal of heat to the surroundings and delivers 428 cal of work. What is the change in internal energy of the system (in cal)?

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Problem 10

What is the change in internal energy (in J) of a system that releases 675 J of thermal energy to its surroundings and has 530 cal of work done on it?

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Problem 11

What is the change in internal energy (in J) of a system that absorbs 0.615 kJ of heat from its surroundings and has 0.247 kcal of work done on it?

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Problem 12

Complete combustion of 2.0 metric tons of coal to gaseous carbon dioxide releases $6.6 \times 10^{10} \mathrm{J}$ of heat. Convert this energy to (a) kilojoules; (b) kilocalories; ( $\mathrm{c} )$ British thermal units.

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Problem 13

Thermal decomposition of 5.0 metric tons of limestone to lime and carbon dioxide absorbs $9.0 \times 10^{6} \mathrm{kJ}$ of heat. Convert this energy to (a) joules; (b) calories; (c) British thermal units.

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Problem 14

The nutritional calorie (Calorie) is equivalent to 1 kcal. One pound of body fat is equivalent to about $4.1 \times 10^{3}$ Calories. Express this quantity of energy in joules and kilojoules.

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Problem 15

If an athlete expends 1950 kJ/h, how long does it take her to work off 1.0 lb of body fat? (See Problem 6.14.)

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Problem 16

Why is the work done when a system expands against a constant external pressure assigned a negative sign?

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Problem 17

Why is it often more convenient to measure $\Delta H$ than $\Delta E ?$

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Problem 18

Hot packs used by skiers use the crystallization of sodium acetate from a concentrated solution. What is the sign of $\Delta H$ for this crystallization? Is the reaction exothermic or endothermic?

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Problem 19

Classify the following processes as exothermic or endothermic: (a) freezing of water; (b) boiling of water; (c) digestion of food; (d) a person running; (e) a person growing; (f) wood being chopped; (g) heating with a furnace.

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Problem 20

What are the two main components of the internal energy of a substance? On what are they based?

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Problem 21

For each process, state whether $\Delta H$ is less than (more negative), equal to, or greater than $\Delta E$ of the system. Explain.
(a) An ideal gas is cooled at constant pressure.
(b) A gas mixture reacts exothermically at fixed volume.
(c) A solid reacts exothermically to yield a mixture of gases in a container of variable volume.

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Problem 22

At constant temperature, a sample of helium gas expands from 922 $\mathrm{mL}$ to 1.14 $\mathrm{L}$ against a pressure of 2.33 atm. Find $w$ (in J) done by the gas $\left(1 \mathrm{J}=9.87 \times 10^{-3} \mathrm{atm} \cdot \mathrm{L}\right) .$

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Problem 23

The external pressure on a gas sample is 2660 mmHg, and the volume changes from 0.88 $\mathrm{L}$ to 0.63 $\mathrm{L}$ at constant temperature. Find $w(\text { in } \mathrm{kJ})$ done on the gas $(1 \mathrm{atm} \cdot \mathrm{L}=101.3 \mathrm{J})$ .

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Problem 24

Draw an enthalpy diagram for a general exothermic reaction; label the axis, reactants, products, and $\Delta H$ with its sign.

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Problem 25

Draw an enthalpy diagram for a general endothermic reaction; label the axis, reactants, products, and $\Delta H$ with its sign.

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Problem 26

Write a balanced equation and draw an approximate enthalpy diagram for: (a) combustion of 1 mol of ethane; (b) freezing of liquid water.

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Problem 27

Write a balanced equation and draw an approximate enthalpy diagram for (a) formation of 1 mol of sodium chloride from its elements (heat is released); (b) vaporization of liquid benzene

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Problem 28

Write a balanced equation and draw an approximate enthalpy diagram for (a) combustion of 1 $\mathrm{mol}$ of liquid methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right) ;(\mathrm{b})$ f rmation of 1 $\mathrm{mol}$ of $\mathrm{NO}_{2}$ , from its elements (heat is absorbed).

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Problem 29

Write a balanced equation and draw an approximate enthalpy diagram for (a) sublimation of dry ice [conversion of $\mathrm{CO}_{2}(s)$ directly to $\mathrm{CO}_{2}(g) ] ;\left(\mathrm{b} \text { ) reaction of } 1 \mathrm{mol} \text { of } \mathrm{SO}_{2} \text { with } \mathrm{O}_{2} .\right.$

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Problem 30

The circles represent a phase change at constant temperature:
Is the value of each of the following positive $(+),$ negative $(-),$ or zero: (a) $q_{\text { sys }} ;\left(\text { b) } \Delta E_{\text { sys }} ;(\mathrm{c}) \Delta E_{\text { univ }} ?\right.$

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Problem 31

he scenes below represent a physical change taking place in a piston-cylinder assembly:
(a) Is $w_{\mathrm{sys}}+,-,$ or 0$?(\mathrm{b})$ Is $\Delta H_{\mathrm{sys}}+,-,$ or 0$?(\mathrm{c})$ Can you determine whether $\Delta E_{\mathrm{surr}}$ is $+,-,$ or 0$?$ Explain.

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Problem 32

Which is larger, the specific heat capacity or the molar heat capacity of a substance? Explain.

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Problem 33

What data do you need to determine the specific heat capacity of a substance?

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Problem 34

Is the specific heat capacity of a substance an intensive or extensive property? Explain.

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Problem 35

Distinguish between specific heat capacity, molar heat capacity, and heat capacity.

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Problem 36

Both a coffee-cup calorimeter and a bomb calorimeter can be used to measure the heat transferred in a reaction. Which measures $\Delta E$ and which measures $\Delta H ?$ Explain.

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Problem 37

Find $q$ when 22.0 g of water is heated from $25.0^{\circ} \mathrm{C}$ to $100 .^{\circ} \mathrm{C}$ .

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Problem 38

Calculate $q$ when 0.10 g of ice is cooled from $10 .^{\circ} \mathrm{C}$ to $-75^{\circ} \mathrm{C}\left(c_{\mathrm{ice}}=2.087 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\right)$

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Problem 39

A 295-g aluminum engine part at an initial temperature of $13.00^{\circ} \mathrm{C}$ absorbs 75.0 $\mathrm{kJ}$ of heat. What is the final temperature of the part $(c \text { of } \mathrm{Al}=0.900 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}) ?$

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Problem 40

A 27.7-g sample of the radiator coolant ethylene glycol releases 688 $\mathrm{J}$ of heat. What was the initial temperature of the sample if the final temperature is $32.5^{\circ} \mathrm{C}(c \text { of ethylene glycol }=$ 2.42 $\mathrm{J} / \mathrm{g} \cdot \mathrm{K} ) ?$

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Problem 41

Two iron bolts of equal mass - one at $100 .^{\circ} \mathrm{C},$ the other at $55^{\circ} \mathrm{C}-$ are placed in an insulated container. Assuming the heat capacity of the container is negligible, what is the final temperature inside the container $(c \text { of iron }=0.450 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}) ?$

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Problem 42

One piece of copper jewelry at $105^{\circ} \mathrm{C}$ has twice the mass of another piece at $45^{\circ} \mathrm{C} .$ Both are placed in a calorimeter of negligible heat capacity. What is the final temperature inside the calorimeter $(c \text { of copper }=0.387 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}) ?$

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Problem 43

When 155 $\mathrm{mL}$ of water at $26^{\circ} \mathrm{C}$ is mixed with 75 $\mathrm{mL}$ of water at $85^{\circ} \mathrm{C},$ what is the final temperature? (Assume that no heat is released to the surroundings; $d$ of water $=1.00 \mathrm{g} / \mathrm{mL}$ .)

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Problem 44

6.44 An unknown volume of water at $18.2^{\circ} \mathrm{C}$ is added to 24.4 $\mathrm{mL}$ of water at $35.0^{\circ} \mathrm{C}$ . If the final temperature is $23.5^{\circ} \mathrm{C},$ what was the unknown volume? (Assume that no heat is released to the surroundings; $d$ of water $=1.00 \mathrm{g} / \mathrm{mL}$ .)

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Problem 45

$\mathrm{A} 455-\mathrm{g}$ piece of copper tubing is heated to $89.5^{\circ} \mathrm{C}$ and placed in an insulated vessel containing 159 $\mathrm{g}$ of water at $22.8^{\circ} \mathrm{C} .$ Assuming no loss of water and a heat capacity of 10.0 $\mathrm{J} / \mathrm{K}$ for the vessel, what is the final temperature $(c \text { of copper }=0.387 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}) ?$

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Problem 46

$\mathrm{A} 30.5$ -g sample of an alloy at $93.0^{\circ} \mathrm{C}$ is placed into 50.0 $\mathrm{g}$ of water at $22.0^{\circ} \mathrm{C}$ in an insulated coffee cup with a heat capacity of 9.2 $\mathrm{J} / \mathrm{K}$ . If the final temperature of the system is $31.1^{\circ} \mathrm{C},$ what is the specific heat capacity of the alloy?

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Problem 47

High-purity benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} ; \Delta H\right.$ for combustion $=-3227 \mathrm{kJ} / \mathrm{mol} )$ is used to calibrate bomb calorimeters. A 1.221 -g sample burns in a calorimeter (heat capacity of 1365 $\mathrm{JJ}^{\prime} \mathrm{C}$ ) that contains 1.200 $\mathrm{kg}$ of water. What is the temperature change?

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Problem 48

Two aircraft rivets, one iron and the other copper, are placed in a calorimeter that has an initial temperature of $20 .^{\circ} \mathrm{C} .$ The data for the rivets are as follows:
$$\begin{array}{lll}{\text { Mass (g) }} & {30.0} & {20.0} \\ {\text { Initial } T\left(^{\circ} \mathrm{C}\right)} & {0.0} & {100.0} \\ {c(\mathrm{J} / \mathrm{g} \cdot \mathrm{K})} & {0.450} & {0.387}\end{array}$$
(a) Will heat flow from Fe to Cu or from Cu to Fe?
(b) What other information is needed to correct any measurements in an actual experiment?
(c) What is the maximum final temperature of the system (assuming the heat capacity of the calorimeter is negligible)?

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Problem 49

A chemical engineer placed 1.520 g of a hydrocarbon in the bomb of a calorimeter (see Figure 6.10, p. 265). The bomb was immersed in 2.550 L of water and the sample was burned. The water temperature rose from $20.00^{\circ} \mathrm{C}$ to $23.55^{\circ} \mathrm{C}$ . If the calorimeter (excluding the water) had a heat capacity of 403 $\mathrm{J} / \mathrm{K}$ , what was the heat released $\left(q_{V}\right)$ per gram of hydrocarbon?

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Problem 50

When 25.0 $\mathrm{mL}$ of 0.500$M \mathrm{H}_{2} \mathrm{SO}_{4}$ is added to 25.0 $\mathrm{mL}$ of 1.00 $\mathrm{M} \mathrm{KOH}$ in a coffee-cup calorimeter at $23.50^{\circ} \mathrm{C},$ the temperature rises to $30.17^{\circ} \mathrm{C}$ . Calculate $\Delta \mathrm{H}$ of this reaction. (Assume that the total volume is the sum of the volumes and that the density and specific heat capacity of the solution are the same as for water.)

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Problem 51

Does a negative $\Delta H$ mean that the heat should be treated as a reactant or as a product?

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Problem 52

Would you expect $\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}(g)$ to have a positive or a negative $\Delta H ?$ Explain.

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Problem 53

Is $\Delta H$ positive or negative when 1 mol of water vapor condenses to liquid water? How does this value compare with $\Delta H$ for the vaporization of 2 mol of liquid water to water vapor?

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Problem 54

Consider the following balanced thermochemical equation for a reaction sometimes used for $\mathrm{H}_{2} \mathrm{S}$ production:
$$^{1}_{8} \mathrm{S}_{8}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{S}(g) \quad \Delta H=-20.2 \mathrm{kJ}$$
(a) Is this an exothermic or endothermic reaction?
(b) What is $\Delta H$ for the reverse reaction?
(c) What is $\Delta H$ when 2.6 $\mathrm{mol}$ of $\mathrm{S}_{8}$ reacts?
(d) What is $\Delta H$ when 25.0 $\mathrm{g}$ of $\mathrm{S}_{8}$ reacts?

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Problem 55

Consider the following balanced thermochemical equation for the decomposition of the mineral magnesite:
$$\mathrm{MgCO}_{3}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H=117.3 \mathrm{kJ}$$
(a) Is heat absorbed or released in the reaction?
(b) What is $\Delta H$ for the reverse reaction?
(c) What is $\Delta H$ when 5.35 mol of $\mathrm{CO}_{2}$ reacts with excess MgO?
(d) What is $\Delta H$ when 35.5 $\mathrm{g}$ of $\mathrm{CO}_{2}$ reacts with excess MgO?

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Problem 56

When 1 mol of $\mathrm{NO}(g)$ forms from its elements, 90.29 $\mathrm{kJ}$ of heat is absorbed. (a) Write a balanced thermochemical equation. (b) What is $\Delta H$ when 3.50 $\mathrm{g}$ of NO decomposes to its elements?

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Problem 57

When 1 mol of $\operatorname{KBr}(s)$ decomposes to its elements, 394 $\mathrm{kJ}$ of heat is absorbed. (a) Write a balanced thermochemical equation. (b) What is $\Delta H$ when 10.0 $\mathrm{kg}$ of $\mathrm{KBr}$ forms from its elements?

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Problem 58

Liquid hydrogen peroxide, an oxidizing agent in many rocket fuel mixtures, releases oxygen gas on decomposition:
$$2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g) \quad \Delta H=-196.1 \mathrm{kJ}$$
How much heat is released when 652 $\mathrm{kg}$ of $\mathrm{H}_{2} \mathrm{O}_{2}$ decomposes?

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Problem 59

Compounds of boron and hydrogen are remarkable for their unusual bonding (described in Section 14.5) and also for their reactivity. With the more reactive halogens, for example, diborane $\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)$ forms trihalides even at low temperatures:
$\mathrm{B}_{2} \mathrm{H}_{6}(g)+6 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{BCl}_{3}(g)+6 \mathrm{HCl}(g)$
$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \Delta H=-755.4 \mathrm{kJ}$
What is $\Delta H$ per kilogram of diborane that reacts?

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Problem 60

Deterioration of buildings, bridges, and other structures through the rusting of iron costs millions of dollars a day. The actual process requires water, but a simplified equation is
$$4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1.65 \times 10^{3} \mathrm{kJ}$$
(a) How much heat is released when 0.250 $\mathrm{kg}$ of iron rusts?
(b) How much rust forms when $4.85 \times 10^{3} \mathrm{kJ}$ of heat is released?

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Problem 61

A mercury mirror forms inside a test tube as a result of the thermal decomposition of mercury(II) oxide:
$$2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \quad \Delta H=181.6 \mathrm{kJ}$$
(a) How much heat is absorbed to decompose 555 $\mathrm{g}$ of the oxide?
(b) If 275 $\mathrm{kJ}$ of heat is absorbed, how many grams of Hg form?

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Problem 62

Most ethylene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),$ the starting material for producing polyethylene, comes from petroleum processing. It also occurs naturally as a fruit-ripening hormone and as a component of natural gas. (a) The heat transferred during combustion of $\mathrm{C}_{2} \mathrm{H}_{4}$ is $-1411 \mathrm{kJ} / \mathrm{mol}$ . Write a balanced thermochemical equation. (b) How many grams of $\mathrm{C}_{2} \mathrm{H}_{4}$ must burn to give 70.0 $\mathrm{kJ}$ of heat?

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Problem 63

Sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}, \text { table sugar) is oxidized in the body }\right.$ by $\mathrm{O}_{2}$ via a complex set of reactions that produces $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$ and releases $5.64 \times 10^{3} \mathrm{kJ} / \mathrm{mol}$ of sucrose. (a) Write a balanced thermochemical equation for the overall process. (b) How much heat is released per gram of sucrose oxidized?

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Problem 64

Express Hess’s law in your own words.

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Problem 65

What is the main application of Hess’s law?

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Problem 66

When carbon burns in a deficiency of $\mathrm{O}_{2},$ a mixture of $\mathrm{CO}$ and $\mathrm{CO}_{2}$ forms. Carbon burns in excess $\mathrm{O}_{2}$ to form only $\mathrm{CO}_{2},$ and CO burns in excess $\mathrm{O}_{2}$ to form only $\mathrm{CO}_{2}$ . Use $\Delta \mathrm{H}$ values of the latter two reactions (from Appendix $\mathrm{B} )$ to calculate $\Delta H$ for
$$\mathrm{C}(\text { graphite })+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}(g)$$

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Problem 67

Calculate $\Delta H$ for
$$\mathrm{Ca}(s)+\frac{1}{2} \mathrm{O}_{2}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{CaCO}_{3}(s)$$
given the following reactions:
$$\begin{array}{ll}{\mathrm{Ca}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CaO}(s)} & {\Delta H=-635.1 \mathrm{kJ}} \\ \quad\quad\quad {\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)} & {\Delta H=178.3 \mathrm{kJ}}\end{array}$$

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Problem 68

Calculate $\Delta H$ for
$$2 \mathrm{NOCl}(g) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{Cl}_{2}(g)$$
given the following reactions:
$$\begin{array}{ll}{\frac{1}{2} \mathrm{N}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \operatorname{NO}(g)} & {\Delta H=90.3 \mathrm{kJ}} \\ {\mathrm{NO}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}(g)} & {\Delta H=-38.6 \mathrm{kJ}}\end{array}$$

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Problem 69

Write the balanced overall equation (equation 3$)$ for the fol- lowing process, calculate $\Delta H_{\text { overall }},$ and match the number of each equation with the letter of the appropriate arrow in Figure P6.69:
(1) $\quad \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) \quad \Delta H=180.6 \mathrm{kJ}$
(2) $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H=-114.2 \mathrm{kJ}$
(3) $\quad\quad\quad\quad\quad \Delta H_{\text { overall }}=?$

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Problem 70

Write the balanced overall equation (equation 3$)$ for the following process, calculate $\Delta H_{\text { overall }},$ and match the number of each equation with the letter of the appropriate arrow in Figure $\mathrm{P} 6.70$ :
(1) $\quad \mathrm{P}_{4}(s)+6 \mathrm{Cl}_{2}(g) \longrightarrow 4 \mathrm{PCl}_{3}(g) \quad \Delta H=-1148 \mathrm{kJ}$
(2) $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H=-114.2 \mathrm{kJ}$
(3) $\quad\quad\quad\quad\quad \Delta H_{\text { overall }}=?$

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Problem 71

At a given set of conditions, 241.8 $\mathrm{kJ}$ of heat is released when 1 $\mathrm{mol}$ of $\mathrm{H}_{2} \mathrm{O}(g)$ froms from its elements. Under the same conditions, 285.8 $\mathrm{kJ}$ is released when 1 $\mathrm{mol}$ of $\mathrm{H}_{2} \mathrm{O}(l)$ forms from its elements. Find $\Delta H$ for the vaporization of water at these conditions.

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Problem 72

When 1 $\mathrm{mol}$ of $\mathrm{CS}_{2}(l)$ forms from its elements at 1 $\mathrm{atm}$ and $25^{\circ} \mathrm{C}, 89.7 \mathrm{kJ}$ of heat is absorbed, and it takes 27.7 $\mathrm{kJ}$ to vaporize 1 $\mathrm{mol}$ of the liquid. How much heat is absorbed when 1 $\mathrm{mol}$ of $\mathrm{CS}_{2}(g)$ forms from its elements at these conditions?

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Problem 73

Diamond and graphite are two crystalline forms of carbon. At 1 atm and $25^{\circ} \mathrm{C}$ , diamond changes to graphite so slowly that the enthalpy change of the process must be obtained indirectly. Using equations from the numbered list below, determine $\Delta H$ for
$$\mathrm{C}(\text { diamond })\longrightarrow \mathrm{C}(\text { graphite })$$
(1) C(diamond) $+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \quad \Delta H=-395.4 \mathrm{kJ}$
(2) $2 \mathrm{CO}_{2}(g) \longrightarrow 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \quad \Delta H=566.0 \mathrm{kJ}$
(3) C(graphite) $+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \quad \Delta H=-393.5 \mathrm{kJ}$
(4) $2 \mathrm{CO}(g) \longrightarrow \mathrm{C}(\text { graphite })+\mathrm{CO}_{2}(g) \quad \Delta H=-172.5 \mathrm{kJ}$

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Problem 74

What is the difference between the standard enthalpy of formation and the standard enthalpy of reaction?

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Problem 75

How are $\Delta H_{\mathrm{f}}^{\circ}$ values used to calculate $\Delta H_{\mathrm{rxn}}^{\circ} ?$

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Problem 76

Make any changes needed in each of the following equations to make the enthalpy change equal to $\Delta H_{\mathrm{f}}^{\circ}$ for the compound:
(a) $\mathrm{Cl}(g)+\mathrm{Na}(s) \longrightarrow \mathrm{NaCl}(s)$
(b) $\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{H}(g)+\frac{1}{2} \mathrm{O}_{2}(g)$
(c) $\frac{1}{2} \mathrm{N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{NH}_{3}(g)$

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Problem 77

Use Table 6.3 or Appendix $\mathrm{B}$ to write a balanced formation equation at standard conditions for each of the following compounds: (a) $\mathrm{CaCl}_{2} ;(\mathrm{b}) \mathrm{NaHCO}_{3} ;(\mathrm{c}) \mathrm{CCl}_{4} ;(\mathrm{d}) \mathrm{HNO}_{3} .$

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Problem 78

Use Table 6.3 or Appendix $\mathrm{B}$ to write a balanced formation equation at standard conditions for each of the following compounds: $(\mathrm{a}) \mathrm{HI} ;(\mathrm{b}) \operatorname{Si} \mathrm{F}_{4} ;(\mathrm{c}) \mathrm{O}_{3} ;(\mathrm{d}) \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}$

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Problem 79

Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for each of the following:
(a) $2 \mathrm{H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
(b) $\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(l)+\mathrm{HCl}(g) \quad[\text { unbalanced }]$

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Problem 80

Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for each of the following:
(a) $\mathrm{SiO}_{2}(s)+4 \mathrm{HF}(g) \longrightarrow \mathrm{SiF}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
(b) $\mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \quad[\text { unbalanced }]$

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Problem 81

Copper(I) oxide can be oxidized to copper(II) oxide:
$$\mathrm{Cu}_{2} \mathrm{O}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CuO}(s) \quad \Delta H_{\mathrm{mn}}^{\circ}=-146.0 \mathrm{kJ}$$
Given $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{Cu}_{2} \mathrm{O}(s)=-168.6 \mathrm{kJ} / \mathrm{mol},$ find $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{CuO}(s)$

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Problem 82

Acetylene burns in air by the following equation:
$\mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
$\quad\quad\quad\quad\quad\quad\quad \Delta H_{\mathrm{rxn}}^{\circ}=-1255.8 \mathrm{kJ}$
Given $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{CO}_{2}(g)=-393.5 \mathrm{kJ} / \mathrm{mol}$ and $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{H}_{2} \mathrm{O}(g)=$ $-241.8 \mathrm{kJ} / \mathrm{mol},$ find $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{C}_{2} \mathrm{H}_{2}(g)$

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Problem 83

The common lead-acid car battery produces a large burst of current, even at low temperatures, and is rechargeable. The reaction that occurs while recharging a “dead” battery is
$$2 \mathrm{PbSO}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{SO}_{4}(l)$$
(a) Use $\Delta H_{\mathrm{f}}^{\mathrm{o}}$ values from Appendix $\mathrm{B}$ to calculate $\Delta H_{\mathrm{ran}}^{\circ}$
(b) Use the following equations to check your answer to part (a):
(1) $\mathrm{Pb}(s)+\mathrm{PbO}_{2}(s)+2 \mathrm{SO}_{3}(g) \longrightarrow 2 \mathrm{PbSO}_{4}(s)$
$\quad\quad\quad\quad\quad\quad\quad\quad \Delta H_{\mathrm{rxn}}^{\circ}=-768 \mathrm{kJ}$
(2) $\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(l) \quad\quad\quad\quad \Delta H_{\mathrm{rxn}}^{\circ}=-132 \mathrm{kJ}$

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Problem 84

Stearic acid $\left(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\right)$ is a fatty acid, a molecule with a long hydrocarbon chain and an organic acid group (COOH) at the end. It is used to make cosmetics, ointments, soaps, and candles and is found in animal tissue as part of many saturated fats. In fact, when you eat meat, you are ingesting some fats containing stearic acid.
(a) Write a balanced equation for the combustion of stearic acid to gaseous products.
(b) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for this combustion $\left(\Delta H_{\mathrm{f}}^{\circ} \text { of } \mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}=\right.$ $-948 \mathrm{kJ} / \mathrm{mol} )$
(c) Calculate the heat $(q)$ released in $\mathrm{kJ}$ and kcal when 1.00 $\mathrm{g}$ of stearic acid is burned completely.
(d) A candy bar contains 11.0 $\mathrm{g}$ of fat and provides $100 .$ Cal from fat; is this consistent with your answer for part ( $(\mathrm{c}) ?$

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Problem 85

Diluting sulfuric acid with water is highly exothermic;
$$\mathrm{H}_{2} \mathrm{SO}_{4}(l) \stackrel{\mathrm{H} \mathrm{O}}{\longrightarrow} \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+\text {heat}$$
(a) Use Appendix $\mathrm{B}$ to find $\Delta H_{\mathrm{rxn}}^{\circ}$ for diluting 1.00 $\mathrm{mol}$ of $\mathrm{H}_{2} \mathrm{SO}_{4}(l)$ $(d=1.83 \mathrm{g} / \mathrm{mL})$ to 1 $\mathrm{L}$ of 1.00$M \mathrm{H}_{2} \mathrm{SO}_{4}(a q)(d=1.060 \mathrm{g} / \mathrm{mL})$
(b) Suppose you carry out the dilution in a calorimeter. The initial $T$ is $25.0^{\circ} \mathrm{C},$ and the specific heat capacity of the final solution is 3.50 $\mathrm{J} / \mathrm{g} \cdot \mathrm{K}$ . What is the final $T ?$
(c) Use the ideas of density and heat capacity to explain why you should add acid to water rather than water to acid.

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Problem 86

A balloonist begins a trip in a helium-filled balloon in early morning when the temperature is $15^{\circ} \mathrm{C}$ . By mid-afternoon, the temperature is $30^{\circ} \mathrm{C}$ . Assuming the pressure remains at 1.00 $\mathrm{atm}$ , for each mole of helium, calculate the following:
(a) The initial and final volumes
(b) The change in internal energy, $\Delta E$ (Hint: Helium behaves like an ideal gas, so $E=\frac{3}{2} n R T .$ Be sure the units of $R$ are consistent with those of $E . )$
(c) The work ( w) done by the helium (in $\mathrm{J} )$
(d) The heat $(q)$ transferred (in $\mathrm{J} )$
(e) $\Delta H$ for the process (in J)
(f) Explain the relationship between the answers to parts (d) and (e).

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Problem 87

In winemaking, the sugars in grapes undergo fermentation by yeast to yield $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$ and $\mathrm{CO}_{2} .$ During cellular respiration (combustion), sugar and ethanol yield water vapor and $\mathrm{CO}_{2}$.
(a) Using $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ for sugar, calculate $\Delta H_{\mathrm{rxn}}^{\mathrm{o}}$ of fermentation and of respiration.
(b) Write a combustion reaction for ethanol. Which has a higher $\Delta H_{\mathrm{rxn}}^{\circ}$ for combustion per mole of $\mathrm{C},$ sugar or ethanol?

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Problem 88

Three of the reactions that occur when the paraffin of a candle (typical formula $\mathrm{C}_{21} \mathrm{H}_{44} )$ burns are as follows:
(1) Complete combustion forms $\mathrm{CO}_{2}$ and water vapor.
(2) Incomplete combustion forms CO and water vapor.
(3) Some wax is oxidized to elemental $\mathrm{C}$ (soot) and water vapor.
(a) Find $\Delta H_{\text { rxa }}^{\circ}$ of each reaction $\left(\Delta H_{\mathrm{f}}^{\circ} \text { of } \mathrm{C}_{21} \mathrm{H}_{44}=-476 \mathrm{kJ} / \mathrm{mol}\right.$ use graphite for elemental carbon).
(b) Find $q(\text { in } \mathrm{kJ})$ when a 254 -g candle burns completely.
(c) Find $q(\text { in } \mathrm{kJ} \text { ) when } 8.00 \% \text { by mass of the candle burns }$ incompletely and 5.00$\%$ by mass of it undergoes soot formation.

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Problem 89

Ethylene oxide (EO) is prepared by the vapor-phase oxidation of ethylene. Its main uses are in the preparation of the antifreeze ethylene glycol and in the production of poly(ethylene terephthalate), which is used to make beverage bottles and fibers. Pure EO vapor can decompose explosively:
$$\mathrm{H}_{2} \mathrm{C}-\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{CO}(g)$$
Liquid EO has $\Delta H_{\mathrm{f}}^{\circ}=-77.4 \mathrm{kJ} / \mathrm{mol}$ and $\Delta H^{\circ}$ for its vaporization $=569.4 \mathrm{JJg.}$ (a) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for the gas-phase reaction.
(b) External heating causes the vapor to decompose at 10 bar and $93^{\circ} \mathrm{C}$ in a distillation column. What is the final temperature if the average specific heat capacity of the products is 2.5 $\mathrm{JJ} / \mathrm{g} \cdot^{\circ} \mathrm{C} ?$

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Problem 90

The following scenes represent a gaseous reaction between compounds of nitrogen ($blue$) and oxygen ($red$) at 298 K:
(a) Write a balanced equation and use Appendix $\mathrm{B}$ to calculate $\Delta H_{\mathrm{rxx}}^{\mathrm{o}}$
(b) If each molecule of product represents $1.50 \times 10^{-2} \mathrm{mol}$ , what quantity of heat (in $\mathrm{J} )$ is released or absorbed?

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Problem 91

Isooctane $\left(\mathrm{C}_{8} \mathrm{H}_{18} ; d=0.692 \mathrm{g} / \mathrm{mL}\right)$ is used as the fuel in a test of a new automobile drive train.
(a) How much energy (in kJ) is released by combustion of 20.4 gal of isooctane to gases $\left(\Delta H_{\mathrm{rxn}}^{\circ}=-5.44 \times 10^{3} \mathrm{kJ} / \mathrm{mol}\right) ?$
(b) The energy delivered to the wheels at 65 $\mathrm{mph}$ is $5.5 \times 10^{4} \mathrm{kJ} / \mathrm{h}$ . Assuming all the energy is transferred as work to the wheels, how far (in $\mathrm{km} )$ can the car travel on the 20.4 gal of fuel?
(c) If the actual range is 455 $\mathrm{mi}$ , explain your answer to (b).

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Problem 92

Four $50 .$ -g samples of different colorless liquids are placed in beakers at $T_{\text { initial }}=25.00^{\circ} \mathrm{C} .$ Each liquid is heated until $450 . \mathrm{J}$ of heat has been absorbed; $T_{\text { final }}$ is shown on each beaker below. Rank the liquids in order of increasing specific heat capacity.

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Problem 93

Reaction of gaseous ClF with $\mathrm{F}_{2}$ yields liquid $\mathrm{ClF}_{3},$ an important fluorinating agent. Use the following thermochemical equations to calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ for this reaction:
(1) $2 \mathrm{ClF}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{Cl}_{2} \mathrm{O}(g)+\mathrm{OF}_{2}(g) \Delta H_{\mathrm{rxn}}^{\circ}=167.5 \mathrm{kJ}$
(2) $2 \mathrm{F}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{OF}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-43.5 \mathrm{kJ}$
(3) $2 \mathrm{ClF}_{3}(l)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{Cl}_{2} \mathrm{O}(g)+3 \mathrm{OF}_{2}(g)$
$\quad\quad\quad\quad\quad\quad \Delta H_{\mathrm{ran}}^{\circ}=394.1 \mathrm{kJ}$

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Problem 94

Silver bromide is used to coat ordinary black-and-white photographic film, while high-speed film uses silver iodide.
(a) When 50.0 $\mathrm{mL}$ of 5.0 $\mathrm{g} / \mathrm{L}$ AgNO $_{3}$ is added to a coffee-cup calorimeter containing 50.0 $\mathrm{mL}$ of 5.0 $\mathrm{g} / \mathrm{L}$ NaI, with both solutions at $25^{\circ} \mathrm{C},$ what mass of AgI forms?
(b) Use Appendix $\mathrm{B}$ to find $\Delta H_{\mathrm{rxn}}^{\circ}$
(c) What is $\Delta T_{\text { soln }}$ (assuming the volumes are additive and the solution has the density and specific heat capacity of water)?

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Problem 95

The calorie (4.184 J) is defined as the quantity of energy needed to raise the temperature of 1.00 g of liquid water by $1.00^{\circ} \mathrm{C} .$ The British thermal unit (Btu) is defined as the quantity of energy needed to raise the temperature of 1.00 $\mathrm{lb}$ of liquid water by $1.00^{\circ} \mathrm{F} .$
(a) How many joules are in 1.00 $\mathrm{Btu}\left(1 \mathrm{lb}=453.6 \mathrm{g} ; 1.0^{\circ} \mathrm{C}=\right.$ $1.8^{\circ} \mathrm{F} ) ?$
(b) The therm is a unit of energy consumption and is defined as $100,000 \mathrm{Btu.}$ How many joules are in 1.00 therm?
(c) How many moles of methane must be burned to give 1.00 therm of energy? (Assume that water forms as a gas.)
(d) If natural gas costs $\$ 0.66$ per therm, what is the cost per mole of methane? (Assume that natural gas is pure methane.)
(e) How much would it cost to warm 318 gal of water in a hot tub from $15.0^{\circ} \mathrm{C}$ to $42.0^{\circ} \mathrm{C}$ by burning methane $(1 \mathrm{gal}=3.78 \mathrm{L}) ?$

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Problem 96

When organic matter decomposes under oxygen-free (anaerobic) conditions, methane is one of the products. Thus, enormous deposits of natural gas, which is almost entirely methane, serve as a major source of fuel for home and industry.
(a) Known deposits of natural gas can produce 5600 EJ of energy $\left(1 \mathrm{EJ}=10^{18} \mathrm{J}\right)$ . Current total global energy usage is $4.0 \times 10^{2} \mathrm{EJ}$ per year. Find the mass (in kg) of known deposits of natural gas $\left(\Delta H_{\mathrm{xn}}^{\circ} \text { for the combustion of } \mathrm{CH}_{4}=-802 \mathrm{kJ} / \mathrm{mol}\right)$
(b) At current rates of usage, for how many years could these deposits supply the world's total energy needs?
(c) What volume (in $\mathrm{ft}^{3} )$ of natural gas, measured at STP, is required to heat 1.00 $\mathrm{qt}$ of water from $25.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C}$ of $\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{g} / \mathrm{mL} ; d$ of $\mathrm{CH}_{4}$ at $\mathrm{STP}=0.72 \mathrm{g} / \mathrm{L} ) ?$
(d) The fission of 1 $\mathrm{mol}$ of uranium (about $4 \times 10^{-4} \mathrm{ft}^{3} )$ in a nuclear reactor produces $2 \times 10^{13} \mathrm{J}$ . What volume (in $\mathrm{ft}^{3} )$ of natural gas would produce the same amount of energy?

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Problem 97

A reaction takes place in a steel vessel within a chamber filled with argon gas. Shown below are atomic-scale views of the argon adjacent to the surface of the container wall of the reaction vessel before and after the reaction. Was the reaction exothermic or endothermic? Explain.

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Problem 98

An aqueous waste stream with a maximum concentration of 0.50$M \mathrm{H}_{2} \mathrm{SO}_{4}\left(d=1.030 \mathrm{g} / \mathrm{mL} \text { at } 25^{\circ} \mathrm{C}\right)$ is neutralized by controlled addition of 40$\% \mathrm{NaOH}(d=1.430 \mathrm{g} / \mathrm{L})$ before it goes to the process sewer and then to the chemical plant waste treatment facility. A safety review finds that the waste stream could meet a small stream of an immiscible organic compound, which could form a flammable vapor in air at $40^{\circ} \mathrm{C}$ . The maximum temperature reached by the NaOH solution and the waste stream is $31^{\circ} \mathrm{C}$ .Could the temperature increase due to the heat transferred by the neutralization cause the organic vapor to explode? Assume that the specific heat capacity of each solution is 4.184 $\mathrm{J} / \mathrm{g} \cdot \mathrm{K}$ .

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Problem 99

Kerosene, a common space-heater fuel, is a mixture of hydrocarbons whose "average" formula is $\mathrm{C}_{12} \mathrm{H}_{26}$
(a) Write a balanced equation, using the simplest whole-number coefficients, for the complete combustion of kerosene to gases.
(b) If $\Delta H_{\mathrm{rxn}}^{\circ}=-1.50 \times 10^{4} \mathrm{kJ}$ for the combustion equation as written in part (a), determine $\Delta H_{\mathrm{f}}^{\circ}$ of kerosene.
(c) Calculate the heat released by combustion of 0.50 gal of kerosene $(d \text { of kerosene }=0.749 \mathrm{g} / \mathrm{mL})$ .
(d) How many gallons of kerosene must be burned for a kerosene furnace to produce $1250 . \mathrm{Btu}(1 \mathrm{Btu}=1.055 \mathrm{kJ}) ?$

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Problem 100

Silicon tetrachloride is produced annually on the multikiloton scale and used in making transistor-grade silicon. It can be produced directly from the elements (reaction 1) or, more cheaply, by heating sand and graphite with chlorine gas (reaction 2). If water is present in reaction 2, some tetrachloride may be lost in an unwanted side reaction (reaction 3):
(1) $\operatorname{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(g)$
(2) $\mathrm{SiO}_{2}(s)+2 \mathrm{C}(\text { graphite })+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(g)+2 \mathrm{CO}(g)$
(3) $\begin{aligned} \operatorname{SiCl}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow & \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g) \\ & \Delta H_{\mathrm{rxn}}^{\circ}=-139.5 \mathrm{kJ} \end{aligned}$
(a) Use reaction 3 to calculate the standard enthalpies of reaction of reactions 1 and 2.
(b) What is the standard enthalpy of reaction for a fourth reaction that is the sum of reactions 2 and 3?

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Problem 101

One mole of nitrogen gas confined within a cylinder by a piston is heated from $0^{\circ} \mathrm{C}$ to $819^{\circ} \mathrm{C}$ at 1.00 $\mathrm{atm} .$
(a) Calculate the work done by the expanding gas in joules $\left(1 \mathrm{J}=9.87 \times 10^{-3} \mathrm{atm} \cdot \mathrm{L}\right) .$ Assume that all the energy is used to do work.
(b) What would be the temperature change if the gas were heated using the same amount of energy in a container of fixed volume? (Assume that the specific heat capacity of $\mathrm{N}_{2}$ is 1.00 $\mathrm{J} / \mathrm{g} \cdot \mathrm{K} .$ )

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Problem 102

The chemistry of nitrogen oxides is very versatile. Given the following reactions and their standard enthalpy changes,
$(1)\mathrm{NO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{3}(g) \quad \quad \quad \quad\quad \Delta H_{\mathrm{rxn}}^{\circ}=-39.8 \mathrm{kJ}$
$(2) \mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-112.5 \mathrm{kJ}$
$(3) 2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g) \quad\quad \quad \quad \quad \quad \quad \quad \Delta H_{\mathrm{rxn}}^{\circ}=-57.2 \mathrm{kJ}$
$(4) 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \quad\quad \quad \quad \Delta H_{\mathrm{rxn}}^{\circ}=-114.2 \mathrm{kJ}$
$(5) \mathrm{N}_{2} \mathrm{O}_{5}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{5}(g) \quad \quad \quad \quad \quad \quad \quad \Delta H_{\mathrm{rxn}}^{\circ}=54.1 \mathrm{kJ}$
calculate the standard enthalpy of reaction for
$$\mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{N}_{2} \mathrm{O}_{5}(s) \longrightarrow 2 \mathrm{N}_{2} \mathrm{O}_{4}(g)$$

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Problem 103

Electric generating plants transport large amounts of hot water through metal pipes, and oxygen dissolved in the water can cause a major corrosion problem. Hydrazine $\left(\mathrm{N}_{2} \mathrm{H}_{4}\right)$ added to the water avoids the problem by reacting with the oxygen:
$$\mathrm{N}_{2} \mathrm{H}_{4}(a q)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$
About $4 \times 10^{7} \mathrm{kg}$ of hydrazine is produced every year by reacting ammonia with sodium hypochlorite in the Raschig process:
$2 \mathrm{NH}_{3}(a q)+\mathrm{NaOCl}(a q) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(a q)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$
$\quad\quad\quad\quad\quad\quad\quad \Delta H_{\mathrm{rxn}}^{\circ}=-151 \mathrm{kJ}$
(a) If $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{NaOCl}(a q)=-346 \mathrm{kJ} / \mathrm{mol},$ find $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{N}_{2} \mathrm{H}_{4}(a q) .$
(b) What is the heat released when aqueous $\mathrm{N}_{2} \mathrm{H}_{4}$ is added to $5.00 \times 10^{3} \mathrm{L}$ of water that is $2.50 \times 10^{-4} \mathrm{M} \mathrm{O}_{2} ?$

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Problem 104

Liquid methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ can be used as an alternative fuel in pickup and SUV engines. An industrial method for preparing it involves the catalytic hydrogenation of carbon monoxide:
$$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \stackrel{\text { catalyst }}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}(l)$$
How much heat (in $\mathrm{kJ} )$ is released when 15.0 $\mathrm{L}$ of $\mathrm{CO}$ at $85^{\circ} \mathrm{C}$ and 112 kPa reacts with 18.5 $\mathrm{L}$ of $\mathrm{H}_{2}$ at $75^{\circ} \mathrm{C}$ and 744 $\mathrm{torr} ?$

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Problem 105

(a) How much heat is released when 25.0 $\mathrm{g}$ of methane burns in excess $\mathrm{O}_{2}$ to form gaseous $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O} ?$
(b) Calculate the temperature of the product mixture if the methane and air are both at an initial temperature of $0.0^{\circ} \mathrm{C}$ Assume a stoichiometric ratio of methane to oxygen from the air, with air being 21$\% \mathrm{O}_{2}$ by volume $\left(c \text { of } \mathrm{CO}_{2}=57.2 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K} ; c \text { of }\right.$ $\mathrm{H}_{2} \mathrm{O}(g)=36.0 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K} ; c$ of $\mathrm{N}_{2}=30.5 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K} )$

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