1. Unit 8
Gases

2. Overview Characteristics of Gas Pressure Gas Laws Ideal Gases
Partial Pressures
Mole Fractions
Gas Laws
Boyles Law
Charles Law
Avogadro’s Law
Guy-Lussac’s Law
Ideal Gas Law
Ideal Gases
Real Gases
Density of Gases
Volumes of Gases
Standard molar volume
Gas stoichiometry
Effusion/Diffusion
Graham’s Law

3. Characteristics of Gases
Expansion – gases expand to fill their containers
Compression – gases can be compressed
Fluids – gas particles flow past each other
Density – gases have low density
1/1000 the density of the equivalent liquid or solid
Gases effuse and diffuse

4. Kinetic Molecular Theory
Gases consist of large numbers of tiny particles that are far apart relative to their size.
Collisions between gas particles and between particles and container walls are elastic.
Elastic collision – collision in which there is no net loss of kinetic energy
Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy.
There are no forces of attraction between gas particles.
The temperature of a gas depends on the average kinetic energy of the particles of the gas.

5. Kinetic Energy of Gas Particles
At the same conditions of temperature, all gases have the same average kinetic energy
m = mass
v = velocity
At the same temperature, small molecules move FASTER than large molecules

6. Speed of Molecules V = velocity of molecules M = molar mass
R = gas constant
T = temperature

7. Pressure
A force that acts on a given area
Pressure =
Force
Area

8. Measuring Pressure
The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century
Called a barometer
The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high

9. Units of Pressure 1 atmosphere (atm)
760 mm Hg (millimeters of mercury)
760 torr
1.013 bar
Pa (pascals)
101.3 kPa (kilopascals)
14.7 psi (pounds per square inch)

10. Temperature

11. STP
Standard Temperature and Pressure (STP)
1 atmosphere
273 K

12. Dalton’s Law of Partial Pressures
Partial pressure – pressure exerted by particular component in a mixture of gases
Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases
Pt = P1 + P2 + P3+…

13. Mole Fraction P1 = Pt or P1 = X1Pt X1 = mole fraction of gas 1
Mole fraction – expresses the ratio of the number of moles of one component to the total number of moles in the mixture
P1 = Pt or P1 = X1Pt
X1 = mole fraction of gas 1
Example: The mole fraction of N2 in air is 0.78 (78% of air is nitrogen). What is the partial pressure of nitrogen in mmHg?
PN2 = (0.78)(760 mmHg) = 590 mmHg

14. Collecting Gas Over Water
Gas collected by water displacement is always mixed with a small amount of water vapor
Must account for the vapor pressure of the water molecules
Ptotal = Pgas + PH2O
Note: The vapor pressure of water varies with temperature

15. The Gas Laws Robert Boyle Amadeo Avogadro Joseph Louis Gay-Lussac
Jacques Charles

16. Boyles Law
Pressure is inversely proportional to volume when temperature is held constant.

17. Temperature MUST be in KELVINS!
Charles Law
The volume of a gas is directly proportional to temperature.
(P = constant)
Temperature MUST be in KELVINS!

18. Temperature MUST be in KELVINS!
Gay-Lussac’s Law
The pressure and temperature of a gas are
directly related, provided that the volume
remains constant.
Temperature MUST be in KELVINS!

19. Combined Gas Law
Expresses the relationship between pressure, volume and temperature of a fixed amount of gas

20. For example, doubling the moles will double the volume of a gas
Avogadro’s Law
For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).
V = constant × n
V = volume of the gas
n = number of moles of gas
For example, doubling the moles will double the volume of a gas

21. Ideal Gases
Imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory

22. Ideal Gas Law PV = nRT P = pressure V = volume n = moles
R = ideal gas constant
T = temperature (Kelvin)
Numerical Value of R
Units
0.0821
(atm∙L)/(mol∙K)
8.314
J/(mol∙K)
62.4
(mmHg∙L)/(mol∙K)
Note: 1 J = 1 Pa∙m3

23. Standard Volume STP of 1 mole of gas = 1 atm and 273K PV = nRT
(1atm)(V) = (1mol)(.0821)(273)
V = 22.4 L
Volume of 1 mole of gas at STP = 22.4 liters

24. Real Gases
Real Gas – does not behave completely according to the assumptions of the kinetic molecular theory
At high pressure (smaller volume) and low temperature gases deviate from ideal behavior
Particles will be closer together so there is insufficient kinetic energy to overcome attractive forces

25. Real Gases
The Van der Waals Equation adjusts for non-ideal behavior of gases (p. 423 of book)
corrected pressure
corrected volume
Pideal
Videal

26. Density of Gases
… so at STP…

27. Density of Gases Combine density with the ideal gas law (V = p/RT)
M = Molar Mass
P = Pressure
R = Gas Constant
T = Temperature in Kelvins

28. Gas Stoichiometry #1
If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.
3 H2(g) N2(g)  NH3(g)
3 moles H mole N  moles NH3
3 liters H liter N  liters NH3

29. Gas Stoichiometry #2 3 H2(g) + N2(g)  2NH3(g)
How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?
3 H2(g) + N2(g)  2NH3(g)
12 L H2 2
L NH3
= L NH3
8.0 3
L H2

30. Gas Stoichiometry #3
How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
22.4 L O2
g KClO3
2 mol KClO3
1 mol O2
= 13.7 L O2

31. Stoichiometry #4
How many liters of oxygen gas, at 37.0C and atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s)  2 KCl(s) + 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
0.612 =
mol O2
g KClO3
2 mol KClO3
= 16.7 L

32. Diffusion
Spontaneous mixing of two substances caused by the random motion of particles
The rate of diffusion is the rate of gas mixing
The rate of diffusion increases with temperature
Small molecules diffuse faster than large molecules

33. Effusion
Process by which gas particles pass through a tiny opening

34. Graham’s Law of Effusion
Rate of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.
M1 = Molar Mass of gas 1
M2 = Molar Mass of gas 2