1. The Gas Laws Chapter 9

2. Kinetic Molecular Theory 1. A gas is composed of small particles (molecules) that are spaced widely apart. Compressible Low density - about a 1000 times less dense than a liquid 2. The molecules of a gas are in rapid, constant motion Pressure – the force of the molecules hitting the side of a container Fill a container (like a balloon) evenly.

3. Kinetic Molecular Theory 3. All collisions are elastic Molecules don’t lose any energy when they collide. 4. Gas molecules have little/no attractive force on one another. Too far apart Mix thoroughly – unlike oil and water (too far apart for polar/non-polar forces to matter)

4. Kinetic Molecular Theory 5. The temperature of a gas is a measure of average kinetic energy Kinetic energy – energy in motion KE = ½ mv 2 Graham’s Law of Diffusion – the higher the molar mass, the slower it moves v 1 =m 2 v 2 m 1

5. Graham’s Law Example At the same temperature, how much faster does an He atom move than an N 2 molecule? (Ans: 2.65 times faster)

6. Graham’s Law Example Which is faster (and by how much): Cl 2 or O 2 ? (Ans: O 2 is about 1.5 times faster)

7. Which is faster and by how much: HCl or NH 3 ?

8. Our Atmosphere 99% N 2 and O 2 78% N 2 21% O 2 1% CO 2 and the Noble Gases

9. Pressure Pressure = Force Area (Needles, High Heels, Snow shoes) Caused by the collisions of gases against a container We live at about 1 atmosphere of pressure

11. Barometer Torricelli (1643) Height of column stayed about 760 mm (760 torr) The higher the elevation, the lower the mercury Weather Rising pressure – calm weather Dropping pressure – storm (fast moving air)

12. Units of Pressure All of the following are equal: 760 mm Hg (760 torr) 29.9 inches Hg (weather reporting) 1 atmosphere (chemistry) 101.3 kPa (kiloPascals, physics) 760 mm = 29.9 in = 1 atmosphere = 101.3 kPa

13. Converting Pressures Examples: 1. Express 485 torr in atmospheres. 2. Convert 2.4 atmospheres to mm Hg 3. Convert 95.0 kPa to atmospheres and mm Hg. 4. Convert 31.4 inches of mm to atmospheres.

14. The Ideal Gas Law Combination of earlier work on gases. Works very well in situations close to Earth’s pressures and temperatures Does not work for “extreme” situations (Jupiter’s atmosphere is too cold and too dense)

15. The Ideal Gas Law PV = nRT P = pressure in atmosphere V = volume in Liters n = number of moles T = Temperature in Kelvin R = gas constant R = 0.0821 L-atm / mol-K

16. The Ideal Gas Law Examples: 1. What is the pressure of a 1.45 mol sample of a gas in a 20.0 L container at 25 o C? 2. What volume will 5.00 grams of H 2 occupy at 10.0 o C and 1 atmosphere of pressure? 3. How many grams of O 2 are needed to occupy a 500.0 mL aerosol can at 20.0 o C and 0.900 atmospheres?

17. STP Standard Temperature & Pressure Standard Temperature = 0 o C (273 K) Standard Pressure = 1 atm 1 mole of a gas occupies 22.4 L at STP 1 moleor22.4 L 22.4 L1 mole

18. STP Examples: 1. What volume will 0.180 moles of nitrogen gas occupy at STP? 2. How many grams of chlorine (Cl 2 ) gas are present in 50.0 L at STP?

19. Comparing Two Situations Sometimes we want to know what happens when a gas is under different conditions Example: What happens to a basketball if you pump it indoors, then take it out on a cold day?

20. Comparing Two Situations P 1 V 1 = n 1 RT 1 P 2 V 2 = n 2 RT 2 Solve both equations for R R = P 1 V 1 R = P 2 V 2 n 1 T 1 n 2 T 2 P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2

21. Comparing Two Situations See what you can cross out (what you are not told) Remember to convert to Kelvin and moles if needed.

22. Boyle’s Law Boyle’s Law Apparatus Demo Boyle’s Law – The pressure and volume of a gas are inversely related Bicycle pump example Piston down – low volume, high pressure Piston up – high volume, low pressure

23. Boyle’s Law Example: 1. The volume of a car’s cylinder is 475 mL at 1.05 atm. What is the volume when the cylinder is compressed and the pressure is 5.65 atm? P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2

24. Boyle’s Law Collapses to: P 1 V 1 = P 2 V 2 (Answer: 88.3 mL)

25. Boyle’s Law Example: 2. A weather balloon has a volume of 40.0 liters on the surface of the earth at 1.00 atm. What will be the volume at 0.400 atm as it rises? P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2

26. Charles Law Charles Law – The temperature and volume of a gas are directly related “HOTTER = BIGGER” A gas increases in volume 1/273 rd per degree celsius Can be used to find absolute zero Temperature must be in Kelvin

27. Charles Law 1. A basketball has a volume of 12.0 L when blown up at 25.00 o C. What will be the volume if it is taken outside on a day when it is only 5.00 o C? P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2

28. Charles Law Collapses to: V 1 = V 2 T 1 T 2

29. Charles Law 2. If a tire contains 30.0 L of air at 10.0 o C, what volume will it occupy when it is driven and warms up to 50.0 o C?

30. Guy-Lussac’s Law Gay-Lussac’s Law = The temperature and pressure of a gas are directly related. Temperature must be in Kelvin 1. Gas in a spray can has a pressure of 5.00 atm at 25.0 o C. What will be the pressure at 400.0 o C? P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2

31. Avagadro’s Law Avagadro’s Law = The volume of a gas is directly proportional to the moles present “MORE = BIGGER” 1. A balloon has a volume of 1.00 L when 50.0 grams of N 2 are in the balloon. What is the volume if an additional 25.0 grams of N 2 are added?

32. Putting it all together Often you change more than one thing at a time. Ex: In a car, volume, temperature, and pressure may change. 1. The volume of 0.0400 mol of a gas is 500.0 mL at 1.00 atm and 20.0 o C. What is the volume at 2.00 atm and 30.0 o C?

33. Gases and Reaction Stoichiometry 1. What mass of Al is needed to produce 50.0 L of H 2 at STP? 2Al(s) + 6HCl(aq)  2AlCl 3 (aq) + 3H 2 (g) (ANS: 40.2 g Al)

34. Gases and Reaction Stoichiometry 2. What volume of NO gas measured at 0.724 atm and 25 o C will be produced from the reaction of 19.5 g of O 2 ? 4NH 3 (g) + 5O 2 (g)  4NO(g) + 6H 2 O(l) (Ans: 16.4 L)

35. Gases and Reaction Stoichiometry 3. Car safety bags are inflated through the decomposition of NaN 3. How many grams of NaN 3 are needed to produce 36.0 L of N 2 at 1.15 atm and 26.0 o C? 2NaN 3 (s)  2Na(s) + 3N 2 (g) (Ans: 72 g)

36. Gases and Reaction Stoichiometry 4. How many liters of H 2 and N 2 at 1.00 atm and 15.0 o C are needed to produce 150.0 grams of NH 3 ? N 2 (g) + 3H 2 (g)  2NH 3 (g)

37. Dalton’s Law of Partial Pressures John Dalton – Dalton’s Atomic Theory Dalton’s Law – the total pressure of a gas is equal to the sum of the partial pressures P tot = P A + P B + P C + P D +….. P atm = P N2 + P O2 + P rest 1 atm = 0.78atm + 0.21atm + 0.01atm

38. Dalton’s Law of Partial Pressures 1. Three gases are mixed in a 5.00 L container. In the container, there are 255 torr of Ar, 228 torr of N 2, and 752 torr of H 2. What is the total pressure?

39. Dalton’s Law of Partial Pressures 2. On a humid day, the partial pressure of water in the atmosphere is 18 torr. a) If the total pressure is 766 torr, what are the pressures of all of the other gases? b) If the atmosphere is 78% N 2 and 21% O 2, what are their pressures on this humid day?

40. Dalton’s Law of Partial Pressures 3. What is the total pressure (in atm) exerted by a mixture of 12.0 g of N 2 and 12.0 g of O 2 in a 2.50 L container at 25.0 o C?

41. 8. CH 4 (16.0) Fastest Ne (20) CO (28.0) Ar (39.9) Cl 2 (71.0) ClO 2 (87.0)Slowest