Deck 17: Thermal Properties of Matter

Question 1

The number of molecules in one mole of a substance

A) depends on the molecular weight of the substance.
B) depends on the atomic weight of the substance.
C) depends on the density of the substance.
D) depends on the temperature of the substance.
E) is the same for all substances.

Answer 1

is the same for all substances.

Question 2

A vertical tube that is closed at the upper end and open at the lower end contains an air pocket. The open end of the tube is under the water of a lake, as shown in the figure. When the lower end of the tube is just under the surface of the lake, where the temperature is 37°C and the pressure is 1.0 × 10⁵ Pa, the air pocket occupies a volume of 630 cm³. Suppose now that the lower end of the tube is at a depth of 86 m in the lake, where the temperature is 7.0°C. What is the volume of the air pocket under these conditions? The density of the water in the lake is 1000 kg/m³.

Answer 2

60 cm³

Question 3

A fixed amount of ideal gas is held in a rigid container that expands negligibly when heated. At 20°C the gas pressure is p. If we add enough heat to increase the temperature from 20°C to 40°C, the pressure will be

A) impossible to determine since we do not know the number of moles of gas in the container.
B) greater than 2p.
C) less than 2p.
D) equal to 2p.
E) impossible to determine since we do not know the volume of gas in the container.

Answer 3

less than 2p.

Question 4

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. What happens to the average speed of the molecules in the sample?

A) It does not change.
B) It becomes 4 times as great.
C) It becomes 2 times as great.
D) It becomes 1/2 as great.
E) It becomes 1/4 as great.

Question 5

A weather balloon contains 12.0 m³ of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the pressure is 101 kPa. The balloon rises to a location where the temperature is -30.0°C and the pressure is 20.0 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

A) 14.0 m³
B) 2.38 m³
C) 49.9 m³
D) 82.6 m³
E) 4.16 m³

Question 6

A mole of oxygen (O₂) molecules and a mole of carbon dioxide (CO₂) molecules at the same temperature and pressure have

A) the same average molecular speeds.
B) the same number of atoms.
C) different average kinetic energy per molecule.
D) the same number of molecules.
E) different volumes.

Question 7

If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that

A) the pressure of the gas will increase.
B) the volume of the gas will increase.
C) the speed of the gas molecules will increase.
D) All of the above statements are correct.

Question 8

For a fixed amount of gas, if the absolute temperature of the gas is doubled, what happens to the pressure of the gas?

A) The answer cannot be determined without volume information.
B) The pressure of the gas becomes double the original pressure.
C) The pressure of the gas becomes eight times the original pressure.
D) The pressure of the gas becomes one half the original pressure.
E) The pressure of the gas becomes four times the original pressure.

Question 9

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average kinetic energy?

A) It is the same for both of the gases because the temperatures are the same.
B) The oxygen molecules do because they are diatomic.
C) The oxygen molecules do because they are more massive.
D) The helium molecules do because they are less massive.
E) The helium molecules do because they are monatomic.

Question 10

A sealed 89-m³ tank is filled with 6000 moles of oxygen gas (O₂) at an initial temperature of 270 K. The gas is heated to a final temperature of 350 K. The ATOMIC mass of oxygen is 16.0 g/mol, and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The initial pressure of the gas is closest to

A) 0.15 MPa.
B) 0.17 MPa.
C) 0.19 MPa.
D) 0.13 MPa.
E) 0.11 MPa.

Question 11

Which contains more moles of material: 80 grams of helium gas (He, having atomic weight 4.0 g/mol) or 400 grams of argon gas (Ar, having atomic weight 40 g/mol)?

A) helium
B) argon
C) Both contain the same number of moles.

Question 12

An ideal gas is kept in a rigid container. When its temperature is 100 K, the mean-free-path of the gas molecules is λ. What will be the mean-free-path of the molecules at 400 K?

A) 4λ
B) 2λ
C) λ
D) λ/2
E) λ/4

Question 13

A 3.2-L volume of neon gas (Ne) is at a pressure of 3.3 atm and a temperature of 330 K. The atomic mass of neon is 20.2 g/mol, Avogadro's number is 6.022 · 10²³ molecules/mol, and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The mass of the neon gas is closest to

A) 7.9 × 10^-3 kg.
B) 4.6 × 10^-3 kg.
C) 3.8 kg.
D) 7.8 kg.
E) 7.8 × 10² kg.

Question 14

2.0 L of an ideal nitrogen gas (N₂) are at 0.00°C and 1.0 atm. The ideal gas constant is R = 8.314 J/mol · K = 0.0821 L ∙ atm/mol ∙ K, Avogadro's number is 6.022 × 10²³ molecules/mol, and the ATOMIC mass of nitrogen is 14 g/mol.
(a) Determine the number of moles of N₂.
(b) How many molecules of N₂ are present?
(c) What is the mass of this gas?

Question 15

If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then

A) its temperature must increase by a factor of 4.
B) its temperature must increase by a factor of 2.
C) its temperature must increase by a factor of .
D) its pressure must increase by a factor of 2.
E) its pressure must increase by a factor of 4.

Question 16

If a certain sample of an ideal gas has a temperature of 109°C and exerts a pressure of 1.2 × 10⁴ Pa on the walls of its container, how many gas molecules are present in each cubic centimeter of volume? The ideal gas constant is 8.314 J/mol · K and Avogadro's number is 6.022 × 10²³ molecules/mol.

Question 17

The average molecular kinetic energy of a gas can be determined by knowing

A) only the number of molecules in the gas.
B) only the volume of the gas.
C) only the pressure of the gas.
D) only the temperature of the gas.
E) All of the above quantities must be known to determine the average molecular kinetic energy.

Question 18

A sealed 26-m³ tank is filled with 2000 moles of oxygen gas (O₂) at an initial temperature of 270 K. The gas is heated to a final temperature of 460 K. The ATOMIC mass of oxygen is 16.0 g/mol, and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The final pressure of the gas is closest to

A) 0.29 MPa.
B) 0.31 MPa.
C) 0.33 MPa.
D) 0.34 MPa.
E) 0.36 MPa.

Question 19

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the container reads 22°C. Which gas molecules have the greater average speed?

A) It is the same for both of the gases because the temperatures are the same.
B) The oxygen molecules do because they are diatomic.
C) The oxygen molecules do because they are more massive.
D) The helium molecules do because they are less massive.
E) The helium molecules do because they are monatomic.

Question 20

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in pressure. If the original root-mean-square speed (thermal speed) of the gas molecules was V, the new speed is

A) V.
B) 2V.
C) V.
D) V/2.
E) V/

Question 21

A 5.0-liter gas tank holds 1.4 moles of helium (He) and 0.70 moles of oxygen (O₂), at a temperature of 260 K. The atomic masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. Avogadro's number is 6.022 × 10²³ molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K. The total random translational kinetic energy of the gas in the tank is closest to

A) 6.8 kJ.
B) 6.1 kJ.
C) 7.6 kJ.
D) 8.3 kJ.
E) 9.1 kJ.

Question 22

The interior of a refrigerator has a volume of 0.600 m³. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator? The ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A) 500 g
B) 560 g
C) 140 g
D) 270 g
E) 750 g

Question 23

How many moles of water (H₂O) molecules are in a 4.00 m3 container at a pressure 8.00 × 10⁵ N/m² and temperature 600°C? The ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A) 7.72 × 10²⁶ mol
B) 641 mol
C) 441 mol
D) 3.86 × 10²⁶ mol
E) 2.65 × 10²⁶ mol

Question 24

The root-mean-square speed (thermal speed) for a certain gas at 100°C is 0.500 km/s. If the temperature of the gas is now increased to 200°C, the root-mean-square (thermal) speed will be closest to

A) 563 m/s.
B) 634 m/s.
C) 707 m/s.
D) 804 m/s.
E) 1000 m/s.

Question 25

The root-mean-square speed (thermal speed) of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mol, is 396 m/s. What is the root-mean-square speed (thermal speed) of water vapor molecules, with a molecular weight of 18 g/mol, at the same temperature?

A) 253 m/s
B) 396 m/s
C) 421 m/s
D) 506 m/s
E) 619 m/s

Question 26

A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O₂), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?

A) 1.4
B) 2.0
C) 2.8
D) 4.0
E) 5.6

Question 27

A hot air balloon has a volume of 2.00 × 10³ m³ when fully inflated, and the air inside the balloon is always at atmospheric pressure of 1.01 × 10⁵ Pa because of the large opening used to fill the balloon and heat the air inside it. What is the mass of hot air inside the balloon if its temperature is 120°C? The universal gas constant is 8.314 J/mol•K. (Assume a molecular weight of 28.8 g/mol for air.)

A) 1780 kg
B) 5850 kg
C) 203 kg
D) 62.0 kg

Question 28

An ideal gas is kept in a rigid container that expands negligibly when heated. The gas starts at a temperature of 20.0°C, and heat is added to increase its temperature. At what temperature will its root-mean-square speed (thermal speed) be double its value at 20.0°C?

A) 40.0°C
B) 141°C
C) 313°C
D) 400°C
E) 899°C

Question 29

Sometimes an experiment requires a certain pure gas to be used at reduced pressure. One way to achieve this is to purchase a sealed glass container filled with the gas, and to introduce the gas into a vacuum by attaching the glass container to the vacuum chamber and breaking the tip of the glass container using a metallic bean and a magnet. If the volume of the glass container is 1.0 L and it is at a pressure of 1.0 × 10⁵ Pa and if the vacuum chamber has a volume of 2.0 L, what will the pressure be after the gas, which is to be assumed to be an ideal gas, is released into the vacuum chamber and the temperature has returned to its original value? (Note that the glass container remains part of the system.)

A) 33 kPa
B) 50 kPa
C) 300 kPa
D) 200 kPa

Question 30

A bag of potato chips contains 2.00 L of air when it is sealed at sea level at a pressure of 1.00 atm and a temperature of 20.0°C. What will be the volume of the air in the bag if you take it with you, still sealed, to the mountains where the temperature is 7.00°C and atmospheric pressure is 70.0 kPa? Assume that the bag behaves like a balloon and that the air in the bag is in thermal equilibrium with the outside air. (1 atm = 1.01 × 10⁵ Pa)

A) 4.13 L
B) 1.01 L
C) 1.38 L
D) 2.76 L

Question 31

The figure shows a 50-kg frictionless cylindrical piston that floats on 0.68 mol of compressed air at 30°C. How far does the piston move if the temperature is increased to 300°C?

A) 120 cm
B) 250 cm
C) 130 cm
D) 1300 cm

Question 32

What is the average translational kinetic energy per molecule of an ideal gas at a temperature of 300 K? The Boltzmann constant is 1.38 × 10^-23 J/K.

A) 1.7 × 10^-21 J
B) 8.3 × 10^-21 J
C) 6.2 × 10^-21 J
D) 2.1 × 10^-21 J
E) 4.1 × 10^-21 J

Question 33

What is the mass density of argon gas at pressure 1.00 × 105 N/m² and at temperature 300 K? The mean atomic mass of argon is 39.948 g/mol and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A) 1.40 kg/m³
B) 1.00 kg/m³
C) 1.20 kg/m³
D) 1.60 kg/m³
E) 1.80 kg/m³

Question 34

An ideal gas is at a pressure 1.00 × 10⁵ N/m² and occupies a volume 2.00 m³. If the gas is compressed to a volume 1.00 m3 while the temperature remains constant, what will be the new pressure in the gas?

A) 0.500 × 10⁵ N/m²
B) 4.00 × 10⁵ N/m²
C) 1.00 × 10⁵ N/m²
D) 2.00 × 10⁵ N/m²
E) The answer depends on the mass of the gas particles.

Question 35

A cold trap is set up to cause molecules to linger near the suction in a vacuum system. If the cold trap has an effective volume of 0.200 L and is maintained at 13.0 K, how many molecules are in it at 10.0 Pa of pressure? (Avogadro's number is 6.022 × 10²³ molecules/mol, and the universal gas constant is 8.314 J/mol•K. Assume the behavior of an ideal gas.)

A) 1.11 × 10¹⁹ molecules
B) 1.10 × 10²² molecules
C) 7.71 × 10²⁰ molecules
D) 7.71 × 10²³ molecules

Question 36

What is the total translational kinetic energy in a test chamber filled with nitrogen (N₂) at 2.16 × 10⁵ Pa and 20.7°C? The dimensions of the chamber are 4.00 m × 5.70 m × 7.40 m. The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 1023 molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K.

Question 37

3.00 moles of an ideal gas at a pressure of 250 kPa are held in a container of volume of 25.0 L. The ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K, and 1 atm = 1.01 x 10⁵ Pa. The temperature of this gas is closest to

A) 240°C.
B) -180°C.
C) 480°C.
D) -1.0°C.
E) -22°C.

Question 38

A 0.10-m³ gas tank holds 5.0 moles of nitrogen gas (N₂), at a temperature of 370 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 × 10^-10 m, and the Boltzmann constant is 1.38 × 10^-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to

A) 570 m/s.
B) 810 m/s.
C) 410 m/s.
D) 22 m/s.
E) 99 m/s.

Question 39

A sealed container holds 0.020 moles of nitrogen (N₂) gas, at a pressure of 1.5 atmospheres and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. The Boltzmann constant is 1.38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The mass density of the gas is closest to

A) 0.90 kg/m³
B) 1.3 kg/m³
C) 1.8 kg/m³.
D) 2.2 kg/m³
E) 2.6 kg/m³

Question 40

A 25-L container holds ideal hydrogen (H₂) gas at a gauge pressure of 0.25 atm and a temperature of 0°C. What mass of hydrogen gas is in this container? The ATOMIC mass of hydrogen is 1.0 g/mol, the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K, and 1.00 atm = 101 kPa.

A) 1.4 g
B) 2.8 g
C) 4.2 g
D) 5.6 g
E) 6.3 g

Question 41

What is the mean free path for the molecules in an ideal gas when the pressure is 100 kPa and the temperature is 300 K given that the collision cross-section for the molecules of that gas is 2.0 × 10^-20 m²? The Boltzmann constant is 1.38 × 10^-23 J/K, Avogadro's number is 6.02 × 10²³ molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A) 1.1 × 10^-6 m
B) 2.1 × 10^-6 m
C) 1.7 × 10^-6 m
D) 5.3 × 10^-6 m
E) 1.5 × 10^-6 m

Question 42

The mean free path of an oxygen molecule is 2.0 × 10-5 m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The atomic mass of oxygen is 16.0 g/mol, the Boltzmann constant is 1.38 × 10^-23 J/K, Avogadro's number is 6.02 × 10²³ molecules/mole, and the ideal gas constant is J/mol•K = 0.0821 L ∙ atm/mol ∙ K. The radius of an oxygen molecule is closest to

A) 0.22 nm.
B) 0.24 nm.
C) 0.26 nm.
D) 0.28 nm.
E) 0.30 nm.

Question 43

A cubic box with sides of 20.0 cm contains 2.00 × 10²³ molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10^-27 kg. What is the average pressure exerted by the molecules on the walls of the container? The Boltzmann constant is 1.38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A) 3.39 kPa
B) 1.13 kPa
C) 570 Pa
D) 2.26 kPa
E) 9.10 Pa

Question 44

At 50.0°C, the average translational kinetic energy of a gas molecule is K. If the temperature is now increased to 100.0°C, the average translational kinetic energy of a molecule will be closest to

A) 1.07K.
B) 1.15K.
C) 1.41K.
D) 2.00K.
E) 4.00K.

Question 45

Dust particles are pulverized rock, which has density 2500 kg/m³. They are approximately spheres 20 μm in diameter. Treating dust as an ideal gas, what is the root-mean-square speed (thermal speed) of a dust particle at 400°C? (The Boltzmann constant is 1.38 × 10^-23 J/K.)

A) 5.2 × 10^-5 m/s
B) 1.7 × 10^-5 m/s
C) 3.0 × 10^-5 m/s
D) 7.3 × 10^-5 m/s

Question 46

What is the root-mean-square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?

A) 5.4 m/s
B) 1.9 m/s
C) 3.1 m/s
D) 3.3 m/s
E) 1.0 m/s

Question 47

What is the mean free path of a gas of randomly-moving hard spheres of radius 2.00 × 10^-9 m when the density of spheres is 3.00 × 10¹⁹ per cubic meter?

A) 1.17 × 10^-4 m
B) 4.00 × 10^-9 m
C) 9.76 × 10^-5 m
D) 1.88 × 10^-3 m
E) 4.69 × 10^-4 m

Question 48

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at 23.0°C. At 227°C the root-mean-square speed (thermal speed) of the molecules will be closest to

A) 160 m/s
B) 330 m/s
C) 260 m/s
D) 630 m/s
E) 2000 m/s

Question 49

On a hot summer day, the temperature is 40.0°C and the pressure is 1.01 × 10⁵ Pa. Let us model the air as all nitrogen of molecular mass 28.0 g/mol having molecules of diameter 0.500 nm that are moving at their root-mean-square speed. Avogadro's number is 6.02 × 10²³ molecules/mol, the ideal gas constant is 8.31 J/mol•K, and the Boltzmann constant is 1.38 × 10^-23 J/K. Calculate reasonable estimates for
(a) the root-mean-square speed of the nitrogen molecules.
(b) the average distance a typical molecule travels between collisions.
(c) the average time a molecule travels between collisions, assuming that the molecules are moving at their root-mean-square speeds.
(d) the number of collisions an average molecule undergoes per second.

Question 50

What is the average kinetic energy of an ideal gas molecule at 569°C? (The Boltzmann constant is 1.38 × 10^-23 J/K.)

A) 1.74 × 10^-20 J
B) 5.81 × 10^-21 J
C) 1.18 × 10^-17 J
D) 3.93 × 10^-19 J

Question 51

A sealed container holds 0.020 moles of nitrogen (N²) gas at a pressure of 1.5 atmospheres and a temperature of 290 K. The atomic mass of nitrogen is 14 g/mol. The Boltzmann constant is 1.38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K. The average translational kinetic energy of a nitrogen molecule is closest to

A) 4.0 × 10^-21 J.
B) 6.0 × 10^-21 J.
C) 8.0 × 10^-21 J.
D) 10 × 10^-21 J.
E) 12 × 10^-21 J.

Question 52

The mean free path of an oxygen molecule is 2.0 × 10^-5 m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The molecular mass of oxygen is 32.0 g/mol and the Boltzmann constant is 1.38 × 10^-23 J/K, Avogadro's number is 6.02 × 10²³ molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K. Assuming that the molecules are moving at their root-mean-square speeds, the average time interval between collisions of an oxygen molecule is closest to

A) 20 ns.
B) 43 ns.
C) 95 ns.
D) 200 ns.
E) 420 ns.

Question 53

Eleven molecules have speeds 16, 17, 18, . . . , 26 m/s. Calculate the root-mean-square of this group of molecules.

A) 21.2 m/s
B) 21.0 m/s
C) 21.5 m/s
D) 21.7 m/s

Question 54

An oxygen molecule falls in a vacuum. From what height must it fall so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 800 K? (The Boltzmann constant is 1.38 × 10^-23 J/K, the molecular weight of oxygen is 32.0 g/mol, and Avogadro's number is 6.022 × 10²³ molecules/mol.)

A) 31.8 km
B) 10.6 km
C) 21.1 km
D) 42.3 km

Question 55

Assuming the radius of diatomic molecules is approximately 1.0 × 10^-10 m, for what pressure will the mean free path in room-temperature (20°C) nitrogen be 4.6 m? The Boltzmann constant is 1.38 × 10^-23 J/K, Avogadro's number is 6.02 × 10²³ molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A) 4.9 × 10^-8 atm
B) 6.9 × 10^-8 atm
C) 1.5 × 10^-7 atm
D) 2.2 × 10^-7 atm

Question 56

The root-mean-square speed (thermal speed) of the molecules of a gas is 200 m/s at a temperature 23.0°C. What is the mass of the individual molecules? The Boltzmann constant is 1.38 × 10^-23 J/K.

A) 2.13 × 10^-25 kg
B) 2.45 × 10^-25 kg
C) 5.66 × 10^-25 kg
D) 1.78 × 10^-25 kg
E) 3.11 × 10^-25 kg

Question 57

What is the mean free path of molecules in an ideal gas in which the mean collision time is 3.00 × 10^-10 s, the temperature is 300 K, and the mass of the molecules is 6.00 × 10^-25 kg? Assume that the molecules are moving at their root-mean-square speeds. The Boltzmann constant is 1.38 × 10^-23 J/K.

A) 7.22 × 10^-8 m
B) 4.32 × 10^-8 m
C) 9.19 × 10^-8 m
D) 1.39 × 10^-8 m
E) 6.71 × 10^-8 m

Question 58

At what temperature would the root-mean-square speed (thermal speed) of oxygen molecules be 13.0 m/s? Assume that oxygen approximates an ideal gas. The mass of one O₂ molecule is 5.312 x 10^-26 kg. The Boltzmann constant is 1.38 × 10^-23 J/K.

A) 0.217 K
B) 1800 K
C) 5410 K
D) 0.0666 K