Chapter 5

Thermochemistry

Educators


Problem 1

Two positively charged spheres, each with a charge of $2.0 \times$ $10^{-5} \mathrm{C},$ a mass of 1.0 $\mathrm{kg}$ , and separated by a distance of $1.0 \mathrm{cm},$ are held in place on a frictionless track. (a) What is the electrostatic potential energy of this system? If the spheres are released, will they move toward or away from each other? (c) What speed will each sphere attain as the distance between the spheres approaches infinity? [Section 5.1$]$

Matthew B.
Numerade Educator

Problem 2

The accompanying photo shows a pipevine swallowtail caterpillar climbing up a twig. (a) As the caterpillar climbs, its potential energy is increasing. What source of energy has been used to effect this change in potential energy? (b) If the caterpillar is the system, can you predict the sign of $q$ as the caterpillar climbs? (c) Does the caterpillar do work in climbing the twig? Explain. (d) Does the amount of work done in climbing a 12 -inch section of the twig depend on the speed of the caterpillar's climb? (e) Does the change in potential energy depend on the caterpillar's speed of climb? [ Section 5.1$]$

James I.
Numerade Educator

Problem 3

Consider the accompanying energy diagram. (a) Does this diagram represent an increase or decrease in the internal energy of the system? (b) What sign is given to $\Delta E$ for this process? (c) If there is no work associated with the process, is it exothermic or endothermic? [Section 5.2$]$

Matthew B.
Numerade Educator

Problem 4

The contents of the closed box in each of the following illustrations represent a system, and the arrows show the changes to the system during some process. The lengths of the arrows represent the relative magnitudes of $q$ and $w .$ (a) Which of these processes is endothermic? (b) For which of these processes, if any, is $\Delta E<0 ?(\mathbf{c})$ For which process, if any, does the system experience a net gain in internal energy? [ Section 5.2$]$

James I.
Numerade Educator

Problem 5

Imagine that you are climbing a mountain. (a) Is the distance you travel to the top a state function? (b) Is the change in elevation between your base camp and the peak a state function? [Section 5.2$]$

Matthew B.
Numerade Educator

Problem 6

The diagram shows four states of a system, each with different internal energy, $E$ . (a) Which of the states of the system has the greatest internal energy? (b) In terms of the $\Delta E$ values, write two expressions for the difference in internal energy between State A and State B. (c) Write an expression for the difference in energy between State $\mathrm{C}$ and State D. (d) Suppose there is another state of the system, State E, and its energy relative to State A is $\Delta E=\Delta E_{1}+\Delta E_{4}$ . Where
would State $E$ be on the diagram? [ Section 5.2$]$

James I.
Numerade Educator

Problem 7

You may have noticed that when you compress the air in a bicycle pump, the body of the pump gets warmer. (a) Assuming the pump and the air in it comprise the system, what is the sign of w when you compress the air? (b) What is the sign of $q$ for this process? (c) Based on your answers to parts (a) and (b), can you determine the sign of $\Delta E$ for compressing the air in the pump? If not, what would you expect for the sign of $\Delta E ?$ What is your reasoning? [Section 5.2$]$

Matthew B.
Numerade Educator

Problem 8

Imagine a container placed in a tub of water, as depicted in the accompanying diagram. (a) If the contents of the container are the system and heat is able to flow through the container walls, what qualitative changes will occur in the temperatures of the system and in its surroundings? From the
system’s perspective, is the process exothermic or endothermic? (b) If neither the volume nor the pressure of the system changes during the process, how is the change in internal energy related to the change in enthalpy? [Sections 5.2 and 5.3]

James I.
Numerade Educator

Problem 9

In the accompanying cylinder diagram, a chemical process occurs at constant temperature and pressure. (a) Is the sign of w indicated by this change positive or negative? (b) If the process is endothermic, does the internal energy of the system within the cylinder increase or decrease during the change and is $\Delta E$ positive or negative? [Sections 5.2 and 5.3$]$

Matthew B.
Numerade Educator

Problem 10

The gas-phase reaction shown, between $\mathrm{N}_{2}$ and $\mathrm{O}_{2},$ was run in an apparatus designed to maintain a constant pressure. (a) Write a balanced chemical equation for the reaction depicted and predict whether $w$ is positive, negative, or zero. (b) Using data from Appendix C, determine $\Delta H$ for the formation of one mole of the product. [Sections 5.3 and 5.7$]$

James I.
Numerade Educator

Problem 11

Consider the two diagrams that follow. (a) Based on (i), write an equation showing how $\Delta H_{A}$ is related to $\Delta H_{B}$ and $\Delta H_{C}$ . (b) Based on (ii), write an equation relating $\Delta H_{Z}$ to the other enthalpy changes in the diagram. (c) The equations you obtained in parts (a) and (b) are based on what law? (d) Would similar relationships hold for the work involved in each process? [Section 5.6$]$

Matthew B.
Numerade Educator

Problem 12

Consider the conversion of compound A into compound B: A $\longrightarrow$ B. For both compounds A and $B, \Delta H_{f}^{\circ}>0 .$ (a) Sketch an enthalpy diagram for the reaction that is analogous to Figure 5.23 . (b) Suppose the overall reaction is exothermic. What can you conclude? [Section 5.7$]$

James I.
Numerade Educator

Problem 13

(a) What is the electrostatic potential energy (in joules) between an electron and a proton that are separated by 53 pm? (b) What is the change in potential energy if the distance separating the electron and proton is increased to 1.0 nm? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

Matthew B.
Numerade Educator

Problem 14

(a) What is the electrostatic potential energy (in joules) between two protons that are separated by 62 pm? (b) What is the change in potential energy if the distance separating the two is increased to 1.0 nm? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

James I.
Numerade Educator

Problem 15

(a) The electrostatic force (not energy) of attraction between two oppositely charged objects is given by the equation $F=\kappa\left(Q_{1} Q_{2} / d^{2}\right)$ where $\kappa=8.99 \times 10^{9} \mathrm{N}-\mathrm{m}^{2} / \mathrm{C}^{2}, Q_{1}$ and $\mathrm{Q}_{2}$ are the charges of the two objects in Coulombs, and $d$ is the distance separating the two objects in meters. What is the electrostatic force of attraction (in Newtons) between an electron and a proton that are separated by $1.00 \times 10^{2}$ pm? (b) The force of gravity acting between two objects is given by the equation $F=G\left(m_{1} m_{2} / d^{2}\right),$ where $G$ is the gravitational constant, $G=6.674 \times 10^{-11} \mathrm{N}-\mathrm{m}^{2} / \mathrm{kg}^{2}, m_{1}$ and $m_{2}$ are the masses of the two objects, and $d$ is the distance separating them. What is the gravitational force of attraction (in Newtons) between the electron and proton? (c) How many times larger is the electrostatic force of attraction?

Matthew B.
Numerade Educator

Problem 16

Use the equations given in Problem 5.15 to calculate: (a) The electrostatic force of repulsion for two protons separated by 75 $\mathrm{pm} .(\mathbf{b})$ The gravitational force of attraction for two
protons separated by 75 $\mathrm{pm} .$ (c) If allowed to move, will the protons be repelled or attracted to one another?

James I.
Numerade Educator

Problem 17

A sodium ion, $\mathrm{Na}^{+},$ with a charge of $1.6 \times 10^{-19} \mathrm{Cand}$ a chloride ion, $\mathrm{Cl}^{-},$ with charge of $-1.6 \times 10^{-19} \mathrm{C}$ , are separated by a distance of 0.50 $\mathrm{nm}$ . How much work would be required to increase the separation of the two ions to an infinite distance?

Matthew B.
Numerade Educator

Problem 18

A magnesium ion, Mg $^{2+},$ with a charge of $3.2 \times 10^{-19} \mathrm{Cand}$ an oxide ion, $\mathrm{O}^{2-},$ with a charge of $-3.2 \times 10^{-19} \mathrm{C}$ , are separated by a distance of 0.35 $\mathrm{nm}$ . How much work would be required to increase the separation of the two ions to an infinite distance?

James I.
Numerade Educator

Problem 19

Identify the force present and explain whether work is being performed in the following cases: (a) You lift a pencil off the top of a desk. $(\mathbf{b})$ A spring is compressed to half its normal length.

Matthew B.
Numerade Educator

Problem 20

Identify the force present and explain whether work is done when (a) a positively charged particle moves in a circle at a fixed distance from a negatively charged particle, (b) an iron nail is pulled off a magnet.

James I.
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Problem 21

(a) Which of the following cannot leave or enter a closed system: heat, work, or matter? (b) Which cannot leave or enter an isolated system? (c) What do we call the part of the universe that is not part of the system?

Matthew B.
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Problem 22

In a thermodynamic study, a scientist focuses on the properties of a solution in an apparatus as illustrated. A solution is continuously flowing into the apparatus at the top and out at the bottom, such that the amount of solution in the apparatus is constant with time. (a) Is the solution in the apparatus a closed system, open system, or isolated system? (b) If the inlet and outlet were closed, what type of system would it be?

James I.
Numerade Educator

Problem 23

(a) According to the first law of thermodynamics, what quantity is conserved? (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

Matthew B.
Numerade Educator

Problem 24

(a) Write an equation that expresses the first law of thermodynamics in terms of heat and work. (b) Under what conditions will the quantities q and w be negative numbers?

James I.
Numerade Educator

Problem 25

Calculate $\Delta E$ and determine whether the process is endothermic or exothermic for the following cases: (a) $q=0.763 \mathrm{kJ}$ and $w=-840 \mathrm{J} .$ (b) A system releases 66.1 $\mathrm{kJ}$ of heat to its surroundings while the surroundings do 44.0 $\mathrm{kJ}$ of work on
the system.

Matthew B.
Numerade Educator

Problem 26

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing 0.655 $\mathrm{kJ}$ of heat. It shrinks on cooling, and the atmosphere does 382 J of work on the balloon. (b) A 100.0 -g bar of gold is heated from $25^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ during which it absorbs 322 $\mathrm{J}$ of heat. Assume the volume of the gold bar remains constant.

James I.
Numerade Educator

Problem 27

A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here: Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (a) In which case does the gas have the higher temperature after addition of the electrical energy? (b) Identify the sign (positive, negative, or zero) of $q$ and $w$ in each case? (c) In which case is $\Delta E$ for the system (the gas in the cylinder) larger?

Matthew B.
Numerade Educator

Problem 28

Consider a system consisting of two oppositely charged spheres hanging by strings and separated by a distance $r_{1}$ as shown in the accompanying illustration. Suppose they are separated to a larger distance $r_{2},$ by moving them apart. (a) What change, if any, has occurred in the potential energy
of the system? (b) What effect, if any, does this process have on the value of $\Delta E ?(\mathbf{c})$ What can you say about $q$ and $w$ for this process?

James I.
Numerade Educator

Problem 29

(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of a system a state function? Why or why not?

Matthew B.
Numerade Educator

Problem 30

Indicate which of the following is independent of the path by which a change occurs: (a) the change in potential energy when a book is transferred from table to shelf, (b) the heat evolved when a cube of sugar is oxidized to $\operatorname{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g),(\mathbf{c})$ the work accomplished in burning a gallon of gasoline.

James I.
Numerade Educator

Problem 31

During a normal breath, our lungs expand about 0.50 L against an external pressure of 1.0 atm. How much work is involved in this process (in J)?

Matthew B.
Numerade Educator

Problem 32

How much work (in J) is involved in a chemical reaction if the volume decreases from 5.00 to 1.26 L against a constant pressure of 0.857 atm?

James I.
Numerade Educator

Problem 33

(a) Why is the change in enthalpy usually easier to measure than the change in internal energy? (b) $H$ is a state function, but $q$ is not a state function. Explain. (c) For a given process at constant pressure, $\Delta H$ is positive. Is the process endothermic or exothermic?

Matthew B.
Numerade Educator

Problem 34

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant-pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, $\Delta H=0 .$ What can you conclude about $\Delta E, q,$ and $w ?$

James I.
Numerade Educator

Problem 35

Assume that the following reaction occurs at constant pressure:
$$2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s)$$
(a) If you are given $\Delta H$ for the reaction, what additional information do you need to determine $\Delta E$ for the process? (b) Which quantity is larger for this reaction? (c) Explain your answer to part (b).

Matthew B.
Numerade Educator

Problem 36

Suppose that the gas-phase reaction $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow$ 2 $\mathrm{NO}_{2}(g)$ were carried out in a constant-volume container at constant temperature. (a) Would the measured heat change represent $\Delta H$ or $\Delta E ?$ (b) If there is a difference, which quantity is larger for this reaction? (c) Explain your answer to part (b).

James I.
Numerade Educator

Problem 37

A gas is confined to a cylinder under constant atmospheric pressure, as illustrated in Figure $5.4 .$ When the gas undergoes a particular chemical reaction, it absorbs 824 $\mathrm{J}$ of heat from its surroundings and has 0.65 $\mathrm{kJ}$ of $P-V$ work done on it by its surroundings. What are the values of $\Delta H$ and $\Delta E$ for this process?

Matthew B.
Numerade Educator

Problem 38

A gas is confined to a cylinder under constant atmospheric pressure, as illustrated in Figure $5.4 .$ When 0.49 kJ of heat is added to the gas, it expands and does 214 J of work on the surroundings. What are the values of $\Delta H$ and $\Delta E$ for this process?

James I.
Numerade Educator

Problem 39

The complete combustion of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l),$ to form
$\mathrm{H}_{2} \mathrm{O}(g)$ and $\mathrm{CO}_{2}(g)$ at constant pressure releases 1235 $\mathrm{kJ}$ of heat per mole of $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.

Matthew B.
Numerade Educator

Problem 40

The decomposition of $\mathrm{Ca}(\mathrm{OH})_{2}(s)$ into $\mathrm{CaO}(s)$ and $\mathrm{H}_{2} \mathrm{O}(g)$ at constant pressure requires the addition of 109 $\mathrm{kJ}$ of heat per mole of $\mathrm{Ca}(\mathrm{OH})_{2}$ . (a) Write a balanced thermochemical equation for the reaction. (b) Draw an enthalpy diagram for the reaction.

James I.
Numerade Educator

Problem 41

Ozone, $\mathrm{O}_{3}(g),$ is a form of elemental oxygen that plays an important role in the absorption of ultraviolet radiation in the stratosphere. It decomposes to $\mathrm{O}_{2}(g)$ at room temperature
and pressure according to the following reaction:
$$2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g) \quad \Delta H=-284.6 \mathrm{kJ}$$
(a) What is the enthalpy change for this reaction per mole of $\mathrm{O}_{3}(g) ?$
(b) Which has the higher enthalpy under these conditions, 2 $\mathrm{O}_{3}(g)$ or 3 $\mathrm{O}_{2}(g) ?$

Matthew B.
Numerade Educator

Problem 42

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) 1 $\mathrm{mol} \mathrm{CO}_{2}(s)$ or 1 $\mathrm{mol} \mathrm{CO}_{2}(g)$ at the same temperature, ( b) 2 $\mathrm{mol}$ of hydrogen atoms or 1 $\mathrm{mol}$ of $\mathrm{H}_{2},(\mathbf{c}) 1 \mathrm{mol} \mathrm{H}_{2}(g)$ and 0.5 $\mathrm{mol} \mathrm{O}_{2}(g)$ at
$25^{\circ} \mathrm{C}$ or 1 $\mathrm{mol} \mathrm{H}_{2} \mathrm{O}(g)$ at $25^{\circ} \mathrm{C},(\mathbf{d}) 1 \mathrm{mol} \mathrm{N}_{2}(g)$ at $100^{\circ} \mathrm{C}$ or
1 $\mathrm{mol} \mathrm{N}_{2}(g)$ at $300^{\circ} \mathrm{C}$ .

James I.
Numerade Educator

Problem 43

Consider the following reaction:
$$2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H=-1204 \mathrm{kJ}$$
(a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when 3.55 $\mathrm{g}$ of $\mathrm{Mg}(s)$ reacts at constant pressure. (c) How many grams of MgO are produced during an enthalpy change of $-234 \mathrm{kJ}$ ? (d) How many kilojoules of heat are absorbed when 40.3 $\mathrm{g}$ of MgO(s) is decomposed into $\mathrm{Mg}(s)$ and $\mathrm{O}_{2}(g)$ at con stant pressure?

Matthew B.
Numerade Educator

Problem 44

Consider the following reaction:
$$2 \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \quad \Delta H=+252.8 \mathrm{kJ}$$
(a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when 24.0 of $\mathrm{CH}_{3} \mathrm{OH}(g)$ is decomposed by this reaction at constant pressure. (c) For a given sample of $\mathrm{CH}_{3} \mathrm{OH},$ the enthalpy change during the reaction is 82.1 kJ. How many grams of methane gas are produced? (\mathbf{d} ) How many kilojoules of heatare released when 38.5 $\mathrm{g}$ of $\mathrm{CH}_{4}(g)$ reacts completely with $\mathrm{O}_{2}(g)$ to form $\mathrm{CH}_{3} \mathrm{OH}(g)$ at constant pressure?

James I.
Numerade Educator

Problem 45

When solutions containing silver ions and chloride ions are mixed, silver chloride precipitates
$$\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s) \quad \Delta H=-65.5 \mathrm{kJ}$$ (a) Calculate $\Delta H$ for the production of 0.450 mol of AgCl by this reaction. (b) Calculate $\Delta H$ for the production of 9.00 $\mathrm{g}$ of AgCl. (c) Calculate $\Delta H$ when $9.25 \times 10^{-4} \mathrm{mol}$ of AgCl dissolves in water.

Matthew B.
Numerade Educator

Problem 46

At one time, a common means of forming small quantities of oxygen gas in the laboratory was to heat $\mathrm{KClO}_{3} :$ $$2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g) \quad \Delta H=-89.4 \mathrm{kJ}$$ For this reaction, calculate $\Delta H$ for the formation of (a) 1.36 $\mathrm{mol}$ of $\mathrm{O}_{2}$ and $(\mathbf{b}) 10.4 \mathrm{g}$ of $\mathrm{KCl}$ (c) The decomposition of $\mathrm{KClO}_{3}$ proceeds spontaneously when it is heated. Do you think that the reverse reaction, the formation of $\mathrm{KClO}_{3}$ from $\mathrm{KCl}$ and $\mathrm{O}_{2},$ is likely to be feasible under ordinary conditions? Explain your answer.

James I.
Numerade Educator

Problem 47

Consider the combustion of liquid methanol, $\mathrm{CH}_{3} \mathrm{OH}(l) :$
$$\begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H &=-726.5 \mathrm{kJ} \end{aligned}$$ (a) What is the enthalpy change for the reverse reaction? (b) Balance the forward reaction with whole-number coefficients. What is $\Delta H$ for the reaction represented by this equation? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If the reaction were written to produce $\mathrm{H}_{2} \mathrm{O}(g)$ instead of $\mathrm{H}_{2} \mathrm{O}(l),$ would you expect the magnitude of $\Delta H$ to increase, decrease, or stay the same? Explain.

Matthew B.
Numerade Educator

Problem 48

Consider the decomposition of liquid benzene, $\mathrm{C}_{6} \mathrm{H}_{6}(l),$ to gaseous acetylene, $\mathrm{C}_{2} \mathrm{H}_{2}(g) :$ $$\mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{kJ}$$ (a) What is the enthalpy change for the reverse reaction? (b) What is $\Delta H$ for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If $\mathrm{C}_{6} \mathrm{H}_{6}(g)$ were consumed instead of $\mathrm{C}_{6} \mathrm{H}_{6}(l),$ would you expect the magnitude of $\Delta H$ to increase, decrease, or stay the same? Explain.

James I.
Numerade Educator

Problem 49

(a) What are the units of molar heat capacity? (b) What are the units of specific heat? (c) If you know the specific heat of copper, what additional information do you need to calculate the heat capacity of a particular piece of copper pipe?

Matthew B.
Numerade Educator

Problem 50

Two solid objects, A and $\mathrm{B},$ are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing 1000 $\mathrm{g}$ water at $10.0^{\circ} \mathrm{C} .$ Object A increases the water temperature by $3.50^{\circ} \mathrm{C} ; \mathrm{B}$ increases the water temperature by $2.60^{\circ} \mathrm{C}$ .
(a) Which object has the larger heat capacity? (b) What can you say about the specific heats of $\mathrm{A}$ and $\mathrm{B} ?$

James I.
Numerade Educator

Problem 51

(a) What is the specific heat of liquid water? (b) What is the molar heat capacity of liquid water? (c) What is the heat capacity of 185 g of liquid water? (d) How many kJ of heat are needed to raise the temperature of 10.00 $\mathrm{kg}$ of liquid water from 24.6 to $46.2^{\circ} \mathrm{C}$ ?

Matthew B.
Numerade Educator

Problem 52

(a) Which substance in Table 5.2 requires the smallest amount of energy to increase the temperature of 50.0 g of that substance by 10 K? (b) Calculate the energy needed for this temperature change.

James I.
Numerade Educator

Problem 53

The specific heat of octane, $\mathrm{C}_{8} \mathrm{H}_{18}(l),$ is $2.22 \mathrm{J} / \mathrm{g}-\mathrm{K}$ . How many J of heat are needed to raise the temperature of 80.0 $\mathrm{g}$ of octane from 10.0 to $25.0^{\circ} \mathrm{C} ?$ (b) Which will require more heat, increasing the temperature of 1 $\mathrm{mol}$ of $\mathrm{C}_{8} \mathrm{H}_{18}(l)$ by a certain amount or increasing the temperature of 1 mol of $\mathrm{H}_{2} \mathrm{O}(l)$ by the same amount?

Matthew B.
Numerade Educator

Problem 54

Consider the data about gold metal in Exercise 5.26$(\mathrm{b})$ . (a) Based on the data, calculate the specific heat of Au(s). (b) Suppose that the same amount of heat is added to two 10.0 -g blocks of metal, both initially at the same temperature. One block is gold metal, and one is iron metal. Which block will have the greater rise in temperature after the addition of the heat? (c) What is the molar heat capacity of $\operatorname{Au}(s) ?$

James I.
Numerade Educator

Problem 55

When a 6.50 -g sample of solid sodium hydroxide dissolves in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18$)$ the temperature rises from 21.6 to to $37.8^{\circ} \mathrm{C}$ . (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate $\Delta H$ (in $\mathrm{kJ} / \mathrm{mol} \mathrm{NaOH} )$ for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

Matthew B.
Numerade Educator

Problem 56

(a) When a 4.25 -g sample of solid ammonium nitrate dissolves in 60.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature drops from 22.0 to $16.9^{\circ} \mathrm{C}$ . Calculate
$\Delta H\left($ in $\mathrm{kJ} / \mathrm{mol} \mathrm{NH}_{4} \mathrm{NO}_{3}\right)$ for the solution process: $$\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)$$ Assume that the specific heat of the solution is the same as that of pure water. (b) Is this process endothermic or exothermic?

James I.
Numerade Educator

Problem 57

A 2.200 -g sample of quinone $\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)$ is burned in a bomb calorimeter whose total heat capacity is 7.854 $\mathrm{kJ} / \mathrm{c}$ . The temperature of the calorimeter increases from 23.44 to $30.57^{\circ} \mathrm{C}$ . What is the heat of combustion per gram of quinone? Per mole of quinone?

Matthew B.
Numerade Educator

Problem 58

A 1.800 -g sample of phenol $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)$ was burned in a bomb calorimeter whose total heat capacity is 11.66 $\mathrm{kJ} /^{\circ} \mathrm{C}$ The temperature of the calorimeter plus contents increased from 21.36 to $26.37^{\circ} \mathrm{C}$ (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol? Per mole of phenol?

James I.
Numerade Educator

Problem 59

Under constant-volume conditions, the heat of combustion of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ is 15.57 $\mathrm{kJ} / \mathrm{g}$ . A 3.500 -g sample of glucose is burned in a bomb calorimeter. The temperature of the calorimeter increases from 20.94 to $24.72^{\circ} \mathrm{C}$ (a) What is the total heat capacity of the calorimeter? (b) If the size of the glucose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

Matthew B.
Numerade Educator

Problem 60

Under constant-volume conditions, the heat of combustion of benzoic acid $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}$ ) is 26.38 $\mathrm{kJ} / \mathrm{g} .$ A 2.760 -g sample of \right.
benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.60 to $29.93^{\circ} \mathrm{C}$ (a) What is the total heat capacity of the calorimeter? $\mathrm{b}$ ) $\mathrm{A} 1.440$ -g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 22.14 to $27.09^{\circ} \mathrm{C} .$ What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

James I.
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Problem 61

Can you use an approach similar to Hess's law to calculate the change in internal energy, $\Delta E,$ for an overall reaction by summing the $\Delta E$ values of individual reactions that add up to give the desired overall reaction?

Matthew B.
Numerade Educator

Problem 62

Consider the following hypothetical reactions:
$$\begin{array}{ll}{\mathrm{A} \longrightarrow \mathrm{B}} & {\Delta H=+30 \mathrm{kJ}} \\ {\mathrm{B} \longrightarrow \mathrm{C}} & {\Delta H=+60 \mathrm{kJ}}\end{array}$$
(a) Use Hess's law to calculate the enthalpy change for the reaction $A \longrightarrow C .$
(b) Construct an enthalpy diagram for substances $A,$ and C, and show how Hess's law applies.

James I.
Numerade Educator

Problem 63

Calculate the enthalpy change for the reaction
$$\mathrm{P}_{4} \mathrm{O}_{6}(s)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s)$$ given the following enthalpies of reaction:
$$\begin{array}{ll}{\mathrm{P}_{4}(s)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{6}(s)} & {\Delta H=-1640.1 \mathrm{kJ}} \\ {\mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s)} & {\Delta H=-2940.1 \mathrm{kJ}}\end{array}$$

Matthew B.
Numerade Educator

Problem 64

From the enthalpies of reaction
$$\begin{aligned} 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) & \Delta H=-221.0 \mathrm{kJ} \\ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{3} \mathrm{OH}(g) & \Delta H=-402.4 \mathrm{kJ} \end{aligned}$$
calculate $\Delta H$ for the reaction $$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)$$

James I.
Numerade Educator

Problem 65

From the enthalpies of reaction
$$\begin{aligned} \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g) & \Delta H=-537 \mathrm{kJ} \\ \mathrm{C}(s)+2 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g) & \Delta H=-680 \mathrm{kJ} \\ 2 \mathrm{C}(s)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g) & \Delta H=+52.3 \mathrm{kJ} \end{aligned}$$
calculate $\Delta H$ for the reaction of ethylene with $\mathrm{F}_{2} :$
$$\mathrm{C}_{2} \mathrm{H}_{4}(g)+6 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$$

Matthew B.
Numerade Educator

Problem 66

Given the data
$$\begin{aligned} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) & \Delta H=+180.7 \mathrm{kJ} \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) & \Delta H=-113.1 \mathrm{kJ} \\ 2 \mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \Delta H=-163.2 \mathrm{kJ} \end{aligned}$$
use Hess's law to calculate $\Delta H$ for the reaction
$$\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{NO}(g)$$

James I.
Numerade Educator

Problem 67

(a) What is meant by the term standard conditions with reference to enthalpy changes? (b) What is meant by the term enthalpy of formation? (c) What is meant by the term standard enthalpy of formation?

Matthew B.
Numerade Educator

Problem 68

(a) What is the value of the standard enthalpy of formation of an element in its most stable form? (b) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of sucrose (table sugar), $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s), \Delta H_{f}^{\circ}\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)\right]$

James I.
Numerade Educator

Problem 69

For each of the following compounds, write a balanced thermochemical equation depicting the formation of one mole of the compound from its elements in their standard states and then look up $\Delta H^{\circ} f$ for each substance in Appendix C. (a) $\mathrm{NO}_{2}(g),(\mathbf{b}) \mathrm{SO}_{3}(g),(\mathbf{c}) \mathrm{NaBr}(s),(\mathbf{d}) \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s) .$

Matthew B.
Numerade Educator

Problem 70

Write balanced equations that describe the formation of the following compounds from elements in their standard states, and then look up the standard enthalpy of formation for each substance in Appendix C: (a) $\mathrm{H}_{2} \mathrm{O}_{2}(g),(\mathbf{b}) \mathrm{CaCO}_{3}(s)$
(c) $\mathrm{POCl}_{3}(l),(\mathbf{d}) \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) .$

James I.
Numerade Educator

Problem 71

The following is known as the thermite reaction:
$$2 \mathrm{Al}(s)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s)$$
This highly exothermic reaction is used for welding massive units, such as propellers for large ships. Using standard enthalpies of formation in Appendix C, calculate $\Delta H^{\circ}$ for this reaction.

Matthew B.
Numerade Educator

Problem 72

Many portable gas heaters and grills use propane, $\mathrm{C}_{3} \mathrm{H}_{8}(g),$ as a fuel. Using standard enthalpies of formation, calculate the quantity of heat produced when 10.0 g of propane is completely combusted in air under standard conditions.

James I.
Numerade Educator

Problem 73

Using values from Appendix $\mathrm{C}$ , calculate the standard enthalpy change for each of the following reactions:
$$
\begin{array}{l}{\text { (a) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)} \\ {\text { (b) } \mathrm{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)}\end{array}
$$

Matthew B.
Numerade Educator

Problem 74

Using values from Appendix $\mathrm{C}$ , calculate the value of $\Delta H^{\circ}$ for each of the following reactions:
$$\begin{array}{l}{\text { (a) } \mathrm{CaO}(s)+2 \mathrm{HCl}(g) \longrightarrow \mathrm{CaCl}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (b) } 4 \mathrm{FeO}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)} \\ {\text { (c) } 2 \mathrm{CuO}(s)+\mathrm{NO}(g) \longrightarrow \mathrm{Cu}_{2} \mathrm{O}(s)+\mathrm{NO}_{2}(g)} \\ {\text { (d) } 4 \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)}\end{array}$$

James I.
Numerade Educator

Problem 75

Complete combustion of 1 mol of acetone $\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)$ liberates $1790 \mathrm{kJ} :$
$$\begin{aligned} \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l)+4 \mathrm{O}_{2}(g) \longrightarrow & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) \\ & \quad \quad \quad \quad \quad \quad \quad \Delta H^{\circ}=-1790 \mathrm{kJ} \end{aligned}$$
Using this information together with the standard enthalpies of formation of $\mathrm{O}_{2}(g), \mathrm{CO}_{2}(g),$ and $\mathrm{H}_{2} \mathrm{O}(l)$ from Appendix $\mathrm{C},$ calculate the standard enthalpy of formation of acetone.

Matthew B.
Numerade Educator

Problem 76

Calcium carbide $\left(\mathrm{CaC}_{2}\right)$ reacts with water to form acetylene
$\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$ and $\mathrm{Ca}(\mathrm{OH})_{2} .$ From the following enthalpy of reaction data and data in Appendix $\mathrm{C},$ calculate $\Delta H_{f}^{\circ}$ for $\mathrm{CaC}_{2}(s) :$
$$\begin{aligned} \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \Delta H^{\circ}=-127.2 \mathrm{kJ} \end{aligned}$$

James I.
Numerade Educator

Problem 77

Gasoline is composed primarily of hydrocarbons, including many with eight carbon atoms, called octanes. One of the cleanest-burning octanes is a compound called $2,3,4-$ trimethylpentane, which has the following structural formula:
$$\begin{array}{c}{\mathrm{CH}_{3} \mathrm{CH}_{3} \mathrm{CH}_{3}} \\ {\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3}}\end{array}$$
The complete combustion of one mole of this com-
pound to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$ leads to $\Delta H^{\circ}=-5064.9 \mathrm{kJ}$ (a) Write a balanced equation for the combustion of 1 mol of $\mathrm{C}_{8} \mathrm{H}_{18}(l) .$ (b) By using the information in this problem and data in Table $5.3,$ calculate $\Delta H_{f}^{\circ}$ for $2,3,4$ -trimethylpentane.

Matthew B.
Numerade Educator

Problem 78

Diethyl ether, $\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l),$ a flammable compound that was once used as a surgical anesthetic, has the structure
$$\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}_{3}$$
The complete combustion of 1 mol of $\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)$ to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ yields $\Delta H^{\circ}=-2723.7 \mathrm{kJ}$ . (a) Write a balanced equation for the combustion of 1 $\mathrm{mol}$ of $\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l) .$ (b) By using the information in this problem and data in Table $5.3,$ calculate $\Delta H_{f}^{\circ}$ for diethyl ether.

James I.
Numerade Educator

Problem 79

Ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ is blended with gasoline as an automobile fuel. (a) Write a balanced equation for the combustion of liquid ethanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming $\mathrm{H}_{2} \mathrm{O}(g)$ as a product.
(c) Calculate the heat produced per liter of ethanol by combustion of ethanol under constant pressure. Ethanol has a density of 0.789 $\mathrm{g} / \mathrm{mL}$ (d) Calculate the mass of $\mathrm{CO}_{2}$ produced per ky of heat emitted.

Matthew B.
Numerade Educator

Problem 80

Methanol (CH $_{3} \mathrm{OH}$ ) is used as a fuel in race cars. (a) Write a balanced equation for the combustion of liquid methanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming $\mathrm{H}_{2} \mathrm{O}(g)$ as a product. (c) Calculate the heat produced by combustion per liter of methanol. Methanol has a density of 0.791 $\mathrm{g} / \mathrm{mL}$ . (d) Calculate the mass of $\mathrm{CO}_{2}$ produced per kJ of heat emitted.

James I.
Numerade Educator

Problem 81

Without doing any calculations, predict the sign of $\Delta H$ for each of the following reactions:
$$\begin{array}{l}{\text { (a) } \mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{Cl}^{-}(\mathrm{g})} \\ {\text { (b) } 2 \mathrm{H}(g) \longrightarrow \mathrm{H}_{2}(g)} \\ {\text { (c) } \mathrm{Na}(g) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{e}^{-}} \\ {\text { (d) } \mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(l)}\end{array}$$

Matthew B.
Numerade Educator

Problem 82

Without doing any calculations, predict the sign of $\Delta H$ for each of the following reactions:
$$\begin{array}{l}{\text { (a) } 2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)} \\ {\text { (b) } 2 \mathrm{F}(g) \longrightarrow \mathrm{F}_{2}(g)} \\ {\text { (c) } \mathrm{Mg}^{2+}(g)+2 \mathrm{Cl}^{-}(g) \longrightarrow \mathrm{MgCl}_{2}(s)} \\ {\text { (d) } \mathrm{HBr}(g) \longrightarrow \mathrm{H}(g)+\mathrm{Br}(g)}\end{array}$$

James I.
Numerade Educator

Problem 83

Use bond enthalpies in Table 5.4 to estimate $\Delta H$ for each of the following reactions:
(a) $\mathrm{H}-\mathrm{H}(g)+\mathrm{Br}-\mathrm{Br}(g) \longrightarrow 2 \mathrm{H}-\mathrm{Br}(g)$
(b)

Matthew B.
Numerade Educator

Problem 84

Use bond enthalpies in Table 5.4 to estimate $\Delta H$ for each of
the following reactions:

James I.
Numerade Educator

Problem 85

(a) Use enthalpies of formation given in Appendix $C$ to calculate $\Delta H$ for the reaction $B r_{2}(g) \longrightarrow 2$ Br $(g),$ and use this value to estimate the bond enthalpy $D(\mathrm{Br}-\mathrm{Br}) .$ (b) How large is the difference between the value calculated in part (a) and the value given in Table 5.4 ?

Matthew B.
Numerade Educator

Problem 86

(a) The nitrogen atoms in an $\mathrm{N}_{2}$ molecule are held together by a triple bond; use enthalpies of formation in Appendix $\mathrm{C}$ to estimate the enthalpy of this bond, $D(\mathrm{N}=\mathrm{N}) .$ (b) Consider the reaction between hydrazine and hydrogen to produce ammonia, $\mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3 (g) .$ Use enthalpies of formation and bond enthalpies to estimate the enthalpy of the nitrogen- nitrogen bond in $\mathrm{N}_{2} \mathrm{H}_{4}$ . (c) Based on your answers to parts (a) and (b), would you predict that the nitrogen-nitrogen bond in hydrazine is weaker than, similar to, or stronger than the bond in $\mathrm{N}_{2}$ ?

James I.
Numerade Educator

Problem 87

Consider the reaction $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)$ (a) Use the bond enthalpies in Table 5.4 to estimate $\Delta H$ for this reaction, ignoring the fact that water is in the liquid state. (b) Without doing a calculation, predict whether your estimate in part (a) is more negative or less negative than the true reaction enthalpy. (c) Use the enthalpies of formation in Appendix $C$ to determine the true reaction enthalpy.

Matthew B.
Numerade Educator

Problem 88

Consider the reaction $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow 2 \mathrm{HI}(g) .(\mathbf{a})$ Use the bond enthalpies in Table 5.4 to estimate $\Delta H$ for this reaction, ignoring the fact that iodine is in the solid state. (b) Without doing a calculation, predict whether your estimate in part (a) is more negative or less negative than the true reaction enthalpy. (c) Use the enthalpies of formation in Appendix $C$ to determine the true reaction enthalpy.

James I.
Numerade Educator

Problem 89

(a) What is meant by the term fuel value? (b) Which is a greater source of energy as food, 5 g of fat or 9 g of carbohydrate? (c) The metabolism of glucose produces $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ How does the human body expel these reaction products?

Matthew B.
Numerade Educator

Problem 90

(a) Which releases the most energy when metabolized, 1 $\mathrm{g}$ of carbohydrates or 1 $\mathrm{g}$ of fat? (b) A particular chip snack food is composed of 12$\%$ protein, 14$\%$ fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as 25 of fat?

James I.
Numerade Educator

Problem 91

(a) A serving of a particular ready-to-serve chicken noodle soup contains 2.5 $\mathrm{g}$ fat, 14 $\mathrm{g}$ carbohydrate, and 7 $\mathrm{g}$ protein. Estimate the number of Calories in a serving. (b) According to its nutrition label, the same soup also contains 690 $\mathrm{mg}$ of sodium. Do you think the sodium contributes to the caloric content of the soup?

Matthew B.
Numerade Educator

Problem 92

A pound of plain M&M candies contains 96 g fat, 320 g carbohydrate, and 21 g protein. What is the fuel value in kJ in a 42-g (about 1.5 oz) serving? How many Calories does it provide?

James I.
Numerade Educator

Problem 93

The heat of combustion of fructose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},$ is $-2812 \mathrm{kJ} / \mathrm{mol} .$ If a fresh golden delicious apple weighing 4.23 oz $(120 \mathrm{g})$ contains 16.0 $\mathrm{g}$ of fructose, what caloric content does the fructose contribute to the apple?

Matthew B.
Numerade Educator

Problem 94

The heat of combustion of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l),$ is $-1367 \mathrm{kJ} / \mathrm{mol} .$ A batch of Sauvignon Blanc wine contains 10.6$\%$ ethanol by mass. Assuming the density of the wine to be $1.0 \mathrm{g} / \mathrm{mL},$ what is the caloric content due to the alcohol (ethanol) in a 6 -oz glass of wine $(177 \mathrm{mL})$ ?

James I.
Numerade Educator

Problem 95

The standard enthalpies of formation of gaseous propyne $\left(\mathrm{C}_{3} \mathrm{H}_{4}\right),$ propylene $\left(\mathrm{C}_{3} \mathrm{H}_{6}\right),$ and propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ are $+185.4,+20.4,$ and $-103.8 \mathrm{kJ} / \mathrm{mol}$ , respectively.(a) Calculate the heat evolved per mole on combustion of each substance to yield $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g) .$ (b) Calculate the heat evolved on combustion of 1 $\mathrm{kg}$ of each substance. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

Matthew B.
Numerade Educator

Problem 96

It is interesting to compare the "fuel value" of a hydro- carbon in a hypothetical world where oxygen is not the combustion agent. The enthalpy of formation of $\mathrm{CF}_{4}(g)$ is $-679.9 \mathrm{kJ} / \mathrm{mol} .$ Which of the following two reactions is the more exothermic?
$$\begin{array}{l}{\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\mathrm{CH}_{4}(g)+4 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)}\end{array}$$

James I.
Numerade Educator

Problem 97

At the end of $2012,$ global population was about 7.0 billion people. What mass of glucose in kg would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l)$ according to the following thermochemical equation:
$$\begin{aligned} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H^{\circ}=&-2803 \mathrm{kJ} \end{aligned}$$

Matthew B.
Numerade Educator

Problem 98

The automobile fuel called $E 85$ consists of 85$\%$ ethanol and 15$\%$ gasoline. E85 can be used in the so-called flex-fuel vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of $\mathrm{C}_{8} \mathrm{H}_{18} ),$ that the average heat of combustion of $\mathrm{C}_{8} \mathrm{H}_{18}(l)$ is 5400 $\mathrm{kJ} / \mathrm{mol}$ , and that gasoline has an average density of 0.70 $\mathrm{g} / \mathrm{mL}$ . The density of ethanol is 0.79 $\mathrm{g} / \mathrm{mL}$ . (a) By using the information given as well as data in Appendix $\mathrm{C},$ compare the energy produced by combustion of 1.0 L of gasoline and of 1.0 . of ethanol. (b) Assume that the density and heat of combustion of E85 can be obtained by using 85$\%$ of the values for ethanol and 15$\%$ of the values for gasoline. How much energy could be released by the combustion of 1.0 L of E85? (\mathbf{c} ) How many gallons of E85 would be needed to provide the same energy as 10 gal of gasoline? (d) If gasoline costs $\$ 3.88$ per gallon in the United States, what is the break-even price per gallon of E85 if the same amount of energy is to be delivered?

James I.
Numerade Educator

Problem 99

The air bags that provide protection in automobiles in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of $q$ and $w$ in this process?

Matthew B.
Numerade Educator

Problem 100

An aluminum can of a soft drink is placed in a freezer. Later, you find that the can is split open and its contents have frozen. Work was done on the can in splitting it open. Where did the energy for this work come from?

James I.
Numerade Educator

Problem 101

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not? (c) Can you determine the value of $\Delta E$ for the process?

Matthew B.
Numerade Educator

Problem 102

A sample of gas is contained in a cylinder-and-piston arrangement. It undergoes the change in state shown in the drawing. (a) Assume first that the cylinder and piston are perfect thermal insulators that do not allow heat to be transferred. What is the value of $q$ for the state change? What is the sign of $w$ for the state change? What can be said about $\Delta E$ for the state change? (b) Now assume that the cylinder and piston are made up of a thermal conductor such as a metal. During the state change, the cylinder gets warmer to the touch. What is the sign of $q$ for the state change in this case? Describe the difference in the state of the system at the end of the process in the two cases. What can you say about the relative values of $\Delta E ?$

James I.
Numerade Educator

Problem 103

Limestone stalactites and stalagmites are formed in caves by
the following reaction:
$$\mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \longrightarrow \mathrm{CaCO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$$
If 1 $\mathrm{mol}$ of $\mathrm{CaCO}_{3}$ forms at 298 $\mathrm{K}$ under 1 atm pressure, the
reaction performs 2.47 $\mathrm{kJ}$ of $P-V$ work, pushing back the atmo-
sphere as the gaseous $\mathrm{CO}_{2}$ forms. At the same time, 3.95 $\mathrm{kJ}$
of heat is absorbed from the environment. What are the
values of $\Delta H$ and of $\Delta E$ for this reaction?

Matthew B.
Numerade Educator

Problem 104

Consider the systems shown in Figure 5.10. In one case the battery becomes completely discharged by running the current through a heater, and in the other case by running a fan. Both processes occur at constant pressure. In both cases the change in state of the system is the same: The battery goes from being fully charged to being fully discharged. Yet in one case the heat evolved is large, and in the other it is small. Is the enthalpy change the same in the two cases? If not, how can enthalpy be considered a state function? If it is, what can you say about the relationship between enthalpy change and$ q $in this case, as compared with others that we have considered?

James I.
Numerade Educator

Problem 105

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately 1.8 $\mathrm{kg}$ . The specific heat of the brick is $0.85 \mathrm{J} / \mathrm{g}-\mathrm{K}$ . How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as $1.7 \times 10^{3}$ gal of water?

Matthew B.
Numerade Educator

Problem 106

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at $25.1^{\circ} \mathrm{C} .$ A $121.0-\mathrm{g}$ block of copper metal is heated to $100.4^{\circ} \mathrm{C}$ by putting it in a beaker of boiling water. The specific heat of $\mathrm{Cu}(s)$ is $0.385 \mathrm{J} / \mathrm{g}-\mathrm{K}$ . The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of $30.1^{\circ} \mathrm{C}$ (a) Determine the amount of heat, in J, lost by the copper block. (b) Determine the amount of heat gained by the water. The specific heat of water is $4.18 \mathrm{J} / \mathrm{g}-\mathrm{K}$ . (c) The difference between your answers for (a) and (b) is due to heat loss through the Styrofoam cups and the heat necessary to raise the temperature of the inner wall of the apparatus. The heat capacity of the calorimeter is the amount of heat necessary to raise the temperature of the apparatus (the cups and the stopper) by 1 K. Calculate the heat capacity of the calorimeter in J/K. (d)What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?

James I.
Numerade Educator

Problem 107

(a) When a 0.235 -g sample of benzoic acid is combusted in a bomb calorimeter (Figure 5.19$)$ , the temperature rises $1.642^{\circ} \mathrm{C} .$ When a $0.265-\mathrm{g}$ sample of caffeine, $\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}$ is burned, the temperature rises $1.525^{\circ} \mathrm{C} .$ Using the value 26.38 $\mathrm{kJ} / \mathrm{g}$ for the heat of combustion of benzoic acid, calculate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of $0.002^{\circ} \mathrm{C}$ in each temperature reading and that the masses of samples are measured to $0.001 \mathrm{g},$ what is the estimated uncertainty in
the value calculated for the heat of combustion per mole of caffeine?

Matthew B.
Numerade Educator

Problem 108

Meals-ready-to-eat (MREs) are military meals that can be heated on a flameless heater. The heat is produced by the following reaction:
$$\mathrm{Mg}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}_{2}(g)$$
(a) Calculate the standard enthalpy change for this reaction. (b) Calculate the number of grams of Mg needed for this reaction to release enougy energy to increase the temperature of 75 mL of water from 21 to $79^{\circ} \mathrm{C}$ .

James I.
Numerade Educator

Problem 109

Burning methane in oxygen can produce three different carbon-containing products: soot (very fine particles of graphite), CO(g), and $\mathrm{CO}_{2}(g) .$ (a) Write three balanced equations for the reaction of methane gas with oxygen to produce these three products. In each case assume that $\mathrm{H}_{2} \mathrm{O}(l)$ is the only other product. (b) Determine the standard enthalpies
for the reactions in part (a).(c) Why, when the oxygen supply is adequate, is $\mathrm{CO}_{2}(g)$ the predominant carbon-containing product of the combustion of methane?

Matthew B.
Numerade Educator

Problem 110

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethylene:
$$2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)$$
Calculate the $\Delta H^{\circ}$ for this reaction using the following thermochemical data:
$$\begin{array}{ll}{\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)} & {\Delta H^{\circ}=-890.3 \mathrm{kJ}} \\ {\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)} & {\Delta H^{\circ}=-136.3 \mathrm{kJ}} \\ {2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)} & {\Delta H^{\circ}=-571.6 \mathrm{kJ}} \\ {2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)} & {\Delta H^{\circ}=-3120.8 \mathrm{kJ}}\end{array}$$

James I.
Numerade Educator

Problem 111

From the following data for three prospective fuels, calculate which could provide the most energy per unit volume:

Matthew B.
Numerade Educator

Problem 112

The hydrocarbons acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$ and benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)$ have the same empirical formula. Benzene is an "aromatic" hydrocarbon, one that is unusually stable because of its structure. (a) By using data in Appendix C, determine the standard enthalpy change for the reaction 3 $\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)$ (b) Which has greater enthalpy, 3 mol of actylene gas or 1 $\mathrm{mol}$ of liquid benzene?(c) Determine the fuel value, in $\mathrm{kJ} / \mathrm{g},$ for acetylene and benzene.

James I.
Numerade Educator

Problem 113

Ammonia $\left(\mathrm{NH}_{3}\right)$ boils at $-33^{\circ} \mathrm{C} ;$ at this temperature it has a density of 0.81 $\mathrm{g} / \mathrm{cm}^{3} .$ The enthalpy of formation of $\mathrm{NH}_{3}(g)$ is $-46.2 \mathrm{kJ} / \mathrm{mol},$ and the enthalpy of vaporization of $\mathrm{NH}_{3}(l)$ is 23.2 $\mathrm{kJ} / \mathrm{mol} .$ Calculate the enthalpy change when 1 $\mathrm{L}$ of liquid $\mathrm{NH}_{3}$ is burned in air to give $\mathrm{N}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g) .$ How does this compare with $\Delta H$ for the complete combustion of 1 Lof liquid methanol, $\mathrm{CH}_{3} \mathrm{OH}(l) ?$ For $\mathrm{CH}_{3} \mathrm{OH}(l),$ the density at $25^{\circ} \mathrm{C}$ is $0.792 \mathrm{g} / \mathrm{cm}^{3},$ and $\Delta \mathrm{H}_{f}^{\circ}=-239 \mathrm{kJ} / \mathrm{mol}$

Matthew B.
Numerade Educator

Problem 114

Three common hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation:
(a) For each of these substances, calculate the molar enthalpy of combustion to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ (b) Calculate the fuel value, in $\mathrm{k} \mathrm{k} / \mathrm{g},$ for each of these compounds. (\mathbf{c} ) \text { For } each hydrocarbon, determine the percentage of hydrogen by mass.( ( ) By comparing your answers for parts (b) and (c), propose a relationship between hydrogen content and fuel value in hydrocarbons.

James I.
Numerade Educator

Problem 115

A $201-$ lb man decides to add to his exercise routine by walking up three flights of stairs $(45 \mathrm{ft}) 20$ times per day. He figures that the work required to increase his potential energy in this way will permit him to eat an extra order of French fries, at 245 Cal, without adding to his weight. Is he correct in this assumption?

Matthew B.
Numerade Educator

Problem 116

The Sun supplies about 1.0 kilowatt of energy for each square meter of surface area $\left(1.0 \mathrm{kW} / \mathrm{m}^{2},$ where a watt $=1 \mathrm{J} / \mathrm{s}\right)$ Plants produce the equivalent of about 0.20 $\mathrm{g}$ of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ per hour per square meter. Assuming that the sucrose is produced as follows, calculate the percentage of sunlight used to produce sucrose.
$$\begin{array}{c}{12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+12 \mathrm{O}_{2}(g)} \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad {\Delta H=5645 \mathrm{kJ}}\end{array}$$

James I.
Numerade Educator

Problem 117

It is estimated that the net amount of carbon dioxide fixed by photosynthesis on the landmass of Earth is $5.5 \times 10^{16} \mathrm{g} / \mathrm{yr}$ of $\mathrm{CO}_{2} .$ Assume that all this carbon is converted into glucose. (a) Calculate the energy stored by photosynthesis on land per year, in kJ. (b) Calculate the average rate of conversion of solar energy into plant energy in megawatts, MW
$(1 \mathrm{W}=1 \mathrm{J} / \mathrm{s}) .$ A large nuclear power plant produces about
$10^{3} \mathrm{MW} .$ The energy of how many such nuclear power plants is equivalent to the solar energy conversion?

Matthew B.
Numerade Educator

Problem 118

At $20^{\circ} \mathrm{C}$ (approximately room temperature) the average velocity of $\mathrm{N}_{2}$ molecules in air is 1050 $\mathrm{mph}$ . (a) What is the average speed in $\mathrm{m} / \mathrm{s} ?(\mathbf{b})$ What is the kinetic energy (in J) of an $\mathrm{N}_{2}$ molecule moving at this speed? (c) What is the total kinetic energy of 1 mol of $\mathrm{N}_{2}$ molecules moving at this speed?

James I.
Numerade Educator

Problem 119

Suppose an Olympic diver who weighs 52.0 kg executes a straight dive from a 10-m platform. At the apex of the dive, the diver is 10.8 m above the surface of the water. (a) What is the potential energy of the diver at the apex of the dive, relative to the surface of the water? (b) Assuming that all the potential energy of the diver is converted into kinetic energy at the surface of the water, at what speed, in m/s, will the diver enter the water? (c) Does the diver do work on entering the water? Explain.

Matthew B.
Numerade Educator

Problem 120

Consider the combustion of a single molecule of $\mathrm{CH}_{4}(g)$ forming $\mathrm{H}_{2} \mathrm{O}(l)$ as a product. (a) How much energy, in J, is produced during this reaction? (b) A typical X-ray light source has an energy of 8 keV (see inside back cover for conversion between eV and J. Is the energy released by the combustion of a $\mathrm{CH}_{4}$ molecule larger or smaller than the energy of an $\mathrm{X}$ -ray from this source?

James I.
Numerade Educator

Problem 121

Consider the following unbalanced oxidation-reduction reactions in aqueous solution:
$$\begin{array}{c}{\operatorname{Ag}^{+}(a q)+\mathrm{Li}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{Li}^{+}(a q)} \\ {\mathrm{Fe}(s)+\mathrm{Na}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Na}(s)} \\ {\mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g)}\end{array}$$
(a) Balance each of the reactions. (b) By using data in Appendix $C,$ calculate $\Delta H^{\circ}$ for each of the reactions. (c) Based on the values you obtain for $\Delta H^{\circ},$ which of the reactions would you expect to be thermodynamically favored? (d) Use the activity series to predict which of these reactions should occur. coo (Section 4.4 ) Are these results in accord with your conclusion in part (c) of this problem?

Matthew B.
Numerade Educator

Problem 122

Consider the following acid-neutralization reactions involving the strong base $\mathrm{NaOH}(a q)$ :
$$\begin{array}{l}{\mathrm{HNO}_{3}(a q)+\mathrm{NaOH}(a q) \longrightarrow \mathrm{NaNO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \longrightarrow \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\mathrm{NH}_{4}^{+}(a q)+\mathrm{NaOH}(a q) \longrightarrow \mathrm{NH}_{3}(a q)+\mathrm{Na}^{+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)}\end{array}$$ (a) By using data in Appendix $\mathrm{C}$ , calculate $\Delta H^{\circ}$ for each of the reactions. (b) As we saw in Section $4.3,$ nitric acid and hydrochloric acid are strong acids. Write net ionic equations = for the neutralization of these acids. (c) Compare the values of $\Delta H^{\circ}$ for the first two reactions. What can you conclude? (d) In the third equation $\mathrm{NH}_{4}^{+}(a q)$ is acting as an acid. Based on the value of $\Delta H^{\circ}$ for this reaction, do you think it is a strong or a weak acid? Explain.

James I.
Numerade Educator

Problem 123

Consider two solutions, the first being 50.0 $\mathrm{mL}$ of 1.00 $\mathrm{MCuSO}_{4}$ and the second 50.0 $\mathrm{mL}$ of 2.00 $\mathrm{M} \mathrm{KOH}$ . When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to $27.7^{\circ} \mathrm{C}$ (a) Before mixing, how many grams of Cu are present in the solution of $\mathrm{CuSO}_{4}$ ? (b) Predict the identity of the precipitate in the reaction. (c) Write complete and net ionic equations for the reaction that occurs when the two solutions are mixed. (d) From the calorimetric data, calculate $\Delta H$ for the reaction that occurs on mixing. Assume that the calorimeter absorbs only a negligible quantity of heat, that the total volume of the solution is 100.0 $\mathrm{mL}$ , and that the specific heat and density of the solution after mixing are the same as those of pure water.

Matthew B.
Numerade Educator

Problem 124

The precipitation reaction between $\mathrm{AgNO}_{3}(a q)$ and $\mathrm{NaCl}(a q)$
proceeds as follows:
$$\mathrm{AgNO}_{3}(a q)+\mathrm{NaCl}(a q) \longrightarrow \mathrm{NaNO}_{3}(a q)+\mathrm{AgCl}(s)$$
(a) By using data in Appendix C, calculate $\Delta H^{\circ}$ for the net ionic equation of this reaction. (b) What would you expect for the value of $\Delta H^{\circ}$ of the overall molecular equation compared to that for the net ionic equation? Explain.(c) Use the results from (a) and (b) along with data in Appendix C to determine the value of $\Delta H_{f}^{\circ}$ for $\operatorname{Ag} \mathrm{NO}_{3}(a q) .$

James I.
Numerade Educator

Problem 125

A sample of a hydrocarbon is combusted completely in $\mathrm{O}_{2}(g)$ to produce $21.83 \mathrm{g} \mathrm{CO}_{2}(g), 4.47 \mathrm{g} \mathrm{H}_{2} \mathrm{O}(g),$ and 311 $\mathrm{kJ}$ of heat. (a) What is the mass of the hydrocarbon sample that was combusted? (b) What is the empirical formula of the hydrocarbon? (c) Calculate the value of $\Delta H_{f}^{\circ}$ per empirical-formula unit of the hydrocarbon. (d) Do you think that the hydrocarbon is one of those listed in Appendix C? Explain your answer.

Matthew B.
Numerade Educator

Problem 126

The methane molecule, $\mathrm{CH}_{4},$ has the geometry shown in Figure $2.17 .$ Imagine a hypothetical process in which the methane molecule is "expanded," by simultaneously extending all four $\mathrm{C}-\mathrm{H}$ bonds to infinity. We then have the process
$$\mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}(g)+4 \mathrm{H}(g)$$
(a) Compare this process with the reverse of the reaction that represents the standard enthalpy of formation of $\mathrm{CH}_{4}(g) .(\mathbf{b})$ Calculate the enthalpy change in each case. Which is the more endothermic process? What accounts for the difference in $\Delta H^{\circ}$ values? (c) Suppose that 3.45 $\mathrm{g}$ $\mathrm{CH}_{4}(g)$ reacts with $1.22 \mathrm{g} \mathrm{F}_{2}(g),$ forming $\mathrm{CF}_{4}(g)$ and $\mathrm{HF}(g)$ as sole products. What is the limiting reagent in this reaction? If the reaction occurs at constant pressure, what amount of heat is evolved?

James I.
Numerade Educator

Problem 127

One of the best-selling light, or low-calorie, beers is 4.2$\%$ alcohol by volume and a 12 -oz serving contains 110 Calories; remember: 1 Calorie $=1000$ cal $=1$ kcal. To estimate the percentage of Calories that comes from the alcohol, consider the following questions. (a) Write a balanced chemical equation for the reaction of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ , with oxygen to make carbon dioxide and water. (b) Use enthalpies of formation in Appendix $\mathrm{C}$ to determine $\Delta H$ for this reaction. $(\mathbf{c})$ If 4.2$\%$ of the total volume is ethanol and the density of ethanol is $0.789 \mathrm{g} / \mathrm{mL},$ what mass of ethanol does a 12 - oz serving of light beer contain? (\boldsymbol{d} ) How many Calories are released by the metabolism of ethanol, the reaction from part (a)? (e) What percentage of the 110 Calories comes from the ethanol?

Matthew B.
Numerade Educator