2. Gases Chapter 12

3. 2 Importance of Gases Airbags fill with N 2 gas in an accident.Airbags fill with N 2 gas in an accident. Gas is generated by the decomposition of sodium azide, NaN 3.Gas is generated by the decomposition of sodium azide, NaN 3. 2 NaN 3  2 Na + 3 N 22 NaN 3  2 Na + 3 N 2 Air Bag VideoAir Bag VideoAir Bag VideoAir Bag Video

4. 3 General Properties of Gases There is a lot of “free” space in a gas.There is a lot of “free” space in a gas. Gases can be expanded infinitely.Gases can be expanded infinitely. Gases fill containers uniformly and completely.Gases fill containers uniformly and completely. Gases diffuse and mix rapidly.Gases diffuse and mix rapidly.

5. 4 Properties of Gases Gas properties can be modeled using math. Model depends on— V = volume of the gas (L, mL, dm 3 )V = volume of the gas (L, mL, dm 3 ) T = temperature (K)T = temperature (K) –ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! n = amount (moles)n = amount (moles) P = pressure (atmospheres or Pascal)P = pressure (atmospheres or Pascal)

6. 5 Pressure Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643)

7. 6 Pressure Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink)

8. 7PressureColumn height measures Pressure of atmosphere 1 standard atmosphere (atm) = 760 mm Hg (or torr) = 29.92 inches Hg = 14.7 pounds/in2 (psi) = about 34 feet of water = 101.3 kPa (SI unit is PASCAL = Pa)

9. 8 Pressure Conversions A. What is 475 mm Hg expressed in atm? 1 atm 760 mm Hg B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 760 mm Hg 14.7 psi = 1.52 x 10 3 mm Hg = 0.625 atm 475 mm Hg x 29.4 psi x

10. 9 Pressure Conversions A. What is 2 atm expressed in torr? B. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa?

11. 10 Boyle’s Law and Kinetic Molecular Theory How are pressure & volume related?

12. 11 Boyle’s Law This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). P goes up as V goes down. P 1 V 1 = P 2 V 2 Robert Boyle (1627-1691). Son of Earl of Cork, Ireland.

13. 12 Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire.

14. 13 Boyle’s Law Problems A high-altitude balloon contains 30.0L of helium gas at 1 atmosphere. What is the volume when the balloon rises to an altitude where the pressure is only 0.25 atm?

15. 14 Charles’s Law and Kinetic Molecular Theory How are volume and temperature related?

16. 15 Charles’s Law V and T are directly proportional. V 1 V 2 = T 1 T 2 If one temperature goes up, the volume goes up!If one temperature goes up, the volume goes up! Jacques Charles (1746- 1823). Isolated boron and studied gases. Balloonist.

17. 16 Charles’s original balloon Modern long-distance balloon

18. A sample of carbon monoxide gas occupies 3.20 L at 125 o C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = 398 K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V1 1.54 L x 398 K 3.20 L = = 192 K 5.3

19. A set amount of gas at 89 o C occupies a volume of 0.67 L. At what Celsius temperature will the volume become to 1.12 L? = 330 o C

20. 19 What happens to the pressure if volume were kept constant and temp. was changed? What happens to the motion of the particles? This is Gay-Lussac’s Law Joseph Louis Gay- Lussac (1778-1850)

21. 20 Gay-Lussac’s Law P and T are directly proportional. P 1 P 2 = T 1 T 2 If one temperature goes up, the pressure goes up!If one temperature goes up, the pressure goes up! Joseph Louis Gay- Lussac (1778-1850)

22. A gas in a sealed container has a pressure of 125 kPa at a temperature of 30.0 o C. If the pressure in the container is increased to 201 kPa, what is the new temperature of the gas? = 214 o C

23. A rigid plastic container holds 1.00 L methane gas at 660 torr pressure when the temperature is 22.0 o C. How much more pressure will the gas exert if the temperature is raised to 44.6 o C? = 51 torr more

24. 23 Combined Gas Law The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION! P 1 V 1 P 2 V 2 = T 1 T 2 No, it’s not related to R2D2

25. 24 Combined Gas Law If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! = P1P1 V1V1 T1T1 P2P2 V2V2 T2T2 Boyle’s Law Charles’ Law Gay-Lussac’s Law

26. 25 And now, we pause for this commercial message from STP OK, so it’s really not THIS kind of STP… STP in chemistry stands for Standard Temperature and Pressure Standard Pressure = 1 atm (or an equivalent) Standard Temperature = 0 o C (273 K) STP allows us to compare amounts of gases between different pressures and temperatures

27. 26 Combined Gas Law Problem A sample of neon gas is collected at a pressure of 2.7 atm and a temperature of 295.0 K. It has a volume of 2.25 L. What would be the volume of this gas at STP? F: P 1 = 2.7 atm V 1 = 2.25 L T 1 = 295.0 K P 2 = 1 atm V 2 = ? T 2 = 0 o C

28. 27 Calculation P 1 = 2.7 atm V 1 = 2.25 L T 1 = 295.0 K P 2 = 1 atm V 2 = ? T 2 = 0 o C P 1 V 1 P 2 V 2 = P 1 V 1 T 2 = P 2 V 2 T 1 T 2 T 1 V 2 = P 1 V 1 T 2 P 2 T 1 V 2 = 2.7 atm x 2.25 L x 273 K 1 atm x 295.0 K 5.62 L = 5.62 L

29. 28 Learning Check A student collects a 3.5 L sample of hydrogen gas at 22.0 o C and 91.9 kPa. What pressure would the hydrogen be at when the temperature is held constant but the volume decreases to 2.0L?

30. 29 One More Practice Problem A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

31. 30 Try This One A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

32. 31 Avogadro’s Hypothesis Avogadro’s Hypothesis Equal volumes of gases at the same T and P have the same number of molecules. V = n (RT/P) = kn V and n are directly related. twice as many molecules

33. 32 Avogadro’s Hypothesis The gases in this experiment are all measured at the same T and P. Animation of Avogadro’s Hypothesis Animation of Avogadro’s Hypothesis

34. 33 IDEAL GAS LAW Brings together gas properties. Can be derived from experiment and theory. BE SURE YOU KNOW THIS EQUATION! P V = n R T

35. 34 Using PV = nRT P = Pressure V = Volume T = Temperature N = number of moles R is a constant, called the Ideal Gas Constant Instead of learning a different value for R for all the possible unit combinations, we can just use one value and convert the units to match R. R = 0.0821 R = 0.0821 L atm mol K

36. 35 Using PV = nRT How much N 2 is required to fill a small room with a volume of 27,000 L to P that is 0.98 atm at 25 o C? Solution Solution 1. Write down what you are given V = 27,000 L V = 27,000 L T = 25 o C + 273 = 298 K T = 25 o C + 273 = 298 K P = 0.98 atm P = 0.98 atm And we always know R, 0.0821 L atm / mol K

37. 36 Using PV = nRT How much N 2 is required to fill a small room with a volume of 27,000 L to P that is 0.98 atm at 25 o C? Solution Solution 2. Now plug in those values and solve for the unknown. PV = nRT n = 1.1 x 10 3 mol RT RT

38. 37 Learning Check Dinitrogen monoxide (N 2 O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (in atmospheres) in the tank in the dentist office?

39. 38 Learning Check A 5.0 L cylinder contains oxygen gas at 20.0°C and 0.97 atm. How many grams of oxygen are in the cylinder?

40. 39 Deviations from Ideal Gas Law Real molecules have volume. The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves. There are intermolecular forces. An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions. –Otherwise a gas could not condense to become a liquid.

41. 40 Gases in the Air The % of gases in air Partial pressure (STP) 78.08% N 2 593.4 mm Hg 20.95% O 2 159.2 mm Hg 0.94% Ar 7.1 mm Hg 0.03% CO 2 0.2 mm Hg P AIR = P N + P O + P Ar + P CO = 760 mm Hg 2 2 2 Total Pressure760 mm Hg

42. 41 Dalton’s Law of Partial Pressures What is the total pressure in the flask? P total in gas mixture = P A + P B +... Therefore, P total = P H 2 O + P O 2 = 0.48 atm Dalton’s Law: total P is sum of PARTIAL pressures. 2 H 2 O 2 (l)  2 H 2 O (g) + O 2 (g) 0.32 atm 0.16 atm 0.32 atm 0.16 atm

43. 42 Dalton’s Law John Dalton 1766-1844

44. 43 Collecting a gas “over water” Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected “over water”, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial Pressures becomes useful.

45. 44 Table of Vapor Pressures for Water p. 395

46. 45 Solve This! A student collects some hydrogen gas over water at 20 degrees C and 768 torr. What is the pressure of the gas?

47. 46 GAS DENSITY Highdensity Lowdensity 22.4 L of ANY gas AT STP = 1 mole

48. 47 Health Note When a scuba diver is several hundred feet under water, the high pressures cause N 2 from the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N 2 will form bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O 2 in scuba tanks used for deep descents.

49. 48 Gases and Stoichiometry 2 H 2 O 2 (l) ---> 2 H 2 O (g) + O 2 (g) Decompose 1.1 g of H 2 O 2 in a flask with a volume of 2.50 L. What is the volume of O 2 at STP? Bombardier beetle uses decomposition of hydrogen peroxide to defend itself.

50. 49 Gas Stoichiometry: Practice! A.What is the volume at STP of 4.00 g of CH 4 ? B. How many grams of He are present in 8.0 L of gas at STP?

51. 50 What if it’s NOT at STP? 1. Do the problem like it was at STP. (V 1 ) 2. Convert from STP (V 1, P 1, T 1 ) to the stated conditions (P 2, T 2 )

52. 51 Try this one! How many L of O 2 are needed to react 28.0 g NH 3 at 24°C and 0.950 atm? 4 NH 3 (g) + 5 O 2 (g) 4 NO(g) + 6 H 2 O(g)

53. 52 How many L of O 2 are needed to react 28.0 g NH 3 at 24°C and 0.950 atm? 4 NH 3 (g) + 5 O 2 (g) 4 NO(g) + 6 H 2 O(g) Find mole of O 2 28.0 g NH 3 x 1 mol NH 3 x 5 mol O 2 x 22.4 L O 2 17.0 g NH 3 4 mol NH 3 1 mol O 2 At STP, V = 46.1 L  V 1, P 1, and T 1 P 1 V 1 P 2 V 2 = P 1 V 1 T 2 = P 2 V 2 T 1 T 1 T 2 V 2 = P 1 V 1 T 2 (1 atm) (46.1 L) (297K) P 2 T 1 (0.950 atm) (273 K) = 52.8 L = 46.1 L AT STP

54. 53 GAS DIFFUSION AND EFFUSION diffusion is the gradual mixing of molecules of different gases.diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container.effusion is the movement of molecules through a small hole into an empty container.

55. 54 GAS DIFFUSION AND EFFUSION Graham’s law governs effusion and diffusion of gas molecules. Thomas Graham, 1805-1869. Professor in Glasgow and London. Rate of effusion is inversely proportional to its molar mass.

56. 55 GAS DIFFUSION AND EFFUSION Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is proportional to Tproportional to T inversely proportional to M.inversely proportional to M. Therefore, He effuses more rapidly than O 2 at same T. He

57. 56 Gas Diffusion relation of mass to rate of diffusion HCl and NH 3 diffuse from opposite ends of tube. Gases meet to form NH 4 Cl HCl heavier than NH 3 Therefore, NH 4 Cl forms closer to HCl end of tube. HCl and NH 3 diffuse from opposite ends of tube. Gases meet to form NH 4 Cl HCl heavier than NH 3 Therefore, NH 4 Cl forms closer to HCl end of tube.