Prentice Hall ©2004 Ppt17b Ppt 18b, Continuation of Gases 1. Kinetic Molecular Theory (continued) Postulates / Model How KMT explains Gas Behavior (Gas

Prentice Hall ©2004 Ppt17b

Ppt 18b, Continuation of GasesPpt 18b, Continuation of Gases

1. Kinetic Molecular Theory (continued)• Postulates / Model• How KMT explains Gas Behavior (Gas Laws)• Speed issues

o Distribution Curves and Associated Ideaso Speed KE! (mparticle affects speed, not KEavg!)

2. Real Gas Behavior (i.e., when conditions are not ideal for gases)

• Relation to KMTo When model assumptions no longer “good”

1

Prentice Hall ©2004 Slide 2

Kinetic Molecular Theory—formal postulatesKinetic Molecular Theory—formal postulates

(Recall the “superball” analogy!):

1) 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.

2) 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”

3) Gas collisions are perfectly elastic & particles do not

exert any forces on one another between collisions

4) Average Kinetic Energyparticle Kelvin Temperature

Prentice Hall ©2004

Kinetic Energy is Energy of MotionKinetic Energy is Energy of Motion

m = mass of (a single) particlev = speed of (a single) particle (strictly speaking, velocity)

21

2particleKE mv

• 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)

2


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.**


Derivation of Ideal Gas Eqn. from KMT—Pressure is a result of collisionsDerivation of Ideal Gas Eqn. from KMT—Pressure is a result of collisions

• The pressure equals the product of the average “force per collision” and the # of collisions per sec (per unit of area):

• 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)

(per unit area)

"force" # of collisions x collision sec

P

Frequency of collisions


Assertions (used to derive Ideal Gas Eq. from KMT)Assertions (used to derive Ideal Gas Eq. from KMT)

• “Force per collision” depends on momentum (mv) of particle

1) If more massive, more “oomph” (at given speed)2) If moving faster, bigger impact (for a given m)

• Collisional frequency depends on1) Concentration of particles (more particles, more

collisions each sec (n/V)2) 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

Slide 6


Substitute in!Substitute in!

Slide 7

(per unit area)

"force" # of collisions x collision sec

P

x x n

P mv vV

2 x n

P mvV

x n

P TV

Ideal Gas Law!!


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

Increased

P


Example: Syringe and Balloon in Syringe(How does KMT explain what you see?)Example: Syringe and Balloon in Syringe(How does KMT explain what you see?)

• Watch the demo (what do you predict?)

Chapter 09 Slide 9

• Can you explain why using KMT?

• NOTE: These are “constant temperature” situations. P collisional frequency concentration (T const)


Simulations of KMTSimulations of KMT

• http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm

• http://celiah.usc.edu/collide/1/ --allows changes in mass / particle and gas mixtures

• http://www.falstad.com/gas/

• http://mc2.cchem.berkeley.edu/Java/molecules/index.html


Any given gas law between two variables can be “explained” using KMTAny given gas law between two variables can be “explained” using KMT

• I’ll show figures from a prior textbook on the next three slides

o

o

o

• Tro gives verbal explanations of laws on p. 207

Chapter 09 Slide 11

1 ( , constant)P T n

V

( , constant)P T V n

( , constant)V T P n

Prentice Hall ©2004 Copyright © Houghton Mifflin Company. All rights reserved. 5–12

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!

Prentice Hall ©2004 5–13

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).

Average KE increases…so

Hitting walls more often

Hitting walls “harder”


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

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)

Prentice Hall ©2004 Chapter 09 Slide 15

Kinetic Molecular Theory—Distribution CurvesKinetic 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?






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]


21

2KE mv

Kinetic Molecular Theory—Speed ≠ KE!!Kinetic Molecular Theory—Speed ≠ KE!!

“Big guys move more slowly at the same T”

Same T Same avg KE if m bigger, v smaller


Figure 5.23 “Big guys” move more slowly at same T”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!


Real Gases Deviate from Ideal Behavior at low T and high PReal Gases Deviate from Ideal Behavior at low T and high P

Chapter 09 Slide 21


At STP, some gases act fairly ideally:At STP, some gases act fairly ideally:



Prentice Hall ©2004 Slide 25

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)


At high P, n/V increases and Vparticle not negligibleAt high P, n/V increases and Vparticle not negligible

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Prentice Hall ©2004 Ppt17b Ppt 18b, Continuation of Gases 1. Kinetic Molecular Theory (continued) Postulates / Model How KMT explains Gas Behavior (Gas