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Chapter 1: Properties of gases!

The perfect gas!Gas laws, perfect gas equation!

Partial pressures! Barometric formula! Real gases!

The van der Waals equation!

Mechanical equilibrium!

Thermal equilibrium!

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Temperature scales: Thermometry!Fahrenheit scale: three reference points:!

a. lowest temperature: 0 degrees (brine: a mixture ice,water and ammonium chloride)!

b. ice melts at 32 degrees (he did not use this in his

original scale)!

c. 96 degrees: the temperature in the mouth or armpit of

his wife (or a living man in good health)!

Later on it was adjusted between the freezing (32 F) and

boiling points of water and (212 F). !

In the original Celsius (Swedish astronomer) scale water

boils at 0 degrees and ice melts at 100 degrees. This was

reversed later.!

TF = 32 + 1.8 TC!

Thermal equilibrium:!

Illustration of zeroth law!Of thermodynamics!

Boyles law:!

!

pV=constant at constant n, T!

Boyles law:!

p1/V!

at constant n, T!

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Charles law:!

VT, at constant n, andp!

Charles law:!

pT, at constant n, and V!

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Partial pressures!

p=JpJ!

pJ

=nJ

RT/V (perfect gas)!

Daltons law: pressure exerted by a mixture of gases is equal

to sum of their partial pressures!

Barometric formula!p=p0 exp(-h/H)!

H7.4 km!

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Example problems!

1. Use the barometric formula to calculate the altitude at

which the pressure is 1/10th of that at sea level.!

Compound! Molar volume(liter/mol)!

C2H6! 6.86!

N2! 2.04!

CH4! 1.99!

Ideal gas law! 2.13!

Compound! Molar volume(liter/mol)!

C2H6! 32.73!

N2! 32.83!

CH4! 32.81!

NH3! 32.73!

Ideal gas law! 32.8!

T= 260 K and p= 10 atm! T=400 K and p= 1 atm!

When & why is the ideal gas equation valid? !

Real gases!Do not obey perfect gas equationexactly!

Characterized by intermolecularinteraction!

!repulsive at short distances!!attractive at intermediateseparations!

Real gases!

Compression factor!Z=Vm/V

0m!

For a perfect gas, Z=1!

Z >1: repulsive interaction!

Z

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Critical temperature, Tc!

Temperature above which !

the gas cannot be liquefied!

Boyle temperature!

Temperature at which

properties of real gases

coincide with that of

the perfect gas!

van der Waals

isotherms!

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Surface of possiblestates allowed by the

van der Waals

equation!

Critical compression factor: Zc=pcVc/RTc=3/8=0.375!

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Reduced variables!

pr=p/pc!

Vr=Vm/Vc!

Tr=T/Tc!

pr=8Tr/(3Vr-1)-3/Vr2!

Reduced van der Waals equation of state!

Vexp! pexp (atm)! Pideal(atm)! pvdW(atm)! pBB (atm)! pBWR(atm)!

28.588! 1! 1.004! 0.9994! 1.0004! 1.000!

5.6119! 5! 5.114! 4.999! 4.10! 4.998!

2.7387! 10! 10.470! 9.998! 9.99! 9.989!

0.13720! 100! 209.184! 99.373! 102.903! 99.073!

0.09840! 150! 291.667! 262.513! 160.709! 147.070!

0.0868! 200! 330.645! 519.193! 209.143! 200.201!

0.07160! 450! 400.838! 2608.65! 348.118! 450.277!

0.07089! 475! 404.853! 2955.56! 358.492! 474.984!

0.07022! 500! 408.715! 3357.07! 368.752! 500.237!

Ethane at 350 K!

vdW: van der Waals equation!

BWR: Benedict-Webb-Rubin equation!

BB: Beattie-Bridgeman equation!

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Benedict - Webb - Rubin Equation (BWR)

p = RT+ (BRT A C0T2)2 + (bRT a)3 +

a6+ cT

2

3(1+ 2) exp(2)

where A, B, C0, a, b, c, ,are constants

Beattie - Bridgeman equation (BB)

pVm2= RT 1

c

VmT3

&

'(

)

*+Vm + B

bB

Vm

&

'(

)

*+ A 1

a

Vm

&

'(

)

*+

where A, B, a, b, c are constants

Summary!

Ideal gas equation: pV=nRT!

No intermolecular interaction between gas molecules

!

Daltons law of partial pressures: p J=xJp; xJ=nJ/n; JpJ=p! Valid for both perfect gases and real gases!

Barometric formula: p=p0exp(-h/H); H=RT/Mg! Real gases: ideal gas equation not valid due to intermolecular forces ! Compressibility factor, Z=Vm/Vm0; Vm0=RT/p; Z=1 for ideal gas! Virial equation of state: PVm=RT(1+B#p+C#p2+)!

! PVm=RT(1+B/Vm+C/Vm2+)! Boyle temperature: Temperature at which real gases exhibit ideal gas

behavior!

van der Waals equation: p=RT/(Vm-b)-a/Vm2! Critical constants: Vc=3b; pc=a/27b2; Tc=8a/27Rb! Reduced variables: pr=p/pc; Vr=V/Vc; Tr=T/Tc! Reduced van der Waals equation of state: pr=8Tr/(3Vr-1)-3/Vr2!