21. Kinetic Theory of Ideal Gases

Oxygen (O2) has a molar mass of 32.0 g/mol. What is (g) How many oxygen molecules traveling at this speed are necessary to produce an average pressure of 1 atm?

Oxygen (O2) has a molar mass of 32.0 g>mol. What is (e) Suppose an oxygen molecule traveling at this speed bounces back and forth between opposite sides of a cubical vessel 0.10 m on a side. What is the average force the molecule exerts on one of the walls of the container? (Assume that the molecule's velocity is perpendicular to the two sides that it strikes.)

For diatomic carbon dioxide gas (CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (c) the root-mean-square speed v_rms.

Smoke particles in the air typically have masses of the order of 10-16 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the rootmean-square speed of Brownian motion for a particle with a mass of 3.00 * 10-16 kg in air at 300 K.

At what temperature is the root-mean-square speed of nitrogen molecules equal to the root-mean-square speed of hydrogen molecules at 20.0°C? (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element. The molar mass of H2 is twice the molar mass of hydrogen atoms, and similarly for N2.)

Oxygen (O2) has a molar mass of 32.0 g>mol. What is (d) the momentum of an oxygen molecule traveling at this speed?

Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.0°C in summer to -100°C in winter. Over the course of a Martian year, what are the ranges of (a) the rms speeds of the CO2 molecules and

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (b) the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)

We have two equal-size boxes, A and B. Each box contains gas that behaves as an ideal gas. We insert a thermometer into each box and find that the gas in box A is at 50°C while the gas in box B is at 10°C. This is all we know about the gas in the boxes. Which of the following statements must be true? Which could be true? Explain your reasoning. (a) The pressure in A is higher than in B. (b) There are more molecules in A than in B. (c) A and B do not contain the same type of gas. (d) The molecules in A have more average kinetic energy per molecule than those in B. (e) The molecules in A are moving faster than those in B.

You are watching a science fiction movie in which the hero shrinks down to the size of an atom and fights villains while jumping from air molecule to air molecule. In one scene, the hero's molecule is about to crash head-on into the molecule on which a villain is riding. The villain's molecule is initially 50 molecular radii away and, in the movie, it takes 3.5 s for the molecules to collide. Estimate the air temperature required for this to be possible. Assume the molecules are nitrogen molecules, each traveling at the rms speed. Is this a plausible temperature for air?

Eleven molecules have speeds 15, 16, 17, …, 25 m/s. Calculate (a) vₐᵥ₉ and (b) vᵣₘₛ.

b. A gas cylinder has a piston at one end that is moving outward at speed vₚᵢₛₜₒₙ during an isobaric expansion of the gas. Find an expression for the rate at which vᵣₘₛ is changing in terms of vₚᵢₛₜₒₙ, the instantaneous value of vᵣₘₛ, and the instantaneous value L of the length of the cylinder.

Uranium has two naturally occurring isotopes. ²³⁸U has a natural abundance of 99.3% and ²³⁵U has an abundance of 0.7%. It is the rarer ²³⁵U that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, UF₆, which is a gas, then allowing it to diffuse through a series of porous membranes. ²³⁵UF₆ has a slightly larger rms speed than ²³⁸UF₆ and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of ²³⁵UF₆ to that of ²³⁸UF₆?

A cylinder contains gas at a pressure of 2.0 atm and a number density of 4.2 x 10²⁵ m⁻³. The rms speed of the atoms is 660 m/s. Identify the gas.

The rms speed of molecules in a gas is 600 m/s. What will be the rms speed if the gas pressure and volume are both halved?

By what factor does the rms speed of a molecule change if the temperature is increased from 10℃ to 1000℃?

Dust particles are ≈ 10 μm in diameter. They are pulverized rock, with p ≈ 2500 kg/m³. If you treat dust as an ideal gas, what is the rms speed of a dust particle at 20℃?