1. CHEM 205 section 01 LECTURE #6 Thurs., Nov.30th, 2004
ASSIGNED READINGS:
FINAL CLASS: rest of Ch.12
Final exam: Thurs. Dec. 16th,
Problem-solving session: during exam period
suggest Mon.Dec.13th evening? 6-8pm?
Office hours Dec.8-14th: 1:30-4:00pm

2. 12.6 Kinetic Molecular Theory of Gases
THEORY PROPOSED (and accepted)
TO EXPLAIN OBSERVED BEHAVIOUR OF GASES:
Gases consist of particles (atoms, molecules), separated by distances much greater than size of particles
Particles in constant, random, rapid motion…
…collide with each other and walls of container
Temperature determines the average kinetic energy of particles (thus: same for any gas at same T!)

3. Molecular speed & kinetic energy
Temperature: describes the average kinetic energy of the particles in a substance
K.E. = ½m u2
Average
velocity (speed)
mass
At higher temperatures: higher average kinetic energy
molecules generally moving faster
In a collection of molecules: DISTRIBUTION OF ENERGIES
Some have high K.E., most have average, some have low K.E.
Meaning: not all molecules in a sample move at same speed…
Possible to calculate (not us…): average or “mean” speed, u
u = n1 u1 + n2 u2 + n3 u3...
n1 + n2 + n3…

4. Figure 12.13: Velocities of N2 molecules at two temperatures
Not average since looking at distribution of speeds
in collection of molecules!

5. Heavier molecules are slower at same temp…
in reality: velocity has direction (a vector quantity)
take SQUARE of average velocity then take square root
 removes sign: get directionless velocity
called “root mean square velocity” urms
K.E. proportional to mean square velocity (urms2) & MASS
If we consider a mole of molecules:
KE = ½ mu2
urms = (3RT/M)1/2
where M = molar mass
the 3 comes from velocities in 3 dimensions… don’t worry about it!
gives rise to…
TAKE HOME MESSAGE:
lighter molecules travel faster
than heavier molecules…
relevant to things like
smelling odours!
Figure 12.14

6. 12.7 Diffusion & Effusion: Movement of molecules
1. Diffusion = mixing of two or more gases due to
random molecular motions
 eventually will mix together completely
 rate of mixing depends on mass of particle
 heavy particles diffuse more slowly…
Graham’s law governs effusion and diffusion of gas molecules:
Thomas Graham,
Rate of diffusion/effusion is inversely proportional to gas’s molar mass.

7. A experiment to demonstrate different rates of motion:
Ammonia molecules are lighter,
so it diffuses more quickly
HCl is heavier, so diffuses more slowly
Zumdahl’s Figure 5.24: HCl(g) + NH3(g) meet 
white ring of NH4Cl(s)….

8. 2. Effusion He air = movement of a gas through tiny hole(s)
= faster for lighter molecules…
WHY DOES IT HAPPEN?
molecules collide with container walls…
but if “hit” the hole: go through!
BALLOONS:
Molecules effuse through holes in
a rubber balloon at a rate (= moles/time)
that is:
proportional to temperature, T
inversely proportional to molar mass, M.
Thus:
a He balloon deflates after a while…
He effuses out more rapidly than
N2 & O2 from air effuse in. He
air

9. 12.8 Interesting real-world applications…
Hot air balloons
Deep sea diving
At surface: normal air, 21% O2  P O2 = 0.21 atm
78% N2  P O2 = 0.78 atm
Using a SCUBA tank: must balance pressures…
pressure of air = pressure exerted on body
= 2 atm at 33 feet below water
 because O2 still 21% of the air in the tank,
P O2 = 0.21 x 2 atm = 0.42 atm
P N2 = 0.78 x 2 atm = 1.56 atm
Problem: high P N2 (depths ~below 100ft) leads to
problems with nerve conduction
 poor judgement, giddyness…
Other problems also arise from increased amount of
nitrogen gas dissolving in blood  more in Chem206…

10. 12.9 Real Gases (things to consider if/when we must be VERY accurate)
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature.
WHY?
Particles closer together
Particles moving slowly
Molecules with dipoles attract each other
Non-polar molecules:
electrons become transiently polarized  temporary dipoles form… (more in Chem206)

11. Particles squished together… Size of each one now matters…
Zumdahl’s Figure 5.29: Our particles DO have volume…but… The volume taken up by the gas particles themselves is less important at large container volume (i.e., low pressure) & more important at small container volume (i.e., high pressure).
HIGH PRESSURE:
Particles squished together…
Size of each one now matters…
will behave NON-IDEALLY
LOW PRESSURE:
Particles very far apart…
will behave IDEALLY

12. To accurately describe real gases: use van der Waals’ equationx
Pressure term
Volume term
= nRT V 2 n a
P + _____ ) (
J. van der Waals , Physics Prof., Amsterdam.
Nobel Prize 1910.
V - nb x
= nRT
Measured P
Measured V
Compensate for
intermolecular forces…
“Volume of particles” correction
Real gas particles do NOT each have zero volume
Total volume occupied by
real gas sample therefore
larger than predicted for
“ideal” gas
Real gas particles “waste” some energy by interacting with each other
Observed pressure is lower
than if behaving ideally

13. A real sample of Cl2 gas: 8.00 moles in a 4.00 L tank at 27.0°C
Using PV=nRT:
P = nRT/V note: mol is ~ 284 g of Cl2
P = (8.00 mol)( Latmmol-1K-1)(300 K) / 4.00 L
= 49.2 atm = P if gas behaves ideally under these conditions
For Cl2, experiments have shown: a = 6.49 atmL2/mol2;
b = L/mol V 2 n a
P + _____ ) (
V - nb x
nRT
= 4.00L – (8.00mol x L/mol)
= 4.00L – ( L of matter! )
= L actual empty space…
=(8.00 mol)2 x (6.49 atmL2/mol2)
(4.00 L)2
=25.96 atm …energy “wasted” by interacting
would be enough to cause this much more P
Thus: (P atm) x (3.550 L) = nRT
(3.550 L) P Latm = (8.00 mol)( Latmmol-1K-1)(300 K)
(3.550 L) P Latm = Latm
 P = 29.5 atm
Thus: the P we’d observe is MUCH lower than predicted…
implies that it must be relatively crowded in the tank!

14. ASSIGNED READINGS Problem-solving session: will email you back…
Final exam: Thurs. Dec. 16th,
Room assigned by last name (check on the portal ! )
CC408: AA – LE
CC320: LF – SZ
CC321: TA - ZZ
They are being VERY STRICT this year:
Student ID card mandatory
No electronic dictionaries (books may be approved)
Arrive to the exam room early !