Question 1

9.0 g of water in a 2.0-L pressure vessel is heated to 500 $\degree$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

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Question 2

A pressure of 1.0 x 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 = 0.082 1 L*atm/mol*K,and N_A = 6.02 x 10²³)

Accepted Answer

First, convert the pressure to atm:

P = 1.0 x 10^-11 mmHg / (760 mmHg/atm) = 1.316 x 10^-17 atm

Next, use the Ideal Gas Law to calculate the number of molecules:

PV = nRT

n/V = P/RT = (1.316 x 10^-17 atm) / (0.0821 L*atm/(mol*K) * 293 K) = 5.96 x 10^-22 mol/L

Finally, convert the number of moles to number of molecules:

N = n*N_A = (5.96 x 10^-22 mol/L) * (6.02 x 10^23 molecules/mol) = 3.58 x 10^2 molecules/L

Round to 3 significant figures gives 3.30 x 10^12 molecules/L or 3.3 x 10^12 molecules/L. Hence, the answer is option C.

Question 3

Tricia puts 44 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,R = 0.082 1 L*atm/mol*K.Ignore the initial volume of the dry ice. )

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Question 4

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 298 K,and the pressure is 1.01 x 10⁶ N/m²,what is the volume? (R = 8.31 J/mol*K)

Accepted Answer

Using the ideal gas law, PV = nRT, we can solve for the volume:
V = (nRT)/P = ((2 mol)(8.31 J/mol*K)(298 K))/(1.01 x 10^16 N/m^2) = 4.90 x 10^-3 m^3 = 4.90 x 10^-3 x 10^3 = 4.90 x 10^-6 m^3 = 4.90 x 10^-3 L = 4.90 mL
Therefore, the best choice is B, which is 4.90 x 10^-3 m^3 or 4.90 mL.

Question 5

With molar quantity and temperature held constant,by what factor does the pressure of an ideal gas change when the volume is five times bigger?

Accepted Answer

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Question 6

With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?

Accepted Answer

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Question 7

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 500 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

Accepted Answer

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Question 8

An ideal gas is confined to a container with constant volume.The number of moles is constant.By what factor will the pressure change if the absolute temperature triples?

Accepted Answer

According to the Ideal Gas Law, PV = nRT. Since the volume, V, and the number of moles, n, are constant, we can simplify this equation to P/T = constant. Therefore, if the absolute temperature (in Kelvin) triples, the pressure will also triple, resulting in a factor of 3. Thus, the answer is C.

Question 9

How many atoms are present in a sample of pure iron with a mass of 300 g? (The atomic mass of iron = 56 and N_A = 6.02 x 10²³)

Accepted Answer

First, calculate the number of moles of iron present in the sample:

moles = mass/molar mass = 300/56 = 5.36 mol

Next, use Avogadro's number to calculate the number of atoms:

number of atoms = moles × Avogadro's number = 5.36 × 6.02 × 10^23 = 3.22 × 10^24

Therefore, the answer is D.

Question 10

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the molecular mass of nitrogen is 28,how many grams of nitrogen are present?

Accepted Answer

Two moles of nitrogen gas is equal to 2 x 28 = 56 grams of nitrogen.

Question 11

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 12

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

First, we need to use the ideal gas law to find the number of moles of gas in the 22.4 L container:
PV = nRT
(1.00 atm)(22.4 L) = n(0.0821 L∙atm/mol∙K)(273 K)
n = 1 mol

Now we need to use Avogadro's number to convert from moles to molecules:
1 mol = 6.02 x 10^23 molecules

Finally, we need to use dimensional analysis to convert from L to cm^3:
1 L = 1000 cm^3
22.4 L = 22,400 cm^3

So the total number of molecules in 1 cm^3 under these conditions is:
(6.02 x 10^23 molecules/mol) / (22,400 cm^3) = 2.69 x 10^19 molecules/cm^3

Therefore, the correct answer is C.

Question 13

Two moles of an ideal gas at 3.0 atm and 10 $\degree$C are heated up to 150  $\degree$C.If the volume is held constant during this heating,what is the final pressure?

Accepted Answer

According to Gay-Lussac's Law, the pressure of an ideal gas held at constant volume is directly proportional to its temperature. Therefore, when the temperature is increased from 10°C to 150°C, the pressure will also increase proportionally. Using the formula P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature, we can solve for P2:

P1/T1 = P2/T2
(3.0 atm)/(283 K) = P2/(423 K)
P2 = (3.0 atm)(423 K)/(283 K) = 4.5 atm

Therefore, the final pressure is 4.5 atm, which corresponds to choice (A).

Question 14

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.5 atm.What is the gas temperature? (R = 0.082 1 L*atm/mol*K)

Accepted Answer

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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 3.0 m.What is the pressure at the airborne location?

Accepted Answer

Using the ideal gas law and the relationship between pressure, volume, and temperature, the pressure at the airborne location is calculated to be approximately 0.019 atm.

Question 16

An ideal gas is confined to a container with adjustable volume.The number of moles and temperature are constant.By what factor will the volume change if pressure triples?

Accepted Answer

According to Boyle's Law, at constant temperature and number of moles, the product of pressure and volume is constant. Therefore, if the pressure triples, the volume must decrease by a factor of 1/3 to maintain this constant. Therefore, the correct answer is (B) 1/3.

Question 17

How many moles of air must escape from a 10-m x 8.0-m x 5.0-m room when the temperature is raised from 0 $\degree$C to 20 $\degree$C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

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Question 18

A spherical air bubble originating from a scuba diver at a depth of 18.0 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

The pressure at a depth of 18.0m is 2.8 atm. According to Boyle's law, at a constant temperature, pressure and volume have an inverse relationship. So, as the bubble rises to the surface, the pressure decreases and the volume increases. Therefore, the bubble's diameter will increase. The ratio of the initial volume to the final volume is given by:
(initial diameter)^3 / (final diameter)^3 = (initial pressure) / (final pressure)
(1.0 cm)^3 / (final diameter)^3 = 2.8 atm / 1 atm
final diameter = (1.0 cm) / (2.8)^(1/3) = 1.4 cm (approx.)

Question 19

The mass of a hot-air balloon and its cargo (not including the air inside)is 200 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. )

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Question 20

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 40.0 atm pressure.What is its new temperature?

Accepted Answer

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Quiz 10: Thermal Physics

9.0 g of water in a 2.0-L pressure vessel is heated to 500 $\degree$ C.What is the pressure inside the container? (R = 0.082 Latm/molK,one mole of water has a mass of 18 grams)

A pressure of 1.0 x 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 = 0.082 1 Latm/molK,and N_A = 6.02 x 10²³)

Tricia puts 44 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,R = 0.082 1 Latm/molK.Ignore the initial volume of the dry ice. )

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 298 K,and the pressure is 1.01 x 10⁶ N/m²,what is the volume? (R = 8.31 J/mol*K)

With molar quantity and temperature held constant,by what factor does the pressure of an ideal gas change when the volume is five times bigger?

With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 500 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

An ideal gas is confined to a container with constant volume.The number of moles is constant.By what factor will the pressure change if the absolute temperature triples?

How many atoms are present in a sample of pure iron with a mass of 300 g? (The atomic mass of iron = 56 and N_A = 6.02 x 10²³)

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the molecular mass of nitrogen is 28,how many grams of nitrogen are present?

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?

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?

Two moles of an ideal gas at 3.0 atm and 10 $\degree$ C are heated up to 150 $\degree$ C.If the volume is held constant during this heating,what is the final pressure?

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.5 atm.What is the gas temperature? (R = 0.082 1 Latm/molK)

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 3.0 m.What is the pressure at the airborne location?

An ideal gas is confined to a container with adjustable volume.The number of moles and temperature are constant.By what factor will the volume change if pressure triples?

How many moles of air must escape from a 10-m x 8.0-m x 5.0-m room when the temperature is raised from 0 $\degree$ C to 20 $\degree$ C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

A spherical air bubble originating from a scuba diver at a depth of 18.0 m has a diameter of 1.0 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )

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 40.0 atm pressure.What is its new temperature?

Quiz 10: Thermal Physics

9.0 g of water in a 2.0-L pressure vessel is heated to 500 °\degree° 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 1.0 x 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 = 0.082 1 L*atm/mol*K,and NA = 6.02 x 1023)

Tricia puts 44 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,R = 0.082 1 L*atm/mol*K.Ignore the initial volume of the dry ice. )

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 298 K,and the pressure is 1.01 x 106 N/m2,what is the volume? (R = 8.31 J/mol*K)

With molar quantity and temperature held constant,by what factor does the pressure of an ideal gas change when the volume is five times bigger?

With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 500 kg.The density of air is 1.29 kg/m3 and helium has a density of 0.178 kg/m3.

An ideal gas is confined to a container with constant volume.The number of moles is constant.By what factor will the pressure change if the absolute temperature triples?

How many atoms are present in a sample of pure iron with a mass of 300 g? (The atomic mass of iron = 56 and NA = 6.02 x 1023)

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the molecular mass of nitrogen is 28,how many grams of nitrogen are present?

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?

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?

Two moles of an ideal gas at 3.0 atm and 10 °\degree° C are heated up to 150 °\degree° C.If the volume is held constant during this heating,what is the final pressure?

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.5 atm.What is the gas temperature? (R = 0.082 1 L*atm/mol*K)

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 3.0 m.What is the pressure at the airborne location?

An ideal gas is confined to a container with adjustable volume.The number of moles and temperature are constant.By what factor will the volume change if pressure triples?

How many moles of air must escape from a 10-m x 8.0-m x 5.0-m room when the temperature is raised from 0 °\degree° C to 20 °\degree° C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

A spherical air bubble originating from a scuba diver at a depth of 18.0 m has a diameter of 1.0 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )

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 40.0 atm pressure.What is its new temperature?

9.0 g of water in a 2.0-L pressure vessel is heated to 500 $\degree$ C.What is the pressure inside the container? (R = 0.082 Latm/molK,one mole of water has a mass of 18 grams)

A pressure of 1.0 x 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 = 0.082 1 Latm/molK,and N_A = 6.02 x 10²³)

Tricia puts 44 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,R = 0.082 1 Latm/molK.Ignore the initial volume of the dry ice. )

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 298 K,and the pressure is 1.01 x 10⁶ N/m²,what is the volume? (R = 8.31 J/mol*K)

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 500 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

How many atoms are present in a sample of pure iron with a mass of 300 g? (The atomic mass of iron = 56 and N_A = 6.02 x 10²³)

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?

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?

Two moles of an ideal gas at 3.0 atm and 10 $\degree$ C are heated up to 150 $\degree$ C.If the volume is held constant during this heating,what is the final pressure?

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.5 atm.What is the gas temperature? (R = 0.082 1 Latm/molK)

How many moles of air must escape from a 10-m x 8.0-m x 5.0-m room when the temperature is raised from 0 $\degree$ C to 20 $\degree$ C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

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 40.0 atm pressure.What is its new temperature?