# Chemistry the Central Science

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### Problem 84

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

James I.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.