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AP Notes Chapter 11 Properties Of Gases. Temperature An indirect measure of the average kinetic energy of a collection of particles An indirect measure.

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Presentation on theme: "AP Notes Chapter 11 Properties Of Gases. Temperature An indirect measure of the average kinetic energy of a collection of particles An indirect measure."— Presentation transcript:

1 AP Notes Chapter 11 Properties Of Gases

2 Temperature An indirect measure of the average kinetic energy of a collection of particles An indirect measure of the average kinetic energy of a collection of particles KE avg = kT Boltzman Plot Boltzman Plot

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4 Pressure Measure of the number of collisions between gas particles and a unit area of the wall of the container Pressure = force / unit area

5 Force/area English system: pounds/in 2 (psi) pounds/in 2 (psi) Metric system: Newton/m 2 (pascal) Newton/m 2 (pascal)

6 Torricelli Barometer h = 760 mm Hg 1 atmosphere pressure

7 1 atm = 760 torr (mm Hg) = kPa = bar =14.70 psi

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9 Manometer P gas P atm h

10 Manometer P gas P atm h

11 Volume Total space of a container that gases occupy due to the free random motion of the gas molecules

12 Relationship between Volume & Pressure of Gases P-V

13 V P (at constant T)

14 V 1/P (at constant T) Slope = k

15 In mathematical terms: y = mx + b Boyles Law

16 Relationship between Volume & Temperature of Gases V-T

17 In mathematical terms: y = mx + b V = mT + b Charles Law

18 Where T must be in Kelvin (K) temperature K = 0 C + 273

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20 Relationship between Pressure & Temperature of Gases P-T

21 In mathematical terms: y = mx + b P = mT + b Gay-Lussacs Law

22 Relationship between Volume & Moles of Gases V-n

23 In mathematical terms: y = mx + b V = mn + b Avogadros Law

24 Avogadros Hypothesis At constant temperature and pressure, equal volumes of gases contain equal number of particles

25 3. Hydrogen gas [8.3 liters] reacts in the presence of 2.5 liters of nitrogen gas at 37 0 C and 100 kPa. What volume of ammonia is produced at these same conditions?

26 Combined Gas Law

27 Ideal & Real Gasses

28 Kinetic Molecular Theory 1. Gases consist of small particles that are far apart in comparison to their own size. These particles are considered to be tiny points occupying a negligible volume compared to that of their container.

29 2. Molecules are in rapid and random straight-line motion. This motion can be described by well-defined and established laws of motion. Kinetic Molecular Theory

30 3. The collisions of molecules with the walls of a container or with other molecules are perfectly elastic. That is, no loss of energy occurs. Kinetic Molecular Theory

31 4. There are no attractive forces between molecules or between molecules and the walls with which they collide. Kinetic Molecular Theory

32 5. At any particular instant, the molecules in a given sample of gas do not all possess the same amount of energy. Kinetic Molecular Theory

33 Have 1 particle, with mass m, with velocity PARTICLE IN THE BOX

34 Consider the P exerted:

35 But: f = ?

36 But: f = ma where

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39 Change in velocity = (

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41 Thus, the pressure exerted by one particle on a wall is:

42 But,

43 and, the distance a particle travels between collisions with the same wall is ?

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45 Substituting into we get:

46 Simplifying:

47 but,

48 This represents the pressure (P) that one particle exerts striking opposite walls in the box.

49 Now assume the box contains N particles. Then, N/3 particles are traveling between opposite walls.

50 Thus, the total pressure on opposite walls is:

51 Substitute & rearrange

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53 From classical physics where k is the Boltzman constant

54 where R = universal gas constant N 0 = Avogadros number

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56 Ideal Gas Equation

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58 Note that is similar to the Combined Gas Law derived earlier.

59 Variations on Ideal Gas Equation

60 4. What is the molar mass of methylamine if g of the gas occupies 125 mL with a pressure of 99.5 kPa at 22 0 C?

61 Variations on Ideal Gas Equation Bromine

62 5. Calculate the density of fluorine gas at: 30 0 C and 725 torr C and 725 torr. STP STP

63 Real Gas Behavior

64 Ideal Gas Equation P V = n R T

65 Ideal gas P (atm) PV nRT CO 2 H2H2 N2N2 CH 4

66 correct for volume of molecules (V - b)

67 also correct for attractive forces between molecules

68 van der Waals Equation for 1 mole

69 van der Waals Equation for n moles

70 from CRC Handbook a* b* He Ne *when P(atm) & V(L)

71 from CRC Handbook a* b* NH H 2 O *when P(atm) & V(L)

72 from CRC Handbook a* b* CCl C 5 H *when P(atm) & V(L)

73 Cl 2 gas has a = 6.49, b = Cl 2 gas has a = 6.49, b = For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. For 8.0 mol Cl 2 in a 4.0 L tank at 27 o C. P (ideal) = nRT/V = 49.3 atm P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm P (van der Waals) = 29.5 atm

74 T & P conditions where a real gas approximates an ideal gas?

75 203 K 293 K 673 K Ideal gas P (atm) PV nRT N 2 gas

76 T & P conditions where a real gas approximates an ideal gas? high temperature low pressure

77 Gaseous Molecular Movement

78 Partial Pressure pressure exerted by each component in a mixture of gases

79 this assumes that NO interactions occurs between the molecules of gas

80 must conclude 1. each gas acts as if it is in container alone 2. each gas collides with the container wall as an event

81 where n = # components or P T = P 1 + P 2 + P

82 P i V = n i R T or

83 thus:

84 or

85 therefore: n T = n i and P T sum of mols of gas

86 Mole Fraction

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88 Since: and

89 Then

90 and P i = X i P T

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92 diffusion is the gradual mixing of molecules of different gases. diffusion is the gradual mixing of molecules of different gases. effusion is the movement of molecules through a small hole into an empty container. effusion is the movement of molecules through a small hole into an empty container.

93 rate of average effusion speed

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95 But... where

96 thus then RMS speed

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99 substituting:

100 simplifying Grahams Law NH 3 -HCl

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102 if d is constant

103 if t is constant

104 GAS LAW STOICHIOMETRY

105 1. Ethanol, C 2 H 5 OH, is often prepared by fermentation of sugars such as glucose, C 6 H 12 O 6, with carbon dioxide as the other product.

106 [A] What volume of CO 2 is produced from 125 g of glucose if the reaction is 97.5% efficient?

107 [B] Ethanol can also be made from ethylene, C 2 H 4 according to the following chemical system:

108 3 C 2 H 4 (g) + 2 H 2 SO 4 C 2 H 5 HSO 4 + (C 2 H 5 ) 2 SO 4 then C 2 H 5 HSO 4 + (C 2 H 5 ) 2 SO 4 + 3H 2 O 3C 2 H 5 OH + 2 H 2 SO 4

109 What volume (mL) of 95% ethanol is produced from dm 3 of C 2 H 4 ? The density of 95% ethanol is g/mL.

110 2. What is the final pressure [kPa] if g uranium reacts with sufficient fluorine gas to produce gaseous uranium hexafluoride at 32 o C in a 300. L container?

111 3. What mass of sodium metal is needed to produce 250 mL of hydrogen gas at 24 o C and 740 Torr?


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