Question 1

Quito, Ecuador, is at an altitude of 2,850 meters above sea level, while New York City is at sea level. If you are preparing a hard-boiled egg in Quito, it would have to be placed in boiling water

Accepted Answer

At higher altitudes, the boiling point of water is lower due to decreased atmospheric pressure, so it takes longer to cook food like eggs.

Question 2

What is the root mean square value of the following speeds: 2.0 m/s, 3.0 m/s, 4.0 m/s?

Accepted Answer

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Question 3

The rms speed of the molecules of a gas is 200 m/s at a temperature 300 K. What is the mass of the individual molecules?

Accepted Answer

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Question 4

What is the root mean square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?

Accepted Answer

The root mean square velocity (vrms) is calculated using the formula:

vrms = sqrt((v1^2 + v2^2 + v3^2 + ...) / n)

where v1, v2, v3, etc. are the individual velocities and n is the total number of velocities.

In this case, we have three velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s.

vrms = sqrt((2.0^2 + (-3.0)^2 + 4.0^2) / 3)
vrms = sqrt((4 + 9 + 16) / 3)
vrms = sqrt(29/3)
vrms ≈ 3.1 m/s

Therefore, the best choice is C, 3.1 m/s.

Question 5

What is the average kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17.0°C?

Accepted Answer

The average kinetic energy of a molecule is given by (3/2)kT, where k is the Boltzmann constant (1.38 × 10^-23 J/K) and T is the temperature in Kelvin. Converting 17.0°C to Kelvin gives 290.15 K. Plugging in the values, the average kinetic energy is approximately 6.01 × 10^-21 J.

Question 6

A gas consists of particles of mass 3.00 × 10^-²⁶ kg. What is the pressure in a gas of these particles if there are 2.00 × 10²⁵ particles per cubic meter of gas and the rms speed of the particles is 400 m/s?

Accepted Answer

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Question 7

What is the average kinetic energy per molecule of an ideal gas at a temperature of 300 K? Boltzmann's constant is k = 1.38 × 10^-23 J/K.

Accepted Answer

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Question 8

The rms speed of the molecules of a gas is 200 m/s at a temperature 300 K. What is the rms speed of the molecules at 500 K?

Accepted Answer

The rms speed of gas molecules is proportional to the square root of the temperature. Therefore, the new rms speed is 200 * sqrt(500/300) = 258 m/s.

Question 9

At what temperature is the rms speed of hydrogen molecules, which have a molecular weight of 2.02 g/mole, equal to 2000 m/s?

Accepted Answer

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Question 10

What is the mean free path of a gas of hard spheres of radius 2.00 × 10^-⁹ m when the number of spheres per volume is 3.00 × 10¹⁹ m^-³?

Accepted Answer

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Question 11

For chlorine gas, the van der Waals constants are: a = 0.658 J∙m³/mol², and b = 5.62 × 10^-5 m³/mol. A 3.0-L tank contains 10.0 moles of chlorine gas at a temperature of 625 K. What is the pressure in the container?

Accepted Answer

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Question 12

The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mole, is 396 m/s. What is the rms speed of water molecules, with a molecular weight of 18 g/mol, at the same temperature?

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Question 13

A cubic box with sides of 20 cm contains 2 × 10²³ molecules of helium with a root-mean-square (rms) speed of 200 m/s. The mass of a helium molecule is 3.4 × 10^-27 kg. What is the average pressure exerted by the molecules on the walls of the container?

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Question 14

For carbon dioxide, the van der Waals constants are: a = 0.364 J∙m³/mol², and b = 4.27 × 10^-5 m³/mol. Assuming that the van der Waals equation holds at the critical point (where the p-V curve first becomes horizontal and has a point of inflection), what is the critical temperature of carbon dioxide?

Accepted Answer

The critical temperature (Tc) can be calculated using the van der Waals constants: Tc = (8a)/(27Rb), where R is the ideal gas constant (8.314 J/mol·K). Substituting the given values, Tc = (8 * 0.364) / (27 * 8.314 * 4.27 × 10^-5) ≈ 304 K.

Question 15

What is the mean free path of molecules in an ideal gas in which the mean collision time is 3.00 × 10^-¹⁰ s, the temperature is 300 K, and the mass of the molecules is 6.00 × 10^-²⁵ kg?

Accepted Answer

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Question 16

What is the mean free path for the molecules in an ideal gas when the pressure is 100 kPa and the temperature is 300 K given that the collision cross-section for the molecules of that gas is 2.0 × 10^-20 m²? Boltzmann's constant is k = 1.38 × 10^-23 J/K.

Accepted Answer

The mean free path λ is given by the formula λ = (kT) / (√2 * π * d² * P), where k is Boltzmann's constant, T is the temperature, d is the collision cross-section, and P is the pressure. Substituting the given values, λ = (1.38 × 10^-23 J/K * 300 K) / (√2 * π * (2.0 × 10^-20 m²) * 100,000 Pa) ≈ 1.5 × 10^-6 m.

Question 17

La Paz, Bolivia, is at an altitude of 3,650 meters above sea level. In La Paz, water will boil

Accepted Answer

Water boils at a lower temperature at high altitudes due to the decrease in air pressure. Thus, in La Paz, which is at a high altitude, water will boil below 100°C.

Quiz 18: Kinetic Theory of Gases

Quito, Ecuador, is at an altitude of 2,850 meters above sea level, while New York City is at sea level. If you are preparing a hard-boiled egg in Quito, it would have to be placed in boiling water

What is the root mean square value of the following speeds: 2.0 m/s, 3.0 m/s, 4.0 m/s?

The rms speed of the molecules of a gas is 200 m/s at a temperature 300 K. What is the mass of the individual molecules?

What is the root mean square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?

What is the average kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17.0°C?

A gas consists of particles of mass 3.00 × 10-26 kg. What is the pressure in a gas of these particles if there are 2.00 × 1025 particles per cubic meter of gas and the rms speed of the particles is 400 m/s?

What is the average kinetic energy per molecule of an ideal gas at a temperature of 300 K? Boltzmann's constant is k = 1.38 × 10-23 J/K.

The rms speed of the molecules of a gas is 200 m/s at a temperature 300 K. What is the rms speed of the molecules at 500 K?

At what temperature is the rms speed of hydrogen molecules, which have a molecular weight of 2.02 g/mole, equal to 2000 m/s?

What is the mean free path of a gas of hard spheres of radius 2.00 × 10-9 m when the number of spheres per volume is 3.00 × 1019 m-3?

For chlorine gas, the van der Waals constants are: a = 0.658 J∙m3/mol2, and b = 5.62 × 10-5 m3/mol. A 3.0-L tank contains 10.0 moles of chlorine gas at a temperature of 625 K. What is the pressure in the container?