1. Plan for Mon, 13 Oct 08 Exp 2 post-lab question Lecture
KMT (5.6)
Effusion and Diffusion (5.7)
Real gases and the van der Waal equation (5.8)
The nature of energy?? (6.1)
Quiz 2 returned

2. What can KMT do for you?
The main ideas you should take from KMT is that we can describe T and P from a molecular perspective.
Pressure: arises from molecules banging into the container walls.
Temperature: arises from the kinetic energy of the gas molecules. The more KE they have, the faster they can move around, the “hotter” they are.

3. Temperature according to KMT
Kinetic energy: The energy an object has by virtue of its motion.
Basically, the energy you must apply to an object to accelerate it from rest to a given velocity (u):
The average Ek of a molecule is directly proportional to the absolute temperature in K.
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4. Metathesis Lab (Exp3)
QUIZ 3
We are here.
QUIZ 4
Vol. Anal. FORMAL RPT (Exp4)
Dr. Villarba subs. QUIZ 5
EXAM 2: Ch 5,6,10
Dr. Schultz subs in lab

5. A Closer Look at Molecular KE
Let’s consider the average KE per molecule and see how it determines molecular speed.
Total KE in a mole of gas:
According to KMT, and beyond the scope of this course.
Where u is an average of molecular velocity, and m is the mass of one molecule.
Average KE per molecule:
We are apportioning the total KE in the mole of gas among all the molecules in an average fashion.

6. A Closer Look at Molecular KE
We are apportioning the total KE in the mole of gas among all the molecules in an average fashion.
Note that mNA = M.
“Root-mean-square” speed, one kind of average molecular speed.
urms is the speed of a molecule that has the average KE.
urms gives us a formal connection between average gas speed, T, and M.

7. Distribution of Molecular Speeds
“Maxwell-Boltzmann” curve (a statistical distribution)
urms – the speed of a molecule with the average molecular kinetic energy
uav – average speed
um – most probable speed
Petrucci, Fig 6.17

8. urms Dependence on T & M E&G, Fig. 5.25 Petrucci, Fig. 6.18
M(O2) = 32 g/mol
E&G, Fig. 5.25
M(H2) = 2 g/mol
Petrucci, Fig. 6.18

9. Trends Increased T  increased average KE  increased urms
Maximum of curve shifts to higher u, and distribution spreads out.
Increased M  decreased urms
Heavier molecules have lower average speed than lighter molecules.
At a given T, are there more molecules at low speeds (u < urms) or high speeds (u > urms)?
There are more molecules at lower speeds than high.

10. Calculating urms What is urms at 25oC for He(g) and N2(g)?
M(He) = g/mol
M(N2) = g/mol
Already we know that urms(N2) < urms(He).
We also need T and R. What units do we need for these values?

11. Calculating urms What is urms at 25oC for He(g) and N2(g)?
M(He) = g/mol
M(N2) = g/mol
T = (25oC + 273) K = 298 K
urms is in units of m/s
Will L atm/mol K work?
How about J/mol K?

12. Calculating urms How about 8.314 J/mol K? What’s a J (joule)?
1 J = 1 N m
What’s a N (newton)?
1 N = 1 kg m/s2
 1 J = 1 kg m2/s2

13. Calculating urms for He(g)
M(He) = g/mol
T = 298 K
R = J/mol K = kg m2/mol K s2

14. Calculating urms for N2(g)
M(N2) = g/mol
T = 298 K
R = J/mol K = kg m2/mol K s2

15. Comparison
At 25oC,
urms(N2) = 515 m/s M(N2) = 28 g/mol
urms(He) = 1.36 x 103 m/s M(He) = 4 g/mol
A car travelling at 60 mph,
ucar = 26.8 m/s
If gases travel so fast, why does it take so long for you to smell a bottle of perfume from across the room?

16. Diffusion
Gas molecules travel in a straight line only until they collide with a container wall or another gas molecule.
Gaseous perfume molecules do not have an uninterrupted path in from of them.
They are constantly colliding with gas molecules in the air.

17. Diffusion Diffusion is the process of mixing gases.
This is analogous to solution formation.
Show Z Fig 5.24 p. 207

18. Diffusion of gases
In a closed container, diffusion will eventually lead to a homogeneous mixture.
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19. Effusion
Effusion is a special case of diffusion, which exploits the difference in velocities of lighter gas molecules.
This process was used during the Manhatten Project to separate 235U and 238U isotopes.
Petrucci, Fig 6.21b

20. Effusion of a Gas
Rate of effusion is proportional to urms. So lighter particles will have a higher rate of effusion.
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21. Real Gases
Generally speaking, there is no such thing as an “Ideal Gas.”
There are conditions under which a gas will behave ideally…
low P
moderate to high T
van der Waal developed some corrections to the Ideal Gas law, based on a molecular picture, to explain these observed deviations.

22. Real Gases: Molecules have volume
At high P, the volume of the individual gas molecules becomes non-negligible.
Macroscopic gas is compressible, individual gas molecules are not.
Under high P conditions, the space available for a gas molecule to move through is decreased by its neighbors, so the volume of the system is reduced relative to the ideal case.

23. Volume correction vdW corrected the volume available to a gas:
P’ is a “corrected” ideal pressure.
What is the result of this volume correction, a higher or lower pressure relative to ideal?
Number of moles of gas
Empirical constant… different for each gas

24. Real Gases: Molecules attract each other
Under high P, gas molecules get very close to each other, so intermolecular forces become significant.
At low T, molecular Ek is reduced, and molecular speed drops, so the molecules become “trapped” by attractions to other molecules.
Under these conditions, the molecules don’t collide with the container as frequently, so the pressure of the system is reduced relative to the ideal case.

25. Pressure Correction
vdW corrected for pressure, by including a mutual attraction term.
Molecular attractions are proportional to concentration, n/V.
What is the result of the pressure correction?
Intermolecular attraction term
Empirical constant… different for each gas

26. vdW Equation b generally increases with the size of the molecule
a seems to depend on the strength of intermolecular forces.

27. vdW Equation
vdW equation corrects two major flaws in ideal gas theory:
Gas molecules have finite volume which becomes important at high P.
Gas molecules have nontrivial attractions that become important at low T and high P.

28. Real Gases
Although nonideal behavior is evident at all temperatures, the deviation is less at higher temperatures.
Why do you think that could be?
N2(g)