10.1 Characteristics of Gases

3. 10.1 Characteristics of Gases • Air behaves physically as one gaseous material • N2 (78%), O2 (21%) and Ar (0.9%) • Only a few elements exist as gases under standard conditions • H2, N2, O2, F2, and Cl2, the noble gases (He, Ne, Ar, Kr, Xe) • Gas molecules are relatively far apart • Each molecule behaves largely as though the others are not present • Readily compressible and expansible • Forms homogeneous mixtures with other gases • Low density

4. 10.1 Characteristics of Gases

5. 10.2 Pressure • Atmospheric Pressure and the Barometer • Pressure is defined as:

6. 10.2 Pressure • Atmospheric Pressure and the Barometer • In the 17th century, people believed that the atmosphere had no weight • Torricelli’s experiment • Proved the atmosphere has weight • Pascal’s experiment • Measured the height of the mercury column at two different places • Supported Torricelli’s explanation • Standard atmospheric pressure Figure 10.2 A mercury barometer invented by Torricelli

7. 10.2 Pressure • Atmospheric Pressure and the Barometer • Manometer • This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

8. 10.3 The Gas Law • Blood pressure is reported by two values • Systolic pressure: maximum pressure (pumping) • Diastolic pressure: resting pressure mercury manometer or related device closed, air-filled cuff stethoscope • Hypertension is abnormally high blood pressure. The usual criterion is a blood pressure greater than 140/90.

9. 10.3 The Gas Law • Boyle’s Law • Pressure-volume relationship • The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure

10. 10.3 The Gas Law • Boyle’s Law • For a fixed quantity of gas at constant temperature, the volume of the gas is inversely proportional to its pressure

11. 10.3 The Gas Law • Charles’s Law Temperature-volume relationship The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

12. 10.3 The Gas Law • Avogadro’s Law Quantity-volume relationship Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas

13. 10.3 The Gas Law • Avogadro’s Law At the same volume, pressure and temperature, samples of different gases have the same number of molecules but different masses

14. 10.4 The Ideal-Gas Equation The term R is called the gas constant R = 0.08206 L-atm/mol-K = 8.314 J/mol-K Molar volume: the volume occupied by one mole of ideal gas at STP (273.15K and 1 atm), 22.41 L

15. 10.4 The Ideal-Gas Equation One mole of an ideal gas at STP occupies a volume of 22.41 L. One mole of various real gases at STP occupies close to this ideal volume ▲ Figure 10.11 Comparison of molar volumes at STP

16. Sample Exercise 10.4 Using the Ideal-Gas equation Calcium carbonate, CaCO3(s), decomposes upon heating to give CaO(s) and CO2(g). A sample of CaCO3 is decomposed, and the carbon dioxide is collected in a 250-mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31 °C. How many moles of CO2 gas were generated?

17. Sample Exercise 10.5 The gas pressure in an aerosol can is 1.5 atm at 25 °C. Assuming that the gas inside obeys the ideal-gas equation, what would the pressure be if the can were heated to 450 °C?

19. 10.5 FurtherApplications • Gas Densities and Molar Mass

20. 10.5 FurtherApplications • Gas Densities and Molar Mass ▲ Figure 10.12 Carbon dioxide gas flows downhill because it is denser than air.

21. 10.5 FurtherApplications • Gas Densities and Molar Mass

22. 10.5 FurtherApplications • Volumes of Gases in Chemical Reactions

23. 10.6 Gas Mixtures and Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. - Dalton’s law of partial pressure Partial pressure The pressure exerted by a particular component of a mixture of gases

24. Sample Exercise 10.10 Applying Dalton’s Law to Partial Pressures A gaseous mixture made from 6.00 g O2 and 9.00 g CH4 is placed in a 15.0-L vessel at 0 °C. What is the partial pressure of each gas, and what is the total pressure in the vessel?

25. 10.6 Gas Mixtures and Partial Pressures • Partial Pressure and Mole Fractions Each gas in a mixture behaves independently We can relate the amount of a given gas in a mixture to its partial pressure

26. Sample Exercise 10.11 Relating Mole Fractions to Partial Pressures A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol% CO2, 18.0 mol% O2, and 80.5 mol% Ar. (a) Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 121-L space at 295 K, how many moles of O2 are needed?

27. 10.6 Gas Mixtures and Partial Pressures • Collecting Gases over Water How to measure the amount of gases generated from a chemical reaction ▲ Figure 10.15 Collecting water-insoluble gas over water.

28. 10.6 Gas Mixtures and Partial Pressures • Collecting Gases over Water

29. 10.6 Gas Mixtures and Partial Pressures 122.6 g/mol

30. 10.7 Kinetic-molecular Theory • This is a model that aids in our understanding of what happens to gas particles as environmental conditions change. • Summaries of the theory • Gases consist of large numbers of molecules that are in continuous, random motion • The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained • Attractive and repulsive forces between gas molecules are negligible

31. 10.7 Kinetic-molecular Theory • This is a model that aids in our understanding of what happens to gas particles as environmental conditions change. • Summaries of the theory • Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant • The average kinetic energy of the molecules is proportional to the absolute temperature • The pressure of a gas is caused by collisions of the molecules with the walls of the container

32. 10.7 Kinetic-molecular Theory • Distributions of Molecular Speed • Although the molecules in a sample of gas have an average kinetic energy and hence an average speed, the Individual molecules move at varying speeds mp: most probable speed av: average speed rms: root-mean-square speed

33. 10.7 Kinetic-molecular Theory • Applications to the Gas Laws • Effect of a volume increase at constant temperature • If the volume is increased, the molecules must move a longer distance between collisions → pressure decreases • Effect of a temperature increase at constant volume • An increase in T means an increase the average kinetic E of the molecule and thus increase in u • If there is no change in volume, there will be more collisions with the walls per unit time → pressure increases

34. 10.7 Kinetic-molecular Theory (a) Constant (b) Constant (c) Increase (d) Increase

35. 10.8 Molecular Effusion and Diffusion • At the same T, two gases have the same KEave, m(μrms)2 • Therefore, the particles of the lighter gas must have a higher rms speed than the particles of the heavier one. ▲ Figure 10.19 The effect of molecular mass on molecular speeds.

36. 10.8 Molecular Effusion and Diffusion • Graham’s Law of Effusion • Effusion (유출) is the escape of gas molecules through a tiny hole into an evacuated space. ▲ Figure 10.19 Effusion. Gas molecules in top half effuse through pinhole only when they happen to hit pinhole

37. 10.8 Molecular Effusion and Diffusion • Graham’s Law of Effusion

38. 10.8 Molecular Effusion and Diffusion • Diffusion and Mean Free Path • Diffusion (확산) is the spread of one substance throughout a space or throughout a second substance • The diffusion of gases is much slower than molecular speeds because of molecular collisions • The mean free path of a molecule is the average distance traveled by the molecule between collisions • The mean free path for air molecule • 60 nm at sea level • 10 cm at 100 km in altitude

39. 10.9 Real Gases • Although the ideal-gas equation is a very useful description of gases, all real gases fail to obey the relationship to some degree ▲ Figure 10.24 Gases behave more ideally at low pressure than at high pressure. The volume of gas molecules is not negligible at high pressure. ▲ Figure 10.25 In any real gas, attractive intermolecular forces reduce pressure to values lower than in an ideal gas.

40. 10.9 Real Gases At high P, gas volumes are not negligible Attractive forces between molecules reduce the pressure ▲ Figure 10.22 The effect of pressure on the behavior of several real gases at constant T. The deviations increases with increasing P.

41. 10.9 Real Gases • Cooling a gas increase the chance for molecules to interact with each other ▲ Figure 10.23 The effect of temperature and pressure on the behavior of nitrogen gas. The deviations increase with decreasing T.

42. 10.9 Real Gases • The van der Waals Equation • The ideal-gas equation can be adjusted to take the deviations from ideal behavior into account • The van der Waals Equation = Videal = Pideal

43. 10.9 Real Gases • The van der Waals Equation • a and b values increase with mass of the molecule and the complexity of its structure

44. 10.9 Real Gases

45. 10.9 Real Gases

46. 10.9 Real Gases Homework Practice Exercises p397, 399, 402, and 412 Due on 06-13 (Thur)