root mean square speed (u_rms)

measure of average speed for a group of particles calculated as the square root of the average squared speed

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Chemistry 2e · 9.5 The Kinetic-Molecular Theory

The Kinetic-Molecular Theory: practice problems

4 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 91
Can the speed of a given molecule in a gas double at constant temperature? Explain your answer.
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Exercises 93
The distribution of molecular speeds in a sample of helium is shown in Figure 9.34. If the sample is cooled, will the distribution of speeds look more like that of H₂ or of H₂O? Explain your answer.
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Exercises 95
A 1-L sample of CO initially at STP is heated to 546 K, and its volume is increased to 2 L.
(a) What effect do these changes have on the pressure exerted by the gas?
(b) What is the effect on the average kinetic energy of the molecules?
(c) What is the effect on the root mean square speed of the molecules?
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Exercises 97
Answer the following questions:
(a) Is the pressure of the gas in the hot-air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?
(b) Is the density of the gas in the hot-air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?
(c) At a pressure of 1 atm and a temperature of 20 °C, dry air has a density of 1.2256 g/L. What is the (average) molar mass of dry air?
(d) The average temperature of the gas in a hot-air balloon is 1.30 $\times$ 10² °F. Calculate its density, assuming the molar mass equals that of dry air.
(e) The lifting capacity of a hot-air balloon is equal to the difference in the mass of the cool air displaced by the balloon and the mass of the gas in the balloon. What is the difference in the mass of 1.00 L of the cool air in part (c) and the hot air in part (d)?
(f) An average balloon has a diameter of 60 feet and a volume of 1.1 $\times$ 10⁵ ft³. What is the lifting power of such a balloon? If the weight of the balloon and its rigging is 500 pounds, what is its capacity for carrying passengers and cargo?
(g) A balloon carries 40.0 gallons of liquid propane (density 0.5005 g/L). What volume of CO₂ and H₂O gas is produced by the combustion of this propane at STP?
(h) A balloon flight can last about 90 minutes. If all of the fuel is burned during this time, what is the approximate rate of heat loss (in kJ/min) from the hot air in the bag during the flight?
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Key terms · 2

kinetic molecular theory: theory based on simple principles and assumptions that effectively explains ideal gas behavior
root mean square speed (u_rms): measure of average speed for a group of particles calculated as the square root of the average squared speed

Learn 9.5 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 9.5 in the textbook · This section on openstax.org

The Kinetic-Molecular Theory: practice problems

4 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 91

Can the speed of a given molecule in a gas double at constant temperature? Explain your answer.

Exercises 93

The distribution of molecular speeds in a sample of helium is shown in Figure 9.34. If the sample is cooled, will the distribution of speeds look more like that of H₂ or of H₂O? Explain your answer.

Exercises 95

A 1-L sample of CO initially at STP is heated to 546 K, and its volume is increased to 2 L.

(a) What effect do these changes have on the pressure exerted by the gas?

(b) What is the effect on the average kinetic energy of the molecules?

Exercises 97

Answer the following questions:

(a) Is the pressure of the gas in the hot-air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?

(b) Is the density of the gas in the hot-air balloon shown at the opening of this chapter greater than, less than, or equal to that of the atmosphere outside the balloon?

(c) At a pressure of 1 atm and a temperature of 20 °C, dry air has a density of 1.2256 g/L. What is the (average) molar mass of dry air?

(d) The average temperature of the gas in a hot-air balloon is 1.30 $\times$ 10² °F. Calculate its density, assuming the molar mass equals that of dry air.

(e) The lifting capacity of a hot-air balloon is equal to the difference in the mass of the cool air displaced by the balloon and the mass of the gas in the balloon. What is the difference in the mass of 1.00 L of the cool air in part (c) and the hot air in part (d)?

(f) An average balloon has a diameter of 60 feet and a volume of 1.1 $\times$ 10⁵ ft³. What is the lifting power of such a balloon? If the weight of the balloon and its rigging is 500 pounds, what is its capacity for carrying passengers and cargo?

(g) A balloon carries 40.0 gallons of liquid propane (density 0.5005 g/L). What volume of CO₂ and H₂O gas is produced by the combustion of this propane at STP?

(h) A balloon flight can last about 90 minutes. If all of the fuel is burned during this time, what is the approximate rate of heat loss (in kJ/min) from the hot air in the bag during the flight?

Key terms · 2

kinetic molecular theory: theory based on simple principles and assumptions that effectively explains ideal gas behavior
root mean square speed (u_rms): measure of average speed for a group of particles calculated as the square root of the average squared speed

Learn 9.5 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 9.5 in the textbook · This section on openstax.org