3. What affects the behavior of a gas? u The number of particles present u Volume (the size of the container) u Temperature 2

4. Behavior of gas?? u Usually refers to pressure u But what is pressure? u Collisions between molecules & container u More collisions = higher pressure 3

5. Number of particles u Assume same volume & temperature… u Increasing the number of particles will increase the number of collisions u Increased collisions means increased pressure 4

6. 1 atm u If you double the number of molecules

7. u You double the pressure. 2 atm

8. Number of particles u Decreasing the number of particles will decrease the number of collisions u Decreased collisions means decreased pressure 7

9. u As you remove molecules from a container 4 atm

10. u As you remove molecules from a container the pressure decreases 2 atm

11. u As you remove molecules from a container the pressure decreases u Until the pressure inside equals the pressure outside 1 atm

12. UNDERSTANDING CHECK 11

13. Volume (the size of the container) u Assume constant number of particles & temperature u If the volume decreases, molecules have less room to move u More collisions = increased pressure

14. 1 atm 4 Liters u As the volume of a gas decreases,

15. 2 atm 2 Liters u As the volume of a gas decreases, the pressure increases

16. Volume (size of the container) u If the volume increases, there is more room for the molecules to move u Fewer collisions = decreased pressure u SO… pressure and volume are INVERSELY related 15

17. UNDERSTANDING CHECK 16

18. Temperature u Assume volume and number of particles are constant u Raising the temperature of a gas makes the particles move faster u Faster movement = more collisions = increased pressure u Decreasing temp = slower movement = less collisions = decreased pressure u DIRECT relationship

19. u Start with 1 liter of gas at 1 atm pressure and 300 K u Heat it to 600 K 300 K

20. 600 K Pressure will increase to 2 atm.

21. u If volume not held constant, the volume will increase to 2 liters at 1 atm 300 K (Start) 600 K

22. What does that mean? u Assume pressure is constant u Increasing the temperature will lead to an increase in volume u And thus decreasing the temperature will lead to a decrease in volume u Temperature & volume have a DIRECT relationship 21

23. UNDERSTANDING CHECK 22

24. Dalton’s Law of Partial Pressures u The total pressure inside a container is equal to the sum of the partial pressure of each gas. u The partial pressure of a gas is the pressure of that individual gas hitting the wall. u P Total = P 1 + P 2 + P 3 + … u For example

25. u We can find out the pressure in the fourth container u By adding up the pressure in the first 3 2 atm1 atm3 atm6 atm

26. 25 Dalton’s Law u This means that we can treat gases in the same container as if they don’t affect each other. u We can figure out their pressures separately u And add them to get total pressure

27. Pressure measurements u Can use 3 different units Kilopascals (kPa) Atmospheres (atm) Millimeters of mercury (mm Hg) u Remember… 1 atm = 101.3 kPa = 760 mm Hg 26

28. Examples u What is the total pressure in a balloon filled with nitrogen & oxygen if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg?

29. Examples In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

30. Gas Laws u To make things easier, we are going to assume the gases behave ideally u Assume particles have no volume u Assume no attractive forces between molecules u Situation does not really exist but it... makes the math easier close approximation to reality

31. Boyle’s Law u At a constant temperature, pressure and volume are inversely related u As one goes up, the other goes down u P 1 V 1 = P 2 V 2

32. P V

33. u A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume? Example

34. u A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to a volume of 43 L? Example

35. 34 A sample of oxygen occupies 47.2 liters under a pressure of 1240 mm Hg at 25 o C. What volume would it occupy at 25 o C if the pressure were decreased to 730 mm Hg? (a) 27.8 L (b) 29.3 L (c) 32.3 L (d) 47.8 L (e) 80.2 L

36. Charles’ Law u The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. u K = degrees Celsius + 273 u V 1 = V 2 T 1 T 2

37. V T

38. Example u What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure?

39. Example u What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC?

40. 39 A sample of nitrogen occupies 5.50 liters under a pressure of 900 mm Hg at 25 o C. At what temperature will it occupy 10.0 liters at the same pressure? (a) 32 o C (b) -109 o C (c) 154 o C (d) 269 o C (e) 370 o C

41. Gay Lussac’s Law u The temperature and the pressure of a gas are directly related at constant volume. u P 1 = P 2 T 1 T 2

42. P T

43. 42 A rigid container at 25  C has a pressure of 430 kPa. What would the pressure be at 125  C? A. 574 kPa B. 320 kPa C. 86 kPa D. 2200 kPa E. 620 kPa

44. Examples u What is the pressure inside a 0.250 L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC?

45. Combined Gas Law u The Combined Gas Law deals with the situation where only the number of molecules stays constant. u Everything else varies u P 1 V 1 = P 2 V 2 T 1 T 2 u Lets us figure out one thing when two of the others change.

46. u The combined gas law contains all the other gas laws! u If the temperature remains constant. P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Boyle’s Law

47. u The combined gas law contains all the other gas laws! u If the pressure remains constant. P1P1 V1V1 T 1 x = P2P2 V2V2 T2T2 x Charles’ Law

48. u The combined gas law contains all the other gas laws! u If the volume remains constant. P1P1 V1V1 T1T1 x = P2P2 V2V2 T2T2 x Gay-Lussac’s Law

49. Examples u A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 17 atm. What is the new volume?

50. Examples u If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas?

51. Adding another variable u Avogadro’s Hypothesis – If T & P constant, 2 equal volumes of gas contain the same # of molecules u 22.4 L = 1 mole = 6.022 x 10 23 molecules u Volume has a DIRECT relationship to number of moles present u More volume = more moles u Add this to the combined gas law

52. The Ideal Gas Law u PV = nRT u Pressure (P) times Volume (V) equals the number of moles (n) times the Ideal Gas Constant (R) times the temperature in Kelvin (T). u Doesn’t compare 2 situations like other gas laws

53. u If pressure is in atm, R = 0.0821 u If pressure is in mm Hg, R = 62.4 u If pressure is in kPa, R = 8.31 The Ideal Gas Constant

54. Example u How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg?

55. Example u What is the pressure exerted by 1.8 g of H 2 gas in a 4.3 L balloon at 27ºC?