1. Gases
Made up of particles that have (relatively) large amounts of ________
No definite _______ or___________
Due to a large amount of empty space, gases are easily __________

2. Gases
Made up of particles that have (relatively) large amounts of _energy__
No definite _shape_ or___volume__
Due to a large amount of empty space, gases are easily _compressed_____

3. 4 Quantities to define the state of a gas
Quantity-moles
Temperature in Kelvin
Volume in liters
Pressure in atmosphere.

4. Pressure F P = A Pressure is the amount of force applied to an area:
Atmospheric pressure is the weight of air per unit of area.

5. Pressure
A pressure is exerted when gas particles collide with the walls of any container it is held in.
Units
1.00 atm=
760. mm Hg=
760. torr=
1.01 x Pa=
kPa

6. Units of Pressure mmHg or torr
These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.
Atmosphere
1.00 atm = 760 torr

7. Manometer
The manometer is used to measure the pressure of a gas in a container.

8. Standard Pressure
Normal atmospheric pressure at sea level is referred to as standard pressure.
It is equal to
1.00 atm
760 torr (760 mmHg)
kPa

9. Exercise 1
The pressure of a gas is measured at 49 torr. Represent this pressure in both atmospheres, mm Hg and pascals: (6.4 x 102 atm, 6.7x 105 Pa)

10. Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

11. Main Tenets of Kinetic-Molecular Theory
1.Gases consist of large numbers of tiny particles that are in constant, random motion.

12. Main Tenets of Kinetic-Molecular Theory
2. Collisions between particles are elastic (the average kinetic energy is remains constant following a collision)
This seems to explain the observation that gases, when left alone in a container, don’t seems to lose energy, and don’t spontaneously convert to a liquid.

13. 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.

14. Main Tenets of Kinetic-Molecular Theory
3. The Attractive and repulsive intermolecular forces between gas molecules are very weak, and are nearly negligible, except when they collide.

15. Main Tenets of Kinetic-Molecular Theory
4.The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.
. This seems to explain why gases are compressible.

16. Main Tenets of Kinetic-Molecular Theory
5. Average kinetic energy of molecules is proportional to its Kelvin Temperature.
ALL CALCULATIONS INVOLVING TEMPERATURE OF GASES MUST BE CONVERTED TO KELVIN TEMPERATURE

17. The pressure of the gas is caused by the collision of the molecules with the walls of the cylinder. The magnitude of the pressure depends on the frequency and the force of the collisions.
The temperature of the gas depends on the average kinetic energy of the molecules

18. Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. P1V1 = k or P1V1 = P2 V2

19. P and V are Inversely Proportional
Since
V = k (1/P)
This means a plot of V versus 1/P will be a straight line.
PV = k
A plot of V versus P results in a curve.

20. Exercise 1 Boyles Law
SO2 is a gas that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider 1.53 L of SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 10 6 PA, what is the new volume of the gas?

21. Exercise 2
If a 1.23 L sample of a gas at 53.0 torr is put under pressure up to a value of 240. torr at a constant temperature, what is the new volume?

22. Charles’s Law
The volume of a fixed amount of gas at constant pressure is directly proportional to its absolyute temperature IN KELVIN!.

23. Charles’s Law
So,
It is a direct proportion. A plot of V versus T will be a straight line. V T
= k

24. Gay Lussac
P1 T2 = P2 T1

25. Combined Gas Law P1 V1T2 = P2V2 T1
Notice the , laws are alphabetical (Boyle P and V, Charles V and T and Gay Lussac T and P (missing variable is held constant

26. The Quantity-Volume Relationship
Gay-Lussacs Law of combining volumes- at a given temperature and pressure, the volumes of gases that react with each other are ratios of small whole numbers
Avogadro’s law-equal volumes of gases at the same temp and press contan the same number of molecules!!

27. 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

28. Example 1
If we have a 17.5 L container which holds 0.60 mol of O2 gas at a pressure of 1 atm and a temperature of 25 C, and all of the O2 is converted to O3, what is the volume of the ozone?

29. If 2. 11 g Ne gas occupies a volume of 12. 0 L at 28. 0 C
If 2.11 g Ne gas occupies a volume of 12.0 L at 28.0 C. What volume will 6.58 g of Neon occupy under the same conditions?

30. Ideal-Gas Equation V  nT P So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
Combining these, we get
V  nT P

31. Ideal-Gas Equation
The constant of proportionality is known as R, the gas constant.

32. Ideal-Gas Equation PV = nRT nT P V  nT P V = R or The relationship
then becomes or
PV = nRT

33. Ideal gas law
Most useful when gases are behaving ideally (under conditions that the molecules will not be attracted to each other. This occurs at :
High temperatures and low pressure

34. Ideal gas Law Example 1
A sample of nitrogen gas (N2) has a volume of 9.95 L at a temperature of 1.00 C and 1.75 atm.
Calculate moles of N2 in this sample
Calculate molecules N2 in this sample

35. Other Gas Laws
Example 1.
A sample of methane gas has a pressure of 455 torr at a temperature of -7.5 C and a volume of 2.25 L. If the conditions are changed so that the temperature rises to 21.0 C and and the pressure increases to 437 torr, what will be the new volume of the sample?

36. Other Gas Laws
Example 2
A sample of helium gas has a volume of 16.2 L and a pressure of 1.81 atm. The gas is compressed to a volume of 8.1 L. Calculate the final pressure of the gas (assume constant temperature)

37. Example 3
Calculate the volume of 1 mole of a gas at STP.
This is the molar volume of a gas at STP!!! Very good to know!!

38. Densities of Gases n P V = RT
If we divide both sides of the ideal-gas equation by V and by RT, we get n V P RT =

39. Densities of Gases n   = m P RT m V = We know that
Moles  molecular mass = mass
n   = m
So multiplying both sides by the molecular mass () gives P RT m V =

41. Molecular Mass P d = RT dRT P M =
We can manipulate the density equation (in g/L) to enable us to find the molecular mass of a gas: P RT
d =
becomes
dRT P
M =

42. Density of gases
The molar mass of air is approximately 29 g/mol at STP. What is its density?

43. Gas density/Molar Mass
The density of a gas was measured at 1.50 atm and 27 C and found to be 1.95 g/L. Calculate the molar mass of the gas.

44. The density of air at room temperature (22C) and 1 atm pressure is 1
The density of air at room temperature (22C) and 1 atm pressure is 1.19 g/L. What is the molar mass of air?

46. 3 gases less dense than air
Neon, hydrogen, methane, ammonia, helium,

47. 3 gases more dense than air
CO2, O2 , propane

48. The density of a gas was measured at 1
The density of a gas was measured at 1.50 atm and 27 C and found to be 1.95 g/L. Is this gas, carbon dioxide, oxygen, or neon?

49. Dalton’s Law of Partial Pressures
In a mixture of gases, the total pressure exerted by the mixture is equal to the sum of the individual partial pressures of each gas.
In other words,
Ptotal = P1 + P2 + P3 + …
Start here 6/18/10

50. 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.

51. Partial Pressures
The total pressure at constant T and V is determined by the total number of moles of gas present, it is not important if it is just
one gas or a mixture of many gases. .

52. Partial Pressures
Assuming ideal gas behavior, the pressure in a mixture of gases is Ptotal = ntotal (RT/V) .

53. Calculate the number of moles of hydrogen present, in a 0
Calculate the number of moles of hydrogen present, in a L mixture of Hydrogen and water vapor, at 21.0 C, that has a total pressure of 750. torr, given that the vapor pressure of water at this temperature is 20.0 torr.

54. Example 2
3.00 liters of carbon monoxide gas at a pressure of 199 kPa and 1.00L of carbon dioxide gas at a pressure of 300 kPa are injected into a 1.25 L container. Assuming no reaction between the two gases, what is the total pressure of the container?

55. Example 3 The partial pressure of a gas was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of this gas.

56. Dalton’s Law II The partial pressure was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction
Moles of gas and pressure are directly proportional. Pressure fraction will equal mole fraction.
156 torr/743 torr= mole fraction=.210

58. A sample of solid potassium chlorate (KClO3) was heated in a test tube and decomposed by the following reaction: 2 KClO3 2 KCl O2 The oxygen produced was collected by displacement of water at 22 C at a total pressure of 754 torr. The volume of gas collected was L, and the vapor pressure of water at 22 C is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed.

59. Example 2
A sample of propane (C3H8) having a volume of 3.25 L at 22 C and a pressure of 1.33 at, was mixed with a sample of oxygen gas having a volume of 15.5 L at 25 C and 1.25 atm. The mixture was then ignites to form CO2 and water. Calculate the volume of CO2 formed at a pressure of 1.50 atm and a temperature of 125 C.

60. Main Tenets of Kinetic-Molecular Theory
The average kinetic energy of the molecules is proportional to the absolute temperature. Changing the temp changes the shape of the curve, but not the area beneath it

62. Root Mean Square Velocity

63. Root Mean Squared Velocity
The square root of the avergages of the squares of the speeds of all of the particles in a gas sample at a particular temperature
R T- Kelvin temperature
M-molar mass gas

64. Exercise 19: Root Mean Square Velocity
Calculate the rms velocity for the following gases at 25 C, and at 50C He O2 Rn

65. Quantitatively, what can be said about the rms speed as it relates to the molar mass of a gas and the temperature of the gas

66. Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.

67. Graham’s Law of Effusion and Diffusion
Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

68. Effusion
The difference in the rates of effusion for helium and nitrogen, for example, explains why a helium balloon would deflate faster.

69. Graham's Law KE1 KE2 = 1/2 m1v12 1/2 m2v22 = = m1 m2 v22 v12 m1

70. Rate of effusion gas 1 = M2 Rate of effusion gas 2 M 1

71. Exercise 20 Calculate the ratio of effusion rates of H2 and UF6
Rate H2 =
Rate UF6

72. Real Gases
In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

73. Real Gases
Even the same gas will show wildly different behavior under high pressure at different temperatures.

74. 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.

75. Corrections for Nonideal Behavior
The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.
The corrected ideal-gas equation is known as the van der Waals equation.

76. The van der Waals Equation
) (V − nb) = nRT
n2a V2
(P +