Topic 1 Gases

1.1 Ideal gases

The pressure-volume relationship — Boyle’s lawV=constant×1/P or PV=constant

The quantity-volume relationship — Avogadro’s law

V=constant×n

The temperature-Volume relationship — Charles’ law

V=constant×T or V/T=constant

V nT/P ∝ PV=nRT R--- Avogadro constant

The state equation of ideal gases

Units of pressure

1 Pa=1 N.m-2

1 kPa=103 Pa

1 MPa=106 Pa

1 torr= 1 mmHg=133.322 Pa

1 atm=760 torr=1.01325×105Pa 1 bar=105 Pa=0.9869 atm =750.06 torr

p

Micro view about pressure of gases

Value of R

8.3145 J.mol-1.K-1

0.083145 L.bar.K-1.mol-1

82.058 cm3.atm.mol-1.K-1 0.082058 L.atm.mol-1.K-1 1.98722 cal.mol-1. K-1

62.364 L.Torr.K-1. mol-1

1.2 Mixture of ideal gases

Dalton law:

VRTnnppp /......)(...... 2121

Amagat law:

pRTnnVVV /......)(...... 2121

1.3 Real gases do not follow the ideal state equation( )in T

UpV

m2m

( )( )a

p V b RTV

2inm

ap

V

Internal pressure: induced by interaction between molecules

van der Waals equation:

Volume of gas molecules

b, molecular volume

Kamerling-Onnes equation:2

mpV RT Bp Cp

Substance a (L2 atm/mol2) b (L/mol)

He 0.0341 0.0237

H2 0.244 0.0266

O2 1.36 0.0318

H2O 5.46 0.0305

CCl4 20.4 0.1383

Numerical Example:

Fugacity of real gasesf p

,fugacity coefficient

The efficient pressure

Determination of fugacity coefficient

1. Graphical method

2. Corresponding states method

0

1PmVln dPRT P

Measure P, Vm, T

Compression factor, Z=pV/nRT

The parameters of critical states of real gases

Critical temperature Tc: Above which the gas can not be liquefied by increasing the pressure

Cricital pressure Pc: The minimum pressure the gas could be liquefied at Tc

Cricital volume Vc: The molar volume of the gas at Tc and Pc

Vc, Tc and Pc the critical parameters

Critical Point Data for Methane: Pc = 46.3 bar, Tc = 190.6 K, Vc =0.099 L mol-1, Zc = 0.29.

A few characteristics of some actual gases :

SubstanceCritical State

Tc pc molar Vc

H2O 647.10 K 22.07 MPa 55.95 mL

CH4 190.56 K 4.59 MPa 98.60 mL

CCl2F2 385 K 4.12 MPa mL

N2 126.21 K 3.39 MPa 90.08 mL

O2 154.58 K 5.036 MPa 73.39 mL

CO2 304.19 K 7.38 MPa 91.90 mL

H2 32.98 K 1.315 MPa 66.93 mL

He 5.19 K 0.227 MPa 57.48 mL

Ne 44.40 K 2.76 MPa 41.70 mL

对比温度CT

T

对比压力CP

P

对比体积CV

V

m2m

( )( )a

p V b RTV

van der Waals equation:

8P

RT b

64

27R a

c

c22

c

c

P

T

The corresponding critical constants

The corresponding states

Corresponding temperature

Corresponding pressure

Corresponding volume

)())(( CCc TZRVP

kRT

VPZ

C

CC

At critical point all gases are equally nonideal.

Principle of corresponding states

T1，P1V1，P2V2，P3V3 ……，

π 1， π 2， π 3 ……，Z1， Z2， Z3 ……， Z—π

T2，Z—π

Z—π —θ

……

Plotting Z-π-θfigure:

0

1PmVln dPRT P

dPP

ZdP

PP

Z PP

00

11

P=π PC0

1Zln d

θ 1，

1Z

—

T，P , Newton diagram

PVm=ZRT