MICRO AND NANOSCALE SYSTEMS - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 181

2.5 VAN DER WAALS EQUATION ( CORRESPONDING STATES LAW)
In 1873, Van der Waals proposed an equation of state is qualitatively good de-
scription of liquid and gaseous systems. It is for one mole (one mole) is:

a

� + −=

( )

p v b RT

€ ‚

(2.2)

ƒ

2

„

v

a

Note that at and this equation becomes the equation of state

p >>

v >> b

v

2

of ideal gas

pv = RT

(2.3)

Van der Waals equation can be obtained from the Clapeyron equation of Men-
deleev by an amendment to the magnitude of the pressure a/v 2 and the amendment
b to the volume, both constant a and b independent of T and v but dependent on
the nature of the gas.
The amendment b takes into account:
1)

the volume occupied by the molecules of real gas (in an ideal gas mol-
ecules are taken as material points, not occupying any volume);

so-called “dead space,” in which cannot penetrate the molecules of real
gas during motion, that is, volume of gaps between the molecules in their
dense packing.
Thus,

2)

  (Fig. 2.3). The amendment a/v 2 takes into account the
interaction force between the molecules of real gases. It is the internal pressure,
which is determined from the following simple considerations. Two adjacent ele-
ments of the gas will react with a force proportional to the product of the quanti-
ties of substances enclosed in these elementary volumes.

bv v

ì î ë . çàç .

FIGURE 2.3 Location scheme ofmoleculesin a real gas.