Question 1

Different units can be used for length: m and cm,and of these two,m is the larger by a factor of 100.Different units can also be used for R: (1)J/mol⋅K, (2)L⋅atm/mol⋅K,and (3)(N/m²)⋅m³/mol⋅K. Which of these units for R is the largest? Hint: When expressing R in each of these units,which expression has the lowest numerical factor? (1 L = 10−³ m³,1 atm = 1.01 × 10⁵ Pa)

Accepted Answer

The answer of Different units can be used for length:...

Question 2

Two one-liter containers each contain 10 moles of a gas.The temperature is the same in both containers.Container A holds helium (molecular mass = 4 u),and Container B holds oxygen (molecular mass = 16 u).Which container has the higher pressure and by what factor?

Accepted Answer

The pressure of a gas in a container (assuming ideal gas behavior) is determined by the equation 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. Since both containers have the same volume, number of moles, and temperature, and since the ideal gas law does not depend on the type of gas, both containers have the same pressure.

Question 3

13.0 g of water in a 3.25-L pressure vessel is heated to 480°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 answer of 13.0 g of water in a 3.25-L...

Question 4

One way to heat a gas is to compress it.A gas at 3.0 atm at 27°C is compressed to three tenths of its original volume,and it reaches 35 atm pressure.What is its new temperature?

Accepted Answer

Using the combined gas law: (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is temperature in Kelvin. Convert initial temperature to Kelvin: 27°C = 300 K. Substitute the values: (3 atm * V1) / 300 K = (35 atm * 0.3 V1) / T2. Solving for T2 gives approximately 1050 K, which is 777°C.

Question 5

The gas,C₃H₈,is used in outside grills,and several moles of this gas will burn during an afternoon's grilling.What is the mass of one molecule of this gas?

Accepted Answer

The answer of The gas,C₃H₈,is used in outside grills,and several...

Question 6

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

Accepted Answer

One cubic centimeter is equal to 0.001 L. Therefore, the number of molecules in one cubic centimeter can be calculated as follows:

n = (1 mol / 22.4 L) x (0.001 L) x (6.022 x 10^23 molecules/mol) = 2.69 x 10^19 molecules

Note that this calculation assumes that the gas behaves ideally at these conditions.

Question 7

Tricia puts 5.30 g of dry ice (solid CO₂)into a 4.00-L container and seals the top.The dry ice turns to gas at room temperature (20.0°C).Find the pressure increase in the 4.00-L container.(One mole of CO₂ has a mass of 5.30 g,R = 0.082 1 L⋅atm/mol⋅K.Ignore the initial volume of the dry ice. )

Accepted Answer

Using the ideal gas law, PV = nRT, where n = 1 mole, R = 0.0821 L⋅atm/mol⋅K, T = 293 K (20°C + 273), and V = 4.00 L, the pressure P is calculated as 6.01 atm.

Question 8

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 9

A pressure of 3.00 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 298 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

Accepted Answer

First, we need to convert the pressure from mmHg to atm:
3.00 × 10^-17 mmHg = 3.00 × 10^-17/760 atm = 3.95 × 10^-20 atm

Next, we can use the ideal gas law to solve for the number of gas molecules:
PV = nRT
n = PV/RT
n = (3.95 × 10^-20 atm)(1 L)/(0.082 L·atm/mol·K)(298 K)
n = 1.62 × 10^-22 mol

Finally, we can convert from moles to molecules:
1 mol = 6.02 × 10^23 molecules
1.62 × 10^-22 mol = 9.75 × 10^1 molecules

Therefore, the number of gas molecules per liter volume is 9.75 × 10^12, which corresponds to choice C.

Question 10

A helium-filled weather balloon has a 0.50-m radius at liftoff where air pressure is 1.00 atm and the temperature is 290 K.When airborne,the temperature is 200 K,and its radius expands to 2.00 m.What is the pressure at the airborne location?

Accepted Answer

The ideal gas law can be expressed as: 
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature.

We can assume that the number of moles of helium in the balloon remains constant during the ascent. Therefore, we can express the pressure at the airborne location as:
P₂V₂ = P₁V₁(T₂/T₁)
where the subscripts ₁ and ₂ denote the liftoff and airborne conditions, respectively.

Using the given values, we have:
- V₁ = (4/3)πr₁³ = (4/3)π(0.50 m)³ = 0.524 m³
- V₂ = (4/3)πr₂³ = (4/3)π(2.00 m)³ = 33.51 m³
- T₁ = 290 K
- T₂ = 200 K

Substituting these values, we obtain:
P₂ = P₁V₁(T₂/T₁)/V₂ = (1.00 atm)(0.524 m³)(200 K/290 K)/(33.51 m³) ≈ 0.0108 atm

Therefore, the best choice is C.

Question 11

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 19.00 u,respectively.What mass does one mole of this gas have?

Accepted Answer

The molecular mass of SF6 can be calculated as follows:

Molecular mass of SF6 = (1 x atomic mass of S) + (6 x atomic mass of F)
= (1 x 32.0 u) + (6 x 19.0 u)
= 32.0 u + 114.0 u
= 146.0 u

One mole of SF6 would have a mass equal to its molecular mass in grams. Therefore, one mole of SF6 would have a mass of 146.0 g. Hence, the correct answer is C) 146 g.

Question 12

For a quantity of ideal gas,which of the following is constant?

Accepted Answer

PV/T is known as the Ideal Gas Law and is constant for a given quantity of ideal gas as long as temperature, pressure, and volume are all kept constant. The other options vary with changes in pressure, volume, and temperature.

Question 13

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 450 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

Accepted Answer

To lift a payload, the buoyant force must equal the weight of the payload. The buoyant force is the weight of the air displaced by the helium, which is (density of air - density of helium) * volume * g. Solving for volume gives: Volume = payload weight / (density of air - density of helium) = 450 kg / (1.29 kg/m³ - 0.178 kg/m³) ≈ 410 m³.

Question 14

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 15

How many moles of air must escape from a 15.0-m × 9.0-m × 6.0-m room when the temperature is raised from 10.0°C to 20.0°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.(R = 8.31 J/mol⋅K)

Accepted Answer

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

Question 16

How many molecules are there in 14 grams of nitrogen gas?

Accepted Answer

14 grams of nitrogen gas (N2) is 0.5 moles, and since 1 mole contains Avogadro's number (N_A) of molecules, 0.5 moles contain N_A/2 molecules.

Question 17

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.0 atm.What is the gas temperature? (R = 0.082 1 L⋅atm/mol⋅K)

Accepted Answer

The answer of A 2.00-L container holds half a mole...

Question 18

A room has a volume of 50 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 26°C? R = 0.082 L⋅atm/mol⋅K

Accepted Answer

We can use the ideal gas law to solve for the mass of the air in the room:

PV = nRT

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

First, we need to convert the volume from m3 to L:

50 m3 = 50,000 L

Next, we can solve for the number of moles of air:

n = PV/RT

= (1.0 atm)(50,000 L)/(0.082 L⋅atm/mol⋅K)(299 K)

= 2073 mol

Finally, we can calculate the mass using the molecular mass:

mass = n x molecular mass

= 2073 mol x 29 g/mol

= 60,117 g = 59 kg (to two significant figures)

Therefore, the best choice is C, 59 kg.

Question 19

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 250 K,and the pressure is 1.10 × 10⁶ N/m²,what is the volume? (R = 8.31 J/mol⋅K)

Accepted Answer

Using the ideal gas law PV = nRT, where n = 2 moles, R = 8.31 J/mol⋅K, T = 250 K, and P = 1.10 × 10^6 N/m^2, the volume V is calculated as V = (nRT)/P = (2 * 8.31 * 250) / (1.10 × 10^6) = 3.78 × 10^−3 m^3.

Question 20

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

When the pressure is tripled and the volume is halved, the gas undergoes an adiabatic compression. During this process, the internal energy of the gas increases. This is because the work done on the gas (by decreasing its volume) is positive, and according to the first law of thermodynamics, the change in internal energy is equal to the heat added to the system minus the work done by the system. Since this is an adiabatic process, there is no heat added to the system, and thus the change in internal energy is equal to the work done on the system, which is positive. Therefore, the answer is (B) it increases.

Quiz 10: Thermal Physics

Two one-liter containers each contain 10 moles of a gas.The temperature is the same in both containers.Container A holds helium (molecular mass = 4 u) ,and Container B holds oxygen (molecular mass = 16 u) .Which container has the higher pressure and by what factor?

13.0 g of water in a 3.25-L pressure vessel is heated to 480°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)

One way to heat a gas is to compress it.A gas at 3.0 atm at 27°C is compressed to three tenths of its original volume,and it reaches 35 atm pressure.What is its new temperature?

The gas,C₃H₈,is used in outside grills,and several moles of this gas will burn during an afternoon's grilling.What is the mass of one molecule of this gas?

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

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 pressure of 3.00 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 298 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

A helium-filled weather balloon has a 0.50-m radius at liftoff where air pressure is 1.00 atm and the temperature is 290 K.When airborne,the temperature is 200 K,and its radius expands to 2.00 m.What is the pressure at the airborne location?

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 19.00 u,respectively.What mass does one mole of this gas have?

For a quantity of ideal gas,which of the following is constant?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 450 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

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?

How many moles of air must escape from a 15.0-m × 9.0-m × 6.0-m room when the temperature is raised from 10.0°C to 20.0°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.(R = 8.31 J/mol⋅K)

How many molecules are there in 14 grams of nitrogen gas?

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.0 atm.What is the gas temperature? (R = 0.082 1 L⋅atm/mol⋅K)

A room has a volume of 50 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 26°C? R = 0.082 L⋅atm/mol⋅K

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 250 K,and the pressure is 1.10 × 10⁶ N/m²,what is the volume? (R = 8.31 J/mol⋅K)

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?

Quiz 10: Thermal Physics

Two one-liter containers each contain 10 moles of a gas.The temperature is the same in both containers.Container A holds helium (molecular mass = 4 u) ,and Container B holds oxygen (molecular mass = 16 u) .Which container has the higher pressure and by what factor?

13.0 g of water in a 3.25-L pressure vessel is heated to 480°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)

One way to heat a gas is to compress it.A gas at 3.0 atm at 27°C is compressed to three tenths of its original volume,and it reaches 35 atm pressure.What is its new temperature?

The gas,C3H8,is used in outside grills,and several moles of this gas will burn during an afternoon's grilling.What is the mass of one molecule of this gas?

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

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 pressure of 3.00 × 10−7 mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 298 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and NA = 6.02 × 1023)

A helium-filled weather balloon has a 0.50-m radius at liftoff where air pressure is 1.00 atm and the temperature is 290 K.When airborne,the temperature is 200 K,and its radius expands to 2.00 m.What is the pressure at the airborne location?

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 19.00 u,respectively.What mass does one mole of this gas have?

For a quantity of ideal gas,which of the following is constant?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 450 kg.The density of air is 1.29 kg/m3 and helium has a density of 0.178 kg/m3.

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?

How many moles of air must escape from a 15.0-m × 9.0-m × 6.0-m room when the temperature is raised from 10.0°C to 20.0°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.(R = 8.31 J/mol⋅K)

How many molecules are there in 14 grams of nitrogen gas?

A 2.00-L container holds half a mole of an ideal gas at a pressure of 12.0 atm.What is the gas temperature? (R = 0.082 1 L⋅atm/mol⋅K)

A room has a volume of 50 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 26°C? R = 0.082 L⋅atm/mol⋅K

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 250 K,and the pressure is 1.10 × 106 N/m2,what is the volume? (R = 8.31 J/mol⋅K)

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?

The gas,C₃H₈,is used in outside grills,and several moles of this gas will burn during an afternoon's grilling.What is the mass of one molecule of this gas?

A pressure of 3.00 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 298 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 450 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

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 room has a volume of 50 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 26°C? R = 0.082 L⋅atm/mol⋅K

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 250 K,and the pressure is 1.10 × 10⁶ N/m²,what is the volume? (R = 8.31 J/mol⋅K)