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Materials Science and Engineering
Stacy Silver

HISTORICAL PERSPECTIVES ON van der Waals ATTRACTIVE FORCES 1873 - J.D. van der Waals (Danish Physicist) It had been noted that Boyle's Gas Law (PV=nRT) was not valid at high gas pressures. van der Waals made two assumptions to correct Boyle's Gas Law: 1. Assumed that there small particles known as molecules (BIG, BIG Assumption in 1873) with finite volume. 2. Assumed that there are attractive forces between the molecules Modified Boyle's Gas Law:  n2a P+ 2 (V −nb = nRT [1]  V  where "a/V 2" accounts for the attractive forces between molecules, "b" accounts for the finite volume of the molecules, and "n" is the number of moles of gas in a volume, V, at a temperature, T, and pressure, P. For one mole of gas P+ a (V− b = RT [2]  V2 For a variety of gases, the coefficients have been determined for the van der Waals correction to Boyles Gas Law. For example: Gas a b 2. 2 (l/mole) (l atm/mole ) Oxygen 1.360 0.03183 Carbon Dioxide 3.592 0.04267 Acetic Acid 17.59 0.1068 Nitrogen 1.390 0.03913 Methane 2.253 0.04278 1 van der Waals corrections applied to a variety of common gases.  R   a  where P = V −b T − V 2 10 1 Oxygen CO2 Acetic Acid Nitrogen PRESSURE (ATM) Methane Boyle's Law .1 0 200 400 600 800 1000 1200 TEMPERATURE (K) Based on 1 mole of gas at a constant volume of 22.4 liters. Note the deviation at low temperature for the acetic acid relative to these other gases. This indicates that acetic acid molecules are attracted toward one another. 2 Depending on the units used, the universal gas constant, R, can take on variety of values including Volume Temperature moles Atm psia mmHg gm 0.00290 0.0426 2.20 ft °K lb 1.31 19.31 999 gm 0.00161 0.02366 1.22 °R lb 0.730 10.73 555 62,0802.051206 cm 3 °K lb 357,7,000 2.83x107 34,0405.6 670 °R lb 203004,000
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