Question 1

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)

Accepted Answer

Using the ideal gas law, PV = nRT, we can find the number of moles (n) and then multiply by Avogadro's number (N_A) to find the number of molecules. Converting pressure to atm: 2.0 × 10⁻⁷ mm Hg × (1 atm / 760 mm Hg) = 2.63 × 10⁻¹⁰ atm. Then, n = PV/RT = (2.63 × 10⁻¹⁰ atm × 1 L) / (0.0821 L·atm/mol·K × 293 K) = 1.09 × 10⁻¹² mol. Finally, molecules = n × N_A = 1.09 × 10⁻¹² mol × 6.02 × 10²³ molecules/mol = 6.6 × 10¹¹ molecules, which matches option B when considering significant figures.

Question 2

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

Accepted Answer

The average kinetic energy of a molecule in a monatomic ideal gas is given by the expression (3/2)kT, where k is the Boltzmann constant and T is the absolute temperature. Therefore, choice B, 11ea7a51_637e_1c49_89bd_671548f779fa_TB5259_11, is the correct answer as it represents the expression (3/2)kT.

Question 3

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

The answer of A quantity of a monatomic ideal gas...

Question 4

If the average kinetic energy of the molecules of a monatomic ideal gas at 60°C is doubled,what is the resulting temperature of the gas?

Accepted Answer

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

Question 5

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°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°C is 1.25 kg/m³. )

Accepted Answer

The answer of The mass of a hot-air balloon and...

Question 6

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

Accepted Answer

The answer of What is the internal energy of 42...

Question 7

If the temperature of a gas triples,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 triples,by...

Question 8

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

Accepted Answer

Internal energy of a monatomic ideal gas is given by U = (3/2)PV. Here, P = 6 × 10⁵ Pa and V = 2 m³. So, U = (3/2) × 6 × 10⁵ Pa × 2 m³ = 18 × 10⁵ J.

Question 9

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 10

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. )

Accepted Answer

According to Boyle's Law, the volume of a gas is inversely proportional to the pressure. As the bubble rises, pressure decreases, causing the volume to increase. Since volume is proportional to the cube of the diameter, the diameter increases by the cube root of the pressure ratio. At 30 m, pressure is 4 atm (1 atm surface + 3 atm water), and at the surface, it's 1 atm. The diameter increases by a factor of (4/1)^(1/3) ≈ 1.587, so the new diameter is approximately 1.6 cm.

Question 11

A tank with a volume of 0.200 m³ contains 27.0°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°C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

Accepted Answer

Using the ideal gas law, calculate the number of moles of helium in the tank. Then, calculate the volume of one balloon using its diameter and the formula for the volume of a sphere. Finally, determine how many such balloons can be filled with the helium from the tank, considering the pressure difference.

Question 12

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?

Accepted Answer

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

Question 13

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°C to 10°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

Accepted Answer

The answer of How many moles of air must escape...

Question 14

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.

Accepted Answer

The answer of Estimate the volume of a helium-filled balloon...

Question 15

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 this problem:

PV = nRT

where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature.

At liftoff:

P = 1.0 atm
V = (4/3)π(0.9 m)^3 = 3.05 m^3
T = 298 K

We can solve for n:

n = PV/RT = (1.0 atm)(3.05 m^3)/(0.0821 L atm/mol K)(298 K) = 0.127 mol

Now we can use the same equation at the airborne location:

V = (4/3)π(3.5 m)^3 = 179.6 m^3
T = 210 K
n = 0.127 mol (since the number of moles of gas does not change)

Solving for P:

P = nRT/V = (0.127 mol)(0.0821 L atm/mol K)(210 K)/(179.6 m^3) = 0.012 atm

Therefore, the answer is B.

Question 16

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°C? R = 0.082 L · atm/mol · K

Accepted Answer

The mass of the air in the room 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 massSubstituting the given values into these equations, we get:n = (1.0 atm * 30 m^3) / (0.082 L · atm/mol · K * 295 K) = 120 molmass = 120 mol * 29 g/mol = 3480 g = 3.48 kgTherefore, the mass of the air in the room is 3.48 kg, which is closest to choice A, 36 kg.

Question 17

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°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. )

Accepted Answer

First, we need to calculate the number of moles of CO₂ in 66 g: Number of moles = mass/molar mass = 66 g/44 g/mol = 1.5 mol Since all the dry ice will turn into gas, the final number of moles of gas will also be 1.5 mol. Next, we use the ideal gas law to calculate the final pressure: PV = nRT P = nRT/V P = (1.5 mol)(0.0821 L·atm/mol·K)(293 K)/(2.0 L) P = 18.15 atm Finally, we need to subtract the initial atmospheric pressure of 1 atm: P increase = 18.15 atm - 1 atm = 17.15 atm Therefore, the pressure increase in the 2.0-L container is approximately 17 atm, closest to choice C (18 atm).

Question 18

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 19

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?

Accepted Answer

The average spacing of molecules is inversely proportional to the cube root of the number of molecules. So, when the number of moles increases by a factor of 7, the average spacing decreases by a factor of the cube root of 7, which is approximately 1.9.

Question 20

9.0 g of water in a 2.0-L pressure vessel is heated to 300°C.What is the pressure inside the container? (R = 0.082 L · atm/mol · K,one mole of water has a mass of 18 grams)

Accepted Answer

The correct answer is A because the pressure inside the container is 12 atm. This can be calculated using the ideal gas law, which states that PV = nRT. In this case, P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. We know that the volume of the container is 2.0 L, the number of moles of gas is 9.0 g / 18 g/mol = 0.5 mol, the ideal gas constant is 0.082 L · atm/mol · K, and the temperature is 300°C = 573 K. Plugging these values into the ideal gas law, we get P = nRT/V = (0.5 mol)(0.082 L · atm/mol · K)(573 K) / (2.0 L) = 12 atm.

Quiz 15: Electric Forces and Electric Fields: Part A

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)

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

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?

If the average kinetic energy of the molecules of a monatomic ideal gas at 60°C is doubled,what is the resulting temperature of the gas?

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

If the temperature of a gas triples,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?

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?

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. )

A tank with a volume of 0.200 m³ contains 27.0°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°C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

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?

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°C to 10°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

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.

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?

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°C? R = 0.082 L · atm/mol · K

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°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. )

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?

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?

9.0 g of water in a 2.0-L pressure vessel is heated to 300°C.What is the pressure inside the container? (R = 0.082 L · atm/mol · K,one mole of water has a mass of 18 grams)

Quiz 15: Electric Forces and Electric Fields: Part A

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)

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

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?

If the average kinetic energy of the molecules of a monatomic ideal gas at 60°C is doubled,what is the resulting temperature of the gas?

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

If the temperature of a gas triples,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?

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?

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. )

A tank with a volume of 0.200 m3 contains 27.0°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°C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

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?

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°C to 10°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

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.

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?

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°C? R = 0.082 L · atm/mol · K

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°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. )

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?

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?

9.0 g of water in a 2.0-L pressure vessel is heated to 300°C.What is the pressure inside the container? (R = 0.082 L · atm/mol · K,one mole of water has a mass of 18 grams)

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)

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?

A tank with a volume of 0.200 m³ contains 27.0°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°C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons.

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.

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°C? R = 0.082 L · atm/mol · K

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°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. )