Question 1

The specific heat at constant volume per mole of  is for what type of molecule?

Accepted Answer

The answer of The specific heat at constant volume per...

Question 2

What is the internal energy of 42 moles of Neon gas (molecular mass = 20 u) at 27$\degree$C? (R = 8.31 J/mol ·K)

Accepted Answer

The internal energy of an ideal monoatomic gas like Neon is given by (3/2)nRT. Converting 27°C to Kelvin gives 300K. Substituting n = 42 moles, R = 8.31 J/mol·K, and T = 300K, the internal energy is calculated as (3/2) * 42 * 8.31 * 300 = 1.6 × 10^5 J.

Question 3

What is (are) the unit(s) for the diffusion constant?

Accepted Answer

The diffusion constant has units of m²/s because it is a measure of the rate at which a substance diffuses through a medium. The rate of diffusion is proportional to the concentration gradient of the substance, and the diffusion constant is a measure of the proportionality constant. The units of the diffusion constant are therefore m²/s, which is the product of the units of concentration (mol/m³) and the units of time (s).

Question 4

Consider two containers with the same volume and temperature. Container One holds "dry" air (a mixture of nitrogen and oxygen). Container Two holds "moist" air. The "moist" air has the same ratio of nitrogen to oxygen molecules but also contains water vapor. According to the ideal gas law, if the pressures are equal, the weight of the gas in Container One will be:

Accepted Answer

The presence of water vapor in Container Two means that there are more gas molecules in the container overall, making it heavier than the dry air in Container One. This is because water vapor has a lower molecular weight than nitrogen and oxygen, so a given volume of moist air contains more molecules than the same volume of dry air. Since the pressures are equal, this means that the weight of the gas in Container One is lighter than the weight of the gas in Container Two.

Question 5

A quantity of a monatomic ideal gas expands to four times the volume while maintaining the same pressure. If the internal energy of the gas were U₀ before the expansion, what is it after the expansion?

Accepted Answer

For a monatomic ideal gas, the internal energy is solely dependent on the temperature. Since the pressure is constant and the gas expands to four times the volume, the temperature remains constant. Thus, the internal energy of the gas remains the same. Therefore, the internal energy after the expansion is 4U₀, which is choice C.

Question 6

Suppose the pressure of 20 g of an ideal monatomic gas is tripled while its volume is halved. What happens to the internal energy of the gas?

Accepted Answer

The internal energy of an ideal monatomic gas is directly proportional to its temperature. Tripling the pressure while halving the volume results in an increase in temperature, thus increasing the internal energy.

Question 7

When a sealed container of ideal gas has its temperature increase from 250 K to 500 K, what happens to the mean free path of the molecules?

Accepted Answer

The answer of When a sealed container of ideal gas...

Question 8

For a monatomic gas,  is

Accepted Answer

The answer of For a monatomic gas,  is
...

Question 9

John rapidly pulls a plunger out of a cylinder, increasing its volume. As the plunger moves away, the gas molecules bouncing elastically off the plunger are:

Accepted Answer

The answer of John rapidly pulls a plunger out of...

Question 10

In a system of ideal gas with P, V, and T constant, if the molecules diffuse an average displacement of 2 cm in 4 s, on the average what would the average displacement be for a time of 200 s?

Accepted Answer

The answer of In a system of ideal gas with...

Question 11

The temperature of a quantity of ideal gas in a sealed container is increased from 0°C to 819°C. What happens to the speed of the molecules with average kinetic energy of the gas as a result of this temperature increase?

Accepted Answer

The average kinetic energy of a gas molecule is directly proportional to the absolute temperature of the gas. Therefore, when the temperature of the gas is increased from 0°C to 819°C, the average kinetic energy of the gas molecules will also increase. Since the average kinetic energy of a gas molecule is proportional to the square of its speed, the speed of the gas molecules will also increase. The speed of the gas molecules will double when the temperature of the gas is increased from 0°C to 819°C.

Question 12

If the temperature of a gas doubles, by what factor does the speed of a molecule with the average kinetic energy change?

Accepted Answer

The answer of If the temperature of a gas doubles,...

Question 13

What is the internal energy of a monatomic ideal gas with pressure 6 *10⁵ Pa and with volume 2 m³?

Accepted Answer

The answer of What is the internal energy of a...

Question 14

If the average kinetic energy of the molecules of a monatomic ideal gas at 30°C is doubled, what is the resulting temperature of the gas?

Accepted Answer

The answer of If the average kinetic energy of the...

Question 15

For an ideal gas of a given mass, if the pressure remains the same and the volume decreases:

Accepted Answer

The answer of For an ideal gas of a given...

Question 16

The internal energy of a monatomic ideal gas is equal to which of the following?

Accepted Answer

The internal energy of a monatomic ideal gas is given by (3/2)PV, where P is the pressure, V is the volume, and n is the number of moles of gas.

Question 17

The noble gases, listed by increasing molecular weight, are He, Ne, Ar, Kr, Xe, and Rn. If samples of 1 mole each of these gases are placed in separate containers and heated to 300 K, which gas has the greatest internal energy and the molecules of which gas have the lowest average speed?

Accepted Answer

All the gases have the same internal energy because they have the same number of moles and are at the same temperature. Rn has the lowest average speed due to its highest molecular weight.

Question 18

If the temperature of an ideal gas contained in a box is increased:

Accepted Answer

When the temperature of an ideal gas is increased, the average kinetic energy of the gas molecules increases as well. This means that the molecules will move faster and have a higher average speed. However, the distance between molecules will not be affected by a change in temperature.

Question 19

If an average molecule diffuses to a displacement of 4 cm in 5 s, how long would it take for such a molecule to diffuse to a displacement of 16 cm?

Accepted Answer

Diffusion time is proportional to the square of the displacement. If 4 cm takes 5 s, then 16 cm (which is 4 times the displacement) will take 4^2 = 16 times longer, so 5 s * 16 = 80 s.

Question 20

The absolute temperature of a monatomic ideal gas is directly proportional to which of the following properties, when taken as an average, of the molecules of that gas?

Accepted Answer

The absolute temperature of a monatomic ideal gas is directly proportional to the average kinetic energy of its molecules.

Quiz 15: Gases and Kinetic Theory

The specific heat at constant volume per mole of is for what type of molecule?

What is the internal energy of 42 moles of Neon gas (molecular mass = 20 u) at 27 $\degree$ C? (R = 8.31 J/mol ·K)

What is (are) the unit(s) for the diffusion constant?

A quantity of a monatomic ideal gas expands to four times the volume while maintaining the same pressure. If the internal energy of the gas were U₀ before the expansion, what is it after the expansion?

Suppose the pressure of 20 g of an ideal monatomic gas is tripled while its volume is halved. What happens to the internal energy of the gas?

When a sealed container of ideal gas has its temperature increase from 250 K to 500 K, what happens to the mean free path of the molecules?

For a monatomic gas, is

John rapidly pulls a plunger out of a cylinder, increasing its volume. As the plunger moves away, the gas molecules bouncing elastically off the plunger are:

In a system of ideal gas with P, V, and T constant, if the molecules diffuse an average displacement of 2 cm in 4 s, on the average what would the average displacement be for a time of 200 s?

The temperature of a quantity of ideal gas in a sealed container is increased from 0°C to 819°C. What happens to the speed of the molecules with average kinetic energy of the gas as a result of this temperature increase?

If the temperature of a gas doubles, by what factor does the speed of a molecule with the average kinetic energy change?

What is the internal energy of a monatomic ideal gas with pressure 6 *10⁵ Pa and with volume 2 m³?

If the average kinetic energy of the molecules of a monatomic ideal gas at 30°C is doubled, what is the resulting temperature of the gas?

For an ideal gas of a given mass, if the pressure remains the same and the volume decreases:

The internal energy of a monatomic ideal gas is equal to which of the following?

The noble gases, listed by increasing molecular weight, are He, Ne, Ar, Kr, Xe, and Rn. If samples of 1 mole each of these gases are placed in separate containers and heated to 300 K, which gas has the greatest internal energy and the molecules of which gas have the lowest average speed?

If the temperature of an ideal gas contained in a box is increased:

If an average molecule diffuses to a displacement of 4 cm in 5 s, how long would it take for such a molecule to diffuse to a displacement of 16 cm?

The absolute temperature of a monatomic ideal gas is directly proportional to which of the following properties, when taken as an average, of the molecules of that gas?

Quiz 15: Gases and Kinetic Theory

The specific heat at constant volume per mole of is for what type of molecule?

What is the internal energy of 42 moles of Neon gas (molecular mass = 20 u) at 27 °\degree° C? (R = 8.31 J/mol ·K)

What is (are) the unit(s) for the diffusion constant?

A quantity of a monatomic ideal gas expands to four times the volume while maintaining the same pressure. If the internal energy of the gas were U0 before the expansion, what is it after the expansion?

Suppose the pressure of 20 g of an ideal monatomic gas is tripled while its volume is halved. What happens to the internal energy of the gas?

When a sealed container of ideal gas has its temperature increase from 250 K to 500 K, what happens to the mean free path of the molecules?

For a monatomic gas, is

John rapidly pulls a plunger out of a cylinder, increasing its volume. As the plunger moves away, the gas molecules bouncing elastically off the plunger are:

In a system of ideal gas with P, V, and T constant, if the molecules diffuse an average displacement of 2 cm in 4 s, on the average what would the average displacement be for a time of 200 s?

The temperature of a quantity of ideal gas in a sealed container is increased from 0°C to 819°C. What happens to the speed of the molecules with average kinetic energy of the gas as a result of this temperature increase?

If the temperature of a gas doubles, by what factor does the speed of a molecule with the average kinetic energy change?

What is the internal energy of a monatomic ideal gas with pressure 6 *105 Pa and with volume 2 m3?

If the average kinetic energy of the molecules of a monatomic ideal gas at 30°C is doubled, what is the resulting temperature of the gas?

For an ideal gas of a given mass, if the pressure remains the same and the volume decreases:

The internal energy of a monatomic ideal gas is equal to which of the following?

The noble gases, listed by increasing molecular weight, are He, Ne, Ar, Kr, Xe, and Rn. If samples of 1 mole each of these gases are placed in separate containers and heated to 300 K, which gas has the greatest internal energy and the molecules of which gas have the lowest average speed?

If the temperature of an ideal gas contained in a box is increased:

If an average molecule diffuses to a displacement of 4 cm in 5 s, how long would it take for such a molecule to diffuse to a displacement of 16 cm?

The absolute temperature of a monatomic ideal gas is directly proportional to which of the following properties, when taken as an average, of the molecules of that gas?

What is the internal energy of 42 moles of Neon gas (molecular mass = 20 u) at 27 $\degree$ C? (R = 8.31 J/mol ·K)

A quantity of a monatomic ideal gas expands to four times the volume while maintaining the same pressure. If the internal energy of the gas were U₀ before the expansion, what is it after the expansion?

What is the internal energy of a monatomic ideal gas with pressure 6 *10⁵ Pa and with volume 2 m³?