1. 5-1 Chapter 5 Gases and the Kinetic-Molecular Theory

2. 5-2 기체와 분자운동론 기체상태의 물질 기체의 압력 기체 법칙 보일의 법칙, 샤를의 법칙, 아보가드로의 법칙 분압 기체분자운동론 온도와 에너지, 확산 실제기체 및 반데르발스 상태방정식

3. 5-3 Gases and the Kinetic Molecular Theory 5.1 An Overview of the Physical States of Matter 5.2 Gas Pressure and Its Measurement 5.3 The Gas Laws and Their Experimental Foundations 5.4 Further Applications of the Ideal Gas Law 5.5 The Ideal Gas Law and Reaction Stoichiometry 5.6 The Kinetic-Molecular Theory: A Model for Gas Behavior 5.7 Real Gases: Deviations from Ideal Behavior

4. 5-4 기체는 왜 공부하는가 ? 역사적인 배경과 의미 1.Boyle’s Law – First Scientific Experiment, 1661 2.Charles’s Law – Definition of Temperature, 1780s 3.Avogadro’s Hypothesis – 4.Combined Ideal Gas Law and Kinetic Theories– First Successful Scientific Law derived from purely mathematical approach. 실용적인 배경과 의미 1. 기체는 열역학의 기초, 열역학 제 1, 2 법칙을 설명 2. 화학 평형, 화학적 퍼텐셜의 기초 3. 화학반응의 근본적 이해를 도움 - 반응동력학

5. 5-5  Gases assume the volume and shape of their containers.  Gases are the most compressible state of matter.  Gases will mix evenly and completely when confined to the same container.  Gases have much lower densities than liquids and solids. Physical Characteristics of Gases

6. 5-6 Barometer Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa bar = 10 5 Pa psi = lb/in 2 = 6894.757 Pa Pressure = Force Area (force = mass x acceleration)

7. 5-7

8. 5-8 Pressure = Force/Area SI Units Force = mass × acceleration Force = kg-m/s 2 = Newton Pressure = Newton/m 2 = Pascal Customary Units Pressure = atm, torr, mmHg, bar, psi Relate SI to customary 1.01325 × 10 5 Pascal = 1 atm = 760 torr bar = 10 5 Pascal PRESSURE Units and Measurement

9. 5-9 Common Units of Pressure Atmospheric PressureUnitScientific Field chemistryatmosphere(atm)1 atm* pascal(Pa); 1.01325 × 10 5 Pa; SI unit; physics, chemistry mm of mercury(Hg)760 mm Hg*chemistry, medicine, biology torr760 torr*chemistry pounds per square inch (psi or lb/in 2 ) 14.7 psiengineering bar1.01325 barmeteorology, chemistry, physics *This is an exact quantity; in calculations, we use as many significant figures as necessary.

10. 5-10 Boyle’s Law(1662)

11. 5-11 Charles’ Law (1780s) Definition of Temperature V = V 0 + at V = aT 0 273.15 Temperature(K) T (K) = t ( 0 C) + 273.15

12. 5-12 Equal volumes of gases contain the same number of molecules at constant T,P 22.414 L of any gas contains 6.022×10 23 atoms (or molecules) at 0 ℃ and 1 atm. Avogadro’s Hypothesis

13. 5-13 Avogadro’s Law(1811) V = constant × n V 1 /n 1 = V 2 /n 2 Constant temperature Constant pressure 3 H 2 (g) + N 2 (g) → 2 NH 3 (g) 3 volume + 1 volume → 2 volume 3 mol + 1 mol → 2 mol 3 molecules + 1 molecule → 2 molecules

14. 5-14 Ideal Gas Equation R is the gas constant PV = nRT

15. 5-15 Dalton’s Law of Partial Pressures V and T : constant P1P1 P2P2 P total = P 1 + P 2

16. 5-16 Consider a case in which two gases, A and B, are in a container of volume V. P A = nARTnART V P B = nBRTnBRT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = x i P T mole fraction (x i ) = nini nTnT

17. 5-17 The Molar Mass of a Gas

18. 5-18 Water Vapor Pressure Table Temperature Pressure (°C) (mmHg) Temperature Pressure (°C) (mmHg) Temperature Pressure (°C) (mmHg) 0.0 4.6 5.0 6.5 10.0 9.2 12.5 10.9 15.0 12.8 15.5 13.2 16.0 13.6 16.5 14.1 17.0 14.5 17.5 15.0 18.0 15.5 18.5 16.0 19.9 16.5 19.5 17.0 20.0 17.5 20.5 18.1 21.0 18.6 21.5 19.2 22.0 19.8 22.5 20.4 23.0 21.1 23.5 21.7 24.0 22.4 24.5 23.1 25.0 23.8 26.0 25.2 27.0 26.7 28.0 28.3 29.0 30.0 30.0 31.8 35.0 42.2 40.0 55.3 50.0 92.5 60.0 149.4 70.0 233.7 80.0 355.1 90.0 525.8 95.0 633.9 100.0 760.0

19. 5-19

20. 5-20 P,V,T of gas A amount (mol) of gas A amount (mol) of gas B P,V,T of gas B ideal gas law molar ratio from balanced equation stoichiometric relationships among the amount (mol,n) of gaseous reactant or product and the gas variables P, V, and T. 3 H 2 (g) + N 2 (g) → 2 NH 3 (g)

21. 5-21 Kinetic Molecular Theory of Gases 1. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume. d(N 2,g) = 0.00125 g/L (273°C) d(N 2,liq) = 0.808 g/mL (-195.8°C) 2. Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic. 3. Gas molecules exert neither attractive nor repulsive forces on one another.(no interaction)

22. 5-22 Avogadro’s Law V  n E k = 1/2 mass x speed 2 E k = 1/2 mass x u  2 u 2 is the root-mean-square speed u rms = √ 3RT M R = 8.314Joule/mol*K Graham’s Law of Effusion The rate of effusion of a gas is inversely related to the square root of its molar mass. rate of effusion  1 √M√M

23. 5-23 Applying Graham’s Law of Effusion PROBLEM: Calculate the ratio of the effusion rates of helium and methane (CH 4 ). SOLUTION: PLAN: The effusion rate is inversely proportional to the square root of the molar mass for each gas. Find the molar mass of both gases and find the inverse square root of their masses. M of CH 4 = 16.04g/mol M of He = 4.003g/mol CH 4 He rate = √ 16.04 4.003 = 2.002

24. 5-24 Figure 5.18 Diffusion of a gas particle through a space filled with other particles. distribution of molecular speeds mean free path collision frequency

25. 5-25 Molar Volume of Some Common Gases at 0 0 C and 1 atm Gas Molar Volume (L/mol) Condensation Point ( 0 C) He H 2 Ne Ideal gas Ar N 2 O 2 CO Cl 2 NH 3 22.435 22.432 22.422 22.414 22.397 22.396 22.390 22.388 22.184 22.079 -268.9 -252.8 -246.1 --- -185.9 -195.8 -183.0 -191.5 -34.0 -33.4

26. 5-26 Figure 5.19 The behavior of several real gases with increasing external pressure.

27. 5-27 Van der Waals Constants for Some Common Gases 0.034 0.211 1.35 2.32 4.19 0.244 1.39 1.36 6.49 3.59 2.25 4.17 5.46 He Ne Ar Kr Xe H 2 N 2 O 2 Cl 2 CO 2 CH 4 NH 3 H 2 O 0.0237 0.0171 0.0322 0.0398 0.0511 0.0266 0.0391 0.0318 0.0562 0.0427 0.0428 0.0371 0.0305 Gas a atm·L 2 mol 2 b L mol Van der Waals equation for n moles of a real gas adjusts P upadjusts V down

28. 5-28 Collisions of Gas Particles

29. 5-29 Collisions of Gas Particles

30. 5-30 The gas molecules in the container are in random motion

31. 5-31 압력과 기체분자 운동 운동량 변화 ∆p = mv x – (–mv x ) = 2mv x 분자의 왕복시간 ∆t = 2a/v x 분자 한 개가 면 A 에 미치는 힘 f = ∆p/ ∆t= 2mv x /(2a/v x )= mv x 2 /a N 개의 분자에 의해 면 A 에 가해지는 압력 P = Σf/a 2 = m(v x1 2 + v x2 2 +... + v xN 2 )/a 3 =Nmv x 2 /V PV=Nmv x 2

32. 5-32 압력과 기체분자 운동 공간 상에서 무작위로 움직이는 분자는 특별한 방향에 대한 선호도가 없을 것이므로 분자당 평균운동에너지 Gas Pressure in the Kinetic Theory

33. 5-33 운동에너지와 온도 이상 기체방정식 기체에 열이 가해지면 기체의 내부에너지와 온도가 증가 ! Boltzmann constant Mean Kinetic Energy per particle

34. 5-34 N = number of molecules, k B = Boltzmann constant, J K -1, n = number of moles = N/N A, R = gas constant, 0.08204 l atm mol -1 K -1 T = temperature, P = gas pressure, V = volume, N A = Avogadro’s number PV = Nk B T = nRT

35. 5-35 Maxwell-Boltzmann Distribution for Molecular Speeds f(u) = speed distribution function, m = molecular mass, k = Boltzmann constant, T = temperature, u = speed u~ u+du 사이의 속도를 가진 분자들의 수

36. 5-36 분자속도와 에너지 분포 (Molecular velocity and energy distribution) 슈테른 (Otto Stern) 의 분자속도 측정 노벨물리학상 수상자 (1943, w/ Gerlach) Schematic diagram of a stern type experiment for determining the distribution of molecular velocities  v ~ v+∆v 사이의 분자개수 ∆N 측정가능 !! http://leifi.physik.uni-muenchen.de/web_ph12/originalarbeiten/stern/molekularstr.htm

37. 5-37 Molecular speed Distribution of N 2 gas Maxwell Boltzmann distribution of molecular speeds in nitrogen gas at two temperatures. The ordinate is the fractional number of molecules per unit speed interval in (km/s) -1.

38. 5-38 Apparatus for studying molecular speed distribution Chopper methodgravitation method

39. 5-39 Chemistry in Action: Super Cold Atoms Gaseous Rb Atoms 1.7 x 10 -7 K(170 nK) Bose-Einstein Condensate 1995, Eric Cornell and Carl Wieman Three images showing formation of Bose-Einstein condensate. picture from JILA

40. 5-40 Gaseous Diffusion/Effusion Diffusion of Ammonia and HCl Effusion enrichment of UF 6 Graham’s Law of Effusion A bank of uranium gas centrifuges Uranium Information Centre

41. 5-41 Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. NH 3 17 g/mol HCl 36 g/mol NH 4 Cl

42. 5-42 Kinetic-Molecular Theory for Gaseous Behavior Principal Issues ( 잠재적 문제점 ) –Negligible Volume and No interaction Hold only at low P, high T; for dilute gases –Elastic Collisions Only in Newtonian mechanics is the reverse of an event as likely as the event itself. In the real world you cannot “unscramble” eggs because of entropy effects resulting from large ensembles of molecules

43. 5-43 Deviations from Ideal Behavior 1 mole of ideal gas PV = RT Z = PV RT = 1.0 Repulsive Forces Attractive Forces compression factor

44. 5-44 Effect of intermolecular forces on the pressure exerted by a gas. Real Gas Has volume Has interaction(usually attractive)

45. 5-45 Van der Waals equation nonideal gas P + (V – nb) = nRT an 2 V2V2 () } corrected pressure } corrected volume Gas a [(L 2 · atm)/mol 2 ] b [10 -2 L/mol] He0.034122.370 Ne0.2111.71 Ar1.343.22 Kr2.323.98 Xe4.192.66 H2H2 0.24442.661 N2N2 1.3903.913 O2O2 1.3603.183 CO 2 3.5924.267 CH 4 2.254.28 CCl 4 20.413.8 C2H2C2H2 4.3905.136 Cl 2 6.4935.622 C 4 H 10 14.4712.26 C 8 H 18 37.3223.68 Selected Values for a and b for the van der Waals Equation

46. 5-46 Hydrogen Economy & Fuel Cell

47. 5-47 Chlorine Destroys Ozone but is not consumed in the process Ozone Depletion

48. 5-48

49. 5-49 Crutzen Molina Rowland Holland (The Netherlands) Max-Planck-Institute for Chemistry Mainz, Germany 1933 - USA (Mexico) Department of Earth, Atmospheric and Planetary Sciences and Department of Chemistry, MIT Cambridge, MA, USA 1943 - USA Department of Chemistry, University of California Irvine, CA, USA 1927 -

50. 5-50 Hindenberg Crew: 40 to 61 Capacity: 50-72 passengers Length: 245 m, Diameter: 41 m Volume: 200,000 m³ Powerplant: 4 × Daimler-Benz diesel engines, 890 kW (1,200 hp) each 기체 : 수소 ( 헬륨으로 계획되었으나, 수소로 대체 ) 부력 :

51. 5-51 Science of Hot Air Balloon 2008 National Balloon Classic in Indianola, Iowa. 부력 = 밖 공기의 무게 – 안 공기의 무게 안 공기의 무게 = 공기의 밀도 (ρ(T hot ))× 풍선의 부피 (V)×g 밖 공기의 무게 = 공기의 밀도 (ρ(T cold ))× 풍선의 부피 (V)×g 공기의 밀도 ρ(T) = w/V = Mp/RT 부피 (m 3 ) 600 ~ 2800 ~ 17,000 T cold ~ 20 ℃ T hot ~ 100 ℃ 부력 ~ 700kg

52. 5-52 Lake Nyos, the killer Lake of Cameroon Clarke, T., Taming Africa’s killer lake, Nature, V. 409, p. 554-555, February 2001.

53. 5-53 Lake Nyos, the killer Lake Clarke, T., Taming Africa’s killer lake, Nature, V. 409, p. 554-555, February 2001. Test of the de-gassing operation in 1995

54. 5-54 Air Bag Chemistry

55. 5-55 Air Bag Chemistry

56. 5-56

57. 5-57 Air Bag Chemistry

58. 5-58 Air Bag Chemistry On ignition:2 NaN 3 →  2Na + 3N 2 Secondary reactions: 10 Na + 2 KNO 3 →  K 2 O + 5 Na 2 O + N 2 K 2 O + Na 2 O + SiO 2 →  K 2 Na 2 SiO 4