Deck 14: The Ideal Gas Law and Kinetic Theory

Question 1

Note the following six properties: Which four of the listed properties are needed to describe an ideal gas?

A)1, 2, 4, 6
B)1, 3, 5, 6
C)1, 3, 4, 6
D)1, 4, 5, 6
E)2, 4, 5, 6

Answer 1

1, 3, 5, 6

Question 2

Neon gas at 305 K is confined within a constant volume at a pressure P₁.If the gas has a pressure P₂ when it is cooled to 125 K, what is the ratio of P₂ to P₁?

A)0.410
B)0.639
C)0.717
D)1.56
E)2.44

Answer 2

0.410

Question 3

An ideal gas with a fixed number of molecules is maintained at a constant pressure.At 30.0 °C, the volume of the gas is 1.25 m³.What is the volume of the gas when the temperature is increased to 150.0 °C?

A)0.90 m³
B)1.50 m³
C)1.75 m³
D)2.45 m³
E)6.25 m³

Answer 3

1.75 m³

Question 4

Which one of the following statements best explains why gases are not commercially sold by volume?

A)Gas volume is negligible.
B)Gas volume is difficult to measure.
C)Gas volume depends on the type of gas.
D)Gases have comparatively low densities.
E)Gas volume depends on temperature and pressure.

Question 5

In the space between two stars, the temperature of a gas cloud is 12 K; and the density of the gas is 1.2 × 10^-8 atom/m³.What is the absolute pressure of the gas?

A)2.0 × 10^-30 Pa
B)1.2 × 10^-28 Pa
C)2.0 × 10^-17 Pa
D)1.2 × 10^-6 Pa
E)1.4 × 10^-4 Pa

Question 6

A sample of a monatomic ideal gas is originally at 20 °C.What is the final temperature of the gas if the pressure is doubled and volume is reduced to one-fourth its initial value?

A)900 °C
B)10 °C
C)80 °C
D)(-130 °C)
E)(-260 °C)

Question 7

A sample of neon gas at 20 °C is confined to a cylinder with a movable piston.The gas is then heated until its pressure is doubled.What is the final temperature of the gas?

A)10 °C
B)40 °C
C)313 °C
D)586 °C
E)This cannot be found since the final and initial volumes are unknown.

Question 8

An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 10⁵ Pa by a piston.The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.What is the final pressure of the gas when its temperature returns to its initial value?

A)9.117 × 10⁵ Pa
B)6.447 × 10⁵ Pa
C)4.559 × 10⁵ Pa
D)3.102 × 10⁵ Pa
E)1.823 × 10⁶ Pa

Question 9

A silver coin has a mass of 17.75 g.If the atomic mass of silver is 107.868 u, how many silver atoms are in the coin?

A)5.724 × 10²²
B)2.158 × 10²³
C)4.812 × 10²³
D)3.660 × 10²⁴
E)1.390 × 10²⁵

Question 10

Helium gas at 20 °C is confined within a rigid vessel.The gas is then heated until its pressure is doubled.What is the final temperature of the gas?

A)10 °C
B)20 °C
C)40 °C
D)313 °C
E)586 °C

Question 11

How many molecules are in 0.044 kg of carbon dioxide, CO₂? (atomic masses: C = 12 u; O = 16 u)

A)3
B)44
C)2.20 × 10²⁴
D)6.02 × 10²³
E)3.85 × 10²⁵

Question 12

How many moles are in a 0.53-kg sample of sulphur dioxide, SO₂? (atomic masses: C = 32 u; O = 16 u)

A)5.2
B)8.3
C)48
D)1.6 × 10⁴
E)5.0 × 10²⁴

Question 13

The density of diamond, a form of carbon, is 3520 kg/m³.If the atomic mass of carbon is 12.011 u, how many carbon atoms are there in a solid diamond sphere with a radius of 0.0125 m?

A)1.15 × 10²⁷ atoms
B)5.76 × 10²⁶ atoms
C)2.88 × 10²⁵ atoms
D)1.44 × 10²⁴ atoms
E)7.21 × 10²³ atoms

Question 14

Complete the following statement: The atomic mass unit (u) is defined so that 1 u is exactly equal to the mass of

A)a single hydrogen atom.
B)1/4 of a helium molecule.
C)1/16 of an oxygen-16 atom.
D)1/32 of an oxygen molecule.
E)1/12 of a carbon-12 atom.

Question 15

An ideal gas at 0 °C is contained within a rigid vessel.The temperature of the gas is increased by 1 C°.What is P_f/P_i, the ratio of the final to initial pressure?

A)273/274
B)274/273
C)1/2
D)1/10
E)1/273

Question 16

Which one of the following statements concerning the mole is false?

A)The mole is related to Avogadro's number.
B)The mole is defined in terms of the carbon-12 isotope.
C)The mole is the SI base unit for expressing the "amount" of a substance.
D)One mole of a substance has the same mass as one mole of any other substance.
E)One mole of a substance contains the same number of particles as one mole of any other substance.

Question 17

What is the mass of 3.0 moles of hydrogen molecules, H₂? (atomic mass of H = 1 u)

A)0.0060 g
B)0.0030 kg
C)0.0090 kg
D)0.015 kg
E)0.030 kg

Question 18

Two pure samples of atoms, labeled A and B, contain titanium (Ti) atoms and carbon (C) atoms, respectively.Each sample contains the same number of atoms.What is the ratio of the mass of sample B to that of sample A, m_B/m_A? Note the following atomic masses: C = 12 u; Ti = 48 u.

A)1.0
B)0.25
C)2.0
D)0.50
E)4.0

Question 19

Heat is supplied to a sample of a monatomic ideal gas at 40 °C.It is observed that the gas expands until its volume and pressure are doubled.What is the final temperature of the gas?

A)10 °C
B)20 °C
C)40 °C
D)980 °C
E)1600 °C

Question 20

What is the approximate mass of an oxygen molecule, O₂, if the atomic mass of oxygen is 15.9994 u?

A)2.657 × 10^-26 kg
B)5.313 × 10^-26 kg
C)3.200 × 10^-25 kg
D)6.400 × 10^-25 kg
E)1.927 × 10^-23 kg

Question 21

Complete the following statement: The pressure exerted by a monatomic, ideal gas on the walls of its containing vessel is a measure of

A)the molecular kinetic energy per unit volume.
B)the average random kinetic energy per molecule.
C)the temperature of the gas, regardless of the volume of the vessel.
D)the total internal energy of the gas, regardless of the volume of the vessel.
E)the momentum per unit volume.

Question 22

Which one of the following factors is directly responsible for the pressure exerted by a confined gas?

A)the atomic mass of the gas
B)the density of the sample of molecules
C)the temperature of the sample of molecules
D)the collision of gas molecules with the sides of the containing vessel
E)the average translational kinetic energy of the molecules

Question 23

A 7.50 × 10^-3-m³ bottle contains 0.0200 kg of oxygen gas, O₂, at 77.0 °C.What is the pressure exerted on the inner walls of the flask by the oxygen gas? Note: the atomic mass of O is 15.9994 u.

A)8.42 × 10⁴ Pa
B)1.45 × 10⁵ Pa
C)2.43 × 10⁵ Pa
D)4.86 × 10⁵ Pa
E)1.46 × 10⁶ Pa

Question 24

Consider two ideal gases, A and B, at the same temperature.The rms speed of the molecules of gas A is twice that of gas B.How does the molecular mass of A compare to that of B?

A)The molecular mass of A is twice that of B.
B)The molecular mass of A is one half that of B.
C)The molecular mass of A is 1.4 times that of B.
D)The molecular mass of A is one fourth that of B.
E)The molecular mass of A is four times that of B.

Question 25

An ideal gas is contained in a vessel with a moveable piston.Initially, the gas has a volume of 0.024 m³, an absolute pressure of 1.8 atm, and a temperature of 35.0 °C.The pressure is 0.90 atm when the volume of the container is decreased to 0.012 m³.What is the final temperature of the gas?

A)77 K
B)85 K
C)170 K
D)154 K
E)282 K

Question 26

A mixture of two ideal gases A and B is in thermal equilibrium at 600 K.A molecule of A has one-fourth the mass of a molecule of B and the rms speed of molecules of A is 400 m/s.Determine the rms speed of molecules of B.

A)100 m/s
B)200 m/s
C)400 m/s
D)800 m/s
E)1600 m/s

Question 27

The volume of a carbon dioxide bubble rising in a glass of beer is observed to nearly double as the bubble rises from the bottom to the top of the glass.Why, according to our textbook, does the volume nearly double?

A)The temperature at the bottom is cooler than it is at the top.
B)The amount of carbon dioxide in the bubble increases.
C)The fluid pressure of the beer is greater at the bottom of the glass than at the top.
D)The pressure inside the bubble decreases as it rises.
E)The shape of the glass determines the net force exerted on the bubble.

Question 28

At what temperature would one mole of molecular nitrogen (N₂) have 7.0 × 10³ J of translational kinetic energy? Note: the atomic mass of N is 14 u.

A)130 °C
B)290 °C
C)480 °C
D)560 °C
E)720 °C

Question 29

A sealed container has a volume of 0.020 m³ and contains 15.0 g of molecular nitrogen (N₂), which has a molecular mass of 28.0 u.The gas is at 525 K.What is the absolute pressure of the nitrogen gas?

A)3.9 × 10^-19 Pa
B)4.3 × 10^-5 Pa
C)1.2 × 10⁵ Pa
D)1.9 × 10⁵ Pa
E)4.3 × 10⁶ Pa

Question 30

A canister containing 115 kg of an ideal gas has a volume of 6.5 m³.If the gas exerts a pressure of 4.0 × 10⁵ Pa, what is the rms speed of the molecules?

A)260 m/s
B)180 m/s
C)310 m/s
D)390 m/s
E)420 m/s

Question 31

Under which of the following conditions would you expect real gases to approach ideal behavior?

A)low temperature and low pressure
B)high temperature and low pressure
C)low temperature and high pressure
D)high temperature and high pressure
E)high temperature and high density

Question 32

Complete the following statement: The internal energy of an ideal monatomic gas is

A)proportional to the pressure and inversely proportional to the volume of the gas.
B)independent of the number of moles of the gas.
C)proportional to the Kelvin temperature of the gas.
D)dependent on both the pressure and the temperature of the gas.
E)a constant that is independent of pressure, volume or temperature.

Question 33

A physics student looks into a microscope and observes that small particles suspended in water are moving about in an irregular motion.Which of the following statements is the best explanation for this observation?

A)Water molecules strike the particles giving them the same average kinetic energy as the water.
B)The particles are carried by convection currents in the water.
C)The small particles may be considered a fluid; and thus, move about randomly.
D)The actual motion is regular, but the speeds of particles are too large to observe the regular motion.
E)The particles are moving to be uniformly distributed throughout the volume of the water.

Question 34

Complete the following statement: The absolute temperature of an ideal gas is directly proportional to

A)the number of molecules in the sample.
B)the average momentum of a molecule of the gas.
C)the average translational kinetic energy of the gas.
D)the amount of heat required to raise the temperature of the gas by 1 C°.
E)the relative increase in volume of the gas for a temperature increase of 1 C°.

Question 35

Which one of the following properties of a gas is not consistent with kinetic theory?

A)The average speed of the gas molecules is smaller at high temperatures.
B)Gas molecules are widely separated.
C)Gases fill whatever space is available to them.
D)Gas molecules move rapidly in a random fashion.
E)Gas molecules make elastic collisions with the walls of the containing vessel.

Question 36

Two moles of a monatomic gas with an rms speed of 294 m/s are contained in a tank that has a volume of 0.12 m³.If each gas particle has a mass of 8.220 × 10^-26 kg, what is the absolute pressure of the gas?

A)2.1 × 10⁵ Pa
B)1.1 × 10⁴ Pa
C)4.8 × 10⁴ Pa
D)2.4 × 10⁴ Pa
E)3.0 × 10⁴ Pa

Question 37

The temperature of a monatomic ideal gas with a mass per mole of 0.00750 kg/mol is 298 K.The absolute pressure of the gas is 1.65 × 10⁵ Pa when its volume is 1.21 × 10^-3 m³.What is the mass of the gas?

A)9.11 × 10^-5 kg
B)2.18 × 10^-4 kg
C)4.22 × 10^-4 kg
D)6.04 × 10^-4 kg
E)2.27 × 10^-3 kg

Question 38

Complete the following statement: A bicycle tire explodes after lying in the hot afternoon sun.This is an illustration of

A)Charles' law.
B)Boyle's law.
C)Fick's law.
D)the ideal gas law.
E)the Maxwell speed distribution.

Question 39

Which one of the following statements concerning a collection of gas molecules at a certain temperature is true?

A)All molecules move with the same velocity.
B)Most of the molecules have the same kinetic energy.
C)The lower the temperature, the greater are the molecular speeds.
D)All molecules possess the same momentum.
E)The molecules have a range of kinetic energies.

Question 40

A five-liter tank contains 2.00 moles of oxygen gas, O₂, at 40 °C.What pressure is exerted on the sides of the tank by the oxygen molecules?

A)83.3 Pa
B)4.01 × 10³ Pa
C)1.33 × 10⁵ Pa
D)4.01 × 10⁵ Pa
E)1.04 × 10⁶ Pa

Question 41

An automobile tire is inflated to a gauge pressure of 32 lb/in² at a temperature of -10.0 °C.Under strenuous driving, the tire heats up to 40.0 °C.What is the new gauge pressure if the volume of the tire remains essentially the same? (atmospheric pressure = 14.7 lb/in²)

A)17.5 lb/in²
B)20.6 lb/in²
C)38.0 lb/in²
D)40.9 lb/in²
E)55.6 lb/in²

Question 42

A bubble with a volume of 1.0 cm³ forms at the bottom of a lake that is 20.0 m deep.The temperature at the bottom of the lake is 10.0 °C.The bubble rises to the surface where the temperature is 25.0 °C.Assume that the bubble is small enough that its temperature always matches that of its surroundings.What is the volume of the bubble just before it breaks the surface of the water?

A)2.1 cm³
B)2.8 cm³
C)3.1 cm³
D)6.0 cm³
E)7.7 cm³

Question 43

On a cold day (-3 °C), the gauge pressure on a tire is 2.0 atm.If the tire is heated to 27 °C, without changing its volume, what will the gauge pressure be?

A)2.1 atm
B)2.3 atm
C)2.9 atm
D)3.3 atm
E)27 atm

Question 44

Calculate the rms speed of the carbon dioxide molecules in the air if the temperature is 15.0 °C.Note: The mass of the carbon dioxide molecule is 44.01 u.

A)316 m/s
B)469 m/s
C)378 m/s
D)404 m/s
E)511 m/s

Question 45

How many air molecules are in a room at temperature 23.8 °C and standard pressure if the dimensions of the room are 3.44 m × 3.26 m × 2.28 m?

A)2.08 × 10²⁴
B)4.20 × 10²⁴
C)3.78 × 10²⁵
D)6.32 × 10²⁶
E)8.05 × 10²⁶

Question 46

A flask contains 1.00 mole of oxygen gas, O₂, at 0.00 °C and 1.013 × 10⁵ Pa.What is the rms speed of the molecules? Note: the atomic mass of O is 16 u.

A)230 m/s
B)460 m/s
C)651 m/s
D)920 m/s
E)1302 m/s

Question 47

A gas molecule with a molecular mass of 32.0 u has a speed of 325 m/s.What is the temperature of the gas molecule?

A)72.0 K
B)136 K
C)305 K
D)459 K
E)A temperature cannot be assigned to a single molecule.

Question 48

A lower tank contains water while an upper tank contains air with a negligible concentration of water vapor.A tube with a circular cross section and radius 0.050 m is inserted between the two tanks.The length of the tube is 0.25 m.The diffusion coefficient of water vapor through air is 2.4 × 10^-5 m²/s.The concentration of water vapor just above the surface of the water is 1.7 × 10^-2 kg/m³.If the water vapor is removed from the upper tank so that the concentration there remains nearly zero, what mass of water vapor diffuses through the tube each hour?

A)4.6 × 10^-5 kg
B)2.0 × 10^-6 kg
C)7.1 × 10^-7 kg
D)1.3 × 10^-8 kg
E)8.2 × 10^-8 kg

Question 49

What is the internal energy of 1.75 kg of helium (atomic mass = 4.00260 u) with a temperature of 100 °C?

A)4.65 × 10³ J
B)5.44 × 10⁵ J
C)2.03 × 10⁶ J
D)8.16 × 10⁶ J
E)1.22 × 10⁷ J

Question 50

Which one of the following statements concerning diffusion is true?

A)Diffusion occurs only in gases.
B)Diffusion occurs in solids and fluids.
C)Diffusion is described by Boyle's law.
D)The SI unit for the diffusion constant D is m/s².
E)Diffusion occurs when molecules move from regions of lower concentration to regions of higher concentration.

Question 51

A concentration difference of a certain solute of 1.0 × 10^-2 kg/m³ is maintained between the ends of a tube with a length of 3.5 m and a cross-sectional area of 0.25 m².When 0.0040 g of the solute is introduced to the tube, it takes 350 minutes for this solute to diffuse through the solvent to the opposite end of the tube.What is the diffusion constant for the solute?

A)2.7 × 10^-7 m²/s
B)4.5 × 10^-9 m²/s
C)7.5 × 10^-10 m²/s
D)6.3 × 10^-8 m²/s
E)1.1 × 10^-11 m²/s

Question 52

An air bubble 20 m below the surface of a lake has a volume of 0.02 m³.The bubble then rises to the surface.Assuming the temperature of the lake is uniform, what is the volume of the bubble just before it breaks through the surface?

A)0.02 m³
B)0.04 m³
C)0.06 m³
D)0.08 m³
E)0.10 m³

Question 53

What is the density of methane, CH₄, (molecular mass = 16 u) at STP?

A)0.357 kg/m³
B)0.386 kg/m³
C)0.431 kg/m³
D)0.712 kg/m³
E)0.951 kg/m³

Question 54

A tank contains 135 moles of the monatomic gas argon at a temperature of 15.3 °C.How much energy must be added to the gas to increase its temperature to 45.0 °C?

A)2.50 × 10³ J
B)3.33 × 10⁴ J
C)5.00 × 10⁴ J
D)5.70 × 10⁵ J
E)7.50 × 10⁶ J

Question 55

On a cold day (-3 °C), the gauge pressure on a tire reads 2.0 atm.If the tire is heated to 27 °C, what will be the absolute pressure of the air inside the tire?

A)2.0 atm
B)2.2 atm
C)2.4 atm
D)2.9 atm
E)3.3 atm