Attractive force types

The virial equation is appropriate for describing deviations from ideality in those systems where moderate attractive forces yield fugacity coefficients not far removed from unity. The systems shown in Figures 2, 3, and 4 are of this type. However, in systems containing carboxylic acids, there prevails an entirely different physical situation since two acid molecules tend to form a pair of stable hydrogen bonds, large negative... 

Van der Waals Equations of State. A logical step to take next is to consider equations of state that contain both a covolume term and an attractive force term, such as the van der Waals equation. De Boer [4] and Ross and Olivier [55] have given this type of equation much emphasis. 

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... 

Atoms combine with one another to give compounds having properties different from the atoms they contain The attractive force between atoms m a compound is a chemical bond One type of chemical bond called an ionic bond, is the force of attraction between oppositely charged species (ions) (Figure 1 4) Ions that are positively charged are referred to as cations, those that are negatively charged are anions... 

A substance exists as a liquid rather than a gas because attractive forces between molecules (mtermolecular attractive forces) are greater m the liquid than m the gas phase Attractive forces between neutral species (atoms or molecules but not ions) are referred to as van der Waals forces and may be of three types... 

Boiling Point When describing the effect of alkane structure on boiling point m Sec tion 2 17 we pointed out that van der Waals attractive forces between neutral molecules are of three types The first two involve induced dipoles and are often referred to as dis persion forces or London forces... 

Critical micelle concentration (Section 19 5) Concentration above which substances such as salts of fatty acids aggre gate to form micelles in aqueous solution Crown ether (Section 16 4) A cyclic polyether that via lon-dipole attractive forces forms stable complexes with metal 10ns Such complexes along with their accompany mg anion are soluble in nonpolar solvents C terminus (Section 27 7) The amino acid at the end of a pep tide or protein chain that has its carboxyl group intact—that IS in which the carboxyl group is not part of a peptide bond Cumulated diene (Section 10 5) Diene of the type C=C=C in which a single carbon atom participates in double bonds with two others... 

Physisorption occurs when, as a result of energy differences and/or electrical attractive forces (weak van der Waals forces), the adsorbate molecules become physically fastened to the adsorbent molecules. This type of adsorption is multilayered that is, each molecular layer forms on top of the previous layer with the number of layers being proportional to the contaminant concentration. More molecular layers form with higher concentrations of contaminant in solution. When a chemical compound is produced by the reaction between the adsorbed molecule and the adsorbent, chemisorption occurs. Unlike physisorption, this process is one molecule thick and irreversible... 

In a solution of a solute in a solvent there can exist noncovalent intermolecular interactions of solvent-solvent, solvent-solute, and solute—solute pairs. The noncovalent attractive forces are of three types, namely, electrostatic, induction, and dispersion forces. We speak of forces, but physical theories make use of intermolecular energies. Let V(r) be the potential energy of interaction of two particles and F(r) be the force of interaction, where r is the interparticle distance of separation. Then these quantities are related by... 

There is a reasonable explanation for this type of deviation. The kinetic theory, which explains the pressure-volume behavior, is based upon the assumption that the particles exert no force on each other. But real molecules do exert force on each other The condensation of every gas on cooling shows that there are always attractive forces. These forces are not very important when the molecules are far apart (that is, at low pressures) but they become noticeable at higher pressures. With this explanation, we see that the kinetic theory is based on an idealized gas—one for which the molecules exert no force on each other whatsoever. Every gas approaches such ideal behavior if the pressure is low enough. Then ihe molecules are, on the average, so far apart that then-attractive forces are negligible. A gas that behaves as though the molecules exert no force on each other is called an ideal gas or a perfect gas. 

The bands of matrix-isolated molecules are frequently observed at the wavelengths which differ from those in gas-phase spectra. These matrix shifts are induced by the repulsive and attractive forces between the isolated molecules and the atoms which form the matrix site. Repulsions lead to small increases (1-15 cm ) of vibrational frequencies, and attractions decrease them. Matrix shifts depend on the type of matrix gas they rise in the sequence from neon to xenon. In general, the shifts are positive (the... 

When a solid bar is loaded axially in tension, it elongates more and more with increasing load. The mechanism by which such elongation occurs can be visualised as a progressive increase in the separation of the atoms of the bar in the direction of loading, i.e., in the axial direction. The displacement of the atoms from their equilibrium positions results in the development of attractive forces between them these forces balance the applied load. This elementary picture can be considered to be applicable to the initial stages of deformation of many types of materials, crystalline as well as amorphous. 

In this category, among the molecular, electrostatic and magnetic interparticle bonds, interest is primarily centered on the van der Waals-type attractive forces that may predominate in the absence of liquid and solid bonds. The force of the van der Waals attraction between two spheres of equal size is (R4)... 

Since the zero-point energy is positive, that is of repulsive type and quite large, it is capable of practically balancing the effect of the attractive forces. Hence, solidification is possible only under elevated pressures. 

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