1. Gases

2. General Characteristics of Gases
Highly compressible.
Occupy the full volume of their containers.
When gas is subjected to pressure, its volume decreases.
Gases always form homogeneous mixtures with other gases.
Gases only occupy about 0.1 % of the volume of their containers.

3. Four Physical Quantities for Gases
Phys. Qty.
Symbol
SI unit
Other common units
pressure P
Pascal (Pa)
atm, mm Hg, torr, psi
volume V m3
dm3, L, mL, cm3
temp. T K
°C, °F
moles n
mol

4. Figure 10.2: Pressure Atmosphere Pressure and the Barometer
Standard atmospheric pressure = 760 mm of Hg
1 atm = 760 mmHg = 760 torr = kPa.

5. Units: Force and Pressure

7. Units: Force and Pressure – F12

8. Figure 10.3: Pressure
Closed Systems => manometers

9. The Empirical Gas Laws
Figure 10.7: The Pressure-Volume Relationship: Boyle’s Law

10. The Empirical Gas Laws The Pressure-Volume Relationship: Boyle’s Law
Mathematically:
A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?

11. A sample of gas contained in a flask with a volume of 1
A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?

12. The Empirical Gas Laws
The Temperature-Volume Relationship: Charles’s Law
Charles’s Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases.
Mathematically:
A sample of gas at 15°C and 1 atm has a volume of L. What will be the new volume if temp. is increased to 38°C at constant pressure?

13. Example Calculation
A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?

14. Figure 10.9

15. The Empirical Gas Laws
The Quantity-Volume Relationship: 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.
Mathematically:

16. The Ideal Gas Equation Boyle’s Law:
We can combine these into a general gas law:
Boyle’s Law:
Charles’s Law:
Avogadro’s Law:

17. The Ideal Gas Equation R = gas constant, then
The ideal gas equation is:
R = L·atm/mol·K = J/mol·K
J = kPa·L = kPa·dm3 = Pa·m3
Real Gases behave ideally at low P and high T.

18. Gas Examples
A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.
At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?
A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas?
What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]

19. A sample of H2 gas has a volume of 8
A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.

20. At a constant temperature of 25°C and a pressure of 1 atm, a 12
At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?

21. A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas?
V2 = 3.07 L
n = mol

22. What is the molar volume of an ideal gas at STP
What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]
Key – F14

23. Density of an Ideal-Gas
Gas Densities and Molar Mass
The molar mass of a gas can be determined as follows:
The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?

24. Density of an Ideal-Gas

25. Density of an Ideal-Gas – F12

26. Density Calculation
The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?
HW Key

27. 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:
Each gas obeys the ideal gas equation:

28. Gas Mixtures and Partial Pressures
Partial Pressures and Mole Fractions
Let ni be the number of moles of gas i exerting a partial pressure Pi, then
where i is the mole fraction (ni/nt).
CyberChem Diving video

29. Kinetic Molecular Theory
Assumptions:
Gases consist of a large number of molecules in constant random motion.
Volume of individual molecules negligible compared to volume of container.
Intermolecular forces (forces between gas molecules) negligible.

30. How fast can gas molecules move?

31. Kinetic Molecular Theory
Graham’s Law of Effusion
Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion).
Figure 10.20

32. Kinetic Molecular Theory
Diffusion
Diffusion of a gas is the spread of the gas through space and the mixing through other gases.
Diffusion is faster for light gas molecules.
Diffusion is slowed by gas molecules colliding with each other.

33. Kinetic Molecular Theory
Graham’s Law of Effusion
Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by:
Also works for Comparison of Diffusion rates

34. Kinetic Molecular Theory
Figure 10.19: Molecular Effusion and Diffusion
The lower the molar mass, M, the higher the rms.

35. Why Low Pressure?...Ideal Figure 10.23
Real Gases behave ideally at low P and high T.
Why Low Pressure?...Ideal
Figure 10.23

36. Why High Temperature?...Ideal
Real Gases behave ideally at low P and high T.
Why High Temperature?...Ideal
Figure 10.24

37. Real Gases: Deviations from Ideal Behavior
The van der Waals Equation
General form of the van der Waals equation:
Corrects for molecular volume
Corrects for molecular attraction

38. Gases