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Reminder: Gas Law Behavior (But let’s “rewrite” Ideal Gas Law in terms of pressure)Reminder: Gas Law Behavior (But let’s “rewrite” Ideal Gas Law in terms of pressure)
Ideal Gas LAW: PV = nRT
xnRT n
P P RTV V
(if T constant) n
PV
(if constant) n
VP T
concentration
**These descriptions of “what happens” are not explanations!!! How KMT explains these laws is on the next slides.**
KMT—Pressure is a result of collisions(Explains gas laws via P and “mechanical equilibrium” idea)KMT—Pressure is a result of collisions(Explains gas laws via P and “mechanical equilibrium” idea)
• 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”)
• 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
A Decrease in Volume increases Pressure by increasing the # collisions per secA 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!
An increase in T increases P by increasing both the # collisions per sec AND the “force” per collisionAn 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).
Distribution Curve Comments (see simulation applet!)Distribution Curve Comments (see simulation applet!)
1) 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).
2) Total area under the curve represents the total number of particles of a certain gas in the sample.
3) 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]
KMT explains why the deviations occur at low T and high P!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!
1. 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
2. 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)