21. Kinetic Theory of Ideal Gases

A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20°C. What is the number density of the oxygen?

How many moles are in a $1.00$-kg bottle of water? How many molecules? The molar mass of water is $18.0$ g/mol.

Use the ideal gas law to show that, for an ideal gas at constant pressure, the coefficient of volume expansion is equal to β = 1/ T, where T is the kelvin temperature. Compare to Table 17–1 for gases at T = 293 K.

Assume that in an alternate universe, the laws of physics are very different from ours and that “ideal” gases behave as follows: At constant temperature, pressure is inversely proportional to the square of the volume.

Hydrogen gas behaves very much like an ideal gas. If you have a sample of Hydrogen gas with a volume of 1000 cm³ at 30°C with a pressure of 1 × 10⁵ Pa, calculate how many hydrogen atoms (particles) there are in the sample.

Consider an ideal gas at $27$°C and $1.00$ atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

A container of gas at 2.0 atm pressure and 127°C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again. Show this process on a pV diagram.

0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What is the volume V₃?

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.

Modern vacuum pumps make it easy to attain pressures of the order of $10^{-13}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. How many molecules would be present at the same temperature but at $1.00$ atm instead?

A 1.0 m ✕ 1.0 m ✕ 1.0 m cube of nitrogen gas is at 20℃ and 1.0 atm. Estimate the number of molecules in the cube with a speed between 700 m/s and 1000 m/s.

A gas with initial state variables p₁, V₁, and T₁ is cooled in an isochoric process until p₂ = (1/3)p₁. What are V₂?

14 g of nitrogen gas at STP are pressurized in an isochoric process to a pressure of 20 atm. What are the final temperature?

If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is $1003$°C and the pressure is $92$ atm?

A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303°C. The air above the piston is at 1.00 atm pressure. What will the height of the piston be if the temperature is lowered to 15°C?