1. The Behavior of Gases

2. Review of KMT of Gases Assumptions
Gases consist of tiny particles far apart from one another
Collision between gas particles are elastic, with no loss of KE
Gas particles are in constant, rapid motion.
No forces of attraction or repulsion exist between gas particles
Average KE of particles depends on absolute temperature of the gas

3. Review of Pressure Pressure is force per unit area
SI unit of force is the Newton (N)
SI unit of pressure is the pascal
1Pa = 1N/m2

4. 14.1 Properties of Gases Compressibility
Factors affecting Gas Pressure
Amount of gas (n)
number of particles, i.e. moles of gas
Volume (V)
space occupied by the gas
Temperature (T, absolute temperature)
Recall TK = TC + 273

5. 14.2 The Gas Laws
The gas laws describe the relationship of the 4 important variables that describe gas behavior
Pressure (P)
Moles (n)
Volume (V)
Temperature (T in Kelvins)

6. Boyle’s Law: Pressure & Volume
Volume is inversely related to Pressure
When Pressure increases, Volume decreases
If temperature and moles are constant

7. Practice Problems page 419
Given a volume of 2.50 L, if the pressure of N2O (an anesthetic) decreases from 105 kPa to 40.5 kPa, what is its new volume? (assume n & T are constant)
If 4.00 L of NH3 at 205 kPa is allowed to expand to 12.0L, what is the new pressure if T and n remain constant?

8. Charles’ Law: Volume and Temperature
Volume is directly proportional to absolute temperature
When temperature of an enclosed gas increases, its volume increases
If pressure is constant

9. Sample Problems page 421
If a sample of CO2 occupies a volume of 6.80 L at 325ºC, what will its volume be at 25ºC if the pressure does not change?
Exactly 5.00 L of air at -50.0ºC is warmed to 100.0ºC. What is the new volume if pressure remains constant?

10. Gay-Lussac Law: Pressure and Temperature
Pressure is directly proportional to absolute temperature
As the temperature of an enclosed gas increases, its pressure increases if volume is constant

11. Gay-Lussac Law

14. Sample Problems page 423
A sample of N2 gas has a pressure of 6.58 kPa at 539K. If the volume does not change, what will the pressure be at 211K?
The pressure in a car tire is 198 kPa at 27ºC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire?

15. The Combined Gas Law: Pressure, Volume and Temperature
Combines Boyle’s, Charles’, and Gay-Lussac’s Laws
Relates pressure, volume and temperature

16. Sample Problems page 424
A gas at 155 kPa and 25ºC has an initial volume of 1.00L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125ºC. What is the new volume?
A 5.00 L sample of air has a pressure of 107 kPa at 50.0ºC. If the temperature is raised to 102ºC and the volume expands to 7.00 L, what will the new pressure be?

17. 14.3 Ideal Gases
Gases at ordinary temperatures and pressures comply with the assumptions of the KMT of gases
These are called ideal gases
Gases at extremely low temperatures and/or extremely high pressures do not
These are called real gases

18. Avagadro’s Law: Moles & Volume
The volume of a confined gas is directly proportional to moles of a gas
If the moles of gas increases, the volume of the gas increases
If temperature and pressure are constant
n = kV n/V = k
n1/V1 = n2/V2

19. Practice Problem
A cylinder of gas with a moveable piston contains mol N2 with a volume of 11.0 L. What is the new volume if 1.50 mol of CO2 is injected into the cylinder? Assume that pressure and temperature are unchanged and that the N2 and CO2 do not react with one another.
19.3 L

20. Molar Volume of Gases: Remember This!
At STP, the standard molar volume of any gas is 22.4L
One mole of a gas has a volume of 22.4L at STP
Use this as a conversion factor when solving stoichiometry problems involving gases

21. Practice Problems
A chemical reaction produces mol of oxygen gas. What is the volume of the gas at STP?
A reaction produced 98.0 mL of SO2 gas at STP.
a. How many moles of SO2 were produced?
b. What was the mass in grams of the gas?
c. What is the density of the gas?

22. 14.3 Ideal Gas Law: Pressure, Volume, Moles, Temperature
A single law that relates pressure, volume, moles, and temperature of a gas
PV=nRT
n is number of moles of gas
R is the ideal gas constant
Value of R varies depending on units used for pressure and volume

23. The Ideal Gas Constant

24. Sample Problems
A rigid hollow sphere containing 685 L He has a temperature of 621K and a pressure of 1.89 x 103 kPa. How many moles of He are in the sphere? (251 mol)
What volume will 12.0 g of methane gas (CH4) occupy at a temperature of 25ºC and pressure of 0.52 atm?
A gaseous product of a reaction is collected in a 30.0 L container at 25ºC. The measured pressure of the gas was kPa. The mass of gas produced was about 116 g. What is the molar mass of the gas?

25. Ideal Gases and Real Gases
Ideal gases are real gases which comply with the ideal gas equation
Real gases deviate from the ideal gas equation at low temperatures and high pressures
This is because the assumptions of KMT are no longer valid at low T and high P

26. Real Gases Deviate from the Ideal

27. 14.4 Gas Mixtures and Movements
Very often gases are mixtures
Pure substances
Homogeneous mixtures
Solutions
The total pressure of a mixture of gases is the sum of the pressures of each individual gas (component gas) in the mixture

28. Dalton’s Law of Partial Pressures

29. Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases is the sum of the partial pressure of each component of the mixture
Partial pressure is the pressure of each gas within a mixture of gases

30. Example of Dalton’s Law
If you mix 2 moles O2 at 0.12 atm with 2 moles of N2 at 0.12 atm, the total pressure is the sum of the partial pressures.
Do Problem 32, p. 434

31. Mole Fraction can be used to calculate partial pressures
The mole fraction of a gas is the moles of a gas divided by the total moles of gas in a mixture
X = moles x/ total moles
In a mixture of 200 moles of O2 and 500 moles N2, what is the mole fraction of O2?
XO2 = 200 mol O2/700 mol = 0.29
Suppose this mixture had a total pressure of 600 kPa. What is the PO2?
PO2 = XO2 · Ptotal = 0.29 x 600 kPa = 174 kPa

32. Graham’s Law of Effusion
Diffusion
Movement of molecules from an area of higher concentration to lower concentration

33. Effusion Effusion Rate of effusion
Movement of gas molecules through a pinhole
Rate of effusion
How much gas effuses per second
Sometimes velocity is used

34. Graham’s Law of Effusion
At a given temperature, lower mass molecules diffuse and effuse faster than greater mass molecules
This is because they have the same KE
KE = ½ mv2