Van der Waals constants

TABLE 5.29 Van der Waals Constants for Gases The van der Waals equation of state for a real gas is  [c.516]

L bar K moLi or 0.082 056 L atm K moLi The van der Waals constants are related to the critical temperature and pressure, C and P, in Table 6.5 by  [c.516]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.517]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.518]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.519]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.520]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.521]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.522]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.523]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.524]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.525]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.526]

TABLE 5.29 Van der Waals Constants for Gases Continued)  [c.527]

Table 3.4 van der Waals constants for some common gases  [c.113]

It must be remembered that, in general, the constants a and b of the van der Waals equation depend on volume and on temperature. Thus a number of variants are possible, and some of these and the corresponding adsorption isotherms are given in Table XVII-2. All of them lead to rather complex adsorption equations, but the general appearance of the family of isotherms from any one of them is as illustrated in Fig. XVII-11. The dotted line in the figure represents the presumed actual course of that particular isotherm and corresponds to a two-dimensional condensation from gas to liquid. Notice the general similarity to the plots of the Langmuir plus the lateral interaction equation shown in Fig. XVII-4.  [c.624]

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data.  [c.2439]

We first note errors in total energy means that are not greater than 0.5% for all LN versions tested. Individual energy components show errors that are generally less than 1%, with the exception of the van der Waals energy that can reach 4% for large k2. Of course, this discussion of relative errors reflects practical rather than mathematical considerations, since constants can be added to individual terms without affecting the dynamics. The relative errors  [c.253]

The parameters necessary for the calculation of a force field energy are the force constants k for bonds and angles, as well as their corresponding reference bond lengths Ifl and angles 6q. The energy contribution of a torsion is described via the "barrier height" the torsion angle a), the multiplicity n, and the phase shift y. The non-bonding van der Waals interactions are characterized by the atom-pair collision parameters [c.361]

The van der Waals equation of state for 1 mol of a nonideal gas contains two constants a and b which are characteristic of a particular gas  [c.530]

These constants can be related to the coordinates of the critical point of the gas p, V and T Outline the strategy by which the van der Waals a and b  [c.530]

Reduced Properties. One of the first attempts at achieving an accurate analytical model to describe fluid behavior was the van der Waals equation, in which corrections to the ideal gas law take the form of constants a and b to account for molecular interactions and the finite volume of gas molecules, respectively.  [c.239]

In 1893, it was shown that corresponding states are not unique to van der Waals equation of state (73). Rather, for any equation of state having not more than three constants, corresponding states are only a mathematical consequence.  [c.239]

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres.  [c.257]

CoMFA methodology is based on the assumption that since, in most cases, the drug-receptor interactions are noncovalent, the changes in biological activity or binding constants of sample compounds correlate with changes in electrostatic and van der Waals fields of these molecules. To initiate the CoMFA process, the test molecules should be structurally aligned in their pharmacophoric conformations the latter are obtained by using, for instance, the AAA described above. After the alignment, steric and electrostatic fields of all molecules are sampled with a probe atom, usually an sp carbon bearing a +1 charge, on a rectangular grid that encompasses structurally aligned molecules. The values of both van der Waals and electrostatic interaction between the probe atom and all atoms of each molecule are calculated in every lattice point on the grid using the force field equation described above and entered into the CoMFA QSAR table. This table thus  [c.359]

Wetting and capillarity can be expressed in terms of dielectric polarisabilities when van der Waals forces dominate the interface interaction (no chemical bond or charge transfer) [37]. For an arbitrary material, polarisabilities can be derived from the dielectric constants (e) using the Clausius-Mossotti expression [38]. Within this approximation, the contact angle can be expressed as  [c.140]

Covalent bonds hold atoms together so that molecules are formed. In contrast, weak chemical forces or noncovalent bonds, (hydrogen bonds, van der Waals forces, ionic interactions, and hydrophobic interactions) are intramolecular or intermolecular attractions between atoms. None of these forces, which typically range from 4 to 30 k[/mol, are strong enough to bind free atoms together (Table 1.3). The average kinetic energy of molecules at 25°C is 2.5 kj/mol, so the energy of weak forces is only several times greater than the dissociating tendency due to thermal motion of molecules. Thus, these weak forces create interactions that are constantly forming and breaking at physiological temperature, unless by cumulative number they impart stability to the structures generated by their collective action. These weak forces merit further discussion because their attributes profoundly influence the nature of the biological structures they build.  [c.14]

The van der Waals distance, Rq, and softness parameters, depend on both atom types. These parameters are in all force fields written in terms of parameters for the individual atom types. There are several ways of combining atomic parameters to diatomic parameters, some of them being quite complicated. A commonly used method is to take the van der Waals minimum distance as the sum of two van der Waals radii, and the interaction parameter as the geometrical mean of atomic softness constants.  [c.22]

One way of reducing the number of parameters is to reduce the dependence on atom types. Torsional parameters, for example, can be taken to depend only on the types of the two central atoms. All C-C single bonds would then have the same set of torsional parameters. This does not mean that the rotational barriers for all C-C bonds are identical, since van der Waals and/or electrostatic tenns also contribute. Such a reduction replaces all tetra-atomic parameters with diatomic constants, i.e.  [c.35]

Table 5.27 Compressibility of Water Table 5.28 Mass of Water Vapor In Saturated Air Table 5.29 Van der Waals Constants for Gases Table 5.30 Triple Points of Various M aterlals 5.9.1 Some Physical Chemistry Equations for Gases Table 5.27 Compressibility of Water Table 5.28 Mass of Water Vapor In Saturated Air Table 5.29 Van der Waals Constants for Gases Table 5.30 Triple Points of Various M aterlals 5.9.1 Some Physical Chemistry Equations for Gases
Although the previous paragraphs hint at the serious failure of the van der Waals equation to fit the shape of the coexistence curve or the heat capacity, failures to be discussed explicitly in later sections, it is important to recognize that many of tlie other predictions of analytic theories are reasonably accurate. For example, analytic equations of state, even ones as approximate as that of van der Waals, yield reasonable values (or at least ball park estmiates ) of the critical constants p, T, and V. Moreover, in two-component systems  [c.622]

The concept that Binnig and co-workers [73] developed, which they named the atomic force microscope (AFM, also known as the scaiming force microscope, SFM), involved mounting a stylus on the end of a cantilever with a spring constant, k, which was lower than that of typical spring constants between atoms. This sample surface was then rastered below the tip, using a piezo system similar to that developed for the STM, and the position of the tip monitored [74], The sample position (z-axis) was altered in an analogous way to STM, so as to maintain a constant displacement of the tip, and the z-piezo signal was displayed as a fiinction of V andy coordinates (figure Bl.19.16). The result is a force map, or image of the sample s surface [75], since displacements in the tip can be related to force by Flooke s Law, F = -Icz, where z is the cantilever displacement. In AFM, the displacement of the cantilever by the sample is very simply considered to be the result of long-range van der Waals forces and Bom repulsion between tip and sample. Flowever, in most practical implementations, meniscus forces and contaminants often dominate the interaction with interaction lengths frequently exceeding those predicted [76]. In addition, an entire family of force microscopies has been developed, where magnetic, electrostatic, and other forces have been measured using essentially the same instmment.  [c.1692]

Mid-infrared combination bands and far-infrared spectra of Van der Waals complexes map out tlie pattern of energy levels associated witli intennolecular bending and stretching vibrations. The principal quantities that can be observed are vibrational frequencies and rotational constants, tliough once again subsidiary quantities such as centrifugal distortion constants, dipole moments and nuclear quadmpole coupling constants may sometimes be extracted. In addition, observation of line broadening due to predissociation can sometimes provide very direct measurements of binding energies (and hence of tlie deptlis of potential wells).  [c.2444]

Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled.  [c.50]

In the absence of reliable experimental data, the methods presented here provide physical property estimates that are sufficiently accurate for many engineering apphcations. These techniques have been selected on the basis of accuracy, generality, and, in most cases, sim-phcity they are divided into 11 categories (1) pure component constants critical properties, normal freezing and ooihng temperatures, acentric factor, radius of gyration, dipole moment, and van der Waals area and volume (2) vapor pressure (3) ideal gas thermal properties heat capacity and enth py, Gibbs energy, ana entropy of formation (4) enthalpy of vaporization and fusion (5) sohd and hquid heat capacity (6) vapor, hquid, and solid density (7) vapor and liquid viscosity (8) vapor and hquid thermal conduc tivity (9) vapor and hquid diffusiv-ity (10) surface tension and (11) flammability properties flash point, flammabihty hmits, and autoignition temperature. The definition of the property and limitations and accuracy of each method of correla-  [c.381]

The effects of the constants in the van der Waals equation become more marked as the pressure is increased above atmospheric. Early measurements by Regnault showed tlrat the PV product for CO2, for example, is considerably less tlran that predicted by Boyle s law  [c.114]

The first major obstacle in studying electron transfer and/or metalloproteins is often the lack of potential energy parameters for metal sites in proteins. Although parameters for hemes existed in some of the earliest parameter sets because of the numerous studies of myoglobin [15], hemoglobin [16], and cytochrome [17], there is adearth of parameters for other metal sites. Parameters for iron-sulfur sites havebeenrecently developed [18-21] based on spectroscopic data for the force constants, crystallographic data for the equilibrium values, and quantum mechanical calculations for the partial charges and for the van der Waals parameters (see Chapter 2). Parameters for other sites have also been developed [22-25].  [c.396]

The intermolecular distance in the H2 crystal (3.79 A) is almost five times longer than the H-H bond length, being close to the equilibrium distance in the linear van der Waals complex H3 (3.5 A) [Silvera 1980]. The hydrogen atom, as a substituting impurity, moves almost freely in the cavity with radius 0.6 A. This allows one, when looking for the rate constants of reactions (6.20) and (6.21), to use the gas-phase model, studied quite thoroughly (see, e.g., Garrett and Truhlar [1983, 1991]), as a first approximation.  [c.113]

Since most SWNTs have diameters in the range of 1 -2 nm, we can expect them to remain cylindrical when they form cables. The stiffness constant of the cable structures will then be the sum of the stiffness constants of the SWNTs. However, just as with MWNTs, the van der Waals binding between the tubes limits tensile strength unless the ends of all the tubes can be fused to a load. In the case of bending, a more exact  [c.145]

See pages that mention the term Van der Waals constants : [c.1284]    [c.24]    [c.136]    [c.444]    [c.445]    [c.625]    [c.531]    [c.408]    [c.254]    [c.343]   
Langes handbook of chemistry (1999) -- [ c.5 , c.157 ]