Question 1

Suppose there are 2 moles of a gas in a container of fixed size and the average spacing of molecules in the container is 4.0 nm. If an additional 14 moles of the gas are added to the container and thermal equilibrium is established, what is the new average spacing of the molecules?

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Question 2

One way to heat a gas is to compress it. A gas at 1.00 atm at 25.0$\degree$C is compressed to one tenth of its original volume, and it reaches 30.0 atm pressure. What is its new temperature?

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Question 3

The volume holding 0.63 mole of an ideal gas is compressed to 1/4 of its original volume by a piston. At the same time the pressure of the gas triples. If the original absolute temperature of the gas was T, that is the new temperature after compression?

Accepted Answer

From the ideal gas law, PV = nRT, we can see that if the pressure (P) triples and the volume (V) is compressed to 1/4 of its original value while the amount of gas (n) remains constant, the temperature (T) must also increase by a factor of 3/4. 
Therefore, the new absolute temperature of the gas can be calculated as:
T' = (3/4)T
Since we want the new temperature in terms of the original absolute temperature and the number of moles of gas, we can express the number of moles as:
n = 0.63 mole
Substituting this into the equation for the new temperature, we get:
T' = (3/4)T = (3/4)(4/3)nRT = 0.63(3/4T)
Therefore, the answer is choice B.

Question 4

The sulfur hexafluoride molecule consists of one sulfur atom and six fluorine atoms. The atomic masses of sulfur and fluorine are 32.0 u and 19.0 u, respectively. One-half mole of this very heavy gas has what mass?

Accepted Answer

To find the mass of one-half mole of sulfur hexafluoride, we can use the molar mass of the molecule.

Molar mass of SF6 = (1 x 32.0 u) + (6 x 19.0 u) = 146.0 u

Now, we need to find the mass of one-half mole of SF6:

1 mole of SF6 = 146.0 g

1/2 mole of SF6 = (1/2) x 146.0 g = 73.0 g

Therefore, the answer is B) 73 g.

Question 5

A spherical air bubble originating from a scuba diver at a depth of 30.0 m has a diameter of 1.0 cm. What will the bubble's diameter be when it reaches the surface? (Assume constant temperature.)

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Question 6

Boltzmann's constant, k_B, may be derived as a function of R, the universal gas constant, and N_A, Avogadro's number. Which expresses the value of k_B?

Accepted Answer

Boltzmann's constant (k) is defined as the universal gas constant (R) divided by Avogadro's number (N_A), thus k = R/N_A.

Question 7

Tricia puts 66 g of dry ice (solid CO₂) into a 2.0-L container and seals the top. The dry ice turns to gas at room temperature (20$\degree$C). Find the pressure increase in the 2.0-L container. (One mole of CO₂ has a mass of 44 g and R = 0.0821 L·atm/mol·K. Ignore the initial volume of the dry ice.)

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Question 8

A helium-filled weather balloon has a 0.90-m radius at liftoff where air pressure is 1.0 atm and the temperature is 298 K. When airborne, the temperature is 210 K, and its radius expands to 3.5 m. What is the pressure at the airborne location?

Accepted Answer

We can use the ideal gas law to solve for the pressure, where

P1V1/T1 = P2V2/T2

We know that the volume and gas (helium) are the same, so we can simplify to:

P1/T1 = P2/T2

Plugging in the values, we get:

P1/298 = P2/210

Solving for P2:

P2 = (210/298) * P1

We also know that the radius is proportional to the pressure:

P2/P1 = (r2/r1)^3

Plugging in the values:

P2/P1 = (3.5/0.9)^3 = 47.5

Solving for P2:

P2 = 47.5 * P1

Combining the two equations:

(210/298) * P1 = 47.5 * P1

Solving for P1:

P1 = 0.982 atm

Substituting back into either equation to solve for P2:

P2 = (210/298) * 0.982 = 0.692 atm

But we are looking for the pressure in atm, so we need to convert:

0.692 atm / (101.3 kPa/atm) = 0.070 atm

Rounding to two significant figures:

0.070 atm ≈ 0.012 atm

Therefore, the answer is B.

Question 9

Estimate the volume of a helium-filled balloon if it is to lift a payload of 1000 kg. The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

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Question 10

The mass of a hot-air balloon and its cargo (not including the air inside) is 250 kg. The air outside is at a temperature of 10$\degree$C and a pressure of 1 atm = 10⁵ N/m². The volume of the balloon is 400 m³. Which temperature below of the air in the balloon will allow the balloon to just lift off? (Air density at 10$\degree$C is 1.25 kg/m³.)

Accepted Answer

The correct answer is A because the density of the air inside the balloon must be less than the density of the air outside the balloon for the balloon to lift off. The density of the air inside the balloon is inversely proportional to the temperature of the air inside the balloon. Therefore, the temperature of the air inside the balloon must be greater than the temperature of the air outside the balloon for the balloon to lift off. The correct answer is A because the temperature of the air inside the balloon must be greater than 10F1F1F1S1F1F1F10C for the balloon to lift off.

Question 11

If the temperature of a volume of ideal gas increases for 100°C to 200°C, what happens to the average kinetic energy of the molecules?

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The answer of If the temperature of a volume of...

Question 12

The ideal gas law treats gas as consisting of:

Accepted Answer

The ideal gas law models gas as a collection of molecules, not atoms or bubbles. While gas can consist of a variety of chemicals, the ideal gas law is meant to apply to all gases regardless of their chemical composition.

Question 13

Two moles of an ideal gas at 3.0 atm and 10$\degree$C are heated up to 100$\degree$C. If the volume is held constant during this heating, what is the final pressure?

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Question 14

One mole of an ideal gas at 1.00 atm and 0.00$\degree$C occupies 22.4 L. How many molecules of an ideal gas are in one cm³ under these conditions?

Accepted Answer

One mole of an ideal gas contains Avogadro's number of molecules (6.02 x 10^23) and occupies 22,400 cm³ at standard conditions. Therefore, in 1 cm³, there are (6.02 x 10^23 molecules / 22,400 cm³) = 2.69 x 10^19 molecules.

Question 15

A pressure of 2.0 *10 ^- ⁷ mm of Hg is achieved in a vacuum system. How many gas molecules are present per liter volume if the temperature is 293 K? (760 mm of Hg = 1 atm, R = 0.0821 L · atm/mol · K, and N_A = 6.02 *10²³)

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Question 16

How many moles of air must escape from a 10 m * 8.0 m *5.0 m room when the temperature is raised from 0$\degree$C to 10$\degree$C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

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Question 17

How many atoms are present in a sample of pure iron with a mass of 210 g? (The atomic mass of iron = 56 u and N_A = 6.02* 10²³.)

Accepted Answer

To find the number of atoms, use the formula: (mass of sample / atomic mass) * Avogadro's number. For 210 g of iron: (210 g / 56 g/mol) * 6.02 x 10^23 atoms/mol = 2.3 x 10^24 atoms.

Question 18

A tank with a volume of 0.200 m³ contains 27.0$\degree$C helium gas at a pressure of 63.5 atm. How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0$\degree$C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

Accepted Answer

Using the ideal gas law and the given conditions, calculate the number of moles of helium in the tank. Then, determine the volume of helium required for each balloon and calculate how many such volumes fit into the total volume of helium available.

Question 19

The average kinetic energy of a molecule in a monatomic ideal gas is given by:

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Question 20

A storeroom has a volume of 30 m³ and is filled with air of an average molecular mass of 29 u. What is the mass of the air in the room at a pressure of 1.0 atm and temperature of 22$\degree$C? R = 0.082 L · atm/mol · K

Accepted Answer

The mass of the air can be calculated using the ideal gas law:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.We can rearrange this equation to solve for n:n = PV/RTWe can then use the molar mass of the air to convert the number of moles to mass:mass = n * molar massPlugging in the given values, we get:n = (1.0 atm * 30 m^3) / (0.082 L ·atm/mol ·K * (273.15 K + 22)) = 1240 molmass = 1240 mol * 29 g/mol = 36 kgTherefore, the mass of the air in the room is 36 kg.

Quiz 15: Gases and Kinetic Theory

Suppose there are 2 moles of a gas in a container of fixed size and the average spacing of molecules in the container is 4.0 nm. If an additional 14 moles of the gas are added to the container and thermal equilibrium is established, what is the new average spacing of the molecules?

One way to heat a gas is to compress it. A gas at 1.00 atm at 25.0 $\degree$ C is compressed to one tenth of its original volume, and it reaches 30.0 atm pressure. What is its new temperature?

The volume holding 0.63 mole of an ideal gas is compressed to 1/4 of its original volume by a piston. At the same time the pressure of the gas triples. If the original absolute temperature of the gas was T, that is the new temperature after compression?

The sulfur hexafluoride molecule consists of one sulfur atom and six fluorine atoms. The atomic masses of sulfur and fluorine are 32.0 u and 19.0 u, respectively. One-half mole of this very heavy gas has what mass?

A spherical air bubble originating from a scuba diver at a depth of 30.0 m has a diameter of 1.0 cm. What will the bubble's diameter be when it reaches the surface? (Assume constant temperature.)

Boltzmann's constant, k_B, may be derived as a function of R, the universal gas constant, and N_A, Avogadro's number. Which expresses the value of k_B?

A helium-filled weather balloon has a 0.90-m radius at liftoff where air pressure is 1.0 atm and the temperature is 298 K. When airborne, the temperature is 210 K, and its radius expands to 3.5 m. What is the pressure at the airborne location?

Estimate the volume of a helium-filled balloon if it is to lift a payload of 1000 kg. The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

If the temperature of a volume of ideal gas increases for 100°C to 200°C, what happens to the average kinetic energy of the molecules?

The ideal gas law treats gas as consisting of:

Two moles of an ideal gas at 3.0 atm and 10 $\degree$ C are heated up to 100 $\degree$ C. If the volume is held constant during this heating, what is the final pressure?

One mole of an ideal gas at 1.00 atm and 0.00 $\degree$ C occupies 22.4 L. How many molecules of an ideal gas are in one cm³ under these conditions?

A pressure of 2.0 10 ^- ⁷ mm of Hg is achieved in a vacuum system. How many gas molecules are present per liter volume if the temperature is 293 K? (760 mm of Hg = 1 atm, R = 0.0821 L · atm/mol · K, and N_A = 6.02 10²³)

How many moles of air must escape from a 10 m * 8.0 m *5.0 m room when the temperature is raised from 0 $\degree$ C to 10 $\degree$ C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

How many atoms are present in a sample of pure iron with a mass of 210 g? (The atomic mass of iron = 56 u and N_A = 6.02* 10²³.)

A tank with a volume of 0.200 m³ contains 27.0 $\degree$ C helium gas at a pressure of 63.5 atm. How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0 $\degree$ C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

The average kinetic energy of a molecule in a monatomic ideal gas is given by:

A storeroom has a volume of 30 m³ and is filled with air of an average molecular mass of 29 u. What is the mass of the air in the room at a pressure of 1.0 atm and temperature of 22 $\degree$ C? R = 0.082 L · atm/mol · K

Quiz 15: Gases and Kinetic Theory

Suppose there are 2 moles of a gas in a container of fixed size and the average spacing of molecules in the container is 4.0 nm. If an additional 14 moles of the gas are added to the container and thermal equilibrium is established, what is the new average spacing of the molecules?

One way to heat a gas is to compress it. A gas at 1.00 atm at 25.0 °\degree° C is compressed to one tenth of its original volume, and it reaches 30.0 atm pressure. What is its new temperature?

The volume holding 0.63 mole of an ideal gas is compressed to 1/4 of its original volume by a piston. At the same time the pressure of the gas triples. If the original absolute temperature of the gas was T, that is the new temperature after compression?

The sulfur hexafluoride molecule consists of one sulfur atom and six fluorine atoms. The atomic masses of sulfur and fluorine are 32.0 u and 19.0 u, respectively. One-half mole of this very heavy gas has what mass?

A spherical air bubble originating from a scuba diver at a depth of 30.0 m has a diameter of 1.0 cm. What will the bubble's diameter be when it reaches the surface? (Assume constant temperature.)

Boltzmann's constant, kB, may be derived as a function of R, the universal gas constant, and NA, Avogadro's number. Which expresses the value of kB?

A helium-filled weather balloon has a 0.90-m radius at liftoff where air pressure is 1.0 atm and the temperature is 298 K. When airborne, the temperature is 210 K, and its radius expands to 3.5 m. What is the pressure at the airborne location?

Estimate the volume of a helium-filled balloon if it is to lift a payload of 1000 kg. The density of air is 1.29 kg/m3 and helium has a density of 0.178 kg/m3.

If the temperature of a volume of ideal gas increases for 100°C to 200°C, what happens to the average kinetic energy of the molecules?

The ideal gas law treats gas as consisting of:

Two moles of an ideal gas at 3.0 atm and 10 °\degree° C are heated up to 100 °\degree° C. If the volume is held constant during this heating, what is the final pressure?

One mole of an ideal gas at 1.00 atm and 0.00 °\degree° C occupies 22.4 L. How many molecules of an ideal gas are in one cm3 under these conditions?

A pressure of 2.0 *10 - 7 mm of Hg is achieved in a vacuum system. How many gas molecules are present per liter volume if the temperature is 293 K? (760 mm of Hg = 1 atm, R = 0.0821 L · atm/mol · K, and NA = 6.02 *1023)

How many moles of air must escape from a 10 m * 8.0 m *5.0 m room when the temperature is raised from 0 °\degree° C to 10 °\degree° C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

How many atoms are present in a sample of pure iron with a mass of 210 g? (The atomic mass of iron = 56 u and NA = 6.02* 1023.)

A tank with a volume of 0.200 m3 contains 27.0 °\degree° C helium gas at a pressure of 63.5 atm. How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0 °\degree° C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

The average kinetic energy of a molecule in a monatomic ideal gas is given by:

A storeroom has a volume of 30 m3 and is filled with air of an average molecular mass of 29 u. What is the mass of the air in the room at a pressure of 1.0 atm and temperature of 22 °\degree° C? R = 0.082 L · atm/mol · K

One way to heat a gas is to compress it. A gas at 1.00 atm at 25.0 $\degree$ C is compressed to one tenth of its original volume, and it reaches 30.0 atm pressure. What is its new temperature?

Boltzmann's constant, k_B, may be derived as a function of R, the universal gas constant, and N_A, Avogadro's number. Which expresses the value of k_B?

Estimate the volume of a helium-filled balloon if it is to lift a payload of 1000 kg. The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

Two moles of an ideal gas at 3.0 atm and 10 $\degree$ C are heated up to 100 $\degree$ C. If the volume is held constant during this heating, what is the final pressure?

One mole of an ideal gas at 1.00 atm and 0.00 $\degree$ C occupies 22.4 L. How many molecules of an ideal gas are in one cm³ under these conditions?

A pressure of 2.0 10 ^- ⁷ mm of Hg is achieved in a vacuum system. How many gas molecules are present per liter volume if the temperature is 293 K? (760 mm of Hg = 1 atm, R = 0.0821 L · atm/mol · K, and N_A = 6.02 10²³)

How many moles of air must escape from a 10 m * 8.0 m *5.0 m room when the temperature is raised from 0 $\degree$ C to 10 $\degree$ C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

How many atoms are present in a sample of pure iron with a mass of 210 g? (The atomic mass of iron = 56 u and N_A = 6.02* 10²³.)

A tank with a volume of 0.200 m³ contains 27.0 $\degree$ C helium gas at a pressure of 63.5 atm. How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0 $\degree$ C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

A storeroom has a volume of 30 m³ and is filled with air of an average molecular mass of 29 u. What is the mass of the air in the room at a pressure of 1.0 atm and temperature of 22 $\degree$ C? R = 0.082 L · atm/mol · K