1. Gases © 2009, Prentice-Hall, Inc. Characteristics of Gases Unlike liquids and solids, gases –expand to fill their containers; –are highly compressible; –have extremely low densities –Vapor = gaseous state of a substance that is ordinarily liquid or solid

2. Gases © 2009, Prentice-Hall, Inc. Pressure is the amount of force applied to an area. Pressure Atmospheric pressure is the weight of air per unit of area. P = FAFA

3. Gases © 2009, Prentice-Hall, Inc. Units of Pressure Pascals 1 Pa = 1 N/m 2 Bar 1 bar = 10 5 Pa = 100 kPa mm Hg or torr the difference in the heights measured in mm ( h ) of two connected columns of mercury. Atmosphere 1.00 atm = 760 torr

4. Gases © 2009, Prentice-Hall, Inc. Standard Pressure Normal atmospheric pressure at sea level is referred to as standard pressure. It is equal to –1.00 atm –760 torr (760 mm Hg) –101.325 kPa

5. Gases © 2009, Prentice-Hall, Inc. Manometer This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

6. Gases Practice with Pressure On a certain day the barometer in a laboratory indicates that the atmospheric pressure is 764.7 torr. A sample of gas is placed in a flask attached to an open-end mercury manometer, shown below. The level of mercury in the open-end arm of the manometer has a height of 136.4 mm, and the mercury in the arm that is in contact with the gas has a height of 103.8 mm. What is the pressure of the gas in torr? in atmospheres? in kPa? © 2009, Prentice-Hall, Inc.

7. Gases © 2009, Prentice-Hall, Inc. The Gas Laws BOYLE’S LAW:The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

8. Gases © 2009, Prentice-Hall, Inc. P and V are inversely proportional A plot of V versus P results in a curve. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line. PV = k

9. Gases Temperature Temperature = Average Kinetic Energy K = °C + 273 0 K = absolute zero Standard temperature = 0 °C © 2009, Prentice-Hall, Inc.

10. Gases © 2009, Prentice-Hall, Inc. Charles’s Law The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. A plot of V versus T will be a straight line. i.e., VTVT = k

11. Gases Combined Gas Law Note: T must be in Kelvin © 2009, Prentice-Hall, Inc.

12. Gases © 2009, Prentice-Hall, Inc. Avogadro’s Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. Mathematically, this means V = kn

13. Gases © 2009, Prentice-Hall, Inc. The Ideal Gas Equation V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avogadro’s law) So far we’ve seen that Combining these, we get V V  nT P

14. Gases © 2009, Prentice-Hall, Inc. Ideal-Gas Equation The constant of proportionality is known as R, the gas constant.

15. Gases © 2009, Prentice-Hall, Inc. Ideal-Gas Equation The relationship then becomes nT P V V  nT P V = R or PV = nRT Make sure T is in Kelvin!

16. Gases Use ideal gas law to derive relationships between 2 other variables PV=nRT if n and T are constant, P 1 V 1 = P 2 V 2 if n and P are constant, V 1 = V 2 T 1 T 2 if n and v are constant, P 1 = P 2 T 1 T 2 © 2009, Prentice-Hall, Inc. Relationships between P, V, and T

17. Gases Molar Volume Molar volume = volume that 1 mole of gas occupies. At STP, what is the molar volume of CO 2 ? N 2 ? © 2009, Prentice-Hall, Inc.

18. Gases Practice with Gas Laws Suppose we have a gas confined to a cylinder. How will each of these changes affect the average distance between molecules, the pressure of the gas, and the number of moles of gas present in the cylinder : (a)Heat the gas from 298 K to 360 K, while maintaining the piston in the same position. (b) Move the piston to reduce the volume of gas from 1 L to 0.5 L. (c) Inject additional gas through the gas inlet valve. © 2009, Prentice-Hall, Inc.

19. Gases More practice Calcium carbonate, CaCO 3 (s), decomposes upon heating to give CaO(s) and CO 2 (g). A sample of CaCO 3 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 CO 2 gas were generated? Tennis balls are usually filled with air or N 2 gas to a pressure above atmospheric pressure to increase their “bounce.” If a particular tennis ball has a volume of 144 cm 3 and contains 0.33 g of N 2 gas, what is the pressure inside the ball at 24 °C? 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? © 2009, Prentice-Hall, Inc.

20. Gases © 2009, Prentice-Hall, Inc. Dividing both sides of the ideal-gas equation by V & RT, we get : Knowing moles  molecular mass = mass, (n   = m) We can multiply both sides by the molecular mass (  ) to get: nVnV P RT = © 2009, Prentice-Hall, Inc. P  RT mVmV = n has units of moles/L V Further Applications of the Ideal Gas Law

21. Gases © 2009, Prentice-Hall, Inc. Densities of Gases Mass  volume = density So, Note: If you know the molecular mass, the pressure, and the temperature to calculate the density of a gas. P  RT mVmV = d =

22. Gases © 2009, Prentice-Hall, Inc. Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: Becomes P  RT d = dRT P  =

23. Gases Practice What happens to the density of a gas as (a) the gas is heated in a constant-volume container; (b) the gas is compressed at constant temperature; (c) additional gas is added to a constant- volume container? A series of measurements are made to determine the molar mass of an unknown gas. First, a large flask is evacuated and found to weigh 134.567 g. It is then filled with the gas to a pressure of 735 torr at 31 °C and reweighed. Its mass is now 137.456 g. Finally, the flask is filled with water at 31 °C and found to weigh 1067.9 g. (The density of the water at this temperature is 0.997 g/mL.) Assume that the ideal-gas equation applies, and calculate the molar mass of the unknown gas. 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. © 2009, Prentice-Hall, Inc.

24. Gases © 2009, Prentice-Hall, Inc. 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. In other words, P total = P 1 + P 2 + P 3 + …

25. Gases © 2009, Prentice-Hall, Inc. 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.

26. Gases 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% Ar7.1 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

27. Gases Partial Pressure & Mole fraction The mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component: x i = P i = n i P n and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression: P i = x i P x i = mole fraction of any individual gas component in a gas mixture P i = partial pressure of any individual gas component in a gas mixture n i = moles of any individual gas component in a gas mixture n= total moles of the gas mixture P= pressure of the gas mixture The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture. © 2009, Prentice-Hall, Inc.

28. Gases Practice What is the total pressure exerted by a mixture of 2.00 g of H 2 and 8.00 g of N 2 at 273 K in a 10.0-L vessel? A gaseous mixture made from 6.00 g O 2 and 9.00 g CH 4 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? 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. (a)Calculate the partial pressure of O 2 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 O 2 are needed? © 2009, Prentice-Hall, Inc.

29. Gases © 2009, Prentice-Hall, Inc. Kinetic-Molecular Theory This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

30. Gases © 2009, Prentice-Hall, Inc. Main Tenets of Kinetic- Molecular Theory Gas particles are in constant random straight line motion

31. Gases © 2009, Prentice-Hall, Inc. Main Tenets of Kinetic- Molecular Theory The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

32. Gases © 2009, Prentice-Hall, Inc. Main Tenets of Kinetic- Molecular Theory Attractive and repulsive forces between gas molecules are negligible. An ideal gas is like an ideal vacation! High Temp & Low pressure

33. Gases © 2009, Prentice-Hall, Inc. Main Tenets of Kinetic- Molecular 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.

34. Gases Maxwell-Boltzman Distribution Scheffler Molecules are in constant motion Not all particles have the same energy The average kinetic energy is related to the temperature An increase in temperature spreads out the distribution and the mean speed is shifted upward

35. Gases Scheffler The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature u rms = 3RT M  Velocity of a Gas

36. Gases © 2009, Prentice-Hall, Inc. A sample of O 2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on (a)the average kinetic energy of O 2 molecules, (b) the average speed of O 2 molecules, (c) the total number of collisions of O 2 molecules with the container walls in a unit time, (d) the number of collisions of O 2 molecules with a unit area of container wall per unit time? PRACTICE

37. Gases © 2009, Prentice-Hall, Inc. Molecular Effusion and Diffusion Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

38. Gases © 2009, Prentice-Hall, Inc. Diffusion Diffusion is the spread of one substance throughout a space or throughout a second substance.

39. Gases 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.

40. Gases © 2009, Prentice-Hall, Inc. Effusion The difference in the rates of effusion for helium and nitrogen, for example, explains why a helium balloon would deflate faster.

41. Gases Practice Calculate the rms speed, u, of an N 2 molecule at 25 °C. What is the rms speed of an He atom at 25 °C? An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only 0.355 times that of O 2 at the same temperature. Calculate the molar mass of the unknown, and identify it. © 2009, Prentice-Hall, Inc.

42. Gases © 2009, Prentice-Hall, Inc. Real Gases: Deviations from Ideal Behavior In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

43. Gases © 2009, Prentice-Hall, Inc. Real Gases Even the same gas will show wildly different behavior under high pressure at different temperatures.

44. Gases © 2009, Prentice-Hall, Inc. 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.

45. Gases © 2009, Prentice-Hall, Inc. Corrections for Nonideal Behavior The corrected ideal-gas equation is known as the van der Waals equation. ) (V − nb) = nRT n2aV2n2aV2 (P +

46. Gases Practice If 1.000 mol of an ideal gas were confined to 22.41 L at 0.0 °C, it would exert a pressure of 1.000 atm. Use the van der Waals equation and the constants in Table 10.3 to estimate the pressure exerted by 1.000 mol of Cl 2 (g) in 22.41 L at 0.0 °C. Consider a sample of 1.000 mol of CO 2 (g) confined to a volume of 3.000 L at 0.0 °C. Calculate the pressure of the gas using (a) the ideal-gas equation and (b) the van der Waals equation. © 2009, Prentice-Hall, Inc.