• Gas Law Development
• Dalton’s Partial pressure law
• Graham’s effusion
• Kinetic Theory
–Root-mean-square velocity
• van der Waals equation of state
• HW: Chpt 5 - pg. 223-231, #s 5, 22, 23, 25,
31, 32, 35, 39, 41, 46, 55, 64, 66, 71, 75, 77,
81, 91, 95, 97, 101, 124 Due Mon 10/4

Pressure is? Units?
The height in mm of mercury above the surface of the resevoir of mercury determines the pressure.
The units are mmHg.
mmHg is also the same unit as
Torr. i.e.
standard pressure is
760 mmHg and 760 Torr

Simple Manometer
Similar to the barometer, the height difference of the Hg relates the pressure difference in the unknown gas bulb side to the current atmospheric pressure.
The higher Hg side has the _____ pressure.
(higher/lower)

• Constant temperature experiments demonstrated the PV=constant graphing this yields an inverse relationship
• Thus if the pressure of volume changes at a constant temperature
P
1
V
1
= P
2
V
2

Plot of PV vs. P for Several Gases
This graph shows
Boyles linear relationship for the
PxV. The constant depends on the gas

• Constant pressure experiments demonstrated that Volume is directly proportional to
Temperature (Kelvin)
V
1
= V
2
T
1
T
2
• Several gases were used & all extrapolate to zero volume and the same temperature at negative 273 o C

º
Charles’s Law
Experiment results
Demonstrates a unique absolute zero at -273.15 o C

P
1
V
1
T
1
= P
2
V
2
T
2
Avogadro’s Law - equal volumes of gas contain equal particles of gas
V = k n
At constant temperature and pressure the volume is directly proportional to the number of moles of gas.

• Putting it all together, we can calculate that constant now. The universal gas constant R.
PV=R or PV=nRT nT R =0.0821 l
*atm/mol*K
=8.31 l
*kpa/mol*K

Molar mass, MM = ?
So, moles = ?
What are the units?
Density, d = ?
So, mass = ?
Use L for density since gas
Combine and get expression for moles n=
N= PV = dV Thus MM = dRT volume will be in Liters
RT MM P

The gases in a mixture act independently and thus the forces (and pressures) are additive.
P total
= P
1
+ P
2
+ P
3
+ …

• Ideal Gas Behavior
– Particles assumed to have zero volume
– Particles in constant motion
– Particles exert no forces on each other
– KE ave is directly proportional to T (K)
• Check out Appendix 2 to see derivation of ideal gas law PV=nRT

• also KE ave
= 3/2 RT
• Root square mean velocity
• u rms
= sqrt(3RT/M)
– Where M is mass of a mole in kg
– So now we can calculate ave velocities of gases

Effusion of Gas into Evacuated
Chamber
If more than one type of gas or more than one isotope, which gas effuses faster?
Lighter gas moves
Faster!!
KE = 1/2 mv 2

Relative Molecular
Speed Distribution of H
2 and UF
6

Diffusion Rates of NH
3 and HCl Molecules Through Air
Relative diffusion/effusion rate pg. 213 textbook rate rate
1
2
= Sqrt(M
2
)
Sqrt(M
1
) lighter gas is faster

• All of the gases are real!!! They just behave “ideally” at certain temperatures and pressures.
• Think of the KMT assumptions, what conditions would gases “fail” to act ideally.
• Low temperatures (gases condense) &
High pressures (force the gases together so they have to interact)

Plots of
PV/nRT vs. P for Several Gases

Plot of PV/nRT vs. P for N
2
Gas
This graph shows that at higher temperatures gases behave closer to ideal even at high pressures.
Recall that gases behave “ideally” at low pressures and high temperatures.

• van der Waals equation is entire gas law relationship with corrections for real volume and molecular attractions. pg.216 textbook with Table 5.3 for some common gases
(P obs
+ correction) x ( V - nb) = nRT
This formula is also given on AP exam sheet.

Values of the van der Waals
Constants for Common Gases a is a measure of intermolecular attractions (it is the correction to the pressure to account for attractions for each other) b is a measure of size of the molecule (it is the volume correction)