Question 1

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?

Accepted Answer

The observed motion is due to water molecules striking the particles, transferring kinetic energy to them. This phenomenon is known as Brownian motion, where particles suspended in a fluid move in a zigzag or irregular path due to collisions with the molecules of the fluid.

Question 2

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

Accepted Answer

High temperature and low pressure are the conditions where real gases are more likely to approach ideal behavior. This is because at high temperatures, the kinetic energy of gas particles is high which leads to increased molecular motion and decreased intermolecular forces. At low pressure, the molecules are separated by larger distances which leads to less interaction between them. Both of these conditions allow the molecules to behave more like ideal gases.

Question 3

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?

Accepted Answer

The answer of An ideal gas is contained in a...

Question 4

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?

Accepted Answer

The answer of The volume of a carbon dioxide bubble...

Question 5

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

Accepted Answer

According to kinetic theory, the average speed of gas molecules increases with an increase in temperature, not decreases. Therefore, option A is not consistent with kinetic theory, making it the correct choice.

Question 6

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?

Accepted Answer

The rms speed of gas molecules is inversely proportional to the square root of their molecular mass. If the speed of A is twice that of B, then the mass of A must be one fourth that of B, according to the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $v_{rms}$ is the root mean square speed, $k$ is the Boltzmann constant, $T$ is the temperature, and $m$ is the molecular mass.

Question 7

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

Accepted Answer

The pressure exerted by a confined gas is directly related to the collision of gas molecules with the sides of the containing vessel. This is because each time a molecule collides with the walls of the container, it exerts a force on the surface. The sum of these forces per unit area is the pressure exerted by the gas.

Question 8

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?

Accepted Answer

The answer of A sealed container has a volume of...

Question 9

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?

Accepted Answer

The answer of A five-liter tank contains 2.00 moles of...

Question 10

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

Accepted Answer

The pressure of an ideal gas is directly related to the molecular kinetic energy per unit volume, as described by the kinetic theory of gases.

Question 11

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

Accepted Answer

The internal energy of an ideal monatomic gas is proportional to the kinetic energy of its particles, which is directly proportional to the absolute temperature of the gas, according to the kinetic theory of gases. Therefore, the internal energy is directly proportional to the Kelvin temperature of the gas.

Question 12

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.

Accepted Answer

The translational kinetic energy (KE) of one mole of an ideal gas is given by the equation KE = (3/2)RT, where R is the ideal gas constant (8.314 J/mol·K), and T is the temperature in Kelvin. Rearranging the formula to solve for T gives T = (2KE)/(3R). Substituting the given kinetic energy (7.0 × 10³ J) into the equation yields T = (2 × 7.0 × 10³ J) / (3 × 8.314 J/mol·K) ≈ 562 K. To convert Kelvin to Celsius, subtract 273 from the Kelvin temperature, resulting in approximately 289 °C, which is closest to option B, 290 °C.

Question 13

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

Accepted Answer

The kinetic energy of a gas molecule is proportional to its velocity squared. Therefore, at a certain temperature, the molecules will have a range of velocities and therefore a range of kinetic energies. Choice A is incorrect because the molecules in a gas will have a range of velocities. Choice B is incorrect because the distribution of kinetic energies will follow a Maxwell-Boltzmann distribution, with some molecules having higher or lower kinetic energies than most. Choice C is incorrect because the higher the temperature, the greater are the molecular speeds. Choice D is incorrect because the momentum of a molecule is equal to its mass times its velocity, so each molecule will have a different momentum due to their different velocities.

Question 14

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.

Accepted Answer

The root-mean-square (rms) speed of a molecule in an ideal gas is inversely proportional to the square root of its mass. Since the mass of a molecule of B is four times that of A, the rms speed of B will be half that of A. Given that the rms speed of A is 400 m/s, the rms speed of B will be 400 m/s divided by 2, which is 200 m/s.

Question 15

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?

Accepted Answer

The answer of The temperature of a monatomic ideal gas...

Question 16

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?

Accepted Answer

The answer of A canister containing 115 kg of an...

Question 17

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

Accepted Answer

The absolute temperature of an ideal gas is directly proportional to the average translational kinetic energy of the gas, as stated by the kinetic theory of gases. The other options are not directly proportional to the temperature of the gas.

Question 18

A 7.50 × 10^-³m³ 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.

Accepted Answer

Using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

We first need to find the number of moles of oxygen gas present:

n = m/M
where m is the mass of the oxygen gas and M is the molar mass of oxygen gas.

M = 2(15.9994 u) = 31.9988 g/mol

Converting the mass of oxygen gas to kg:

m = 0.0200 kg

n = 0.0200 kg/31.9988 g/mol = 0.000625 mol

Next, we need to convert the volume to m³:

V = 7.50 × 10¹¹ P0³m³ = 7.50 × 10¹⁷ nm³

V = 7.50 × 10¹⁷ nm³ × (1 m³/10⁰⁹ nm³) = 7.50 m³

Finally, we can solve for the pressure:

P = nRT/V

R = 8.314 J/mol·K
T = 77.0 °C = 350.15 K

P = (0.000625 mol)(8.314 J/mol·K)(350.15 K)/(7.50 m³)
P = 2.43 × 10⁵ Pa

Therefore, the answer is choice C.

Question 19

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?

Accepted Answer

The absolute pressure of the gas can be calculated using the formula derived from the ideal gas law and the kinetic theory of gases: $P = \frac{2}{3} \cdot \frac{N}{V} \cdot \frac{1}{2}m(v_{rms})^2$, where $N$ is the number of molecules, $V$ is the volume, $m$ is the mass of a single molecule, and $v_{rms}$ is the root mean square speed of the molecules. Given $N = 2 \cdot N_A$ (where $N_A$ is Avogadro's number, since we have 2 moles), $V = 0.12 m^3$, $m = 8.220 \times 10^{-26} kg$, and $v_{rms} = 294 m/s$, substituting these values into the formula gives the pressure $P$, which after calculation results in approximately $2.4 \times 10^4 Pa$.

Question 20

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

Accepted Answer

The answer of Complete the following statement: A bicycle tire...

Quiz 14: The Ideal Gas Law and Kinetic Theory

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?

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

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?

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?

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

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?

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

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 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?

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

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

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.

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

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.

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 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?

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

A 7.50 × 10^-³m³ 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.

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?

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

Quiz 14: The Ideal Gas Law and Kinetic Theory

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?

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

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?

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?

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

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?

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

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 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?

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

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

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.

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

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.

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 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?

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

A 7.50 × 10-³m³ 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.

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?

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

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 7.50 × 10^-³m³ 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.

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?