1. Gases and Kinetic Molecular Theory12
Gases and Kinetic Molecular Theory

2. CHAPTER GOALS Comparison of Solids, Liquids, and Gases
Composition of the Atmosphere and Some Common Properties of Gases
Pressure
Boyle’s Law: The Volume-Pressure Relationship
Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale
Standard Temperature and Pressure
The Combined Gas Law Equation
Avogadro’s Law and the Standard Molar Volume

3. CHAPTER GOALS Summary of Gas Laws: The Ideal Gas Equation
Determination of Molecular Weights and Molecular Formulas of Gaseous Substances
Dalton’s Law of Partial Pressures
Mass-Volume Relationships in Reactions Involving Gases
The Kinetic-Molecular Theory
Diffusion and Effusion of Gases
Real Gases: Deviations from Ideality

4. Comparison of Solids, Liquids, and Gases
The density of gases is much less than that of solids or liquids.
Densities (g/mL)
Solid
Liquid
Gas
H2O
0.917
0.998
CCl4
1.70
1.59
Gas molecules must be very far apart compared to liquids and solids.

5. Composition of the Atmosphere and Some Common Properties of Gases
Composition of Dry Air
Gas
% by Volume N2
78.09 O2
20.94 Ar
0.93
CO2
0.03
He, Ne, Kr, Xe
0.002
CH4 H2

6. Pressure Pressure is force per unit area.
lb/in2
N/m2
Gas pressure as most people think of it.

7. Pressure Atmospheric pressure is measured using a barometer.
Definitions of standard pressure
76 cm Hg
760 mm Hg
760 torr
1 atmosphere
101.3 kPa
Hg density = 13.6 g/mL

8. Boyle’s Law: The Volume-Pressure Relationship
V  1/P or
V= k (1/P) or PV = k
P1V1 = k1 for one sample of a gas.
P2V2 = k2 for a second sample of a gas.
k1 = k2 for the same sample of a gas at the same T.
Thus we can write Boyle’s Law mathematically as P1V1 = P2V2

9. Boyle’s Law: The Volume-Pressure Relationship
Example 12-1: At 25oC a sample of He has a volume of 4.00 x 102 mL under a pressure of 7.60 x 102 torr. What volume would it occupy under a pressure of 2.00 atm at the same T?

10. Boyle’s Law: The Volume-Pressure Relationship
Notice that in Boyle’s law we can use any pressure or volume units as long as we consistently use the same units for both P1 and P2 or V1 and V2.
Use your intuition to help you decide if the volume will go up or down as the pressure is changed and vice versa.

11. Charles’ Law: The Volume-Temperature Relationship
absolute zero = C

12. Charles’ Law: The Volume-Temperature Relationship
Charles’s law states that the volume of a gas is directly proportional to the absolute temperature at constant pressure.
Gas laws must use the Kelvin scale to be correct.
Relationship between Kelvin and centigrade.

13. Charles’ Law: The Volume-Temperature Relationship
Mathematical form of Charles’ law.

14. Charles’ Law: The Volume-Temperature Relationship
Example 12-2: A sample of hydrogen, H2, occupies 1.00 x 102 mL at 25.0oC and 1.00 atm. What volume would it occupy at 50.0oC under the same pressure?
T1 = = 298
T2 = = 323

15. Standard Temperature and Pressure
Standard temperature and pressure is given the symbol STP.
It is a reference point for some gas calculations.
Standard P  atm or kPa
Standard T  K or 0.00oC

16. The Combined Gas Law Equation
Boyle’s and Charles’ Laws combined into one statement is called the combined gas law equation.
Useful when the V, T, and P of a gas are changing.

17. The Combined Gas Law Equation
Example 12-3: A sample of nitrogen gas, N2, occupies 7.50 x 102 mL at 75.00C under a pressure of 8.10 x 102 torr. What volume would it occupy at STP?

18. The Combined Gas Law Equation
Example 12-4 : A sample of methane, CH4, occupies 2.60 x 102 mL at 32oC under a pressure of atm. At what temperature would it occupy 5.00 x 102 mL under a pressure of 1.20 x 103 torr?
You do it!

19. The Combined Gas Law Equation

20. Avogadro’s Law and the Standard Molar Volume

21. Avogadro’s Law and the Standard Molar Volume
Avogadro’s Law states that at the same temperature and pressure, equal volumes of two gases contain the same number of molecules (or moles) of gas.
If we set the temperature and pressure for any gas to be STP, then one mole of that gas has a volume called the standard molar volume.
The standard molar volume is 22.4 L at STP.
This is another way to measure moles.
For gases, the volume is proportional to the number of moles.
11.2 L of a gas at STP = mole
44.8 L = ? moles

22. Avogadro’s Law and the Standard Molar Volume
Example 12-5: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given temperature and pressure. (a) What is its molar mass? (b) What is its density at STP?

23. Summary of Gas Laws: The Ideal Gas Law
Boyle’s Law - V  1/P (at constant T & n)
Charles’ Law – V  T (at constant P & n)
Avogadro’s Law – V  n (at constant T & P)
Combine these three laws into one statement
V  nT/P
Convert the proportionality into an equality.
V = nRT/P
This provides the Ideal Gas Law.
PV = nRT
R is a proportionality constant called the universal gas constant.

24. Summary of Gas Laws: The Ideal Gas Law
We must determine the value of R.
Recognize that for one mole of a gas at 1.00 atm, and 273 K (STP), the volume is 22.4 L.
Use these values in the ideal gas law.

25. Summary of Gas Laws: The Ideal Gas Law
R has other values if the units are changed.
R = J/mol K
Use this value in thermodynamics.
R = kg m2/s2 K mol
Use this later in this chapter for gas velocities.
R = dm3 kPa/K mol
This is R in all metric units.
R = cal/K mol
This the value of R in calories rather than J.

26. Summary of Gas Laws: The Ideal Gas Law
Example 12-6: What volume would 50.0 g of ethane, C2H6, occupy at 1.40 x 102 oC under a pressure of x 103 torr?
To use the ideal gas law correctly, it is very important that all of your values be in the correct units!
T = = 413 K
P = 1820 torr (1 atm/760 torr) = 2.39 atm
50 g (1 mol/30 g) = 1.67 mol

27. Summary of Gas Laws: The Ideal Gas Law

28. Summary of Gas Laws: The Ideal Gas Law
Example 12-7: Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH4, measured at standard conditions.
You do it!

29. Summary of Gas Laws: The Ideal Gas Law

30. Summary of Gas Laws: The Ideal Gas Law
Example 12-8: Calculate the pressure exerted by 50.0 g of ethane, C2H6, in a 25.0 L container at 25.0oC.
You do it!

31. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances
Example 12-9: A compound that contains only carbon and hydrogen is 80.0% carbon and 20.0% hydrogen by mass. At STP, 546 mL of the gas has a mass of g . What is the molecular (true) formula for the compound?
100 g of compound contains 80 g of C and 20 g of H.

32. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

33. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

34. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances
Example 12-10: A 1.74 g sample of a compound that contains only carbon and hydrogen contains 1.44 g of carbon and g of hydrogen. At STP 101 mL of the gas has a mass of gram. What is its molecular formula?
You do it!

35. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

36. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

37. Dalton’s Law of Partial Pressures
Dalton’s law states that the pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases.
Ptotal = PA + PB + PC

38. Dalton’s Law of Partial Pressures
Example 12-11: If 1.00 x 102 mL of hydrogen, measured at 25.0 oC and 3.00 atm pressure, and 1.00 x 102 mL of oxygen, measured at 25.0 oC and 2.00 atm pressure, were forced into one of the containers at 25.0 oC, what would be the pressure of the mixture of gases?

39. Dalton’s Law of Partial Pressures
Vapor Pressure is the pressure exerted by a substance’s vapor over the substance’s liquid at equilibrium.

40. Dalton’s Law of Partial Pressures
Example 12-12: A sample of hydrogen was collected by displacement of water at 25.0 oC. The atmospheric pressure was 748 torr. What pressure would the dry hydrogen exert in the same container?

41. Dalton’s Law of Partial Pressures
Example 12-13: A sample of oxygen was collected by displacement of water. The oxygen occupied 742 mL at 27.0 oC. The barometric pressure was 753 torr. What volume would the dry oxygen occupy at STP?
You do it!

42. Dalton’s Law of Partial Pressures

43. Mass-Volume Relationships in Reactions Involving Gases
In this section we are looking at reaction stoichiometry, like in Chapter 3, just including gases in the calculations.
2 mol KClO3 yields mol KCl and 3 mol O2
2(122.6g) yields (74.6g) and 3 (32.0g)
Those 3 moles of O2 can also be thought of as:
3(22.4L) or 67.2 L at STP

44. Mass-Volume Relationships in Reactions Involving Gases
Example 12-14: What volume of oxygen measured at STP, can be produced by the thermal decomposition of g of KClO3?
You do it!

45. Mass-Volume Relationships in Reactions Involving Gases

46. 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.

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

48. 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.

49. 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.

50. 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.

51. 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.
Charles’ Law
V  T
An increase in temperature raises the molecular velocities, thus the V increases to keep the P constant.

52. The Kinetic-Molecular Theory

53. 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 = kg m2/s2 K mol
And M must be in kg/mol.

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

55. The Kinetic-Molecular Theory
Example 12-18: What is the root mean square velocity of He atoms at room T, 25.0oC?
You do it!

56. 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?

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

58. Diffusion and Effusion of Gases
This is a demonstration of diffusion.

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

60. Diffusion and Effusion of Gases
Example 12-15: Calculate the ratio of the rate of effusion of He to that of sulfur dioxide, SO2, at the same temperature and pressure.

61. 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?
You do it!

62. Real Gases: Deviations from Ideality
Real gases behave ideally at ordinary temperatures and pressures.
At low temperatures and high pressures real gases do not behave ideally.
The reasons for the deviations from ideality are:
The molecules are very close to one another, thus their volume is important.
The molecular interactions also become important.

63. Real Gases: Deviations from Ideality
van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures.
The van der Waals constants a and b take into account two things:
a accounts for intermolecular attraction
b accounts for volume of gas molecules
At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.

64. Real Gases: Deviations from Ideality
What are the intermolecular forces in gases that cause them to deviate from ideality?
For nonpolar gases the attractive forces are London Forces.
For polar gases the attractive forces are dipole-dipole attractions or hydrogen bonds.

65. Real Gases: Deviations from Ideality
Example 12-19: Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the ideal gas law.
You do it!

66. Real Gases: Deviations from Ideality
Example 12-20: Solve Example using the van der Waal’s equation.

67. Real Gases: Deviations from Ideality

68. Gases and Kinetic Molecular Theory12
Gases and Kinetic Molecular Theory