Gases

1. Gases • Properties of Gases • Gas Laws (pressure, volume, temperature, moles) • Gases in Chemical Reactions • The Kinetic Model of Gases

3. Gaseous elements

4. Pressure = Force/Area

6. Boyle’s Law V ~ 1/P If a fixed amount of gas is released into a larger container, how much force does it exert?

7. If the volume of a gas is constrained to a smaller container, how much force does it exert? P ~ 1/V Boyle’s Law: P1V1 = P2V2

8. Relationship between volume and pressure. V1 P1 P1V1 = P2V2 Decrease volume  more collisions V2

9. Ex. 1 A sample of gas occupies 21 liters at a pressure of 2.2 atm. What would be the volume if the pressure was increased to 6.2 atm? • Ex. 2 A sample of O2 occupies 10.0 L at 785 torr. At what pressure would it occupy 14.5 L?

10. If the temperature of gas is increased, how will its volume respond (if the pressure is kept constant)? Charle’s Law: V1/T1 = V2 / T2

11. Gas 1 Gas 2 Gas 3 Gas 4 The point where a gas would have zero volume!

12. If a gas is heated, how much force does it exert (if the volume is kept constant)? P ~ T

13. Combined Gas Law (Boyle and Charle’s) P1 V1 = P2 V2 T1 T2

14. Re-cap of Gases: Boyle’s Law: Charles’s Law: P1 V1 = P2 V2 V1/T1 = V2 / T2 P1 V1 = P2 V2 T1 T2 • Gas equations should make sense: volume, pressure, temperature • Watch your units! (K, L, atm)

15. One standardized set of conditions = “STP” • 0o C (273 K) • 1 atm (760 Torr)

16. Ex. 3 A balloon filled with He occupies 413 mL at 100.oC. At what temperature would it occupy 577 mL if the pressure was constant? • Ex. 4 A sample of hydrogen sulfide (H2S) occupies 210 L at 27oC at 1200 T. What volume would it occupy at STP?

17. How much volume does 1 mole of gas occupy at 0o C, 1 atm? If one mole of Argon occupies 22.1 L, how much volume will be occupied by: one mole CO2 one mole N2 one mole O2 one mole H2

18. How much volume does 1 mole of gas occupy at 0o C, 1 atm? Liters Ideal gas: 22.41 L per mole

19. Ex. 5 What is the density of a gas that has a molar mass of 44.01 g/mol at STP?

20. Ideal Gas Law: PV = nRT (where n = moles) What is “R”?

21. “STP” = 0 o C and 1 atm

22. Ex. 6 What is the volume of a balloon filled with 32.02 grams of Helium when the atmospheric pressure is 722 torr and the temperature is 40o C? • Ex. 7 The Goodyear blimp must be inflated with Helium prior to a football game. Its volume is 7601 ft3. How many grams of He are needed for a pressure of 740 torr at 22o C? (1 ft3 = 28.3 L)

23. Ex. 9 A 0.723 g sample of a gas occupies 176 mL at 100.o C and 750. torr. What is its molar mass?

24. Stoichiometric Calculations Involving Gases C3H8 + 5O2 3CO2 + 4H2O 25.0 g of propane produces how many moles of CO2? 25.0 g of propane produces how many liters of CO2 at STP? How many grams of propane are need to react with 50.0 L of O2 at 25o C and 1.0 atm?

25. Key Concepts: • Ideal Gas Law PV = nRT • STP (0o C and 1 atm) • Standard molar volume: 22.4 L/mole at STP • Gases in stoichiometric calculations

26. An airbag inflates in less than 50 msec by the reaction of NaN3 to produce Na and nitrogen gas: NaN3 Na + N2 The volume of the airbag is about 30 L when inflated, and it is filled to a pressure of 1.4 atm. How many grams of NaN3 must be used for each air bag? The molar mass of NaN3 is 65.1 g/mole. Assume the process occurs at room temperature.

27. Gas mixtures • Dalton’s Law of 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 PT=P1+P2+P3+….Pn Exercise: A gaseous mixture is made from 6.00g oxygen and 9.00g methane placed in a 15L vessel at 0oC. What is the partial pressure of each gas and the total pressure in the vessel?

28. Dalton’s law of partial pressures PT = Pa + Pb + Pc + Pd = … Remember that each pressure is also equal to: nXRT/V

29. Mole Fractions • The ratio n1/nT is called the mole fraction (denoted x1), a dimensionless number between 0 and 1. Mole fraction of N2 in air is 0.78, therefore if the total barometric pressure is 760 torr, the partial pressure of N2 is (0.78)(760) = 590 torr.

30. Kinetic –Molecular Theory Theory describing why gas laws are obeyed (explains both pressure and temperature of gases on a molecular level). • Complete form of theory, developed over 100 years or so, published by Clausius in 1857. • Gases consist of large numbers of molecules that are in continuous, random motion • Volume of all molecules of the gas is negligible, as are attractive/repulsive interactions • Interactions are brief, through elastic collisions (average kinetic energy does not change) • Average kinetic energy of molecules is proportional to T, and all gases have the same average kinetic energy at any given T. Because each molecule of gas will have an individual kinetic energy, and thus individual speed, the speed of molecules in the gas phase is usually characterised by the root-mean-squared (rms) speed, u,(not the same though similar to the average speed). Average kinetic energy є = ½mu2

31. Application to Gas Laws • Increasing V at constant T: Constant T means that u is unchanged. But if V is increased the likelihood of collision with the walls decreases, thus the pressure decreases (Boyle’s Law) • Increasing T at constant V: Increasing T increases u, increasing collisional frequency with the walls, thus the pressure increases (Ideal Gas Equation).

32. Ex. 10 A 20.5 L bulb contains 0.200 moles of methane, 0.300 moles of hydrogen, and 0.400 moles of nitrogen at 20.0 o C. It is stinky and explosive. What is the pressure inside the bulb? How much pressure is contributed by each of the three gases? • Ex. 12 One tank of gas contains 5.00 L of N2 at 32.0 atm. A second tank contains 3.00 L of O2 at 24.0 atm. What pressure is attained when the valve between the tanks is opened?

33. Mole fraction: the portion of a specific substance within a mixture What is the portion (mole fraction) of red spheres?

34. Kinetic model of gases each dot is one gas molecule

35. The Kinetic-Molecular Theory • The basic assumptions of kinetic-molecular theory are: • Postulate 1 • Gases consist of discrete molecules that are relatively far apart. • Gases have few intermolecular attractions. • The volume of individual molecules is very small compared to the gas’s volume. • Proof - Gases are easily compressible.

36. The Kinetic-Molecular Theory • Postulate 2 • Gas molecules are in constant, random, straight line motion with varying velocities. • Proof - Brownian motion displays molecular motion.

37. The Kinetic-Molecular Theory • Postulate 3 • Gas molecules have elastic collisions with themselves and the container. • Total energy is conserved during a collision. • Proof - A sealed, confined gas exhibits no pressure drop over time.

38. The Kinetic-Molecular Theory • Postulate 4 • The kinetic energy of the molecules is proportional to the absolute temperature. • The average kinetic energies of molecules of different gases are equal at a given temperature. • Proof - Brownian motion increases as temperature increases.

39. The Kinetic-Molecular Theory • The kinetic energy of the molecules is proportional to the absolute temperature. The kinetic energy of the molecules is proportional to the absolute temperature. • Displayed in a Maxwellian distribution.

40. The Kinetic-Molecular Theory • The gas laws that we have looked at earlier in this chapter are proofs that kinetic-molecular theory is the basis of gaseous behavior. • Boyle’s Law • P  1/V • As the V increases the molecular collisions with container walls decrease and the P decreases. • Dalton’s Law • Ptotal = PA + PB + PC + ..... • Because gases have few intermolecular attractions, their pressures are independent of other gases in the container.

41. Charles’ Law • V  T • An increase in temperature raises the molecular velocities, thus the V increases to keep the P constant.

42. The Kinetic-Molecular Theory • The root-mean square velocity of gases is a very close approximation to the average gas velocity. • Calculating the root-mean square velocity is simple: • To calculate this correctly: • The value of R = 8.314 kg m2/s2 K mol • And M must be in kg/mol.

43. The Kinetic-Molecular Theory • Example 12-17: What is the root mean square velocity of N2 molecules at room T, 25.0oC?

44. The Kinetic-Molecular Theory • What is the root mean square velocity of He atoms at room T, 25.0oC?

45. The Kinetic-Molecular Theory • Can you think of a physical situation that proves He molecules have a velocity that is so much greater than N2 molecules? • What happens to your voice when you breathe He?

46. Diffusion and Effusion of Gases • Diffusion is the intermingling of gases. • Effusion is the escape of gases through tiny holes.

47. Diffusion and Effusion of Gases • This is a demonstration of diffusion.

48. Diffusion and Effusion of Gases • The rate of effusion is inversely proportional to the square roots of the molecular weights or densities.

49. Diffusion and Effusion of Gases • Calculate the ratio of the rate of effusion of He to that of sulfur dioxide, SO2, at the same temperature and pressure.

50. Diffusion and Effusion of Gases • Example 12-16: A sample of hydrogen, H2, was found to effuse through a pinhole 5.2 times as rapidly as the same volume of unknown gas (at the same temperature and pressure). What is the molecular weight of the unknown gas?