Download lecture# 21

CHEM 1711 & 1811 Lecture # 21
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EFFUSION and DIFFUSION
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recall
kinetic theory of gases
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gas molecules move with random directions and speeds
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average speed depends on molar mass (kg/mol) and temperature
v rms = { 3 R T / M }1/2
v ∝ T1/2
so
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diffusion:
mixing caused by random motion of fluid molecules
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not the same idea as convection (bulk flow)
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diffusion rate for gases depends on speed
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rate means mass moved per time
t ∝ T -1/2
initial
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v ∝ M-1/2
or
effusion:
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r ∝ v rms
(faster is less time)
t ∝ M1/2
final
gas molecules escape into vacuum
pressure drop across a pinhole or porous plug
CHEM 1711 & 1811 Lecture # 21
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pressure decreases in time as molecules escape
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calibrate using gas with known molar mass
effusion time t ∝ M1/2
Graham's Law:
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heavier gases effuse more slowly (i.e. smaller rate, more time)
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same relationships as diffusion, just a different way to measure
EXAMPLE
molecular formula from effusion data
Ethyl butyrate (essence of pineapple) has the empirical formula C3H6O. In a
gas effusion experiment, it took 1.62 times as long as CO2 to effuse. What
is its molecular formula?
t ∝ M1/2
so
M ∝ t2
Mx / MCO2 = (tx / tCO2)2
Mx = (44.0 g/mol) (1.62)2 = 115.5 g/mol
C3H6O = 58.1 g/mol
∴
C6H12O2
REAL GASES
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no gas is actually ideal
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molecules do take up space and attract/repel each other
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most noticeable at high p and/or low T
PV =nRT
FAILS !
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need to modify (make more complicated)
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each gas substance behaves a bit differently
(why?)
CHEM 1711 & 1811 Lecture # 21
e.g.
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van der Waals equ. of state :
( P + a n2 / V2 ) ( V - n b ) = n R T
where
a and b are constants specific to each type of molecule
a
represents attractive forces ("stickiness")
b
represents actual volume (size) of molecules
SHOW
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table of van der Waals constants
molecular properties are correlated with van der Waals constants
e.g.
boiling point
substance (l) → substance (g)
trade-off between molecular motion (T) and sticking
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(real) gases may be used to do work
e.g.
refrigerators, air conditioners, heat pumps
NH3
CFCs
HCFCs
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compression (lower V, higher P) causes heating
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expansion (higher V, lower P) causes cooling
DEMO
CO2 fire extinguisher
CHEM 1711 & 1811 Lecture # 21
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ATMOSPHERIC CHEMISTRY
sunlight
stratosphere
O2 + hν → O + O
O + O2 → O3
troposphere
hν
50 km
(ozone)
O3 + hν' → O2 + O
Earth
10 km
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"good" ozone in stratosphere protects life from UV light
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"bad" ozone (a.k.a. smog) in troposphere harms respiration
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HOx tpye free radicals oxidize organics
O* + H2O → OH + OH
(hydroxyl radical)
C3H8 + OH → H2O + C3H7
natural OH concentration < 108 molecules/cm3
(108 OH molecules/cm3) (1000 cm3/L) (1 mol/6.02 x 1023)
= 1.66 x 10-13 mol/L = 0.166 pM
ideally at STP
VM = 22.4 L/mol
molar concentration of air = 1 / VM = 0.0446 mol/L
mole fraction OH
χOH
= 0.166 pM / 44.6 mM = 3.72 x 10-12
= 3.72 pptv
CHEM 1711 & 1811 Lecture # 21
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where
pptv = parts per trillion by volume
(10-12)
likewise
ppbv = parts per billion by volume
(10-9)
and
ppmv = parts per million by volume
(10-6)
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other oxidizing free radicals include
HO2 (hydroperoxy radical)
typically 50 pptv
RO2 (organic peroxy radicals)
e.g.
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C3H7 + O2 → C3H7O2
(propyl peroxy radical)
acid anhydrides
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SOx type molecules from coal combustion
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NOx type molecules from engines
SOx , NOx + HOx + H2O → acid rain
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lower pH in lakes harms aquatic life