1. Ppt 18b, Continuation of Gases
Kinetic Molecular Theory (continued)
Postulates / Model
How KMT explains Gas Behavior (Gas Laws)
Speed issues
Distribution Curves and Associated Ideas
Speed  KE! (mparticle affects speed, not KEavg!)
Real Gas Behavior (i.e., when conditions are not ideal for gases)
Relation to KMT
When model assumptions no longer “good”
Ppt18b

2. Kinetic Molecular Theory—formal postulates
(Recall the “superball” analogy!):
Gas “particles” (atoms or molecules) move in straight lines until they collide with something; Collisions with a surface are the cause of the pressure exerted on it.
Particle volume is negligible (technically, zero) compared to gas volume (vessel volume)
Distance between particles is HUGE compared to particle diameter; Most volume is “empty space”
Gas collisions are perfectly elastic & particles do not exert any forces on one another between collisions
Average Kinetic Energyparticle  Kelvin Temperature
Ppt18b

3. Kinetic Energy is Energy of Motion
m = mass of (a single) particle
v = speed of (a single) particle (strictly speaking, velocity)
At any temperature, particles are always moving and colliding with “walls” (surfaces)
Average KEparticle  TKelvin
 If T increases, particles mover faster and collide “harder” [NOTE: If you double T, speed does not double! It increases by times (~1.4 x)
Ppt18b

4. Reminder: Gas Law Behavior (But let’s “rewrite” Ideal Gas Law in terms of pressure)
Ideal Gas LAW: PV = nRT
concentration
**These descriptions of “what happens” are not explanations!!! How KMT explains these laws is on the next slides.**
Ppt18b

5. Frequency of collisions
Derivation of Ideal Gas Eqn. from KMT—Pressure is a result of collisions
The pressure exerted by a gas comes from the sum of huge numbers of collisions against a surface in a given period of time (say a second)
The pressure equals the product of the average “force per collision” and the # of collisions per sec (per unit of area):
Frequency of collisions
Ppt18b

6. Assertions (used to derive Ideal Gas Eq. from KMT)
“Force per collision” depends on momentum (mv) of particle
If more massive, more “oomph” (at given speed)
If moving faster, bigger impact (for a given m)
Collisional frequency depends on
Concentration of particles (more particles, more collisions each sec (n/V)
Speed of particles (if they move faster, more can “reach” the wall in a given sec) (v)
*Tro gives a more detailed description and derivation
Ppt18b

7. Substitute in!
Ideal Gas Law!!
Ppt18b

8. T, 3/18/08
KMT—Pressure is a result of collisions (Explains gas laws via P and “mechanical equilibrium” idea)
At a given T (and for a given gas), the frequency of collisions depends on the concentration of gas particles:
→ More particles in a given volume  more collisions per second with each m2 of “wall”  increased P
At a given concentration, higher T  higher average KE, which results in:
1) More collisions per second (at a given [gas])
→ because speed increases [but not proportionately!]
2) “Harder” (more forceful) collisions
→ because speed increases (greater “momentum”)
Increased P
Ppt18b

9. Example: Syringe and Balloon in Syringe (How does KMT explain what you see?)
Watch the demo (what do you predict?)
Can you explain why using KMT?
NOTE: These are “constant temperature” situations.
 P  collisional frequency  concentration (T const)
Ppt18b

10. Simulations of KMT
--allows changes in mass / particle and gas mixtures
Ppt18b

11. Any given gas law between two variables can be “explained” using KMT
I’ll show figures from a prior textbook on the next three slides
Tro gives verbal explanations of laws on p. 207
Ppt18b

12. A Decrease in Volume increases Pressure by increasing the # collisions per sec
Is the average speed of the particles different in the second box? (Hint: is T different?) ____
NO!
Greater concentration (n/V) at same T leads to greater collision frequency without a speed increase!
Ppt18b

13. An increase in T increases P by increasing both the # collisions per sec AND the “force” per collision
This assumes that the V is kept constant (could be a rigid container, although here a flexible container is shown with extra masses on the piston).
Average KE increases…so
Hitting walls more often
Hitting walls “harder”
Ppt18b

14. T, 3/18/08
An increase in T at constant P leads to an increase in V so that collisional frequency can decrease to offset increased force per collision
Why? After T , Pgas > Pext  not in mech equilib  piston moves out!
and concentration ends up decreasing to compensate (P “held constant” here)
Ppt18b

15. Kinetic Molecular Theory—Distribution Curves
What does it mean if the bar is “taller” on this plot?
Which bar represents the highest temperature?
How would the plot for Los Angeles be expected to differ from the plot below during this same time period?
Ppt18b

16. Kinetic Molecular Theory—Distribution Curves
Ppt18b 16 16

17. Kinetic Molecular Theory—Distribution Curves
Ppt18b

18. Distribution Curve Comments (see simulation applet!)
When T is raised, average KE goes up, so a given sample’s average speed will go up, shifting the distribution curve to the right (max is further right).
Total area under the curve represents the total number of particles of a certain gas in the sample.
If TWO gases are present in the same container, each one’s distribution curve will have a different height, proportional to how much of that gas is present (and thus partial pressure [this topic will be covered later]).
4) Also, if T is the same, the average speed of MORE MASSIVE particles will be LOWER than less massive ones (maximum further to the LEFT). [See next slide]
Ppt18b

19. Kinetic Molecular Theory—Speed ≠ KE!!
“Big guys move more slowly at the same T”
Same T  Same avg KE  if m bigger, v smaller
Ppt18b

20. Figure 5.23 “Big guys” move more slowly at same T”
Which gas has the greater average kinetic energy?
Ans: Neither! Same T  Same KEavg!
REMEMBER: KE ≠ speed!
Ppt18b

21. Real Gases Deviate from Ideal Behavior at low T and high P
Ppt18b

22. At STP, some gases act fairly ideally:
Chapter 5, Figure 5.22
Molar Volumes of Real Gases
Ppt18b

23. Chapter 5, Figure 5.25
The Effect of Intermolecular Forces
Ppt18b

24. Chapter 5, Figure 5.24
The Effect of Particle Volume
Ppt18b

25. KMT explains why the deviations occur at low T and high P!
Deviations from ideal behavior occur under conditions where the assumptions of the model (of an ideal gas) are no longer “good” assumptions for real gases!
Molecules in gaseous state do not exert any force on one another between collisions.
NOT ACTUALLY TRUE! [intermolecular forces exist between “real” molecules]
but good approximation if T is large! (High KE “overcomes” weak forces)
ASSUMPTION “BREAKS DOWN” at low T
Volume of the molecules is negligibly small compared with that of the container.
NOT TRUE if really compressed!! BAD ASSUMPTION at high P (high n/V)
Ppt18b

26. At high P, n/V increases and Vparticle not negligible
Chapter 5, Figure 5.23
Particle Volume and Ideal Behavior
Ppt18b