Chapter 10 Gases

1. Chapter 10Gases Mrs. Warren Kings High School AP Chemistry 2013-2014

2. Characteristics of Gases • Unlike liquids and solids, gases • Expand spontaneously to fill their containers. • Volume of gas = volume of container • Are highly compressible. • Have extremely low densities.

3. F A P = Pressure • Pressure is the amount of force applied to an area: • Atmospheric pressure is the force (weight) of air per unit of surface area.

4. Units of Pressure • Pascals • 1 Pa = 1 N/m2 • Bar • 1 bar = 105 Pa = 100 kPa Quick Check: Assume the top of your head has a surface area on 10 in. x 10 in. How many pounds of air are you carrying on your head if you are at sea level?

5. Units of Pressure • mmHg or torr • These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury. • Atmosphere • 1.00 atm = 760 torr

6. Standard Pressure • Normal atmospheric pressure at sea level is referred to as standard pressure. • It is equal to • 1.00 atm • 760 torr (760 mmHg) • 101.325 kPa

7. Converting Between Units of Pressure • Convert 0.357 atm to torr • Convert 6.6 x 10-2 torr to atm • Convert 147.2 kPa to torr • Convert 745 torr to kPa • Convert 902 mbar to atm

8. Manometer The manometer is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

9. Manometer • On a certain day the atmospheric pressure is 764.7 torr. A sample of gas is placed in a flask attached to an open-end Hg manometer. The heights are given in the figure to the right. What is the pressure of the gas in the flask in atmospheres and in kPa?

10. Gas Laws • Four variables are needed to define the physical condition, or state, of a gas: • What are they?

11. Pressure-Volume Relationship

12. Boyle’s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

13. PV = k • Since • V = k (1/P) • This means a plot of V versus 1/P will be a straight line. P and V are Inversely Proportional A plot of V versus P results in a curve.

14. Charles’s Law • The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

15. V T = k • So, • A plot of V versus T will be a straight line. Charles’s Law

16. V = kn • Mathematically, this means Avogadro’s Law • Avogadro’s Hypothesis: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. • Avogadro’s Law: The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.

17. Lussac’s Law • What variables are related in Lussac’s law? • What variables remain constant? • Mathematical equation? • Direct/Inverse Relationship?

18. Gas Law Variable Effects • Suppose we have a gas confined to a cylinder with a movable piston. Consider the following changes (assuming no leaks) • Heat the gas from 298K to 360K at constant pressure. • Reduce the volume from 1L to 0.5L at constant temperature. • Inject additional gas, keeping temperature and volume constant. • Indicate how each change affects the average distance between molecules, the pressure, and the number of moles of gas in the cylinder. • What happens to the density of a gas as • The gas is heated in a constant-volume container • The gas is compressed at constant temperature • Additional gas is added to a constant-volume container

19. nT P V Ideal-Gas Equation • So far we’ve seen that V 1/P (Boyle’s law) VT (Charles’s law) Vn (Avogadro’s law) • Combining these, we get

20. Ideal-Gas Equation The constant of proportionality is known as R, the gas constant.

21. nT P V nT P V= R Ideal-Gas Equation The relationship then becomes or PV = nRT

22. Ideal Gases • What is an Ideal Gas? • In deriving the ideal gas law we assume the following: • Molecules of an ideal gas do not interact with one another • The combined volume of the molecules is much smaller than the volume the gas occupies; thus we consider the molecules taking up no space in the container.

23. Ideal Gases v. Real Gases

24. Ideal Gas Law • Calcium carbonate decomposes upon heating. The carbon dioxide produced in the reaction is collected in a 250 mL flask. After 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? • Tennis balls are usually filled with either air or nitrogen gas to a pressure above atmospheric pressure to increase their bounce. If a tennis ball has a volume of 144 cm3 and contains 0.33 g of nitrogen gas, what is the pressure inside the ball at 24°C?

25. Gas Laws • The gas pressure in an aerosol can is 1.5 atm at 25°C. Assume that the gas obeys ideal conditions, what is the pressure when the can is heated to 450°C? • An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend until the pressure is 0.45 atm. During ascent, the temperature of the gas falls from 22°C to -21°C. Calculate the volume of the balloon at its final altitude.

26. n V P RT = Densities of Gases If we divide both sides of the ideal-gas equation by V and by RT, we get

27. m V P RT = Densities of Gases • We know that • Moles  molecular mass = mass n  = m • So multiplying both sides by the molecular mass () gives

28. m V P RT d = = Densities of Gases • Mass  volume = density • So, Note: One needs to know only the molecular mass, the pressure, and the temperature to calculate the density of a gas.

29. P RT d = dRT P  = Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: becomes

30. Density and Molecular Mass • What is the density of carbon tetrachloride vapor at 714 torr and 125°C? • Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21°C and 740.0 torr. • 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 31°C, its mass is 137.456g. When the flask is evacuated again and then filled with water at 31°C, its mass is 1067.9g (the density of water at this temperature is 0.997 g/mL). Calculate the molar mass. • The mean molar mass of the atmosphere at the surface of Titan is 28.6 g/mol. The surface temperature is 95K and the pressure is 1.6 atm. Calculate the density.

31. Dalton’s Law ofPartial Pressures • The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. • In other words, • Ptotal = P1 + P2 + P3 + …

32. Partial Pressures • A mixture of 6.00 g of O2 and 9.00 g of CH4 is placed in a 15.0 L vessel at 0°C. What is the partial pressure of each gas, and the total pressure in the vessel? • What is the total pressure exerted by a mixture of 2.00 g of H2 and 8.00 g of N2 at 273K in a 10.0 L vessel?

33. Mole Fractions • A study of certain gas effects on plant growth requires a synthetic atmosphere composed of 1.5 mol% CO2, 18.0 mol% O2, and 80.5 mol% Ar. • Calculate the partial pressure of O2 in the mixture if the total pressure of the atmosphere is to be 745 torr. • If this atmosphere is to be held in a 121 L space at 295 K, how many moles of O2 are needed?

34. Partial Pressures • When one collects a gas over water, there is water vapor mixed in with the gas. • To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure. • When a sample of KClO3 is partially decomposed, the volume is 0.250L at 26°C and 765 torr total pressure. How many moles of O2 are collected? How many grams of KClO3 were decomposed?

35. Kinetic-Molecular Theory This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

36. Main Tenets of Kinetic-Molecular 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.

37. Main Tenets of Kinetic-Molecular Theory 4. The average kinetic energy of the molecules is proportional to the absolute temperature.

38. Main Tenets of Kinetic-Molecular Theory 5. 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.

39. Applying Kinetic Molecular Theory • A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on • The average kinetic energy of the molecules • Their average speed • The number of collisions they make with the container walls per unit time. • The number of collisions they make with a unit area of container wall per unit time.

40. Molecular Speeds • Root Mean Square Speed: √3RT M • Most Probable Speed: √2RT M • Calculate the rms speed of the molecules in a sample of nitrogen gas at 25°C.

41. High Temperatures Increase Average Speed

43. Effusion Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

44. Graham's Law • r1 = √M1 r2 √M2 • An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is 0.355 times the rate at which oxygen gas effuses at the same temperature. Calculate the molar mass of the unknown and identify it.

45. Effusion The difference in the rates of effusion for helium and nitrogen, for example, explains why a helium balloon would deflate faster.

46. Diffusion Diffusion is the spread of one substance throughout a space or throughout a second substance.

47. Real Gases In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

48. Real Gases Even the same gas will show wildly different behavior under high pressure at different temperatures.

49. Deviations from Ideal Behavior The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

50. Corrections for Nonideal Behavior • The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. • The corrected ideal-gas equation is known as the van der Waals equation.