1. Gases Pressure Boyle’s Law Charles’ Law Gay-Lussac’s Law
Avogadro’s Law
Ideal Gas Equation
Dalton’s Law
Effusion and Diffusion
Kinetic-Molecular Theory
Real Gases

2. Elemental states at 25oC Solid Liquid Gas He Rn Xe I Kr Br Se Ar Cl SNe F O P N C H Li Na Cs Rb K Tl Hg Au Hf Ls Ba Fr Pt Ir Os Re W Ta Po Bi Pb Be Mg Sr Ca Cd Ag Zr Y Pd Rh Ru Tc Mo Nb Ac Ra Zn Cu Ti Sc Ni Co Fe Mn Cr V In Sb Sn Ga Ge Al Gd Cm Tb Bk Sm Pu Eu Am Nd U Pm Np Ce Th Pr Pa Yb No Lu Lr Er Fm Tm Md Dy Cf Ho Es At Te As Si B
5 - 2
Solid
Liquid
Gas

3. Observed properties of matter
State
Property Solid Liquid Gas
Density High High Low
(like solids)
Shape Fixed Takes shape Expands
of lower part to fill the
of container container
Compressibility Small Small Large
Thermal Very Small Moderate
expansion Small

4. The gaseous state
In this state, the particles have sufficient energy to overcome all forces that attract them to each other.
Each particle is completely
separated from the others.
This results in low densities
and the fact that gases completely fill the container that holds them.

5. Gas pressure Gases exhibit pressure on any container they are in.
Pressure is defined as a force per unit of area.
Pressure = Force / Area
Several common units
1.00 atm = 760 torr
760 mm Hg
29.9 in Hg
14.7 lb/in2
1.01 x 105 Pa
force
area

6. Barometer Device used to measure atmospheric pressure. One atm
vacuum
One
atm
760 mmHg
29.9 inHg

7. The gas laws
Since gases are highly compressible and will expand when heated, these properties have been studied extensively.
The relationships between volume, pressure, temperature and moles are referred to as the gas laws.
To understand the relationships, we must introduce a few concepts.

8. Units we will be using
Volume liters, although other units could be used.
Temperature Must use an absolute scale.
K - Kelvin is most often used.
Pressure Atm, torr, mmHg, lb/in2.
- use what is appropriate.
Moles We specify the amounts in
molar quantities.

9. Gas laws
Laws that show the relationship between volume and various properties of gases
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
Avogadro’s Law
The Ideal Gas Equation combines several of these laws into a single relationship.

10. Temperature and number of moles must be held constant!
Boyle’s law
The volume of a gas is inversely proportional to its pressure.
PV = k or
P1 V1 = P2 V2
Temperature and number of moles must be held constant!

11. Boyle’s law Increasing the pressure on a sample on gas
decreases it volume at
constant temperature.
Note the effect here
as weight is added.

12. Pressure and number of moles
Charles’ law
The volume of a gas is directly proportional
to the absolute temperature (K). V T
= k
V V2
T T2 or =
Pressure and number of moles
must be held constant!

13. Charles’ law When you heat a sample of a gas, its volume increases.
The pressure and number
of moles must be held constant.

14. Charles’ Law Placing an air filled balloon near liquid nitrogen (77 K)
will cause the volume to be reduced. Pressure and
the number of moles are constant.

15. Gay-Lussac’s Law Law of of Combining Volumes.
At constant temperature and pressure, the volumes of gases involved in a chemical reaction are in the ratios of small whole numbers.
Studies by Joseph Gay-Lussac led to a better understanding of molecules and their reactions.

16. Gay-Lussac’s Law Example. Reaction of hydrogen and oxygen gases.
Two ‘volumes’ of hydrogen will combine with one ‘volume’ of oxygen to produce two volumes of water.
We now know that the equation is:
2 H2 (g) + O2 (g) H2O (g) + H2 O2
H2O

17. Avogadro’s law
Equal volumes of gas at the same temperature and pressure contain equal numbers of molecules.
V = k n
V V2
n n2 =

18. Avogadro’s law If you have more moles of a gas, it takes up more
space at the same temperature and pressure.

19. Standard conditions (STP)
Remember the following standard conditions.
Standard temperature = K
Standard pressure = 1 atm
At these conditions:
One mole of a gas has
a volume of 22.4 liters.

20. The ideal gas law
A combination of Boyle’s, Charles’ and Avogadro’s Laws
PV = nRT
P = pressure, atm
V = volume, L
n = moles
T = temperature, K
R = L atm/K mol
(gas law constant)

21. Example What is the volume of 2.00 moles of gas at
3.50 atm and K?
PV = nRT
V = nRT / P
= (2.00 mol)( L atm K-1mol-1)(310.0 K)
(3.50 atm)
= 14.5 L

22. Ideal gas law PV R = nT R = = 0.08206 atm L mol-1 K-1
R can be determined from standard conditions. PV nT
R =
( 1 atm ) ( 22.4 L )
( 1 mol ) ( K)
R =
= atm L mol-1 K-1

23. Ideal gas law
When you only allow volume and one other factor to vary, you end up with one of the other gas laws.
Just remember
Boyle Pressure
Charles Temperature
Avogadro Moles

24. Ideal gas law P1V1 P2V2 n1T1 n2T2 = R = This one equation says it all.
Anything held constant will
“cancels out” of the equation

25. Ideal gas law P1V1 P2V2 n1T1 n2T2 = P1V1 = P2V2
Example - if n and T are held constant
P1V1
n1T1
P2V2
n2T2 =
This leaves us
P1V1 = P2V2
Boyle’s Law

26. Example If a gas has a volume of 3.0 liters at 250 K,
what volume will it have at 450 K ?
Cancel P and n
They don’t change
P1V1
n1T1
P2V2
n2T2 =
We end up with
Charles’ Law V1 T1 V2 T2 =

27. Example If a gas has a volume of 3.0 liters at 250 K,
what volume will it have at 450 K ?
P1V1
n1T1
P2V2
n2T2 V1 T1 = V2 T2 =
V2 = (3.0 l) (450 K)
(250 K)
= 5.4 L

28. Dalton’s law of partial pressures
The total pressure of a gaseous mixture is the sum of the partial pressure of all the gases.
PT = P1 + P2 + P
Air is a mixture of gases - each adds it own pressure to the total.
Pair = PN2 + PO2 + PAr + PCO2 + PH2O

29. Partial pressure example
Mixtures of helium and oxygen are used in scuba diving tanks to help prevent “the bends.”
For a particular dive, 46 liters of O2 and 12 liters of He were pumped in to a 5 liter tank. Both gases were added at 1.0 atm pressure at 25oC.
Determine the partial pressure for both gases in the scuba tank at 25oC.

30. Partial pressure example
First calculate the number of moles of each gas using PV = nRT.
nO2 = = 1.9 mol
nHe = = 0.49 mol
(1.0 atm) (46 l)
( l atm K-1 mol-1)(298.15K)
(1.0 atm) (12 l)
( l atm K-1 mol-1)(298.15K)

31. Partial pressure example
Now calculate the partial pressures of each.
PO2 = = 9.3 atm
PO2 = = 2.4 atm
Total pressure in the tank is 11.7 atm.
(1.9 mol) ( K) ( l atm K-1 mol-1)
(5.0 l)
(0.49 mol) ( K) ( l atm K-1 mol-1)
(5.0 l)

32. Graham’s law
Relates the rates of effusion of two gases to their molar masses.
This law notes that larger molecules move more slowly.
Rate A MM B
Rate B MM A =

33. Diffusion

34. Diffusion and effusion
The random and spontaneous mixing of molecules.
Effusion
The escape of
molecules through
small holes in a
barrier.

35. Kinetic-molecular theory
This theory explains the behavior of gases.
Gases consist of very small particles (molecules) which are separated by large distances.
Gas molecules move at very high speeds - hydrogen molecules travel at almost 4000 mph at 25oC.
Pressure is the result of molecules hitting the container. At 25 oC and 1 atm, a molecule hits another molecule and average of 1010 times/sec.

36. Kinetic-molecular theory
No attractive forces exist between ideal gas molecules or the container they are in.
Energy of motion is called kinetic energy.
Average kinetic energy = mv2
Because gas molecules hit each other frequently, their speed and direction is constantly changing.
The distribution of gas molecule speeds can be calculated for various temperatures. 1 2

37. Kinetic-molecular theory
Fraction having each speed
Molecular speed (m/s)
O2 at 25oC
O2 at 700oC
H2 at 25oC
Average speed

38. Real gases We can plot the compressibility factor (PV/nRT)
for gases. If the gas is ideal, it should always
give a value of 1.
Obviously, none of these gases are ‘ideal.’ H2 N2
Compressibility
factor
CH4
C2H4
NH3
Pressure, atm

39. Real gases
As pressure approaches zero, all gases approach ideal behavior.
At high pressure, gases deviate significantly from ideal behavior.
Why?
Attractive forces actually do exist between molecules.
Molecules are not points -- they have volume.

40. ( ) Van der Waals equation
This equation is a modification of the ideal gas relationship. It accounts for attractive forces and molecular volume.
P +
an2 V2
(V - nb) = nRT ( )
Correction for
Molecular volume
Correction for attractive
forces between molecules

41. Van der Waals constants
a b
Gas Formula L2 atm mol-2 L mol-1
Ammonia NH
Argon Ar
Chlorine Cl
Helium He
Hydrogen H
Nitrogen N
Water H2O
Xenon Xe