Van der Waal’s constants

Schuster calculated the molecular co-volume at the b.p. from 0b= Vmb--bb =RTblBby where bb is van der Waals s constant at the b.p. and Bb is the internal pressure. For normal substances, fe6=0 646c, 6=0 236 =0 147Z>c-Unlike Traube s co-volume, Schuster s depends on the nature of the substance. If the degree of association at the critical point is assumed to be 1, that for an abnormal substance was calculated from the observed and normal 0b values as in the case of Traube s equation. 

The atomic and molecular volumes of inorganic liquids were considered from the point of view of the Lewis-Langmuir theory of atomic structure by Pease.2 Tasiro gave the formula log v=[ml /(p+k)]+log Voo, where Vao=sp. vol. at infinite pressure, iw=tangent of the angle between the isotherm and the abscissa axis, fc=an arbitrary constant 2 5651 Voo=b (van der Waals s constant). 

If 1 jvg is neglected in comparison with 1 jvi, the law of rectilinear diameter of Cailletet and Mathias ( 5.VIIB) gives llvi=A—BTy where A and B are constants, and r=abs. temp. Hence, from Bakker s equation ( 4.VIIIL), l. =alvi, it foUows that l —a A—BT), where a is van der Waals s constant. From Stefan s equation ( 6.VIII G),... 

Valson s law of moduli, 32, 198 van der Waals s constants, 23, 154-5 surface tension equations, 141, 151 vapour pressure equation, 267... 

An estimation of van der Waal s constant could be made from surface tension of the material following a simple treatment suggested by Overbeek and give in Void s paper (19, 20). According to this, the interaction energy per square centimeter of two semi-infinite slabs of material separated by a distance a is given by - A and... 

Van der Waal s constant as calculated with the help of equation 16 and found to be 2.1 x 10 ergs. It was also evaluated by... 

It makes allowance both for the volume occupied by the molecules and for the attractive force between the molecules b is the effective volume of molecules in 1 mol of gas and n is a measure of the attractive force between the molecules. For values of R, a, and b see a table of van der Waal s constants for gases in hide DR (ed) (2004) CRC handbook of chemistry and physics. CRC Press, Boca Raton, FL. 

The integrand of (7.24), like that of van der Waals s constant, m, is always short-ranged, and so m(p) does not have the weak divergence at the critical point that is correctly given by (4.162). We discuss the significance of this divergence in S 9.2. 

Replacement of gas by the nonpolar (e.g., hydrocarbon) phase (oil phase) has been sometimes used to modify the interactions among molecules in a spread film of long-chain substances. The nonpolar solvent/water interface possesses an advantage over that between gas and water in that cohesion (i.e., interactions between adsorbed molecules) due to dipole and van der Waals s forces is negligible. Thus, at the oil/water interfaces, the behavior of adsorbates is much more ideal, but quantitative interpretation may be uncertain, in particular for the higher chains, which are predominantly dissolved in the oil phase to an unknown extent. The oil phase is poured on the surface of an aqueous solution. Thus, the hydrocarbon, such as heptane or decane, forms a membrane a few millimeters thick. It is thicker than the adsorbed monolayer. Owing to the small difference in dielectric constant between the air and a hydrocarbon oil, the... 

The concept ofmetastability in this elementary setting has exactly the same meaning as in the closely related case of van der Waals s fluid. Consider the simplest equilibrium treatment of a bar loaded by a constant stress Oo,. The static problem reduces to the minimization of the functional... 

Charton used statistical methods to investigate the contributions to Taft s s values of the size of the groups concerned and their polar effects. As a measure of group size he took the van der Waal s radius, rv, and he used o-, and crR as measures of inductive and mesomeric effects. Correlations of steric substituent constants were then carried out250 using the equation (for group x)... 

The ortho substituent constants, s°, on the other hand, gave no significant correlation with van der Waal s radii. The effects of groups in the ortho position are fully accounted for in terms of o-, and steric effects of groups in the ortho position are constant, negligible, or non-existent251. This result was confirmed by an analysis of the data for acid-catalyzed ester hydrolysis and formation, including those of Tables 20 and 22. 

Cohesion Pressure. A term in Van der Waal s equation introduced to take care of the effect of molecular attraction. It is usually expressed as a/Vwhere at is a constant and V is the volume of the gas. 

A gaseous mixture at 25°C (298 K) and 120 atm (12,162 kPa) contains 3% helium, 40% argon, and 57% ethylene on a mole basis. Compute the volume of the mixture per mole using the following (a) ideal-gas law, (b) compressibility factor based on pseudoreduced conditions (Kay s method), (c) mean compressibility factor and Dalton s law, (d) van der Waal s equation and Dalton s law, and (e) van der Waal s equation based on averaged constants. 

Calculate the volume using van der Waal s equation with averaged constants. In this method it is convenient to rearrange the van der Waal equation into the form... 

Auluck and Rai, from the hole theory of liquids, calculated that van der Waals s a constant is given hy a—k Vm oipQ fh ) where is a constant, theoretically 2 4 but experimentally 1-44, and h is Planck s constant,... 

Young found from van der Waals s equation that the ratio of the actual density at the critical point to the theoretical density for the ideal gas should be (8/3)- /2=3 77 for all substances. The actual values are not far from this, except for alcohols and acetic acid, which have values of 4 to nearly 5. The density of saturated vapour is equal to the ideal gas density at the same corresponding temperature multiplied by a constant k ... 

According to Foa the law of corresponding states shows that for each value of d =TjTc there is the same value of the molecular heat of the liquid along the iimiting curve and of the molecular heat at constant pressure in the ideal gas state the experimental agreement is moderate. Baynes calculated or and or" from van der Waals s and Clausius s characteristic equations, and related the sign to the number of atoms in the molecule. 

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