Chapter 14 The Behavior of Gases

1. Chapter 14The Behavior of Gases

2. Compressibility The measure of how much the volume of matter decreases under pressure.

3. Properties of a Gas • They are easy to compress. • They expand to fill their containers. • They occupy far more space than the liquids or solids from which they form.

4. Variables that describe a Gas • The four variables and their common units: 1. pressure (P) in kilopascals(kPa) 2. volume (V) in Liters(L) 3. temperature (T) in Kelvin(K) 4. number of moles (n) (mol)

5. Amount of Gas • When we inflate a balloon, we are adding gas molecules. • Increasing the number of gas particles increases the number of collisions • thus, the pressure increases • If temp. is constant- doubling the number of particles doubles pressure

6. Pressure and the number of molecules are directly related • More molecules means more collisions. • Fewer molecules means fewer collisions.

7. Common use? • Aerosol (spray) cans • gas moves from higher pressure to lower pressure • a propellant forces the product out • whipped cream, hair spray, paint

8. 2. Volume of Gas • In a smaller container, molecules have less room to move. • Hit the sides of the container more often. • As volume decreases, pressure increases. (think of a syringe)

9. 3. Temperature of Gas • Raising the temperature of a gas increases the pressure, if the volume is held constant. • The molecules hit the walls harder, and more frequently! • The only way to increase the temperature at constant pressure is to increase the volume.

11. Homework Section: 14.1 Practice Problems Review Due: 3/17/06

12. The Gas Laws • These will describe HOW gases behave. • Can be predicted by the theory. • Amount of change can be calculated with mathematical equations.

13. Boyle’s Law • At a constant temperature, gas pressure and volume are inversely related. • As one goes up the other goes down P1 x V1= P2 x V2

16. 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?

17. P1 = 1 atm V1 = 25 L P2 = 1.5atm V2 = ? L

18. P1 x V1 = V2 P2 1atm x 25L = V2 1.5atm P1 x V1= P2 x V2 16.7 L = V2

20. A balloon is filled with 73 L of air at 1.3atm pressure. What pressure is needed to change the volume to 43L?

21. P1 = 1.3atm V1 = 73 L P2 = ? atm V2 = 43 L

22. P1 x V1 = P2 V2 1.3atm x 73L = P2 43 L P1 x V1= P2 x V2 16.7 L = V2

23. V1 V2 T1 T2 = Charles’s Law • The volume of a gas is directly proportional to the Kelvin temperature, if the pressure is held constant.

26. What is the temperature of a gas expanded from 2.5 L at 25 ºC to 4.1L at constant pressure? V1 = 2.5L T1 = 25ºC + 273 = 298K V2 = 4.1L T2 = ?ºC

27. V1 V2 T1 T2 = T2 T1 x V2 V1 = T2 298K x 4.1L 2.5L = T2 = 488K = 216°C

28. What is the final volume of a gas that starts at 8.3 L and 17ºC, and is heated to 96ºC? V1 = 8.3L T1 = 17ºC + 273 = 290K T2 = 96°C + 273 = 369K V2 = ?ºC

29. V1 V2 T1 T2 = V1 x T2 V2 T1 = 8.3L x 369K V2 290K = V2 = 10.6L

30. P1 P2 T1 T2 = Gay-Lussac’s Law • The temperature and the pressure of a gas are directly related, at constant volume.

31. What is the pressure inside a 0.250 L can of deodorant that starts at 25 ºC and 1.2 atm if the temperature is raised to 100 ºC? P1 = 1.2atm T1 = 25ºC + 273 = 298K T2 = 100ºC + 273 = 373K P2 = ? atm

32. P2 T2 P1 T1 = P2 (373K)(1.2atm) 298K = P1 P2 T1 T2 = P2 = 1.5 atm

33. Combined Gas Law • The Combined Gas Law deals with the situation where only the number of molecules stays constant. • Formula: (P1 x V1)/T1= (P2 x V2)/T2 • This lets us figure out one thing when two of the others change.

34. A 15 L cylinder of gas at 4.8 atm pressure and 25 ºC is heated to 75 ºC and compressed to 17 atm. What is the new volume? P1 = 4.8 atm V1 = 15 L T1 = 25ºC + 273 = 298K P2 = 17 atm V2 = ? L T2 = 75ºC + 273 = 348K

35. P1 V1 P2 V2 T1 T2 = V2 P1 V1T2 P2 T1 = V1 (4.8 atm)(15L)(348K) (17 atm)(298K) = V1 = 4.9 L

36. P1 V1 P2 x V2 x = T1 T2 • The combined gas law contains all the other gas laws! • If the temperature remains constant... Boyle’s Law

37. P1 V1 P2 x V2 x = T1 T2 • The combined gas law contains all the other gas laws! • If the pressure remains constant... Charles’s Law

38. P1 V1 P2 x V2 x = T1 T2 • The combined gas law contains all the other gas laws! • If the volume remains constant... Gay-Lussac’s Law

39. Homework Section: 14.2 Practice Problems Review Due: 3/21/06

40. Ideal Gases • We are going to assume the gases behave “ideally”- obeys the Gas Laws under all temp. and pres.

41. Ideal Gases • An ideal gas does not really exist, but it makes the math easier and is a close approximation. • Particles have no volume. • No attractive forces.

42. Ideal Gases • There are no gases for which this is true; however, • Real gases behave this way at high temperature and low pressure.

43. The Ideal Gas Law #1 • Equation: P x V = n x R x T • Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. • This time R does not depend on anything, it is really constant • R = 8.31 (L x kPa) / (mol x K)

44. The Ideal Gas Law • We now have a new way to count moles (amount of matter), by measuring T, P, and V. We aren’t restricted to STP conditions P x V R x T n =

45. Examples • How many moles of air are there in a 2.0 L bottle at 19 ºC and 747 mm Hg? • What is the pressure exerted by 1.8 g of H2 gas in a 4.3 L balloon at 27 ºC? • Samples 12-5, 12-6 on pages 342 and 343

46. 6. Ideal Gas Law #2 • P x V = m x R x T M • Allows LOTS of calculations! • m = mass, in grams • M = molar mass, in g/mol • Molar mass = m R T P V

47. Density • Density is mass divided by volume m V so, m M P V R T D = D = =

49. Ideal Gases don’t exist • Molecules do take up space • There are attractive forces • Otherwise there would be no liquids formed

50. Real Gases behave like Ideal Gases. • When the molecules are far apart • The molecules do not take up as big a percentage of the space • We can ignore their volume. • This is at low pressure