Question 1

What is the total translational kinetic energy of the gas in a classroom filled with nitrogen at $1.01 \times 10 ^ { 5 } \mathrm {~Pa}$ at $20.7 ^ { \circ } \mathrm { C } \text { ? }$ The dimensions of the classroom are $4.60 \mathrm {~m} \times 5.20 \mathrm {~m} \times 8.80 \mathrm {~m} .$ The Boltzmann constant is 1.3806503 × 10^-23 J/K,R = 8.31 J/mol ∙ K,and N_A = 6.022 × 10²³ molecules/mol.

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Question 2

A sealed container holds 0.020 moles of ideal nitrogen (N₂)gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is 1.38 × 10^-23 J/K.

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Question 3

The molecular weight of nitrogen,N₂,is 28 g/mol.What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

Accepted Answer

The rms speed of nitrogen molecules can be calculated using the formula:
rms speed = √(3kT/m)
where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molecular weight of nitrogen.
Converting the temperature of 8.0°C to Kelvin:
T = 8.0°C + 273 = 281 K
Substituting the values:
rms speed = √(3 * 1.38 × 10^-23 J/K * 281 K / 28 g/mol * 1 mol/6.022 × 10^23 molecules)
rms speed = 499.7 m/s which is approximately 500 m/s
Therefore, the best choice is B.

Question 4

A 24.0-L tank contains ideal helium gas at 27°C and a pressure of 22.0 atm.How many moles of gas are in the tank? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

Accepted Answer

First we need to convert the temperature to Kelvin:

27°C + 273.15 = 300.15 K

We also need to convert the pressure to kPa:

22.0 atm × 101 kPa/atm = 2222 kPa

Now we can use the ideal gas law:

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 in Kelvin. Solving for n:

n = PV/RT

Plugging in the numbers:

n = (2222 kPa × 24.0 L)/(8.31 J/mol ∙ K × 300.15 K)

n ≈ 21.4 mol

So the answer is D, 21.4 mol.

Question 5

What is the average translational kinetic energy of an ideal gas at $819 \mathrm {~K} \text { ? }$ The Boltzmann constant is 1.38 × 10^-23 J/K.

Accepted Answer

The average translational kinetic energy of an ideal gas is given by $\frac{3}{2}kT$. Substituting $k = 1.38 \times 10^{-23} \, \text{J/K}$ and $T = 819 \, \text{K}$, the energy is $1.70 \times 10^{-20} \, \text{J}$.

Question 6

At what temperature would the root mean square speed of oxygen molecules,O₂,be $14.0 \mathrm {~m} / \mathrm { s }$ if oxygen behaves like an ideal gas? The mass of one O₂ molecule is 5.312 × 10^-26 kg,and the Boltzmann constant is 1.38 × 10^-23 J/K.

Accepted Answer

The root mean square speed $v_{rms}$ is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$. Solving for $T$, we get $T = \frac{mv_{rms}^2}{3k}$. Substituting the given values, $m = 5.312 \times 10^{-26} \, \text{kg}$, $v_{rms} = 14.0 \, \text{m/s}$, and $k = 1.38 \times 10^{-23} \, \text{J/K}$, we find $T \approx 0.251 \, \text{K}$.

Question 7

If the temperature of a gas is increased from 20°C to 100°C,by what factor does the rms speed of an ideal molecule change?

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Question 8

A flask contains a mixture of argon and neon gases at a stabilized temperature.The root-mean-square speed of the argon gas is determined to be 1.21 km/s.What is the root-mean-square speed of the neon gas? The atomic mass of argon is 39.95 g/mol,and that of neon is 20.18 g/mol.

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Question 9

A 5.3 L flask of ideal neon gas (which is monatomic)is at a pressure of 6.0 atm and a temperature of $290 \mathrm {~K} .$ The atomic mass of neon is 20.2 g/mol.What is the mass of the neon gas in the flask.(R = 8.31 J/mol ∙ K,1 atm = 101 kPa,N_A = 6.022 × 10²³ molecules/mol)

Accepted Answer

The ideal gas law is PV = nRT, where 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/RT. We are given P = 6.0 atm, V = 5.3 L, R = 8.31 J/mol ∙ K, and T = 290 K. Plugging these values into the equation, we get: n = (6.0 atm)(5.3 L)/(8.31 J/mol ∙ K)(290 K) = 0.13 mol. The mass of the neon gas is then: mass = n × molar mass = (0.13 mol)(20.2 g/mol) = 2.7 × 10^-2 g.

Question 10

A sealed container holds 0.020 moles of ideal nitrogen (N₂)gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.How many molecules of nitrogen are in the container? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

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Question 11

A 0.50 $m ^ { 3 }$ gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of $350 \mathrm {~K} .$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ What is the rms speed of the molecules? (The Boltzmann constant is 1.38 × 10^-23 J/K,N_A = 6.022 × 10²³ molecules/mol.)

Accepted Answer

The rms speed of the molecules is given by:$$v_{rms}=\sqrt{\frac{3RT}{M}}$$where R is the gas constant, T is the temperature, and M is the molar mass.Plugging in the given values, we get:$$v_{rms}=\sqrt{\frac{3(8.31 J/molK)(350 K)}{28 g/mol}}$$$$v_{rms}=560 m/s$$Therefore, the rms speed of the molecules is 560 m/s.

Question 12

At what temperature is the rms speed of hydrogen molecules,H₂,which have a molecular weight of 2.02 g/mole,equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

Accepted Answer

To solve this problem, we can use the equation for the root-mean-square speed of gas molecules:

v(rms) = √(3kT/m)

where v(rms) is the root-mean-square speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molecular weight of the gas.

Rearranging this equation, we get:

T = (m * v(rms)^2) / (3k)

Plugging in the given values, we get:

T = (2.02 g/mol * (2000 m/s)^2) / (3 * 1.38 x 10^-23 J/K)

Note that we convert the given speed from km/s to m/s.

Simplifying this expression, we get:

T ≈ 51°C

Therefore, the answer is choice C.

Question 13

A 4.2-L flask of ideal neon gas (which is monatomic)is at a pressure of 3.3 atm and a temperature of 450 K.The atomic mass of neon is 20.2 g/mol.How many neon atoms are in the flask? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa,N_A = 6.022 × 10²³ molecules/mol)

Accepted Answer

To find the number of neon atoms in the flask, we can use the ideal gas law, PV = nRT, where 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. First, we need to convert the pressure from atm to kPa because the given R value is in J/mol·K, which requires pressure in kPa: 3.3 atm × 101 kPa/atm = 333.3 kPa. Then, we solve for n:$$n = \frac{PV}{RT} = \frac{333.3 \, \text{kPa} \times 4.2 \, \text{L}}{8.31 \, \text{J/mol·K} \times 450 \, \text{K}}$$Note that 1 L·kPa = 1 J, so the units of volume and pressure are compatible with R's units:$$n \approx \frac{1400}{3739.5} \, \text{mol} \approx 0.374 \, \text{mol}$$Finally, to find the number of atoms, we multiply the number of moles by Avogadro's number (6.022 × 10^23 molecules/mol):$$0.374 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 2.3 \times 10^{23}$$Therefore, the correct answer is 2.3 × 10^23 neon atoms in the flask.

Question 14

An oxygen molecule,O₂,falls in a vacuum.From what height must it fall so that its translational kinetic energy at the bottom of its fall equals the average translational kinetic energy of an oxygen molecule at 920 K? The mass of one O₂ molecule is 5.312 × 10^-26 kg,and the Boltzmann constant is 1.38 × 10^-23 J/K.Neglect air resistance and assume that g remains constant at 9.8 m/s² throughout the fall of the molecule.

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Question 15

The rms speed of a certain sample of carbon dioxide molecules,with a molecular weight of 44.0 g/mole,is 396 m/s.What is the rms speed of water vapor molecules,with a molecular weight of 18.0 g/mol,at the same temperature as the carbon dioxide?

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Question 16

What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? The Boltzmann constant is 1.38 × 10^-23 J/K.

Accepted Answer

The average translational kinetic energy ($E_k$) of a molecule in a gas is given by the equation $E_k = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature in Kelvin. To convert 17°C to Kelvin, add 273.15, giving 290.15 K. Plugging in the values: $E_k = \frac{3}{2} \times 1.38 \times 10^{-23} \times 290.15$, which calculates to approximately $6.01 \times 10^{-21}$ J.

Question 17

A sealed cylinder fitted with a movable piston contains ideal gas at 27°C,pressure 0.500 × 10⁵ Pa,and volume 1.25 m³.What will be the final temperature if the gas is compressed to 0.800 m³ and the pressure rises to 0.820 × 10⁵ Pa?

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Question 18

A 3.9-L volume of ideal neon gas (monatomic)is at a pressure of 5.6 aym and a temperature of $330 \mathrm {~K} .$ The atomic mass of neon is $20.2 \mathrm {~g} / \mathrm { mol }$ The temperature of the gas is now increased to 430 K and the volume is increased to $5.9 \text { L. }$ What is the final pressure of the gas?

Accepted Answer

Using the ideal gas law, we can write:$$PV = nRT$$where 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 P:$$P = \frac{nRT}{V}$$We can now plug in the given values:$$n = \frac{3.9 	ext{ L}}{22.4 	ext{ L/mol}} = 0.174 	ext{ mol}$$$$R = 0.0821 	ext{ L atm/(mol K)}$$$$T_1 = 330 	ext{ K}$$$$V_1 = 3.9 	ext{ L}$$$$T_2 = 430 	ext{ K}$$$$V_2 = 5.9 	ext{ L}$$We can now solve for P:$$P = \frac{(0.174 	ext{ mol})(0.0821 	ext{ L atm/(mol K)})(430 	ext{ K})}{5.9 	ext{ L}} = 4.8 	ext{ atm}$$Therefore, the final pressure of the gas is 4.8 atm.

Question 19

(a)At what Celsius temperature is the average kinetic energy of a helium gas atom equal to 6.21 × 10^-21 J? The Boltzmann constant is 1.38 × 10^-23 J/K . (b)What would be the temperature for radon gas?

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Question 20

A 0.40- $m ^ { 3 }$ gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of $290 \mathrm {~K} .$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ What is the pressure of the gas? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

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Quiz 10: Gases

A sealed container holds 0.020 moles of ideal nitrogen (N₂) gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is 1.38 × 10^-23 J/K.

The molecular weight of nitrogen,N₂,is 28 g/mol.What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

A 24.0-L tank contains ideal helium gas at 27°C and a pressure of 22.0 atm.How many moles of gas are in the tank? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

What is the average translational kinetic energy of an ideal gas at $819 \mathrm {~K} \text { ? }$ The Boltzmann constant is 1.38 × 10^-23 J/K.

At what temperature would the root mean square speed of oxygen molecules,O₂,be $14.0 \mathrm {~m} / \mathrm { s }$ if oxygen behaves like an ideal gas? The mass of one O₂ molecule is 5.312 × 10^-26 kg,and the Boltzmann constant is 1.38 × 10^-23 J/K.

If the temperature of a gas is increased from 20°C to 100°C,by what factor does the rms speed of an ideal molecule change?

A flask contains a mixture of argon and neon gases at a stabilized temperature.The root-mean-square speed of the argon gas is determined to be 1.21 km/s.What is the root-mean-square speed of the neon gas? The atomic mass of argon is 39.95 g/mol,and that of neon is 20.18 g/mol.

A 5.3 L flask of ideal neon gas (which is monatomic) is at a pressure of 6.0 atm and a temperature of $290 \mathrm {~K} .$ The atomic mass of neon is 20.2 g/mol.What is the mass of the neon gas in the flask.(R = 8.31 J/mol ∙ K,1 atm = 101 kPa,N_A = 6.022 × 10²³ molecules/mol)

A sealed container holds 0.020 moles of ideal nitrogen (N₂) gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.How many molecules of nitrogen are in the container? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

At what temperature is the rms speed of hydrogen molecules,H₂,which have a molecular weight of 2.02 g/mole,equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

A 4.2-L flask of ideal neon gas (which is monatomic) is at a pressure of 3.3 atm and a temperature of 450 K.The atomic mass of neon is 20.2 g/mol.How many neon atoms are in the flask? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa,N_A = 6.022 × 10²³ molecules/mol)

The rms speed of a certain sample of carbon dioxide molecules,with a molecular weight of 44.0 g/mole,is 396 m/s.What is the rms speed of water vapor molecules,with a molecular weight of 18.0 g/mol,at the same temperature as the carbon dioxide?

What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? The Boltzmann constant is 1.38 × 10^-23 J/K.

A sealed cylinder fitted with a movable piston contains ideal gas at 27°C,pressure 0.500 × 10⁵ Pa,and volume 1.25 m³.What will be the final temperature if the gas is compressed to 0.800 m³ and the pressure rises to 0.820 × 10⁵ Pa?

(a)At what Celsius temperature is the average kinetic energy of a helium gas atom equal to 6.21 × 10^-21 J? The Boltzmann constant is 1.38 × 10^-23 J/K . (b)What would be the temperature for radon gas?

A 0.40- $m ^ { 3 }$ gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of $290 \mathrm {~K} .$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ What is the pressure of the gas? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

Quiz 10: Gases

A sealed container holds 0.020 moles of ideal nitrogen (N2) gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is 1.38 × 10-23 J/K.

The molecular weight of nitrogen,N2,is 28 g/mol.What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10-23 J/K and NA = 6.022 × 1023 molecules/mol.

A 24.0-L tank contains ideal helium gas at 27°C and a pressure of 22.0 atm.How many moles of gas are in the tank? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

What is the average translational kinetic energy of an ideal gas at 819 K ? 819 \mathrm {~K} \text { ? }819 K ? The Boltzmann constant is 1.38 × 10-23 J/K.

At what temperature would the root mean square speed of oxygen molecules,O2,be 14.0 m/s14.0 \mathrm {~m} / \mathrm { s }14.0 m/s if oxygen behaves like an ideal gas? The mass of one O2 molecule is 5.312 × 10-26 kg,and the Boltzmann constant is 1.38 × 10-23 J/K.

If the temperature of a gas is increased from 20°C to 100°C,by what factor does the rms speed of an ideal molecule change?

A flask contains a mixture of argon and neon gases at a stabilized temperature.The root-mean-square speed of the argon gas is determined to be 1.21 km/s.What is the root-mean-square speed of the neon gas? The atomic mass of argon is 39.95 g/mol,and that of neon is 20.18 g/mol.

A 5.3 L flask of ideal neon gas (which is monatomic) is at a pressure of 6.0 atm and a temperature of 290 K.290 \mathrm {~K} .290 K. The atomic mass of neon is 20.2 g/mol.What is the mass of the neon gas in the flask.(R = 8.31 J/mol ∙ K,1 atm = 101 kPa,NA = 6.022 × 1023 molecules/mol)

A sealed container holds 0.020 moles of ideal nitrogen (N2) gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.How many molecules of nitrogen are in the container? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

At what temperature is the rms speed of hydrogen molecules,H2,which have a molecular weight of 2.02 g/mole,equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10-23 J/K and NA = 6.022 × 1023 molecules/mol.

A 4.2-L flask of ideal neon gas (which is monatomic) is at a pressure of 3.3 atm and a temperature of 450 K.The atomic mass of neon is 20.2 g/mol.How many neon atoms are in the flask? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa,NA = 6.022 × 1023 molecules/mol)

The rms speed of a certain sample of carbon dioxide molecules,with a molecular weight of 44.0 g/mole,is 396 m/s.What is the rms speed of water vapor molecules,with a molecular weight of 18.0 g/mol,at the same temperature as the carbon dioxide?

What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? The Boltzmann constant is 1.38 × 10-23 J/K.

A sealed cylinder fitted with a movable piston contains ideal gas at 27°C,pressure 0.500 × 105 Pa,and volume 1.25 m3.What will be the final temperature if the gas is compressed to 0.800 m3 and the pressure rises to 0.820 × 105 Pa?

(a)At what Celsius temperature is the average kinetic energy of a helium gas atom equal to 6.21 × 10-21 J? The Boltzmann constant is 1.38 × 10-23 J/K . (b)What would be the temperature for radon gas?

A 0.40- m3m ^ { 3 }m3 gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of 290 K.290 \mathrm {~K} .290 K. The atomic mass of nitrogen is 14.0 g/mol14.0 \mathrm {~g} / \mathrm { mol }14.0 g/mol What is the pressure of the gas? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

A sealed container holds 0.020 moles of ideal nitrogen (N₂) gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is 1.38 × 10^-23 J/K.

The molecular weight of nitrogen,N₂,is 28 g/mol.What is the rms speed of nitrogen molecules in a cooler at 8.0°C? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

What is the average translational kinetic energy of an ideal gas at $819 \mathrm {~K} \text { ? }$ The Boltzmann constant is 1.38 × 10^-23 J/K.

At what temperature would the root mean square speed of oxygen molecules,O₂,be $14.0 \mathrm {~m} / \mathrm { s }$ if oxygen behaves like an ideal gas? The mass of one O₂ molecule is 5.312 × 10^-26 kg,and the Boltzmann constant is 1.38 × 10^-23 J/K.

A 5.3 L flask of ideal neon gas (which is monatomic) is at a pressure of 6.0 atm and a temperature of $290 \mathrm {~K} .$ The atomic mass of neon is 20.2 g/mol.What is the mass of the neon gas in the flask.(R = 8.31 J/mol ∙ K,1 atm = 101 kPa,N_A = 6.022 × 10²³ molecules/mol)

A sealed container holds 0.020 moles of ideal nitrogen (N₂) gas,at a pressure of 1.5 atm and a temperature of 290 K.The atomic mass of nitrogen is 14.0 g/mol.How many molecules of nitrogen are in the container? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)

At what temperature is the rms speed of hydrogen molecules,H₂,which have a molecular weight of 2.02 g/mole,equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol.

A 4.2-L flask of ideal neon gas (which is monatomic) is at a pressure of 3.3 atm and a temperature of 450 K.The atomic mass of neon is 20.2 g/mol.How many neon atoms are in the flask? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa,N_A = 6.022 × 10²³ molecules/mol)

What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? The Boltzmann constant is 1.38 × 10^-23 J/K.

A sealed cylinder fitted with a movable piston contains ideal gas at 27°C,pressure 0.500 × 10⁵ Pa,and volume 1.25 m³.What will be the final temperature if the gas is compressed to 0.800 m³ and the pressure rises to 0.820 × 10⁵ Pa?

(a)At what Celsius temperature is the average kinetic energy of a helium gas atom equal to 6.21 × 10^-21 J? The Boltzmann constant is 1.38 × 10^-23 J/K . (b)What would be the temperature for radon gas?

A 0.40- $m ^ { 3 }$ gas tank holds 7.0 moles of ideal diatomic nitrogen gas at a temperature of $290 \mathrm {~K} .$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ What is the pressure of the gas? (R = 8.31 J/mol ∙ K,1 atm = 101 kPa)