1. Gases Chapter 13

2. Solids, liquids, and Gases Chapter 132 Compare the position and motion of the three states of matter.

3. Energy Potential Energy –Stored energy – due to position –Particles are attracted to one another. More energy is required to keep particles farther apart. –Which of the 3 states has the highest potential energy? Chapter 133 Kinetic Energy –Motion energy – related to temperature –The faster the particles are moving, the higher the kinetic energy, the higher the temperature (average kinetic energy) –Which of the 3 states has the highest kinetic energy?

4. Chapter 134 Kinetic-Molecular Theory -Theory developed to explain gas behavior -To describe the behavior of a gas, we must first describe what a gas is: –Gases consist of very small particles each of which have a mass. –The distance between gas particles are relatively large. Volume of individual molecules is negligible compared to volume of container. –Gas particles in rapid, constant, random motion.

5. Chapter 135 –Collisions between gas particles are perfectly elastic. Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. Kinetic-Molecular Theory (Cont’d) No energy is lost during collisions.

6. Chapter 136 Kinetic-Molecular Theory (Cont’d) The average kinetic energy of gas particles depends only on the temperature of the gas. Gas particles exert no forces on each other. Intermolecular forces (forces between gas molecules) are negligible. What happens as temperature increases? Which statements in KMT are assumptions?

7. Chapter 137 Let’s generate some gas -Expand to fill a volume (expandability) -Compressible -Takes shape of container -Diffuses and flows Properties of a gas

8. Chapter 138 Variables that can be measured for gases –Temperature –Volume –Amount –Pressure

9. Temperature (T) Measured in Fahrenheit, Celsius, or Kelvin. For this chapter, we have to use Kelvin. ◦ C = K – 273K = ◦ C + 273 Chapter 139 Volume (V) Measured in Liters, cubic meters, gallons, etc… Amount (n) Measured in moles

10. Chapter 1310 Pressure (P) – what causes pressure? 1 atm = 760 mmHg = 760 torr = 101.3 kPa The pressure of a gas is measured using a manometer. *Atomspheric pressure is measured using a Barometer.

11. Unit Conversions 22 ◦ C = ______ K37 K = ______ ◦ C 18 mL = ______ L 4.3 L = ______ cm 3 500 cm 3 = ______ mL 2.2 dm 3 = _______ L Chapter 1311

12. Unit Conversions 2.8 g N 2 = ______ mol 612 mol SO 3 = _______ g 22 kPa = ______ atm 289 mmHg = _______ kPa 4.3 atm = ______ torr 518 kPa = _______ mmHg Chapter 1312

13. Chapter 1313 The Gas Laws -There are four variables required to describe a gas: -Amount of substance: moles (n) -Volume of substance: volume (V) -Pressures of substance: pressure (P) -Temperature of substance: temperature (T) -The gas laws will hold two of the variables constant and see how the other two vary (n,V,P,T)

14. Chapter 1314 Today’s Lab – Boyle’s Law We will maintain a constant temperature and number of moles of gas. So we will vary the Pressure and the Volume and see how they relate. PV = kor P/V = k inverse direct

15. Bolyle’s Law Lab – 16 pts total Heading – 1 pt Purpose – 1 pt Procedure – 1 pt Data – 4 pts (make sure they have units for the 3 rd and 4 th columns. Graph – 3 pts (should have a title and labeled axis) Questions – 6 pts (in complete sentences) 1) 1/2 2) doubled 3) inverse 4) PV=k 5) The pressure and volume of a gas at a constant temperature are inversely proportional to each other. 6) Source of error. Chapter 1315

16. Chapter 1316 Variables for Gases Discussed Before T – Temperature V – Volume P – Pressure n – Amount of a substance (moles)

17. Chapter 1317 Boyle’s Law – peeps in bell jar demo The Pressure-Volume Relationship Boyle’s Law - The volume of a fixed quantity of gas is inversely proportional to its pressure at a constant temperature.

18. Chapter 1318 A gas occupies 22 L at 2.43 atm. What is the new volume if the pressure changed to 5.11 atm?

19. Chapter 1319 Gay-Lussac’s Law – can crush demo Gay-Lussac’s Law – As the temperature of an enclosed gas increases, the pressure increases if the volume is constant. The Pressure-Temperature Relationship:

20. Chapter 1320 A gas has a pressure of 1.47 atm at 303 K. What is the new temperature if the pressure changed to 680 mmHg?

21. Chapter 1321 Charles Law – ivory soap demo Charles’s Law - the volume of a fixed quantity of gas at constant pressure increases as the temperature increases. The Temperature-Volume Relationship:

22. Chapter 1322 A gas occupies 14 L at 275 K. What is the new volume if the temperature changed to 297 K?

23. Chapter 1323 Avogadro’s Law Avogadro’s Law - The volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas. The Quantity-Volume Relationship:

24. Chapter 1324 A balloon contains 1.98 mol of a gas and has a volume of 4.2 L. Some of the gas was let out to give a volume of 3.1 L. What is the amount of gas left in the balloon?

25. Chapter 1325 The Gas Laws Summary Boyle’s Law Charles’ Law Avogadro’s Law Guy-Lussac’s Law

26. Chapter 1326 The Ideal Gas Equation Ideal gas equation: PV = nRT P = pressure (atm or mmHg or kPa) V = volume (L)n = amount (mol) R = gas constantT = temperature (K) Combine the gas laws (Boyle, Charles, Guy- Lussac, Avogadro) yields a new law or equation.

27. Chapter 1327 Finding R with Dry Ice Lab PV = nRT What units are used for R?

28. Calculating R with Dry Ice Lab – 20 pts total Heading – 1 pt Purpose – 1 pt Procedure – 1 pt Data – 10 pts (make sure they have units) Calculations – 2pts Conclusion – 5 pts –Their value for R –Literature value for R –% error –Sources of error –How they affected their results (higher or lower and must be consistent with their result for R) Chapter 1328

29. Chapter 1329 Calculating R We define STP (standard temperature and pressure) as 0  C = 273 K, and 1 atm = 760 mmHg = 101.3 kPa Volume of 1 mol of gas at STP is 22.4 L. PV = nRT

30. Chapter 1330 The Ideal Gas Equation-Finding R

31. Chapter 1331 Combined Gas Law So in cases with changing conditions and

32. Chapter 1332 Ideal vs. Combined Gas Law-When Use Ideal Gas Law: Conditions not changing Combined Gas Law: Conditions Changing

33. Chapter 1333 Example 1 How many moles of a gas at 100 degrees C does it take to fill a 1.0 L flask to a pressure of 1.50 atm? Not a changing situation so use Ideal Gas Law PV=nRT

34. At 60 Celsius a 0.10 L sample of a gas has a pressure of 75.6 kPa. What would its volume be at STP? Chapter 1334 Changing situation so use combined gas law. Example 2

35. Chapter 1335 What pressure would 3.55 grams of argon gas be under in a 2.40 L cylinder at -35 Celsius? Not a changing situation so use Ideal Gas Law PV=nRT Example 3

36. Chapter 1336 What is the density of bromine gas the gas fills a 52.5 L cylinder at 145 K and 583 mmHg? Not a changing situation so use Ideal Gas Law PV=nRT Example 4

37. Chapter 1337 Example 5 A gas occupies 4430 mL at 30 Celsius. It was transferred in a 3.5 L cylinder. What is the new temperature. Changing situation so use combined gas law.

38. Chapter 1338Demos Egg in E-flask Fountain

39. Tank Car This tank car was cleaned with steam then all the valves were shut and tank car was sealed. The workers went home and when they came back the next morning this is what they saw. Chapter 1339

40. Chapter 1340

41. Chapter 1341

42. Chapter 1342

43. Chapter 1343 Ideal vs. Real gases Ideal gases behave “ideally” according to the kinetic molecular theory and follow the ideal gas law PV = nRT. But kinetic molecular theory has several assumptions that work most of the time but not always.

44. Chapter 1344 Kinetic Molecular Theory Assumptions 1) The volume of gas particles are so small and the spaces between particles are so large. Therefore KMT assumes that gas particles have no volume. 2) The distance between gas particles are very large. Therefore KMT assumes that there is no attraction (IMF) between gas particles.

45. Chapter 1345 But Real gases have volume Under most conditions the volume of gas particles is negligible. To compensate, we plug in the following equation for V in PV = nRT But at small volumes or if the gas particles are large, the volume of the gas particles become significant.

46. Chapter 1346 And real gases have attractive forces (IMF) Under most conditions, the intermolecular forces between gas particles are negligible. To compensate for the pressure difference caused by IMF we plug in the following equation instead of P in PV = nRT But at high pressure and low temperatures, the attractive forces become significant.

47. Chapter 1347 Ideal vs. Real gases Which gas behaves more ideally? Ne or HCl? Neon because it’s particles have a smaller volume and weaker intermolecular forces.

48. Chapter 1348 Ideal vs. Real gases In PV = nRT, plugging in We get the Van der Waals Equation

49. Example Use the Van der Waals equation to calculate the temperature of 3.6 moles of nitrogen gas in a 4.6 L cylinder at 2.5 atm if a and b for nitrogen are 1.390 and 0.03910 respectively. Chapter 1349

50. Chapter 1350 Gas Mixtures and Partial Pressures Dalton’s Law - In a gas mixture the total pressure is given by the sum of partial pressures of each component: P t = P 1 + P 2 + P 3 + … - The pressure due to an individual gas is called a partial pressure. Dalton’s Law

51. Chapter 1351 Partial Pressure of Dry Air At top of Mt. Everest, total atmospheric pressure is 33.73 kPa (about 1/3 that of sea level). So partial pressure of O 2 is 7.06 kPa. To support respiration the partial pressure must be 10.76 kPa or higher so oxygen tanks are needed.

52. Example Chapter 1352 What is the total pressure of a mixture of gases containing oxygen, hydrogen, and water vapor if their partial pressures are 120 kPa, 94 kPa, and 137 kPa respectively?

53. Chapter 1353 Molecular Effusion and Diffusion Graham’s Law of Diffusion or Effusion Effusion – The escape of gas through a small opening. Diffusion – The movement of gas particles through another gas.

54. Chapter 1354 Molecular Effusion and Diffusion Graham’s Law of Effusion or Diffusion

55. Chapter 1355 Kinetic-Molecular Theory As kinetic energy increases, the velocity of the gas molecules increases. Average kinetic energy, KE, is related to root mean square speed: KE= ½mv 2 Molecular Speed

56. Chapter 1356 Graham’s Law of Effusion or Diffusion Gases at same temperature – tell me about them –They have the same kinetic energy (KE) Which would move faster? CO 2 or O 2 –O 2 would move faster because KE=1/2 mv 2 and O 2 has the lower mass Thomas Graham noticed how rate of diffusion (or effusion) related to molar mass

57. Chapter 1357 Molecular Effusion and Diffusion Graham’s Law of Effusion – The rate of effusion of a gas is inversely proportional to the square root of its molecular mass. Graham’s Law of Effusion or Diffusion m 1 and m 2 are molar mass and v 1 and v 2 are effusion/diffusion rates

58. Chapter 1358 Molecular Effusion and Diffusion Graham’s Law of Effusion/Diffusion – The rate of effusion/diffusion of a gas is inversely proportional to the square root of its molecular mass. Graham’s Law of Effusion/Diffusion

59. Example Chapter 1359 Find the relative rate of diffusion for the gases krypton and bromine.

60. Chapter 1360 Gas Laws & Stoichiometry PV = nRT calculations in reactions with molar ratios Link? Moles!!

61. Chapter 1361 Example 1 -What mass of NaCl could be produced form excess sodium and 10.0 L of chlorine gas at 23 o C and 1.02 atm?

62. Chapter 1362 Example 2 -Calcium carbonate decomposes to form carbon dioxide and calcium oxide. What volume of carbon dioxide at 25 o C and 99.8 kPa is produced if 25.0 g of calcium carbonate is decomposed?