Molecules have a finite size

Our immediate purpose is to measure the mean free path by detecting the deviation of a molecule from a straight-line trajectory. Next we shall argue that the mean free path must surely depend on the density of the other molecules. If there are few molecules available to collide with, the mean free path will necessarily be long and vice versa. The collision cross-section results when we factor out the role of the density of target molecules in determining the mean free path. What remains is the cross-section, a molecular measure of size, with units of area. The final point of this section is that this size does depend on the energy with which the two molecules collide and that this dependence reflects the influence of the intermolecular potential on the distance that the molecules can approach one another. 

1 Direct determination of the mean free path by a scattering experiment 

Newton s first law is directly invoked in the analysis of the scattering experiment an A molecule is said to have collided with a target molecule if it changed its direction of velocity and thereby leaves the well-collimated beam. In other words, the experiment demonstrates that a force acted between A and B molecules and it measures the resulting attennation of the beam of A molecnles. Here is where we define when a collision occurs it is when a force acted between the two molecules. 

The direction of die beam of A molecules is taken as the x axis. The flux is defined as the number of beam molecules crossing a unit area (perpendicular to the direction of the beam) per unit time. The flux, I(x), at distance x along the 

Owing to collisions with molecules of the target gas, A molecules are deflected fiom the beam and so the beam flux decreases down the length of the scattering cell. The fractional loss in beam intensity when an A molecule traverses a short distance Ax is determined by the likelihood of a collision with a B molecule in the 

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The original van der Waals idea was that pressure in a fluid is the result of both repulsive forces or excluded volume effects, which increase as the molar volume decreases, and attractive forces which reduce the pressure. Since the molecules have a finite size, there would be a limiting molar volume, b, which could be achieved only at infinite pressure. At large intermolcular separations, London dispersion theory establishes that attractive forces increase as r6, where r is the intermolecular distance. Since volume is proportional to r3, this provides some explanation also for the attractive term in the van der Waals equation of state. 

The surface excess can be defined in various ways. Actually, there is no true dividing plane, but rather an AW interface that is not sharp, since molecules have a finite size and moreover exhibit Brownian motion. Flence the interface extends over a layer of some molecular diameters. In the derivation of Eq. (10.2), the position of the dividing plane has been chosen so that the surface excess of the solvent is zero. In Figure 10.5 the concentration of the solute is depicted as a function of the distance from the dividing plane (z). In Figure 10.5a, there is no adsorption the two hatched areas on either side of the dividing plane are equal. (Because of the definition... 

It is important to realise that the Gibbs model does not imply that the surface excess is concentrated at the Gibbs dividing surface this is clearly physically impossible since molecules have a finite size and cannot occupy a mathematical surface. What the Gibbs method docs is to recognise the existence of concentration profiles such as those shown in Figure 5.3, whose exact form cannot yet be measured experimentally, and to provide a method of expressing the observable consequences of their existence. 

Real gases, on the other hand, consist of atoms or molecules that interact through intermolecular forces. Atoms/molecules attract at distant range and repel at near range they may be thought of as having a finite size. The theory of real gases accounts for these facts by means of a virial expansion,... 

The size distribution of emulsions is controlled by the rate of diffusion of functional molecules to the interface [4]. Emulsifier molecules diffuse to the interface while coalescence is occurring [4]. If the coating of fat globules were instantaneous, the emulsion would have a particle size distribution identical to that at the moment of emulsification. In actuality, emulsifier molecules require a finite time to reach the interface and be adsorbed. The rate of droplet coating is determined by (1) the rate of fat droplet coalescence, (2) the rate at which emulsifiers reach the interface, and (3) their rate of absorption. The... 

The above analysis of intermolecular stabilizing interactions with its breakdown into coulombic, polarization, and dispersion attractive terms has the advantage of clarifying, at least to some extent, the nature of these attractions in terms of chemically understandable interactions between charge densities. The price that has to be paid is that for a complete description of the interaction, some kind of repulsive effect must also be partitioned out of total energies. As already mentioned, repulsion must account for the scarce compressibility of condensed media - and, indeed, for the very fact that molecules just do not eollapse onto one another, and macroscopic bodies have a finite spatial size. 

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