Exam 17: Thermal Properties of Matter

What is the mass density of argon gas at pressure 1.00 × 105 N/m² and at temperature 300 K? The mean atomic mass of argon is 39.948 g/mol and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

The root-mean-square speed (thermal speed) of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mol, is 396 m/s. What is the root-mean-square speed (thermal speed) of water vapor molecules, with a molecular weight of 18 g/mol, at the same temperature?

The figure shows a 50-kg frictionless cylindrical piston that floats on 0.68 mol of compressed air at 30°C. How far does the piston move if the temperature is increased to 300°C?

On a hot summer day, the temperature is 40.0°C and the pressure is 1.01 × 10⁵ Pa. Let us model the air as all nitrogen of molecular mass 28.0 g/mol having molecules of diameter 0.500 nm that are moving at their root-mean-square speed. Avogadro's number is 6.02 × 10²³ molecules/mol, the ideal gas constant is 8.31 J/mol•K, and the Boltzmann constant is 1.38 × 10^-23 J/K. Calculate reasonable estimates for (a) the root-mean-square speed of the nitrogen molecules. (b) the average distance a typical molecule travels between collisions. (c) the average time a molecule travels between collisions, assuming that the molecules are moving at their root-mean-square speeds. (d) the number of collisions an average molecule undergoes per second.

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? The Boltzmann constant is 1.38 × 10^-23 J/K, Avogadro's number is 6.02 × 10²³ molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

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

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in temperature. What happens to the average speed of the molecules in the sample?

A weather balloon contains 12.0 m³ of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the pressure is 101 kPa. The balloon rises to a location where the temperature is -30.0°C and the pressure is 20.0 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

3.00 moles of an ideal gas at a pressure of 250 kPa are held in a container of volume of 25.0 L. The ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K, and 1 atm = 1.01 x 10⁵ Pa. The temperature of this gas is closest to

What is the average kinetic energy of an ideal gas molecule at 569°C? (The Boltzmann constant is 1.38 × 10^-23 J/K.)

The average molecular kinetic energy of a gas can be determined by knowing

What is the total translational kinetic energy in a test chamber filled with nitrogen (N₂) at 2.16 × 10⁵ Pa and 20.7°C? The dimensions of the chamber are 4.00 m × 5.70 m × 7.40 m. The ATOMIC weight of nitrogen is 28.0 g/mol, Avogadro's number is 6.022 × 1023 molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K.

If a certain sample of an ideal gas has a temperature of 109°C and exerts a pressure of 1.2 × 10⁴ Pa on the walls of its container, how many gas molecules are present in each cubic centimeter of volume? The ideal gas constant is 8.314 J/mol · K and Avogadro's number is 6.022 × 10²³ molecules/mol.

A cubic box with sides of 20.0 cm contains 2.00 × 10²³ molecules of helium with a root-mean-square speed (thermal speed) of 200 m/s. The mass of a helium molecule is 3.40 × 10^-27 kg. What is the average pressure exerted by the molecules on the walls of the container? The Boltzmann constant is 1.38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K.

A sealed container holds 0.020 moles of nitrogen (N²) gas at a pressure of 1.5 atmospheres and a temperature of 290 K. The atomic mass of nitrogen is 14 g/mol. The Boltzmann constant is 1.38 × 10^-23 J/K and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K. The average translational kinetic energy of a nitrogen molecule is closest to

The root-mean-square speed (thermal speed) for a certain gas at 100°C is 0.500 km/s. If the temperature of the gas is now increased to 200°C, the root-mean-square (thermal) speed will be closest to

A sealed 26-m³ tank is filled with 2000 moles of oxygen gas (O₂) at an initial temperature of 270 K. The gas is heated to a final temperature of 460 K. The ATOMIC mass of oxygen is 16.0 g/mol, and the ideal gas constant is R = 8.314 J/mol · K = 0.0821 L · atm/mol · K. The final pressure of the gas is closest to

A 25-L container holds ideal hydrogen (H₂) gas at a gauge pressure of 0.25 atm and a temperature of 0°C. What mass of hydrogen gas is in this container? The ATOMIC mass of hydrogen is 1.0 g/mol, the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K, and 1.00 atm = 101 kPa.

A cold trap is set up to cause molecules to linger near the suction in a vacuum system. If the cold trap has an effective volume of 0.200 L and is maintained at 13.0 K, how many molecules are in it at 10.0 Pa of pressure? (Avogadro's number is 6.022 × 10²³ molecules/mol, and the universal gas constant is 8.314 J/mol•K. Assume the behavior of an ideal gas.)

An oxygen molecule falls in a vacuum. From what height must it fall so that its kinetic energy at the bottom equals the average energy of an oxygen molecule at 800 K? (The Boltzmann constant is 1.38 × 10^-23 J/K, the molecular weight of oxygen is 32.0 g/mol, and Avogadro's number is 6.022 × 10²³ molecules/mol.)