Chemistry

Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson

Chapter 9

Gases - all with Video Answers

Educators

+ 7 more educators

Chapter Questions

Problem 1

Why are sharp knives more effective than dull knives (Hint: think about the definition of pressure)?

Lottie Adams

Lottie Adams

Numerade Educator

Problem 2

Why do some small bridges have weight limits that depend on how many wheels or axles the crossing vehicle has?

Lottie Adams

Numerade Educator

Problem 3

Why should you roll or belly-crawl rather than walk across a thinly-frozen pond?

Lottie Adams

Numerade Educator

Problem 4

A typical barometric pressure in Redding, California, is about 750 mm Hg. Calculate this pressure in atm and kPa.

Lottie Adams

Numerade Educator

Problem 5

A typical barometric pressure in Denver, Colorado, is 615 mm Hg. What is this pressure in atmospheres and kilopascals?

Lottie Adams

Numerade Educator

Problem 6

A typical barometric pressure in Kansas City is 740 torr. What is this pressure in atmospheres, in millimeters of mercury, and in kilopascals?

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 7

Canadian tire pressure gauges are marked in units of kilopascals. What reading on such a gauge corresponds to 32 psi?

Lottie Adams

Numerade Educator

Problem 8

During the Viking landings on Mars, the atmospheric pressure was determined to be on the average about 6.50 millibars (1 bar = 0.987 atm). What is that pressure in torr and kPa?

Dominique Jan Tan

Dominique Jan Tan

Numerade Educator

Problem 9

The pressure of the atmosphere on the surface of the planet Venus is about 88.8 atm. Compare that pressure in psi to the normal pressure on earth at sea level in psi.

Lottie Adams

Numerade Educator

Problem 10

A medical laboratory catalog describes the pressure in a cylinder of a gas as 14.82 MPa. What is the pressure of this gas in atmospheres and torr?

Lottie Adams

Numerade Educator

Problem 11

Consider this scenario and answer the following questions: On a mid-August day in the northeastern United States, the following information appeared in the local newspaper: atmospheric pressure at sea level 29.97 in. Hg, 1013.9 mbar.

(a) What was the pressure in kPa?
(b) The pressure near the seacoast in the northeastern United States is usually reported near 30.0 in. Hg. During a hurricane, the pressure may fall to near 28.0 in. Hg. Calculate the drop in pressure in torr

Nicole Smina

Numerade Educator

Problem 12

Why is it necessary to use a nonvolatile liquid in a barometer or manometer?

Lottie Adams

Numerade Educator

Problem 13

The pressure of a sample of gas is measured at sea level with a closed-end manometer. The liquid in the manometer is mercury. Determine the pressure of the gas in:

(a) torr
(b) Pa
(c) bar

Lottie Adams

Numerade Educator

Problem 14

The pressure of a sample of gas is measured with an open-end manometer, partially shown to the right. The liquid in the manometer is mercury. Assuming atmospheric pressure is 29.92 in. Hg, determine the pressure of the

gas in:
(a) torr
(b) Pa
(c) bar

Lottie Adams

Numerade Educator

Problem 15

The pressure of a sample of gas is measured at sea level with an open-end mercury manometer. Assuming atmospheric pressure is 760.0 mm Hg, determine the pressure of the gas in:

(a) mm Hg
(b) atm
(c) kPa

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 16

The pressure of a sample of gas is measured at sea level with an open-end mercury manometer. Assuming atmospheric pressure is 760 mm Hg, determine the pressure of the gas in:

(a) mm Hg
(b) atm
(c) kPa

Lottie Adams

Numerade Educator

Problem 17

How would the use of a volatile liquid affect the measurement of a gas using open-ended manometers vs. closed-end manometers?

Lottie Adams

Numerade Educator

Problem 18

Sometimes leaving a bicycle in the sun on a hot day will cause a blowout. Why?

Glyniss A

Numerade Educator

Problem 19

Explain how the volume of the bubbles exhausted by a scuba diver (Figure 9.16) change as they rise to the surface, assuming that they remain intact.

Lottie Adams

Numerade Educator

Problem 20

One way to state Boyle’s law is “All other things being equal, the pressure of a gas is inversely proportional to its volume.” (a) What is the meaning of the term “inversely proportional?” (b) What are the “other things” that must be equal?

Lottie Adams

Numerade Educator

Problem 21

An alternate way to state Avogadro’s law is “All other things being equal, the number of molecules in a gas is directly proportional to the volume of the gas.” (a) What is the meaning of the term “directly proportional?” (b) What are the “other things” that must be equal?

Lottie Adams

Numerade Educator

Problem 22

How would the graph in Figure 9.12 change if the number of moles of gas in the sample used to determine the curve were doubled?

Lottie Adams

Numerade Educator

Problem 23

How would the graph in Figure 9.13 change if the number of moles of gas in the sample used to determine the curve were doubled?

Lottie Adams

Numerade Educator

Problem 24

In addition to the data found in Figure 9.13, what other information do we need to find the mass of the sample of air used to determine the graph?

Lottie Adams

Numerade Educator

Problem 25

Determine the volume of 1 $\mathrm{mol}$ of $\mathrm{CH}_{4}$ gas at 150 $\mathrm{K}$ and 1 $\mathrm{atm}$ , using Figure 9.12 .

Lottie Adams

Numerade Educator

Problem 26

Determine the pressure of the gas in the syringe shown in Figure 9.13 when its volume is 12.5 mL, using:

(a) the appropriate graph
(b) Boyle’s law

Lottie Adams

Numerade Educator

Problem 27

A spray can is used until it is empty except for the propellant gas, which has a pressure of 1344 torr at $23^{\circ} C.$ If the can is thrown into a fire $\left(T=475^{\circ} C\right),$ what will be the pressure in the hot can?

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 28

What is the temperature of an $11.2-L$ sample of carbon monoxide, $CO,$ at 744 torr if it occupies 13.3 $L$ at $55^{\circ} C$ and 744 tor?

Dominique Jan Tan

Dominique Jan Tan

Numerade Educator

Problem 29

A $2.50-$ L volume of hydrogen measured at $-196^{\circ} C$ is warmed to $100^{\circ} C$ . Calculate the volume of the gas at the higher temperature, assuming no change in pressure.

Lottie Adams

Numerade Educator

Problem 30

A balloon inflated with three breaths of air has a volume of 1.7 L. At the same temperature and pressure, what is the volume of the balloon if five more same-sized breaths are added to the balloon?

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 31

A weather balloon contains 8.80 moles of helium at a pressure of 0.992 atm and a temperature of 25 °C at ground level. What is the volume of the balloon under these conditions?

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 32

The volume of an automobile air bag was 66.8 L when inflated at 25 °C with 77.8 g of nitrogen gas. What was the pressure in the bag in kPa?

Lottie Adams

Numerade Educator

Problem 33

How many moles of gaseous boron trifluoride, $BF_{3}$, are contained in a 4.3410-L bulb at 788.0 K if the pressure is 1.220 atm? How many grams of $BF_{3} ?$

Lottie Adams

Numerade Educator

Problem 34

Iodine, $I_{2},$ is a solid at room temperature but sublimes (converts from a solid into a gas) when warmed. What is the temperature in a 73.3-mL bulb that contains 0.292 g of $I_{2}$ vapor at a pressure of 0.462 atm?

Lottie Adams

Numerade Educator

Problem 35

How many grams of gas are present in each of the following cases?

(a) 0.100 $L$ of $CO_{2}$ at 307 torr and $26^{\circ} \mathrm{C}$
(b) 8.75 $L$ of $\mathrm{C}_{2} \mathrm{H}_{4},$ at 378.3 $\mathrm{kPa}$ and 483 $\mathrm{K}$
(c) 221 $mL$of $\mathrm{Ar}$ at 0.23 $\mathrm{torr}$ and $-54^{\circ} \mathrm{C}$

Lottie Adams

Numerade Educator

Problem 36

A high altitude balloon is filled with $1.41 \times 10^{4}$ L of hydrogen at a temperature of $21^{\circ} \mathrm{C}$ and a pressure of 745 torr. What is the volume of the balloon at a height of 20 $\mathrm{km}$ , where the temperature is $-48^{\circ} C$ and the pressure is 63.1 $tor?$

Lottie Adams

Numerade Educator

Problem 37

A cylinder of medical oxygen has a volume of 35.4 $\mathrm{L}$ , and contains $\mathrm{O}_{2}$ at a pressure of 151 $atm$ and a temperature of $25^{\circ} \mathrm{C}$ . What volume of $\mathrm{O}_{2}$ does this correspond to at normal body conditions, that is, 1 atm and 37 $^{\circ} C ?$

Lottie Adams

Numerade Educator

Problem 38

A large scuba tank (Figure 9.16) with a volume of 18 L is rated for a pressure of 220 bar. The tank is filled at 20 °C and contains enough air to supply 1860 L of air to a diver at a pressure of 2.37 atm (a depth of 45 feet). Was the tank filled to capacity at 20 °C?

David Collins

Numerade Educator

Problem 39

A 20.0-L cylinder containing 11.34 kg of butane $C_{4} H_{10},$ was opened to the atmosphere. Calculate the mass of the gas remaining in the cylinder if it were opened and the gas escaped until the pressure in the cylinder was equal to the atmospheric pressure, 0.983 atm, and a temperature of 27 °C.

David Collins

Numerade Educator

Problem 40

While resting, the average 70-kg human male consumes 14 L of pure $O_{2}$. per hour at 25 °C and 100 kPa. How many moles of $O_{2}$ are consumed by a 70 kg man while resting for 1.0 h?

Dominique Jan Tan

Dominique Jan Tan

Numerade Educator

Problem 41

For a given amount of gas showing ideal behavior, draw labeled graphs of:

(a) the variation of P with V
(b) the variation of V with T
(c) the variation of P with T
(d) the variation of $\frac{1}{P}$ with V

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 42

A liter of methane gas, $CH_{4}$ , at $STP$ contains more atoms of hydrogen than does a liter of pure hydrogen gas, $H_{2},$ at $STP$ . Using Avogadro's law as a starting point, explain why.

Lottie Adams

Numerade Educator

Problem 43

The effect of chlorofluorocarbons (such as $CCl_{2} F_{2} )$ on the depletion of the ozone layer is well known. The use of substitutes, such as $CH_{3} CH_{2} F(g),$ for the chlorofluorocarbons, has largely corrected the problem. Calculate the volume occupied by 10.0 g of each of these compounds at STP:

(a) $\mathrm{CCl}_{2} \mathrm{F}_{2}(g)$
(b) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{F}(g)$

Lottie Adams

Numerade Educator

Problem 44

As 1 g of the radioactive element radium decays over 1 year, it produces $1.16 \times 10^{18}$ alpha particles (helium nuclei). Each alpha particle becomes an atom of helium gas. What is the pressure in pascal of the helium gas produced if it occupies a volume of 125 mL at a temperature of 25 °C?

Lottie Adams

Numerade Educator

Problem 45

A balloon that is 100.21 L at 21 °C and 0.981 atm is released and just barely clears the top of Mount Crumpet in British Columbia. If the final volume of the balloon is 144.53 L at a temperature of 5.24 °C, what is the pressure experienced by the balloon as it clears Mount Crumpet?

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 46

If the temperature of a fixed amount of a gas is doubled at constant volume, what happens to the pressure?

Lottie Adams

Numerade Educator

Problem 47

If the volume of a fixed amount of a gas is tripled at constant temperature, what happens to the pressure?

Lottie Adams

Numerade Educator

Problem 48

What is the density of laughing gas, dinitrogen monoxide, $N_{2} O,$ at a temperature of 325 K and a pressure of 113.0 kPa?

Lottie Adams

Numerade Educator

Problem 49

Calculate the density of Freon $12, CF_{2} Cl_{2},$ at $30.0^{\circ} C$ and 0.954 atm.

Lottie Adams

Numerade Educator

Problem 50

Which is denser at the same temperature and pressure, dry air or air saturated with water vapor? Explain.

Lottie Adams

Numerade Educator

Problem 51

A cylinder of $O_{2}(g)$ used in breathing by emphysema patients has a volume of 3.00 $L$ at a pressure of 10.0 $atm$ . If the temperature of the cylinder is $28.0^{\circ} C,$ what mass of oxygen is in the cylinder?

Oluwapelumi Kolawole

Oluwapelumi Kolawole

Numerade Educator

Problem 52

What is the molar mass of a gas if 0.0494 g of the gas occupies a volume of 0.100 L at a temperature 26 °C and a pressure of 307 torr?

Lottie Adams

Numerade Educator

Problem 53

What is the molar mass of a gas if 0.281 g of the gas occupies a volume of 125 mL at a temperature 126 °C and a pressure of 777 torr?

Lottie Adams

Numerade Educator

Problem 54

How could you show experimentally that the molecular formula of propene is $C_{3} H_{6},$ not $CH_{2} ?$

Lottie Adams

Numerade Educator

Problem 55

The density of a certain gaseous fluoride of phosphorus is 3.93 g/L at STP. Calculate the molar mass of this fluoride and determine its molecular formula.

Christopher Nilsen

Christopher Nilsen

Numerade Educator

Problem 56

Consider this question: What is the molecular formula of a compound that contains 39% C, 45% N, and 16% H if 0.157 g of the compound occupies 125 mL with a pressure of 99.5 kPa at 22 °C?

(a) Outline the steps necessary to answer the question.
(b) Answer the question

Tianyu Li

Numerade Educator

Problem 57

A 36.0–L cylinder of a gas used for calibration of blood gas analyzers in medical laboratories contains 350 g $\mathrm{CO}_{2}, 805 \mathrm{g} \mathrm{O}_{2},$ and $4,880 \mathrm{g} \mathrm{N}_{2} .$ At 25 degrees $\mathrm{C}$

Lottie Adams

Numerade Educator

Problem 58

A cylinder of a gas mixture used for calibration of blood gas analyzers in medical laboratories contains 5.0% $CO_{2}, 12.0 \% O_{2},$ and the remainder $N_{2}$ at a total pressure of 146 atm. What is the partial pressure of each component of this gas? (The percentages given indicate the percent of the total pressure that is due to each component.)

Lottie Adams

Numerade Educator

Problem 59

A sample of gas isolated from unrefined petroleum contains $90.0 \% \mathrm{CH}_{4}, 8.9 \% \mathrm{C}_{2} \mathrm{H}_{6}, \mathrm{C}_{3} \mathrm{H}_{8}$ at a total pressure of 307.2 kPa. What is the partial pressure of each component of this gas? (The percentages given indicate
the percent of the total pressure that is due to each component.)

Lottie Adams

Numerade Educator

Problem 60

A mixture of 0.200 g of $\mathrm{H}_{2}, 1.00 \mathrm{g}$ of $\mathrm{N}_{2},$ and 0.820 $g$ of Ar is stored in a closed container at STP. Find the volume of the container, assuming that the gases exhibit ideal behavior

Lottie Adams

Numerade Educator

Problem 61

Most mixtures of hydrogen gas with oxygen gas are explosive. However, a mixture that contains less than 3.0 $\% O_{2}$ is not. If enough $\mathrm{O}_{2}$ is added to a cylinder of $\mathrm{H}_{2}$ at 33.2 $atm$ to bring the total pressure to $34.5 atm,$ is the mixture explosive?

Lottie Adams

Numerade Educator

Problem 62

A commercial mercury vapor analyzer can detect, in air, concentrations of gaseous Hg atoms (which are poisonous) as low as $2 \times 10^{-6} mg /L$ of air. At this concentration, what is the partial pressure of gaseous mercury if the atmospheric pressure is 733 torr at 26 °C?

Aadit Sharma

Numerade Educator

Problem 63

A sample of carbon monoxide was collected over water at a total pressure of 756 torr and a temperature of 18 °C. What is the pressure of the carbon monoxide? (See Table 9.2 for the vapor pressure of water.)

Lottie Adams

Numerade Educator

Problem 64

In an experiment in a general chemistry laboratory, a student collected a sample of a gas over water. The volume of the gas was 265 mL at a pressure of 753 torr and a temperature of 27 °C. The mass of the gas was 0.472 g. What was the molar mass of the gas?

Lottie Adams

Numerade Educator

Problem 65

Joseph Priestley first prepared pure oxygen by heating mercuric oxide, $HgO:$
$2 HgO(s) \longrightarrow 2 Hg(l)+O_{2}(g)$

(a) Outline the steps necessary to answer the following question: What volume of O2 at 23 °C and 0.975 atm is produced by the decomposition of 5.36 g of HgO?
(b) Answer the question.

Lottie Adams

Numerade Educator

Problem 66

Cavendish prepared hydrogen in 1766 by the novel method of passing steam through a red-hot gun barrel:
$4 H_{2} O(g)+3 Fe(s) \longrightarrow Fe_{3} O_{4}(s)+4 H_{2}(g)$

(a) Outline the steps necessary to answer the following question: What volume of $H_{2}$ at a pressure of 745 torr and a temperature of 20 °C can be prepared from the reaction of 15.0 $\mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O} ?$
(b) Answer the question.

Lottie Adams

Numerade Educator

Problem 67

The chlorofluorocarbon $CCl_{2}F_{2}$ can be recycled into a different compound by reaction with hydrogen to produce $\mathrm{CH}_{2} \mathrm{F}_{2}(g),$ a compound useful in chemical manufacturing: $\mathrm{CCl}_{2} \mathrm{F}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{2} \mathrm{F}_{2}(g)+2 \mathrm{HCl}(g)$

(a) Outline the steps necessary to answer the following question: What volume of hydrogen at 225 atm and 35.5 °C would be required to react with 1 ton $\left(1.000 \times 10^{3} \mathrm{kg}\right)$ of $CCl_{2} F_{2} ?$
(b) Answer the question

Lottie Adams

Numerade Educator

Problem 68

Automobile air bags are inflated with nitrogen gas, which is formed by the decomposition of solid sodium azide $\left(NaN_{3}\right)$. The other product is sodium metal. Calculate the volume of nitrogen gas at 27 °C and 756 torr formed by the decomposition of 125 g of sodium azide

Lottie Adams

Numerade Educator

Problem 69

Lime, $CaO,$ is produced by heating calcium calcium carbonate, $CaCO_{3} ;$ carbon dioxide is the other product.

(a) Outline the steps necessary to answer the following question: What volume of carbon dioxide at 875 K and 0.966 atm is produced by the decomposition of 1 ton $\left(1.000 \times 10^{3} kg\right)$ of calcium carbonate?
(b) Answer the question

Lottie Adams

Numerade Educator

Problem 70

Before small batteries were available, carbide lamps were used for bicycle lights. Acetylene gas, $C_{2} H_{2},$ and solid calcium hydroxide were formed by the reaction of calcium carbide, $CaC_{2},$ with water. The ignition of the acetylene gas provided the light. Currently, the same lamps are used by some cavers, and calcium carbide is used to produce acetylene for carbide cannons

(a) Outline the steps necessary to answer the following question: What volume of $C_{2} H_{2}$ at 1.005 atm and $12.2^{\circ} C$ is formed by the reaction of 15.48 $g$ of $\mathrm{CaC}_{2}$ with water?
(b) Answer the question.

Lottie Adams

Numerade Educator

Problem 71

Calculate the volume of oxygen required to burn 12.00 $L$ of ethane gas, $C_{2}$ , to produce carbon dioxide and water, if the volumes of $\mathrm{C}_{2} H_{6}$ and $O_{2}$ are measured under the same conditions of temperature and pressure.

Lottie Adams

Numerade Educator

Problem 72

What volume of $\mathrm{O}_{2}$ at $\mathrm{STP}$ is required to oxidize 8.0 $\mathrm{L}$ of NO at $\mathrm{STP}$ to $\mathrm{NO}_{2}$ ? What volume of $\mathrm{NO}_{2}$ is produced at STP?

Lottie Adams

Numerade Educator

Problem 73

Consider the following questions:

(a) What is the total volume of the $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$ at $600^{\circ} \mathrm{C}$ and 0.888 atm produced by the combustion of 1.00 L of $\mathrm{C}_{2} \mathrm{H}_{6}(g)$ measured at STP?
(b) What is the partial pressure of $H_{2} \mathrm{O}$ in the product gases?

Lottie Adams

Numerade Educator

Problem 74

Methanol, $CH_{3} \mathrm{OH}$, is produced industrially by the following reaction:

$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \frac{\text { copper catalyst } 300 \mathrm{C}, 300 \mathrm{atm}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{OH}(g)$

Assuming that the gases behave as ideal gases, find the ratio of the total volume of the reactants to the final volume.

Lottie Adams

Numerade Educator

Problem 75

What volume of oxygen at 423.0 $K$ and a pressure of 127.4 $\mathrm{kPa}$ is produced by the decomposition of 129.7 $g$ of $\mathrm{BaO}_{2}$ to BaO and $\mathrm{O}_{2} ?$

Lottie Adams

Numerade Educator

Problem 76

A 2.50 -L sample of a colorless gas at STP decomposed to give 2.50 $\mathrm{L}$ of $N_{2}$ and 1.25 $\mathrm{L}$ of $\mathrm{O}_{2}$ at $\mathrm{STP}$ . What is the colorless gas?

Lottie Adams

Numerade Educator

Problem 77

Ethanol, $C_{2} H_{5} OH$, is produced industrially from ethylene,$C_{2} H_{4}$, by the following sequence of reactions:

$3 \mathrm{C}_{2} \mathrm{H}_{4}+2 \mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{HSO}_{4}+\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{SO}_{4}$
$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{HSO}_{4}+\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{SO}_{4}+3 \mathrm{H}_{2} \mathrm{O} \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{H}_{2} \mathrm{SO}_{4}$

What volume of ethylene at STP is required to produce 1.000 metric ton (1000 kg) of ethanol if the overall yield of ethanol is 90.1%?

Lottie Adams

Numerade Educator

Problem 78

One molecule of hemoglobin will combine with four molecules of oxygen. If 1.0 g of hemoglobin combines with 1.53 mL of oxygen at body temperature (37 °C) and a pressure of 743 torr, what is the molar mass of hemoglobin?

Lottie Adams

Numerade Educator

Problem 79

A sample of a compound of xenon and fluorine was confined in a bulb with a pressure of 18 torr. Hydrogen was added to the bulb until the pressure was 72 torr. Passage of an electric spark through the mixture produced Xe and HF. After the HF was removed by reaction with solid KOH, the final pressure of xenon and unreacted hydrogen in the bulb was 36 torr. What is the empirical formula of the xenon fluoride in the original sample? (Note: Xenon fluorides contain only one xenon atom per molecule.)

Lottie Adams

Numerade Educator

Problem 80

One method of analyzing amino acids is the van Slyke method. The characteristic amino groups $\left(-\mathrm{NH}_{2}\right)$ in protein material are allowed to react with nitrous acid, $\mathrm{HNO}_{2},$ to form $\mathrm{N}_{2}$ gas. From the volume of the gas, the amount of amino acid can be determined. A 0.0604-g sample of a biological sample containing glycine, $\mathrm{CH}_{2}\left(\mathrm{NH}_{2}\right) \mathrm{COOH},$ was analyzed by the van Slyke method and vielded 3.70 $\mathrm{mL}$ of $\mathrm{N}_{2}$ collected over water at a pressure of 735 torr and 29 °C. What was the percentage of glycine in the sample?
$\mathrm{CH}_{2}\left(\mathrm{NH}_{2}\right) \mathrm{CO}_{2} \mathrm{H}+\mathrm{HNO}_{2} \longrightarrow \mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CO}_{2} \mathrm{H}+\mathrm{H}_{2} \mathrm{O}+\mathrm{N}_{2}$

Lottie Adams

Numerade Educator

Problem 81

A balloon filled with helium gas is found to take 6 hours to deflate to 50% of its original volume. How long will it take for an identical balloon filled with the same volume of hydrogen gas (instead of helium) to decrease its volume by 50%?

Lottie Adams

Numerade Educator

Problem 82

Explain why the numbers of molecules are not identical in the left- and right-hand bulbs shown in the center illustration of Figure 9.27.

Lottie Adams

Numerade Educator

Problem 83

Starting with the definition of rate of effusion and Graham’s finding relating rate and molar mass, show how to derive the Graham’s law equation, relating the relative rates of effusion for two gases to their molecular masses.

Lottie Adams

Numerade Educator

Problem 84

Heavy water, $\mathrm{D}_{2} \mathrm{O}$ (molar mass $=20.03 \mathrm{g} \mathrm{mol}^{-1} ),$ can be separated from ordinary water, $\mathrm{H}_{2} \mathrm{O}$ (molar mass $=$ 18.01), as a result of the difference in the relative rates of diffusion of the molecules in the gas phase. Calculate the
relative rates of diffusion of $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{D}_{2} \mathrm{O}$

Lottie Adams

Numerade Educator

Problem 85

Which of the following gases diffuse more slowly than oxygen? $\mathrm{F}_{2},$ Ne, $\mathrm{N}_{2} \mathrm{O}, \mathrm{C}_{2} \mathrm{H}_{2}, \mathrm{NO}, \mathrm{Cl}_{2}, \mathrm{H}_{2} \mathrm{S}$

Lottie Adams

Numerade Educator

Problem 86

During the discussion of gaseous diffusion for enriching uranium, it was claimed that 2 $^{235} \mathrm{UF}_{6}$ diffuses 0.4% $^{238} \mathrm{UF}_{6}$ faster than Show the calculation that supports this value. The molar mass of $^{235} \mathrm{UF}_{6}= 235.043930 + 6 ×
18.998403 = 349.034348 g/mol,$ and the molar mass of $^{238} \mathrm{UF}_{6} = 238.050788 + 6 × 18.998403 = 352.041206 g/ mol.$

Lottie Adams

Numerade Educator

Problem 87

Calculate the relative rate of diffusion of $^{1} \mathrm{H}_{2}$ (molar mass 2.0 g/mol) compared to that of $^{2} \mathrm{H}_{2}$ (molar mass 4.0 g/mol) and the relative rate of diffusion of $\mathrm{O}_{2}$ (molar mass 32 g/mol) compared to that of $\mathrm{O}_{3}$ (molar mass 48 g/mol).

Lottie Adams

Numerade Educator

Problem 88

A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 mL/s. Calculate the molecular mass of the unknown gas.

Lottie Adams

Numerade Educator

Problem 89

When two cotton plugs, one moistened with ammonia and the other with hydrochloric acid, are simultaneously inserted into opposite ends of a glass tube that is 87.0 cm long, a white ring of $\mathrm{NH}_{4} \mathrm{Cl}$ forms where gaseous $\mathrm{NH}_{3}$ and gaseous HCl first come into contact $\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$ At approximately what distance from the ammonia moistened plug does this occur? (Hint: Calculate the rates of diffusion for both $\mathrm{NH}_{3}$ and $\mathrm{HCl}$ and find out
how much faster $\mathrm{NH}_{3}$ diffuses than HCl.)

Lottie Adams

Numerade Educator

Problem 90

Using the postulates of the kinetic molecular theory, explain why a gas uniformly fills a container of any
shape

Lottie Adams

Numerade Educator

Problem 91

Can the speed of a given molecule in a gas double at constant temperature? Explain your answer.

Lottie Adams

Numerade Educator

Problem 92

Describe what happens to the average kinetic energy of ideal gas molecules when the conditions are changed as follows:

(a) The pressure of the gas is increased by reducing the volume at constant temperature.
(b) The pressure of the gas is increased by increasing the temperature at constant volume.
(c) The average velocity of the molecules is increased by a factor of 2.

Lottie Adams

Numerade Educator

Problem 93

The distribution of molecular velocities in a sample of helium is shown in Figure 9.34. If the sample is
cooled, will the distribution of velocities look more like that of $\mathrm{H}_{2}$ or of $\mathrm{H}_{2} \mathrm{O}$ ? Explain your answer.

Lottie Adams

Numerade Educator

Problem 94

What is the ratio of the average kinetic energy of a $SO_{2}$ molecule to that of an $\mathrm{O}_{2}$ molecule in a mixture of two gases? What is the ratio of the root mean square speeds, $u_{\mathrm{rms}},$ of the two gases?

Lottie Adams

Numerade Educator

Problem 95

A 1-L sample of CO initially at STP is heated to 546 K, and its volume is increased to 2 L.

(a) What effect do these changes have on the number of collisions of the molecules of the gas per unit area of the container wall?
(b) What is the effect on the average kinetic energy of the molecules?
(c) What is the effect on the root mean square speed of the molecules?

Lottie Adams

Numerade Educator

Problem 96

The root mean square speed of $H_{2}$ molecules at 25 °C is about 1.6 km/s. What is the root mean square speed of a $N_{2}$ molecule at 25 °C?

Lottie Adams

Numerade Educator

Problem 97

Answer the following questions:

(a) Is the pressure of the gas in the hot air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?
(b) Is the density of the gas in the hot air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?
(c) At a pressure of 1 atm and a temperature of 20 °C, dry air has a density of 1.2256 g/L. What is the (average) molar mass of dry air?
(d) The average temperature of the gas in a hot air balloon is $1.30 \times 10^{2} \circ F$ Calculate its density, assuming the molar mass equals that of dry air.
(e) The lifting capacity of a hot air balloon is equal to the difference in the mass of the cool air displaced by the balloon and the mass of the gas in the balloon. What is the difference in the mass of 1.00 L of the cool air in part (c) and the hot air in part (d)?
(f) An average balloon has a diameter of 60 feet and a volume of $1.1 \times 10^{5} \mathrm{ft}^{3}.$ What is the lifting power of such a balloon? If the weight of the balloon and its rigging is 500 pounds, what is its capacity for carrying passengers and cargo?
(g) A balloon carries 40.0 gallons of liquid propane(density 0.5005 $\mathrm{g} / \mathrm{L} )$ . What volume of $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ gas is produced by the combustion of this propane?
(h) A balloon flight can last about 90 minutes. If all of the fuel is burned during this time, what is the approximate rate of heat loss (in kJ/min) from the hot air in the bag during the flight?

Lottie Adams

Numerade Educator

Problem 98

Show that the ratio of the rate of diffusion of Gas 1 to the rate of diffusion of Gas $2, \frac{R_{1}}{R_{2}}$ is the same at 0 °C and 100 °C.

Lottie Adams

Numerade Educator

Problem 99

Graphs showing the behavior of several different gases follow. Which of these gases exhibit behavior significantly different from that expected for ideal gases?

Lottie Adams

Numerade Educator

Problem 100

Explain why the plot of PV for $CO_{2}$ differs from that of an ideal gas

Lottie Adams

Numerade Educator

Problem 101

Under which of the following sets of conditions does a real gas behave most like an ideal gas, and for which conditions is a real gas expected to deviate from ideal behavior? Explain.

(a) high pressure, small volume
(b) high temperature, low pressure
(c) low temperature, high pressure

Lottie Adams

Numerade Educator

Problem 102

Describe the factors responsible for the deviation of the behavior of real gases from that of an ideal gas.

Lottie Adams

Numerade Educator

Problem 103

For which of the following gases should the correction for the molecular volume be largest:
$CO, CO_{2}, H_{2}, He, NH_{3}, SF_{6} ?$

Cheryl Glor

Numerade Educator

Problem 104

A 0.245-L flask contains 0.467 mol $CO_{2}$ at 159 °C. Calculate the pressure:

(a) using the ideal gas law
(b) using the van der Waals equation
(c) Explain the reason for the difference.
(d) Identify which correction (that for P or V) is dominant and why

Rabia Shuaib

Numerade Educator

Problem 105

Answer the following questions:

(a) If XX behaved as an ideal gas, what would its graph of Z vs. P look like?
(b) For most of this chapter, we performed calculations treating gases as ideal. Was this justified?
(c) What is the effect of the volume of gas molecules on Z? Under what conditions is this effect small? When is it large? Explain using an appropriate diagram.
(d) What is the effect of inter molecular attractions on the value of Z? Under what conditions is this effect small? When is it large? Explain using an appropriate diagram.
(e) In general, under what temperature conditions would you expect Z to have the largest deviations from the Z for an ideal gas?

Lottie Adams

Numerade Educator