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This figure includes two diagrams. Each involves two lavender shaded boxes that contain 14 relatively evenly distributed, purple spheres. In the first box in a, a nearly centrally located purple sphere has 6 double-headed arrows extending outward from it to nearby spheres. A single purple arrow is pointing right into open space. This box is labeled, “real.” There is a second box that looks slightly larger than the first box in a. It has the same number of particles but no arrows. This box is labeled, “ideal.” In b, the first box has a purple sphere at the right side which has 4 double-headed arrows radiating out to the top, bottom, and left to other spheres. A single purple arrow points right through open space to the edge of the box. This box has no spheres positioned near its right edge This box is labeled, “real.” The second box is the same size as the first box and contains the same number of particles. There are no arrows in it, except for the purple arrow which appears to be bigger and bolder. This box is labeled, “ideal.”
(a) Attractions between gas molecules serve to decrease the gas volume at constant pressure compared to an ideal gas whose molecules experience no attractive forces. (b) These attractive forces will decrease the force of collisions between the molecules and container walls, therefore reducing the pressure exerted compared to an ideal gas.

There are several different equations that better approximate gas behavior than does the ideal gas law. The first, and simplest, of these was developed by the Dutch scientist Johannes van der Waals in 1879. The van der Waals equation    improves upon the ideal gas law by adding two terms: one to account for the volume of the gas molecules and another for the attractive forces between them.

This figure shows the equation P V equals n R T, with the P in blue text and the V in red text. This equation is followed by a right pointing arrow. Following this arrow, to the right in blue text appears the equation ( P minus a n superscript 2 divided by V squared ),” which is followed by the red text ( V minus n b ). This is followed in black text with equals n R T. Beneath the second equation appears the label, “Correction for molecular attraction” which is connected with a line segment to V squared. A second label, “Correction for volume of molecules,” is similarly connected to n b which appears in red.

The constant a corresponds to the strength of the attraction between molecules of a particular gas, and the constant b corresponds to the size of the molecules of a particular gas. The “correction” to the pressure term in the ideal gas law is n 2 a V 2 , and the “correction” to the volume is nb . Note that when V is relatively large and n is relatively small, both of these correction terms become negligible, and the van der Waals equation reduces to the ideal gas law, PV = nRT . Such a condition corresponds to a gas in which a relatively low number of molecules is occupying a relatively large volume, that is, a gas at a relatively low pressure. Experimental values for the van der Waals constants of some common gases are given in [link] .

Values of van der Waals Constants for Some Common Gases
Gas a (L 2 atm/mol 2 ) b (L/mol)
N 2 1.39 0.0391
O 2 1.36 0.0318
CO 2 3.59 0.0427
H 2 O 5.46 0.0305
He 0.0342 0.0237
CCl 4 20.4 0.1383

At low pressures, the correction for intermolecular attraction, a , is more important than the one for molecular volume, b . At high pressures and small volumes, the correction for the volume of the molecules becomes important because the molecules themselves are incompressible and constitute an appreciable fraction of the total volume. At some intermediate pressure, the two corrections have opposing influences and the gas appears to follow the relationship given by PV = nRT over a small range of pressures. This behavior is reflected by the “dips” in several of the compressibility curves shown in [link] . The attractive force between molecules initially makes the gas more compressible than an ideal gas, as pressure is raised (Z decreases with increasing P ). At very high pressures, the gas becomes less compressible (Z increases with P ), as the gas molecules begin to occupy an increasingly significant fraction of the total gas volume.

Strictly speaking, the ideal gas equation functions well when intermolecular attractions between gas molecules are negligible and the gas molecules themselves do not occupy an appreciable part of the whole volume. These criteria are satisfied under conditions of low pressure and high temperature . Under such conditions, the gas is said to behave ideally, and deviations from the gas laws are small enough that they may be disregarded—this is, however, very often not the case.

Practice Key Terms 2

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Source:  OpenStax, Ut austin - principles of chemistry. OpenStax CNX. Mar 31, 2016 Download for free at http://legacy.cnx.org/content/col11830/1.13
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