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

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

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

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

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

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

Substitute in! Ideal Gas Law!! Ppt18b

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

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

Simulations 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://chemconnections.org/Java/molecules/index.html http://phet.colorado.edu/en/simulation/gas-properties Ppt18b

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

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

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

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

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

Kinetic Molecular Theory—Distribution Curves Ppt18b 16 16

Kinetic Molecular Theory—Distribution Curves Ppt18b

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

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

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

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

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

Chapter 5, Figure 5.25 The Effect of Intermolecular Forces Ppt18b

Chapter 5, Figure 5.24 The Effect of Particle Volume Ppt18b

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

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