Exam 20: The Micromacro Connection

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

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?

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 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.

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

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.)

Eleven molecules have speeds 16,17,18,...,26 m/s.Calculate the root-mean-square of this group of molecules.

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

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

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?

The root-mean-square speed (thermal speed)of the molecules of a gas is 200 m/s at a temperature 23.0°C.What is the mass of the individual molecules? The Boltzmann constant is 1.38 × 10^-23 J/K.

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

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in pressure.If the original root-mean-square speed (thermal speed)of the gas molecules was V,the new speed is

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?

As a result of any natural process,the total entropy of any system plus that of its environment

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

An ideal gas is kept in a rigid container.When its temperature is 100 K,the mean-free-path of the gas molecules is λ.What will be the mean-free-path of the molecules at 400 K?

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? Assume that the molecules are moving at their root-mean-square speeds.The Boltzmann constant is 1.38 × 10^-23 J/K.

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