1. Chapter 10 Gases

2. 10.7: Ideal Gases and KMT Ideal gases fit all assumptions of kinetic molecular theory: Gas particles are far apart (mostly empty space) Lower density; compressible Elastic collisions Kinetic energy doesn’t change (KE related to temp) Constant, random motion KE is greater than attractive forces keeping a substance liquid/solid No attraction/repulsion Average KE depends on temperature All gases at same temp have same KE KE=1/2mv 2  lighter gases are faster than heavier gases

3. 10.7: Real Gases and KMT KMT only applies to Ideal Gases (don’t exist) Real gases DO behave NEARLY ideally if temperature isn’t too low or pressure too high -gases that have little attraction for each other behave more like ideal gases -noble gases, nonpolar diatomic molecules

4. 10.1 Gases ● Expand to fill container ● Volume of gas = volume of container ● Highly compressible ● Form homogeneous mixtures ● Example: liquid gas/water = 2 separate layers; vapors above the liquids homogeneous mixture ● Diffusion and effusion ● Diffusion – mixing gases from spontaneous motion ● Effusion – particle under pressure pass through a tiny opening ● Which would diffuse/effuse faster – He or Ne?

5. Do the compounds in Table 10.1 have small (less than 100g/mol) or large molecular weights?

6. 10.2 Pressure ● Pressure : force that acts on a given area – P=F/A ● Gravitational force causes atmosphere to push down on the earth – What happens to bottle on airplane? ● Units: pascal – 1bar = 10 5 Pa or 100kPa = 1 bar – Psi, lbs/in 2 – Sea level = 14.7psi

7. 10.2 Pressure ● Barometer – Torricelli (1600's) – 760 mm long tube filled with mercury and put in a mercury filled dish – Hg level moves up/down in response to atmospheric pressure ● Standard atmospheric pressure – 760 mmHg = 101.3kPa = 1 atm = 760 torr = 101.3 bar ● Manometer – fluid filled U-shaped tube; one end open, other end attached to gas being measured – Also: sphygmomanometer

8. 10.2: Pressure ● Convert: a. 0.357 atm to torr b. 6.6x10 -2 torr to atm c. 147.2kPa to torr d. 745 torr to kPa e. 902mbar to atm

9. 10.3: Gas Laws ● Define state of a gas: – Temperature – Pressure – Volume – Amount (usually moles) ● Gas Laws: relationships between above factors (keeping 2 constant)

10. 10.3: Gas Laws ● Boyle's Law: pressure-volume ● inverse relationship

11. 10.3: Gas Laws ● Charles Law: temperature-volume ● Direct relationship – Notice dashed line through -273C

12. 10.3: Gay-Lussac’s Law Relates pressure and temperature Also a direct relationship

13. 10.3: Gas Laws ● Avogadro's Law: quantity-volume – Hypothesis: equal volume of gases at the same temp and pressure contain equal number of molecules (1mol = 22.4L) – Volume and number of moles directly proportional

14. 10.3: Gas Laws ● A gas is confined to a cylinder with a movable piston. Consider the following: a. heat the gas from 298K to 360K at constant P b. reduce the volume from 1L to 0.5L at constant T c. inject additional gas, keeping T&V constant ● How will the change affect the average distance between molecules, the pressure of the gas and the number of moles of gas in the cylinder?

15. 10.3: Gas Laws

16. ● What happens to the density of a gas as: a. gas is heated to a constant-volume container b. gas is compressed at constant temp c. additional gas is added at constant volume

17. 10.4: Ideal Gas Equation ● PV = nRT ● R = gas constant – Different values – Book uses 0.08206 Latm/molK ● p. 392 has other values ● Standard Temperature and Pressure – 273K; 1 atm – 1 mole of gas at STP = 22.4L

18. 10.4: Ideal Gas Equation ● Suggest an explanation for the “ideal” nature of helium compared to the other gases

19. 10.4: Ideal Gas Equation ● Calcium carbonate, the principal compound in limestone, decomposes upon heating to CaO(s) and CO 2 (g). A sample of CaCO 3 is decomposed and the CO 2 collected in a 250ml flask. After decomposition is complete, the gas has a pressure of 1.3 atm at 31C. How many moles of CO 2 were generated?

20. 10.4: Ideal Gas Equation ● Tennis balls are usually filled with either air or N 2 gas to a pressure above atmospheric pressure to increase their bounce. If a tennis ball has a volume of 144cm 3 and contains 0.33g of N 2 gas, what is the pressure inside the ball at 24C?

21. 10.4: Ideal Gas Equation ● Combined Gas Law – used for a fixed amount of a gas under changing conditions P 1 V 1 = P 2 V 2 T 1 T 2

22. 10.4: Ideal Gas Equation ● The gas pressure in an aerosol can is 1.5atm at 25C. Assuming the gas obeys the ideal gas equation, what is the pressure when the can is heated to 450C?

23. 10.4: Ideal Gas Equation ● The pressure in a natural gas tank is maintained at 2.20atm. On a day when the temperature is -15C, the volume of gas in the tank is 3.25x10 3 m 3. What is the volume of the same quantity of gas on a day when the temperature is 31C?

24. 10.4: Ideal Gas Equation ● An inflated balloon has a volume of 6.0L at sea level (1.0atm) and is allowed to ascend until the pressure is 0.45atm. During ascent the temperature of the gas falls from 22C to -21C. Calculate the volume of the balloon at its final altitude.

25. 10.4: Ideal Gas Equation ● A 0.50 mol sample of oxygen gas is confined at 0C and 1.0atm in a cylinder with a movable piston. The piston compresses the gas so that the final volume is half the initial volume and the final pressure is 2.2 atm. What is the final temperature of the gas in degrees C?

26. 10.5: Gas Density & Molar Mass d=m/V  n/V = P/RT n times molar mass = m d= P x molar mass/RT SO…can solve for density using the ideal gas law What is the density of carbon tetrachloride vapor at 714 torr and 125C?

27. 10.5: Gas Density and Molar Mass The mean molar mass of the atmosphere at the surface of Titan (Saturn’s largest moon) is 28.6g/mol. The surface temperature is 95K and the pressure is 1.6atm. Assuming ideal behavior, calculate the density of Titan’s atmosphere.

28. 10.5: Gas Density and Molar Mass A large evacuated flask initially has a mass of 134.567g. When the flask is filled with a gas of unknown molar mass to a pressure of 735 torr at 31C, its mass is 137.456g. When the flask is evacuated again and filled with water at 31C, its mass is 1067.9g. The density of water at this temperature is 0.997g/mL. Assuming the ideal gas equation applies, calculate the molar mass of the gas.

29. 10.5: Gas Density and Molar Mass Calculate the average molar mass of dry air if it has a density of 1.17g/L at 21C and 740.0 torr.

30. 10.5: Volume of Gases in Chemical Reactions Coefficients in balanced chemical equation gives the relative amount (moles) of reactants and products Ideal gas equation relates moles to P, V, T Automobile air bags are inflated by nitrogen gas generated by the rapid decomposition of sodium azide (NaN 3 ). If an air bag has a volume of 36L and is to be filled with nitrogen gas at 1.15atm and 26.0C, how many grams of sodium azide must be decomposed?

31. 10.5: Volume of Gases in Chemical Reactions In the first step in the industrial process for making nitric acid, ammonia reacts with oxygen in the presence of a suitable catalyst to form nitric oxide (NO) and water vapor. How many liters of ammonia at 850C and 5.00 atm are required to react with 1.00mol of oxygen in this reaction?

32. 10.6: Gas Mixtures and Partial Pressure Dalton’s Law of Partial Pressure: the total pressure of a mixture of gases is equal to the sum of the individual pressures of the gases -partial pressure: pressure exerted by an individual gas in a mixture of gases P T = P A + P B + P C +…

33. 10.6: Gas Mixtures and Partial Pressure How is the pressure exerted by N 2 gas affected when some O 2 gas is introduced into a container if the temperature and volume remain constant?

34. Dalton's Law of Partial Pressures What is the pressure of oxygen gas if a mixture contains 4 moles oxygen, 2 moles nitrogen and 2 moles of carbon dioxide. The total pressure is 1.00 atm.

35. Dalton's Law of Partial Pressures A sample of hydrogen gas is collected over water at 25ºC. The vapor pressure of water at 25ºC is 23.8 mmHg. If the total pressure is 523.8 mmHg, what is the partial pressure of the hydrogen?

36. 10.6: Gas Mixtures and Partial Pressure A mixture of 6.00g O 2 (g) and 9.00g CH 4 (g) is placed in a 15.0L vessel at 0C. What is the partial pressure of each gas and what is the total pressure in the vessel?

37. 10.6: Gas Mixtures and Partial Pressure Looking at PV= nRT, at constant V&T, the pressure of a gas is determined by the moles of gas -mole fraction: ratio of moles of part of the mixture to the total moles in the mixture X A =n A /n T P A = X A xP T

38. 10.6: Gas Mixtures and Partial Pressure Air is 72% N 2 (the mole fraction would be 0.72). What is the partial pressure of N 2 if the barometric pressure is 760torr? -because N 2 is 72% of the mixture, it contributes 72% of the total pressure

39. 10.6: Gas Mixtures and Partial Pressure A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent CO 2, 18.0 mol percent O 2 and 80.5 mol percent Ar. -What is the partial pressure of O 2 if the total pressure is 745torr? -If the atmosphere is to be held in a 121L space at 295K, how many moles of O 2 are needed?

40. 10.6: Gas Mixtures and Partial Pressure From data gathered by Voyager I, scientists have estimated the composition of the atmosphere of Titan, Saturn’s largest moon. The pressure on the surface of Titan is 1220 torr. The atmosphere consists of 82 mol percent N 2, 12 mol percent Ar, and 6.0 mol percent CH 4. Calculate the partial pressure of each gas.

41. 10.6: Gas Mixtures and Partial Pressure Collecting Gases over Water

42. 10.6: Gas Mixtures and Partial Pressure When a sample of KClO 3 is partially decomposed in the setup shown in the previous slide, the volume of gas collected is 0.250L at 26C and 765torr total pressure. a. how many moles of O 2 is collected? b. how many grams of KClO 3 were decomposed

43. 10.6: Gas Mixtures and Partial Pressure Ammonium nitrite decomposes on heating to form nitrogen gas and liquid water. When a sample of ammonium nitrite is decomposed and N 2 gas is collected over water at 26C and 745 torr total pressure. How many grams of ammonium nitrite were decomposed?

44. 10.8: Molecular Effusion & Diffusion Diffusion: movement of gas particles from an area of high concentration to an area of low concentration -occurs in a space where other gas particles are present Effusion: movement of gas particles through a tiny hole

45. 10.8: Molecular Effusion & Diffusion Because pressure and temperature are constant in this figure but volume changes, which other quantity in the ideal gas equation must also change?

46. Graham’s Law of Effusion: The rate of effusion of a gas is inversely proportional to the square root of its molecular weight. Rate 1 = “Rate” refers to molecules that effuse per second or liters of gas that effuse per second (it is not time!) 10.8: Molecular Effusion & Diffusion

47. An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is 0.355 times the rate at which O 2 gas effuses at the same temperature. Calculate the molar mass of the unknown and identify it.

48. 10.8: Molecular Effusion & Diffusion Calculate the ratio of the effusion rates of nitrogen gas and oxygen gas

49. 10.8: Molecular Effusion & Diffusion Notice how fast the speeds are... Why is it that it could take several minutes for a gas (like perfume) to spread throughout a room?

50. 10.8: Molecular Effusion & Diffusion Mean free path Average distance traveled by a molecule between collisions Pressure

51. 10.9: Real Gases n = PV/RT For 1 mole of gas, PV/RT should = 1 at all pressure Plot PV/RT vs Pressure, notice that it is not 1 – does not behave like an ideal gas at high pressure For lower pressures (inset) the gases do behave more ideally

52. 10.9: Real Gases Under which conditions do you expect helium gas to deviate most from ideal behavior? a. 100K and 1atm b. 100K and 5 atm c. 300K and 2 atm

53. 10.9: Real Gases Most ideal to least ideal: 1. light nonpolar molecules 2. heavier nonpolar molecules 3. polar molecules 4. molecules with hydrogen bonding

54. 10.9: Real Gases Real gases do have attractions for each other and have volume High temp and low pressure case the gas to behave more ideally Van der Waals equation takes into account these attractions: (P + n 2 a/V 2 )(V-nb) = nRT a and b are constants (see p. 412)

55. Avogadro's Law Equal volumes of gas at the same temperature and pressure contain the same number of particles V 1 /n 1 = V 2 /n 2