21. Kinetic Theory of Ideal Gases

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.

At an altitude of $11,000$ m (a typical cruising altitude for a jet airliner), the air temperature is $-56.5$°C and the air density is $0.364$ kg/m³ . What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the earth, so the calculation of Example $18.4$ in Section $18.1$ doesn't apply.)

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?

Calculate the density of the atmosphere at the surface of Mars (where the pressure is $650$ Pa and the temperature is typically $253$ K, with a CO₂ atmosphere), Venus (with an average temperature of $730$ K and pressure of $92$ atm, with a CO₂ atmosphere), and Saturn's moon Titan (where the pressure is $1.5$ atm and the temperature is $-178$°C, with a N₂ atmosphere).

A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains $0.110$ m³ of air at a pressure of $0.355$ atm. The piston is slowly pulled out until the volume of the gas is increased to $0.390$ m³. If the temperature remains constant, what is the final value of the pressure?

Helium gas with a volume of $3.20$ L, under a pressure of $0.180$ atm and at $41.0$°C, is warmed until both pressure and volume are doubled. What is the final temperature?

The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about 2×10⁶ K. The gas pressure in the corona is about 0.03 Pa. Estimate the number density of particles in the solar corona.

The total lung capacity of a typical adult is 5.0 L. Approximately 20% of the air is oxygen. At sea level and at a body temperature of 37°C, how many oxygen molecules do the lungs contain at the end of a strong inhalation?

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10^-10 mm of Hg. At T=20°C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?

An inflated bicycle inner tube is 2.2 cm in diameter and 200 cm in circumference. A small leak causes the gauge pressure to decrease from 110 psi to 80 psi on a day when the temperature is 20°C. What mass of air is lost? Assume the air is pure nitrogen.

In Problems $67, 68, 69,$ and $70$ you are given the equation(s) used to solve a problem. For each of these, you are to draw a pV diagram.

$(T_2 + 273) \text{ K} = \frac{200 \text{ kPa}}{500 \text{ kPa}} \times 1 \times (400 + 273) \text{ K}$

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10^-10 mm of Hg. What fraction is this of atmospheric pressure?

In Problems $67,68,69,$ and $70$ you are given the equation(s) used to solve a problem. For each of these, you are to write a realistic problem for which this is the correct equation(s).

$(T_2+273)\text{ K}=\frac{200\text{ kPa}}{500\text{ kPa}}\times 1\times (400+273)\text{ K}$

In Problems $67,68,69,$ and $70$ you are given the equation(s) used to solve a problem. For each of these, you are to write a realistic problem for which this is the correct equation(s).

$p_2=\frac{300{\text{ cm}}^3}{100{\text{ cm}}^3}\times 1\times 2\text{ atm}$

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20°C undergo an isobaric expansion until the volume has tripled. What is the gas temperature after the expansion (in °C)? The gas pressure is then decreased at constant volume until the original temperature is reached.