nils walter: chem 260 the properties of perfect gaseschem260/fall01/lecture18.pdfnils walter: chem...
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Nils Walter: Chem 260
The properties of perfect gasesAtkins, Chapter 1
Gases have V(olume), p(ressure), T(emperature) and n (amount)as observables that can fully describe their state
Avogadro’s principle:[1811]
nV ∝nVVm =or = constant (if T and
p don’t change)
Boyle’s law:[1661] V
p 1∝ at constant T
Charles’s law:[1787] (+ Gay-Lussac 1802)
BTVV C += °0 [T in oC]
Nils Walter: Chem 260
Summary: The perfect gas equation of state
nRTpV =
VnRTp =
Boyle:
Avogadro:
pRT
nV = = 24.465 l/mol
in 3Dp
V
T
Nils Walter: Chem 260
The perfect gas temperature:The Kelvin scale
TpnRV = Only holds when T is
measured in K(elvin)
Charles: BTVV C += °0[T in oC]
p
V
T
in 3D:
For all gases:Extrapolation toV = 0 yields same
T = -273.15 oC= absolute zero = 0 K
Nils Walter: Chem 260
Applying the perfect gas law
nRTpV = ����
2
22
1
11
TVp
TVp =
change in conditions
���� Mount Everestis not for everyone
Nils Walter: Chem 260
Dalton’s law
mole fractionsxA + xB = 1
nn
nnnx A
BA
AA =
+=
nn
nnnx B
BA
BB =
+=
pxpxVRTnx
VRTnxp BABA +=+=
partial pressureBA ppp +=
VRTn
VRTn
VRTnp BA +== since
nA+ nB = n
Nils Walter: Chem 260
Description of a perfect gas bythe kinetic model
Three assumptions→ A gas consists of molecules in ceaseless motion in 3D→ The size of the molecules is small compared to theiraverage distance traveled→ The molecules do not interact
� Many moleculescontinuously collide with the
wall and produce pressure
;3
2
VnMcp = N
sssc N22
22
1 ...+++=����
root-mean-square speed
Nils Walter: Chem 260
The Maxwell distribution of speeds
sesRTMsf RT
Ms∆=
−222
3 2
24)(
ππ
Maxwell [late 1800’s]:
perfect gas law
VnRT
VnMcp ==
3
2
����
MRTc 3= an average speed
What are the individual speeds?