Exam 18: The Micromacro Connection

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.

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.)

If the temperature of a fixed amount of an ideal gas is increased, it NECESSARILY follows that

At 50.0°C, the average translational kinetic energy of a gas molecule is K. If the temperature is now increased to 100.0°C, the average translational kinetic energy of a molecule will be closest to

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?

The entropy of an isolated system must be conserved, so it never changes.

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.

The mean free path of an oxygen molecule is 2.0 × 10^-5 m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The atomic mass of oxygen is 16.0 g/mol, 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 J/mol•K = 0.0821 L ∙ atm/mol ∙ K. The radius of an oxygen molecule is closest to

What is the mean free path of a gas of randomly-moving hard spheres of radius 2.00 × 10^-9 m when the density of spheres is 3.00 × 10¹⁹ per cubic meter?

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

A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the reads 22°C. Which gas molecules have the greater average speed?

At what temperature would the root-mean-square speed (thermal speed) of oxygen molecules be 13.0 m/s? Assume that oxygen approximates an ideal gas. The mass of one O₂ molecule is 5.312 x 10^-26 kg. The Boltzmann constant is 1.38 × 10^-23 J/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.

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

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 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?

If we double the root-mean-square speed (thermal speed) of the molecules of a gas, then

A 5.0-liter gas tank holds 1.7 moles of monatomic helium (He) and 1.10 mole of diatomic oxygen (O₂), at a temperature of 260 K. The ATOMIC masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. What is the ratio of the root-mean-square (thermal) speed of helium to that of oxygen?