the kinetic-molecular theory (the theory of moving particles) 1. gas particles are in constant,...
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The Kinetic-Molecular Theory(the theory of moving particles)
1. Gas particles are in constant, random motion.
2. The volume of the particles is negligible compared to the container volume.
3. The attractive-repulsive forces between particles are negligible.
4. Collisions are elastic.
5. KEavg of particles is proportional to absolute temperature. K) (in T KE
(i.e., no energy is lost).
v T (in K)
At a given temp., the gas particlesof Sample A have the same avg. KEas the gas particles of Sample B.
pressure = “ ” and “ ” gas particlescollide with the sides of the containerhow hard how often
containerwall A
containerwall B
1 mol Ne @ 25oC ina 5.0-L container…
1 mol Ne @ 350oC ina 5.0-L container…
1 mol Ne @ 25oC ina 5.0-L container…
5 mol Ne @ 25oC ina 5.0-L container…
Particle-Velocity Distribution(___________, same T and P)
# of
part
icle
s
Speed ofparticles (m/s)
(SLOW)
most massive gas (e.g., CO2)
least massive gas (e.g., He)
various gases
(FAST)
rms (root-mean-square) speed
a gas of intermediatemass (e.g., N2)
Particle-Velocity Distribution(same gas, same P, ________)
# of
part
icle
s
Speed ofparticles (m/s)
(SLOW)
coldest gas
warmest gas
various T
(FAST)
T = 80.0oC
Equation for the rms speed of a gas:
T R 3 u
R = 8.314 J/mol-K
= molar mass, in kg
KEavg for a particle = ½ m u2 in kg
Find the rms speed of chlorine gas at 80.0oC.
= 353 K = 71.0 g = 0.0710 kg
T R 3 u
0710.0(353) (8.314) 3
= 352 m/s
diffusion: effusion: the net movement of
a substance from high
to low conc.
the escape of gas particles
through a tiny holeinto an evacuated space
NET MOVEMENT
more massive = slow;less massive = fast
NET MOVEMENT
[ HIGH ] [ LOW ]
For gases, rates of diffusion & effusion obey Graham’s law:
** To use Graham’s Law, both gases must be at the… same temp.
r = rates
= molar masses
The rate of diffusion of gases is slower than themolecular speeds because of...collisions.
-- ~10 x 109 collisions/sec per particle
The mean free path is the average distancetraveled by a particle between collisions.
-- it is shorter when the pressure is…high
t = times
1
2
1
2
2
1
t
t
r
r
He2
4.003
Ne10
20.180
Ar18
39.948
Kr36
83.80
Xe54
131.29
Rn86
(222)
1
2
2
1
rr
4
4
CH
unk
unk
CH r
r
16
1.58 unk2
mm = 16.0 g/mol
2unk (1.58) 16 = 39.9 g/mol
Ar
16
11.58 unk
CH4 moves 1.58 times faster than which noble gas?
“Ar?”
“Aahhrrrr! Buckets o’ blood!Swab de decks, ye scurvy dogs!”
Ne2
or Ar?