1. Gases
AP Chemistry
Chapter 5

2. Tenets of the Kinetic Molecular Theory of Gases
Gas particles are in constant random motion. Each molecule moves in a straight line until it collides with another object. These collisions are elastic (no net loss of kinetic energy)
Gas particles exert no forces on each other (they neither attract nor repel each other)
The volume of the gas molecule is negligible compared to the distance between the particles
The average kinetic energy of the particles is directly proportional to the Kelvin temperature of the gas.

3. Visualizing Molecular Motion: Many Molecules
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4. Real vs Ideal Gases
Kinetic Molecular Theory helps to explain the behavior of Ideal Gases.
Important to note that gases do not always behave ideally… Why?
Real gases DO have attractive forces between them
Real gases DO have a volume associated with the particles

5. When do real gases deviate from Ideal behavior?
Under conditions of very low temperature – Molecules are moving slowly and attractive forces may be significant
Under conditions of high pressure – molecules are close together and molecular volume may be significant
Molecules that behave least ideally would be polar and large.

6. Gas Pressure
Gas pressure results from molecules colliding with the walls of their container.
Pressure = force
area
Common gas pressure units:
mmHg, torr, atm, kPa

7. A barometer is a tube completely full of mercury that is inverted in a dish of mercury.
The Hg flows out of the tube until the pressure applied by the column of Hg is equal to the pressure applied by the atmosphere on the Hg in the dish.
760 mmHg = atmospheric pressure at sea level

8. Manometers are used to determine the pressure difference between the atmosphere and a reaction vessel.
In the diagram, assume that the right side (low pressure) is open to the atmosphere (760 mmHg). If the left side (high pressure) is connected to a flask, the pressure in that flask would be 768 mmHg.

9. Pressure Conversions 1 atm = 760 mmHg = 760 torr = 101.3 kPa
Convert 54.8 kPa to mmHg.
54.8 kPa x 760 mmHg
101.3 kPa
= 411 mmHg

10. Boyle’s Law
The pressure of a sample of gas is inversely related to the volume of the gas at constant temperature
P1V1 = P2V2

11. Boyle's Law: A Molecular-Level View
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12. Charles’ Law
The volume of a sample of gas is directly proportional to the absolute (Kelvin) temperature of the gas at constant pressure
V1 V2
T1 T2 =
Reminder: K = ºC

13. Charles's Law: A Molecular-Level View
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14. Gay-Lussac’s Law
The pressure of a sample of gas is directly proportional to the absolute (Kelvin) temperature of the gas at constant volume
P1 P2
T T2 =

15. Avogadro’s Law
Equal volumes of gases at the same temperature and pressure will contain the same number of molecules
In other words: The volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.
V1 V2
n1 n2 =

16. Ideal Gas Law
Combines relationships between volume, pressure, absolute temperature, and number of moles of gas
PV = nRT
R = ideal gas law constant
R = L·atm/K·mol
R = 8.31 L·kPa/K·mol
Pay attention to units!

17. The Ideal Gas Law, PV = nRT
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18. Ideal Gas Law and Molar Mass
molar mass = grams/mole
rearrange to:
moles = grams/molar mass
Plug into Ideal Gas Law:
PV = _(mass)RT__
(molar mass)

19. Ideal Gas Law and Density
Density = mass /volume
Rearrange Ideal Gas Law
Mass P(molar mass)
V RT
Density = =

20. Dalton’s Law
Dalton’s Law of Partial Pressures says that for a mixture of gases in a container, the total pressure is equal to the sum of the partial pressures of each gas.
Ptotal = PA+ PB + PC + etc

21. Use: PT(XA) = PA where XA is the mole fraction of substance A.
Ex: A container holds 2.00 moles of He, 1.50 moles of Ne, and 0.80 moles of Ar. The total pressure in the container is 50.0 kPa. Determine the partial pressure of each gas in the mixture.
Use: PT(XA) = PA where XA is the mole fraction of substance A.
PHe = 50.0 kPa (2.00 mol/4.30 mol) = 23.3 kPa

22. Gas Collection over Water
When you collect a gas sample over water, the “gas” collected contains both water vapor as well as the gas being produced.
PT = Pgas + Pwater

23. Temperature and KE
The Kelvin temperature of a gas is directly proportional to the average kinetic energy of the molecules
For a mole of gas:
(KE)ave = 3/2 RT
where: R = 8.31 J/mol*K
T = Kelvin Temp
Note: 1 joule = 1 kg*m2/s2

24. Root Mean Square Velocity
Root mean square velocity (urms) is an average molecular speed of molecules in a sample.
Reminder: for a particle, KE = ½ mu2
Where KE = average KE in joules
u2 = mean (ave) square speed in m/s
m = mass of the molecule in kg

25. urms = u2 = 3RT where M = molar mass M
Combining average KE equations results in
NA(½ mu2) = 3/2 RT
where: NA = Avogadro’s #
Since NA*m = molar mass and with simplifying
urms = u2 = 3RT where M = molar mass M

26. Ex: Calculate the root mean square velocity of nitrogen gas at 25ºC.
urms = 3(8.31J/K*mol)(298K)
kg/mol
= 515 m/s

27. Diffusion and Effusion
Diffusion is the gradual mixing of one gas with another gas.
Effusion is the passage of a gas through a small hole into a vacuum

28. Graham’s Law of Effusion
The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles
Rate of effusion gas 1 M2
Rate of effusion gas 2 M1 =