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

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)

I. Gas PropertiesCharles law 1787

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

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

1660 () . () .1662 . () ().1671 . . . 1660 () . 2 . . , , .1661 14 () . .1662 () . () . .1663 .1660

1784 .1785 ( ). .1787 , .1788 .1792 6 . .1784 .1785 (~1786).1786 2 (~1798). .1787 () . (~1792). (~1791).1788 . .1789 . 1787

1804 ,1806 40 . 50 . 1807 1808 , .1811 . 1813 () .1814 , .1804 . 1805 .1806 (962~) 1807 (~1814) . .1811 (~1812). .1812 , . , (~1814). 1814 . 18 . (~1815) . .1811

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)

Collisions of Gas Particles

Collisions of Gas Particles

*The gas molecules in the container are in random motion

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

Gas Pressure in the Kinetic Theory

! Boltzmann constantMean Kinetic Energy per particle

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)

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)

Maxwell-Boltzmann Distribution for Molecular Speedsf(u) = speed distribution function, m = molecular mass,k = Boltzmann constant,T = temperature, u = speedu~ u+du

(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

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.

Apparatus for studying molecular speed distributionChopper methodgravitation method

The distribution of speedsfor nitrogen gas moleculesat three different temperatures

Chemistry in Action: Super Cold AtomsGaseous Rb Atoms1.7 x 10-7 KBose-Einstein Condensate

Gaseous Diffusion/EffusionDiffusion of Ammonia and HCl

Effusion enrichment of UF6

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

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

Deviations from Ideal Behavior1 mole of ideal gaspV = nRTRepulsive ForcesAttractive Forces

Effect of intermolecular forces on the pressure exerted by a gas.Real GasHas volumeHas interaction(usually attractive)

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

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

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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