1. Kinetic Molecular Theory
Postulates of the Kinetic Molecular Theory of Gases
Gases consist of particles (atoms or molecules) in constant, straight-line motion.
Gas particles do not attract or repel each other (no interactions). Particles collide with each other and surfaces elastically. Collisions with walls of container define pressure (P = F/A).
Gas particles are small, compared with the distances between
them. Hence, the volume (size) of the individual particles can be assumed
to be negligible (zero).
4. The average kinetic energy of the gas particles is directly proportional
to the Kelvin temperature of the gas

2. Properties of Gases Gases expand to fill any container.
random motion, no attraction
Gases are fluids (like liquids).
particles flow easily
Gases have very low densities.
lots of empty space; particles spaced far apart
Gases are easily compressible.
empty space reduced to smaller volume
Courtesy Christy Johannesson

3. Collisions of Gas Particles Pressure = collisions on container walls

4. Changing the Size of the Container
In a smaller container - particles have less room to move.
Particles hit the sides of the container more often.
This causes an increase in pressure.
As volume decreases: pressure increases.

5. Pressure = Force/Area
KEY UNITS AT SEA LEVEL (also known as standard pressure)
kPa (kilopascal)
1 atm
760 mm Hg
760 torr
14.7 psi
Sea level
Courtesy Christy Johannesson

6. Barometers
Mount Everest
Sea level
Sea level On top of Mount Everest

7. Temperature K = ºC + 273 ºF ºC K
Always use temperature in Kelvin when working with gases. Std temperature = 273 K ºF
-459 32
212 ºC
-273
100 K
273
373
K = ºC + 273
Courtesy Christy Johannesson

8. Standard Temperature & Pressure
STP
STP
Standard Temperature & Pressure
0°C K
1 atm kPa
- OR -
Courtesy Christy Johannesson

9. Boyle’s Law As the pressure on a gas increases - the volume decreases
1 atm
As the pressure on a gas increases -
the volume decreases
Pressure and volume are inversely related
As the pressure on a gas increases
2 atm
4 Liters
2 Liters

10. Boyle’s Law Illustrated
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 404

11. PV = k Boyle’s Law P1 x V1 = P2 x V2
Volume
(mL)
Pressure
(torr)
P.V
(mL.torr)
10.0
20.0
30.0
40.0
760.0
379.6
253.2
191.0
7.60 x 103
7.59 x 103
7.64 x 103
The pressure and volume of a gas are inversely related
at constant mass & temp
PV = k
P1 x V1 = P2 x V2
Courtesy Christy Johannesson

12. Boyle’s Law example
A quantity of gas under a pressure of kPa has a volume
of 380 cm3. What is the volume of the gas at standard
pressure, if the temperature is held constant?
P1 x V1 = P2 x V2
(106.6 kPa) x (380 cm3) = (101.3 kPa) x (V2)
V2 = 400 cm3

13. Charles’s Law
Timberlake, Chemistry 7th Edition, page 259

14. If you start with 1 liter of gas at 1 atm pressure and 300 K
and heat it to 600 K one of 2 things happens

15. Either the volume will increase to 2 liters at 1 atm
600 K
300 K
Either the volume will increase to 2 liters at 1 atm

16. 300 K
600 K
Or the pressure will increase to 2 atm.

17. Charles’ Law
Volume
(mL)
Temperature
(K)
V / T
(mL / K)
40.0
44.0
47.7
51.3
273.2
298.2
323.2
348.2
0.146
0.148
0.147
The volume and absolute temperature (K) of a gas are directly related
at constant mass & pressure
V1 / T1 = V2 / T2
Courtesy Christy Johannesson

18. Gay-Lussac’s Law P1 / T1 = P2 / T2
The pressure and absolute temperature (K) of a gas are directly related
at constant mass & volume
Temperature (K)
Pressure
(torr)
P/T
(torr/K)
248
691.6
2.79
273
760.0
2.78
298
828.4
373
1,041.2
Joseph Louis Gay-Lussac ( , France) His experiments led him to propose in 1808 the Law of Combining Volumes, which states that the volume of gases involved in a chemical reaction are in a small whole number ratio.
P1 / T1 = P2 / T2
Courtesy Christy Johannesson

19. V T PV T P T PV = k P1V1 T1 = P2V2 T2 P1V1T2 = P2V2T1
Combined Gas Law V T PV T P T PV
= k
P1V1 T1 =
P2V2 T2
P1V1T2 = P2V2T1
Courtesy Christy Johannesson

20. The Combined Gas Law
A quantity of gas has a volume of 400 cm3 at STP. What volume will it occupy at 35oC and 83.3 kPa?
( kPa) x (400 cm3) = (83.3 kPa) x (V2)
273 K
308 K
P1 = kPa
T1 = 273 K
V1 = 400 cm3
P2 = kPa
T2 = 35oC = 308 K
V2 = ? cm3
V2 = cm3

21. The Combined Gas Law
When measured at STP, a quantity of gas has a volume of 500 cm3. What volume will it occupy at 20oC and 93.3 kPa?
( kPa) x (500 cm3) = (93.3 kPa) x (V2)
273 K
293 K
P1 = kPa
T1 = 273 K
V1 = 500 cm3
P2 = kPa
T2 = 20oC = 293 K
V2 = ? cm3
V2 = cm3

22. Molar Volume (Avogadro)
1 mol of all STP have a volume of 22.4 L
Avogadro’s Law V1/n1 = V2/n2
MOLAR VOLUME
One mole of any gas occupies 22.4 liters at standard temperature and pressure (STP).
Timberlake, Chemistry 7th Edition, page 268

23. PV = nRT Ideal Gas Law Brings together all gas properties.
P = pressure
V = volume (must be in liters)
n = moles
R = universal gas constant (0.082 or 8.314)
T = temperature (must be in Kelvin)
Can be derived from experiment and theory.

24. Ideal Gas Law
What is the pressure of 0.18 mol of a gas in a 1.2 L flask at 298 K?
PV = nRT
P x (1.2 L) = (0.18 mol) x (.082) x (298 K)
P = ? atm
n = 0.18 mol
T = 298 K
V = 1.2 L
R = .082 (L x atm)/(mol x K)
P = 3.7 atm

25. D = (MM)P/RT Gas Density
Larger particles are more dense. Gases are more dense at
higher pressures and lower temperatures
D = density (in g/L)
P = pressure
MM = molar mass (g/mol)
R = universal gas constant
T = temperature (must be in Kelvin)
Can be derived from experiment and theory.

26. Gas Problems
1. The density of an unknown gas is 0.010g/ml. What is the molar mass of this gas measured at C and 3.25 atm? Use proper sig figs.
g/mol = (0.010g/ml) x (.082atm L/mol K) x (262 K) x (1/3.25 atm) x (1000ml/1 L)
Molar mass = ? g/mol
D = g/ml
T = 262 K
P = 3.25 atm
R = .082 (L atm)/(mol K)
P = 66 g/mol

27. Gas Problems
2. What is the volume of 3.35 mol of gas which has a measured temperature of 47.00C and a pressure of 185 kPa? Use proper sig figs.
(185 kPa) x (V) = (3.35 mol) x (8.314 L kPa/mol K) x (320 K)
PV = nRT
V = ? L
n = 3.35 mol
T = 320 K
P = 185 kPa
R = (L kPa)/(mol K)
V = L

28. Ptotal = P1 + P2 + ... Dalton’s Law
The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.
Ptotal = P1 + P
In a gaseous mixture, a gas’s partial pressure is the one the gas would exert if it were by itself in the container.
The mole ratio in a mixture of gases determines each gas’s partial pressure.
Courtesy Christy Johannesson

29. Gas Mixtures and Dalton’s Law

30. Gas Collected Over Water
When a H2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H2 and water vapor.

31. Look up water-vapor pressure on p.10 for 22°C.
Dalton’s Law
Hydrogen gas is collected over water at 22°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.
The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H2 and water vapor.
GIVEN:
PH2 = ?
Ptotal = 94.4 kPa
PH2O = 2.6 kPa
WORK:
Ptotal = PH2 + PH2O
94.4 kPa = PH kPa
PH2 = 91.8 kPa
Look up water-vapor pressure on p.10 for 22°C.
Courtesy Christy Johannesson

32. Dalton’s Law
The total pressure of mixture (3.0 mol He and 4.0 mol Ne) is 97.4
kPa. What is the partial pressure of each gas.
3 mol He
7 mol gas
PHe =
(97.4 kPa) =
41.7 kPa
4 mol Ne
7 mol gas
PNe =
(97.4 kPa) =
55.7 kPa

33. Dalton’s Law
Suppose you are given four containers – three filled with noble gases.
The first 1 L container is filled with argon and exerts a pressure of 2 atm.
The second 3 liter container is filled with krypton and has a pressure of
380 mm Hg. The third 0.5 L container is filled with xenon and has a
pressure of kPa. If all these gases were transferred into an empty
2 L container…what would be the pressure in the “new” container?
PKr = 380 mm Hg
Ptotal = ?
PAr = 2 atm
Pxe
607.8 kPa
V = 1 liter V = 3 liters V = 0.5 liter V = 2 liters

34. “Total Pressure = Sum of the Partial Pressures”
…just add them up
PKr = 380 mm Hg
Ptotal = ?
PAr = 2 atm
Pxe
607.8 kPa
V = 1 liter V = 3 liters V = 0.5 liter V = 2 liters
Dalton’s Law of Partial Pressures
“Total Pressure = Sum of the Partial Pressures”
PT = PAr + PKr + PXe + …
P1 x V1 = P2 x V2
P1 x V1 = P2 x V2
(0.5 atm) (3L) = (X atm) (2L)
(6 atm) (0.5 L) = (X atm) (2L)
PKr = atm
Pxe = 1.5 atm
PT = 1 atm atm atm
PT = atm

35. Partial Pressure
A gas is collected over water at 649 torr and 26.00C. If its volume when collected is 2.99 L, what is its volume at STP? Use proper sig figs.
(83.1 x 2.99) / 299 = ( x V2) / 273
P1V1/T1 = P2V2/T PT = PG + Pw
V2 = ? L
V1 = 2.99 L
T1 = 299 K
T2 = 273 K
PT = 649 torr
P1 = 86.5 kPa – 3.4 kPa = 83.1 kPa
P2 = kPa
V2 = L

36. Gas Stoichiometry
Find the volume of hydrogen gas made when 38.2 g zinc react with excess hydrochloric
acid. Pressure =107.3 kPa; temperature = 88oC.
Zn (s) HCl (aq)  ZnCl2 (aq) + H2 (g)

37. Gas Stoichiometry
Find the volume of hydrogen gas made when 38.2 g zinc react with excess hydrochloric
acid. Pressure =107.3 kPa; temperature = 88oC.
Zn (s) HCl (aq)  ZnCl2 (aq) + H2 (g)
38.2 g excess V = ? L H2
P = kPa
T = 88oC (361 K)
At STP, we’d use 22.4 L per mol, but we aren’t at STP.

38. Pressure and Balloons B When balloon is being filled: PA > PB A
When balloon is filled and tied:
PA = PB
When balloon deflates:
PA < PB
A = pressure exerted BY balloon
B = pressure exerted ON balloon

39. Balloon Riddle A B C When the balloons are untied,
will the large balloon (A) inflate
the small balloon (B); will they
end up the same size or will the
small balloon inflate the large
balloon?
Why? B C