1. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Chemistry FIFTH EDITION by Steven S. Zumdahl University of Illinois

2. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2 Chemistry FIFTH EDITION Chapter 5 Gases

3. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 3 Section 5.6 The Kinetic Molecular Theory of Gases Simple Model which attempts to explain the properties of an Ideal Gas. Before -- experimental point of view Now -- theory to explain the behavior.

4. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 1.Volume of individual particles is  zero. 2.Collisions of particles with container walls cause pressure exerted by gas. 3.Particles exert no forces on each other. 4.Average kinetic energy  Kelvin temperature of a gas.

5. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5 Figure 5.14 The Effects of Decreasing the Volume of a Sample of Gas at Constant Temperature Boyle’s Law: P V = kP = (nRT) 1/V

6. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Figure 5.15 The Effects of Increasing the Temperature of a Sample of Gas at Constant Volume P = (nR) T V

7. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7 Figure 5.16 The Effects of Increasing the Temperature of a Sample of Gas at Constant Pressure Charles’ Law: V = (n R) T P

8. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 Figure 5.17 The Effects of Increasing the Number of Moles of Gas Particles at Constant Temperature and Pressure Avogadro’s Law: V = (RT) n P

9. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 9 The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.) ☻ See Exercise #72!! ☻ R = 8.3145 J/ K mole

10. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 Root Mean Square Velocity Ave. Velocity of gas particles is a special kind of average. The square root of the average of the squares of the individual velocities of the gas particles. u rms = ( √ ū 2 ) = √(3RT/M)

11. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 Root Mean Square Velocity u rms = √(3RT/M) (units are m/s) where M = mass of a mole of gas particles in kg R = 8.3145 J/mole K J = kg m 2 / s 2 Read Sample Exercise 5.19 on page 217.

12. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 12 Real gases experience a large # of collisions. A given particle will continuously change its course as a result of collisions with other particles, as well as with the walls of the container. See figure in next slide.

13. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 13 Figure 5.18 Path of One Particle in a Gas is typically very erratic.

14. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 Gas particles actually have a large range of velocities. Root mean square velocity gives us a feel for the average velocity of a gas particles. However, Most gas particles do not have this velocity.

15. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 Figure 5.19 A Plot of the Relative Number of O 2 Molecules That Have a Given Velocity at STP u rms ≈ 500 m/s

16. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 Figure 5.20 A Plot of the Relative Number of N 2 Molecules That Have a Given Velocity at Three Temperatures

17. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 Effusion: describes the passage of gas into an evacuated chamber. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

18. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 Figure 5.21 The Effusion of a Gas into an Evacuated Chamber

19. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 Graham’s Law of Effusion: Diffusion: M = molar mass

20. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 Figure 5.23 HCl(g) and NH 3 (g) Meet in a Tube Diffusion Careful Experiments show observed ratio is less than expected from calculations.

21. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 Diffusion Mixing of Gases Quite complicated to describe theoretically. So many collisions occur as the molecules travel. Previous equation used as a first approximation.