11.1 and 11.2 Development of the Kinetic Theory of Gases
• The kinetic Theory of Gases
– Gases are made up of molecules with lots of empty space between
– Particles move quickly - pressure is caused by this motion
– Collisions are completely elastic
– There are no attractive or repulsive forces between molecules
– KE = ½ mv 2

• Properties of Gases resulting from the KTG
– Expansion - no definite shape or definite volume
– Fluidity - particles glide past each other ( gases and liquids are both fluids)
– Low Density - gases are roughly 1/1000 the density of solids and liquids
– Compressibility
– Diffusion - spontaneous mixing of 2 substances due to random molecular motion
– Effusion - a gas spreads through a small opening between containers

• A qualitative description of gases:
– P = Pressure (mmHg, kPa, atm)
– T = Temperature (K, C o )
– V = Volume (mL, L)
– n = moles

• Describes the relationship between Pressure,
Temperature, and Volume.
• Formula:
– P
1
V
1
= P
2
V
2
T1 T
2
• STP = standard temperature and pressure:
– Pressure units: 101.3 kPa, 760 torr, 1 atm, 760 mmHg
– Temperature units: 273 K, O C 0 ( must use K with gas laws)
– Volume: if one mole is present, then 22.4 L

• 2.0 atm = ______ Kpa
• 560mmHg = ______ torr
• 35 o c = _____ K
• 298 K = _____ c o
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• The volume of a gas varies inversely with pressure at constant temperature.
– Formula:
P
1
V
1
= P
2
V
2
T1 T
2
• P
1
V
1
= P
2
V
2
– As the applied (outside pressure) increases, the volume decreases.
• Graph:
V
P

• Ex1: If 150. ml of a sample of O
2 at 720.0 mm
Hg has the pressure increased to 750.0 mm Hg, what is the new volume?
x = 144 mL

• The volume of a fixed mass of gas varies directly with temperature at constant pressure.
– Formula:
P
1
V
1
= P
2
V
2
T1 T
2
• V
1
= V
2
T
1
T
2
• As the temperature increases, the volume v increases. (hot air balloon)
When the graph is extrapolated to 0 K, the volume is 0.
This is impossible as the gas would have volume of all the particles with no space between them. Of course, this is impossible to test since no gases exist at - 273 C 0 (only solids and liquids).
t

• If 753 ml of nitrogen at 25 C 0 is heated to
50. C 0 , then what is the new volume?
820 mL

• The pressure of a fixed mass of gas varies directly with temperature at constant volume
– Formula: P
1
V
1
= P
2
V
2
T1 T
2
• P
1
= P
2
T
1
T
2
– As the temperature increases, the pressure increases. p t

• If a gas at 3.0 atm and 25 C0 is heated to
52 C0, what is the new pressure?
3.3 atm

• The relationship between pressure, volume, and temperature when the amount of gas is fixed
– Formula
P
1
V
1
= P
2
V
2
T
1
T
2

• If a sample of gas at 22.0
o c and 31 kPa occupies 200.0 cm 3 , what space will it occupy at
STP?

• A 350 mL air sample collected at 35 o C has a pressure of 550 mmHg. What pressure will the air exert if it is allow to expand to 425 mL and
57 o C?
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• The total pressure of a collection of gases in a mixture is equal to the sum of the pressures that each gas would exert by itself in the same volume.
– Formula: P
T
= P
1
+ P
– Collecting gas over water:
2
.....
P total
= P water
+ P hydrogen
H
2
O
(g)
H
2
O
(g)
H
2
O
(g)
Zn
(s)
+ H
2
SO
4(aq)

ZnSO
4(aq)
+ H
2(g)

• A student collects oxygen gas over water at an atmospheric pressure of 100.0 kPa and a temperature of 29.0 C 0 . What is the partial pressure of the oxygen?
At 29.0 C 0 water has a pressure of 30.0 mmHg (or 4.00 kPa).
100.0 kPa = 4.00 kPa + P oxygen
P oxygen
= 96.0 kPa

• Graham noticed that gases with low densities diffuse faster than gases with higher densities.
• Under the same conditions of temperature and pressure, gases diffuse at a rate inversely proportional to the square roots of their densities
(or molecular mass).

• Formulas: rate of gas “A” = rate of gas “B” density of gas “B” density of gas “A” velocity of gas “A” = velocity of gas “B” molecular weight of gas “B” molecular weight of gas “A”
This comes from KE = ½ mv 2

• If CO
2 molecules travel at 200.0 mph, how fast do H
2 molecules go? x = 938.1 mph

• If He atoms travel at 800.0 mph, how fast do nitrogen molecules go?
x = 330.8 mph

• In Boyle’s Law, Pressure = Force/Area. So….
½ the volume means 2x the particles So, 2x the pressure
• In Charle’s Law, temperature is proportional to KE.
So....
-doubling temperature = doubling KE
-doubling KE = doubling pressure (doubles the number of collisions)
-in order to keep pressure the same (constant), volume must double instead

• In Gay-Lussac’s Law, temperature is proportional to KE. So...
– doubling temperature = doubling KE
– doubling KE = doubling pressure (doubles the number of collisions)
– volume is constant, so the pressure does change
• In Dalton’s Law of Partial Pressures, if gas A exerts a pressure of 5 collisions/second and gas B exerts a pressure of 5 collisions/second, then the total # of collisions/second should = 10 (their sum).

• To what temperature must a sample of nitrogen at 27 o C and 0.625 atm be heated so that its pressure becomes 855 mmHg at constant volume?
• If the pressure exerted on a 240 mL sample of hydrogen gas at constant temperature is increased from 325 mmHg to 550 mmHg, what will be the final volume of the sample?

• A sample of gas is collected over water at a temperature of 35.0
o when the barometric pressure reading is 742 mmHg. What is the partial pressure of the dry gas?
• A sample of air has a volume of 140 mL at 67 o C.
To what temperature must the gas be lowered to reduce its volume to 50 mL at constant pressure?

• If CO atoms travel at 300.0 mph, how fast do chlorine molecules go?
• A gas measures of 1.75 L at -23 o C and
150 kPa. At what temperature would the gas occupy 1.30 L at 210 kPa?

http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm