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I. Gas PropertiesBoyles law 1660
pascal(Pa)bar (atm)torr(psi)1 Pa 1 N/m2 105 9.8692106 7.5006103
145.04106 1 bar100,000 106dyn/cm2 0.98692750.0614.5041
at98,066.500.980670.96784735.5614.2231 atm101,3251.01325 1 atm
76014.6961 torr133.3221.3332103 1.3158103 1 Torr; 1mmHg19.337103 1
psi6.894103 68.948103 68.046103 51.715 1 lbf/in2
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Units of Pressure1 pascal (Pa) = 1 N/m21 atm = 760 mmHg = 760
torr1 atm = 101,325 Pabar = 105 Papsi = lb/in2 = 6894.757
Pa5.2Pressure = (force = mass x acceleration)
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I. Gas PropertiesCharles law 1787
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I. Gas PropertiesCharless law, temperature and thermometer1593
Galileo Galilei invented a rudimentary water thermometer in which,
for the first time, allowed temperature variations to be
measured.
1714, Gabriel Fahrenheit invented the first mercury thermometer,
the modern thermometer.
1742, Anders Celsius (17011744) created Celsius temperature
scale 1848, Lord William Thomson Kelvin developed the idea of
absolute temperature, what is called the "Second Law of
Thermodynamics", and developed the dynamical theory of heat.By
Guy-Lussac, 1802
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I. Gas PropertiesAvogadro number of gas 1811 R= 8.314472 J K-1
mol-11865 Josef Loschmidt(1821-1895), using the new Kinetic
Molecular Theory (KMT) calculated the number of molecules/cm3 = 2.6
x 10191910 Jean Perrin, by direct measurements of the mean square
displacement and application of Einsteins equation, using
suspensions of particles of gamboge and of mastic of uniform size =
7.12 x 1023Daltons law 1801
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1660 () . () .1662 . () ().1671 . . . 1660 () . 2 . . , , .1661
14 () . .1662 () . () . .1663 .1660
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1784 .1785 ( ). .1787 , .1788 .1792 6 . .1784 .1785 (~1786).1786
2 (~1798). .1787 () . (~1792). (~1791).1788 . .1789 . 1787
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1804 ,1806 40 . 50 . 1807 1808 , .1811 . 1813 () .1814 , .1804 .
1805 .1806 (962~) 1807 (~1814) . .1811 (~1812). .1812 , . ,
(~1814). 1814 . 18 . (~1815) . .1811
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Kinetic Molecular Theory of Gases1. A gas is composed of
molecules that are separated from each other by distances far
greater than their own dimensions. The molecules can be considered
to be points; that is, they possess mass but have negligible
volume.
d(N2,g) = 0.00125 g/L (273C)d(N2,liq) = 0.808 g/mL (-195.8C)2.
Gas molecules are in constant motion in random directions.
Collisions among molecules are perfectly elastic.3. Gas molecules
exert neither attractive nor repulsive forces on one another.(no
interaction)
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Collisions of Gas Particles
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Collisions of Gas Particles
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*The gas molecules in the container are in random motion
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p = mvx (mvx) = 2mvx t = 2a/vx A f = p/ t= 2mvx/(2a/vx)= mvx2/aN
A p = f/a2 = m(vx12 + vx22 + ... + vxN2)/a3 =Nmvx2/V pV=Nmvx2
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Gas Pressure in the Kinetic Theory
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! Boltzmann constantMean Kinetic Energy per particle
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p = gas pressure, V=volume = mean square velocityN = number of
gas moleculesn = mole number of gas molecules = N/NANA = Avogadros
numberm = mass of the gas moleculeM = molar mass of the gas
molecule(Kinetic Molecular Theory for Gases)
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N = number of molecules, k = Boltzmann constant, J K-1,n =
number of moles = N/NA,R = gas constant, 0.08204 l atm mol-1 K-1T =
temperature, P = gas pressure, V = volume,NA = Avogadros number pV
= NkT = nRT (Ideal Gas Equation)
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Maxwell-Boltzmann Distribution for Molecular Speedsf(u) = speed
distribution function, m = molecular mass,k = Boltzmann constant,T
= temperature, u = speedu~ u+du
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(Molecular velocity and energy distribution)(Otto Stern) (1943,
w/ Gerlach)Schematic diagram of a stern type experiment for
determining the distributionof molecular velocities v ~ v+v N!!
http://leifi.physik.uni-muenchen.de/web_ph12/originalarbeiten/stern/molekularstr.htm
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Molecular speed Distribution of N2 gasMaxwell Boltzmann
distribution of molecular speeds in nitrogen gas at two
temperatures. The ordinate is the fractional number of molecules
per unit speed interval in (km/s)-1.
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Apparatus for studying molecular speed distributionChopper
methodgravitation method
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The distribution of speedsfor nitrogen gas moleculesat three
different temperatures
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Chemistry in Action: Super Cold AtomsGaseous Rb Atoms1.7 x 10-7
KBose-Einstein Condensate
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Gaseous Diffusion/EffusionDiffusion of Ammonia and HCl
Effusion enrichment of UF6
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Gas diffusion is the gradual mixing of molecules of one gas with
molecules of another by virtue of their kinetic properties.NH317
g/molHCl36 g/mol
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Kinetic-Molecular Theory for Gaseous BehaviorPrincipal Issues (
)
Negligible Volume and No interactionHold only at low P, high T;
for dilute gasesElastic CollisionsOnly in Neutonian mechanics is
the reverse of an event as likely as the event itself. In the real
world you cannot unscramble eggs because of entropy effects
resulting from large ensembles of molecules
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Deviations from Ideal Behavior1 mole of ideal gaspV =
nRTRepulsive ForcesAttractive Forces
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Effect of intermolecular forces on the pressure exerted by a
gas.Real GasHas volumeHas interaction(usually attractive)
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Van der Waals equationnonideal gasSelected Values for a and b
for the van der Waals Equation
Gasa [(L2 atm)/mol2]b [10-2
L/mol]He0.034122.370Ne0.2111.71Ar1.343.22Kr2.323.98Xe4.192.66H20.24442.661N21.3903.913O21.3603.183CO23.5924.267CH42.254.28CCl420.413.8C2H24.3905.136Cl26.4935.622C4H1014.4712.26C8H1837.3223.68
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Distribution of Molecular VelocitiesN molecules at equilibrium
at Tmagnitude u of the velocity vector The fraction of molecules
having simultaneouslya velocity component between ux and ux + dux,
uy and uy + duy, and uz and uz + duz is
-. fraction of molecules with a speed between u and u + du
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Velocity DistributionThe distribution of particle velocities by
Maxwell & Boltzmann The most probable velocity The average
velocity The root mean square velocity
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