Molecule per volume

Z) 1/P. Higher pressure generally is due to more molecules per volume, so the number of molecules is proportional to pressure, and diffusivity is inversely proportional to the number of molecules. More molecules means less distance before the diffusing molecule hits another molecule and bounces back. 

Recall that N is the number of molecules per volume V and that the molar density is n/V, where n = N/A. Substituting into Eq. 12.53 gives... 

One of the mayor drawbacks is that only volatile and temperature-resistant compounds can be investigated. Gases are magnetized faster than liquids, because they have shorter spin-lattice relaxation times (T ), due to an effective spin rotation mechanism. Therefore, pulse repetition times in flow experiments can be in the range of 1 s and some dozen transients can be accumulated per separated peak. Nevertheless, the sample amounts used nowadays in capillary GC are far from the detection limit of NMR spectroscopy, and therefore the sensitivity is low or insufficient, due to the small number of gas molecules per volume at atmospheric pressure in the NMR flow cell. In addition, high-boiling components (> 100 °C) are not easy to handle in NMR flow probes and can condense on colder parts of the apparatus, thus reducing their sensitivity in NMR spectroscopy. 

It is obvious that a consistent system for the description of concentrations in the gas phase is necessary. Usually, fractional or percentage concentrations are used. Mixing ratios of low concentrated volatile compounds and gases are based on the parts per... unit system. This unit is obsolete but is still used in the current literature. It cannot be utihzed for particle concentrations. Therefore, the WHO (1999) has adopted a mass per volume system with concentrations [C] in mgm . Other units frequently employed to express the concentration of gases include moles per volume or molecules per volume (vanLoon and Duffy, 2000, Kurzweil, 1999). 

Chemists usually characterize the concentration of a solution by a measure of the number of molecules per volume rather than the number of grams per volume because reactions happen when one molecule reacts with one molecule, not when one gram reacts with one gram. The difficulty is that molecules are very small, and a good many of them are required to make up a measurable amount. For instance, it requires about a trillion trillion water molecules in the liquid state to fill a 240-milliliter (one-cup) container. Therefore, it is infinitely easier to speak of collections of molecules rather than individual molecules. The name that chemists agreed on for a collection of molecules is a mole, and a mole is like a dozen—only different. 

Here N/V is the number of the dissolved polyelectrolyte molecules per volume whereas /o (r/) denotes the scattering intensity of an isolated macromolecule. S(q) is the effective structure factor that takes into account the effect of finite concentrations. As shown further below its influence can be disregarded for higher scattering angles. 

Tne greater the random translational kinetic energy of gas molecules per volume, the greater the pressure... 

The average number of molecules per volume unit, the concentration, is ... 

Here, a and <72 are the surface charge densities of probe and sample, eo is the permittivity of free space, s is the dielectric constant, e is the unit charge. The Debye length 2.d is determined by the salt concentration oo is the bulk concentration of a monovalent salt in molecules per volume. For more detailed... 

Vapor permeation differs from pervaporation, as stated above, insofar as the feed mixture to be separated is supplied as a vapor. At least the more-permeable component is kept as close to saturation conditions as possible. Thermodynamically there is no difference between a liquid and ifs equilibrium vapor, the partial vapor pressure and thus the driving force for the transport through the membrane are identical and the same solution-diffusion mechanism is valid. However, the density of the vaporous feed and thus the concentration of molecules per volume is lower by two to three orders of magnitude than that of the liquid. As a consequence the membrane is usually less swollen than when in contact with a liquid feed. As the feed mixture getting in contact with the membrane is already in the vapor phase no phase change occurs across the membrane and thus no temperature polarization will be observed. Concentration polarization, however, is still an issue. Although the diffusion coefficient is much higher in a vapor than in a liquid, this is at least partially outbalanced by the lower density of the vapor, and therefore concentration polarization effects may be observed at all concentrations of the component to be removed. Minimum... 

The reduced density or packing fraction T) is related to an effective and temperature-dependent co-volume b(T) by T) = r b(T)p/4, with p being the number density, i.e., the number of molecules per volume. However, PHSC-theory does not use an analytical intermolecular potential to estimate the temperature dependence of a(T) and b(T). Instead, empirical temperature functions are fitted to experimental data of argon and mefliane (see also ). 

Another way to reduce the number of nearest neighbors is by increasing the total surface area per volume, since molecules on surface lack the molecules above the surface. In addition, for extremely small particles (for instance, nuclei with radii of curvature less than 10 nm), the number of molecules per volume is reduced due to steric hindrance. This is one source of the Kelvin effect, in which the solubility of a substance increases with decreasing radius of curvature (Adamson and Gast 1997). 

Pure Rotational Diffusion Here we consider the rotational motion of the rodhke molecule in details. We do not pay attention to the center-of-mass position. Let us define by u(t) the unit vector along the rod axis at time t and place the rodlike molecule in the spherical polar coordinate system (Fig. 3.59). The orientation vector u(0 is represented by the polar angle d and the azimuthal angle solute molecules per volume. The probabihty to find u(0 between 6 and 6 + dO and between

[Pg.263]

Since v is inversely proportional to the buffer gas number density N, the mobility K is also inversely proportional to N. Here N (in units of molecules per volume) is used as the relevant quantity to express pressure because N is, in contrast to pressure p, decoupled from the temperature T. Because K depends on N it is practical to convert K into the pressure-independent quantity [Pg.4]

The time correlation function C(t) from (19) is a description of the transition statistics in the equilibrium system described in terms of the microscopic degrees of freedom. To make contact with a macroscopic description, appropriate for an experiment in which many molecules of type A and B are present in the sample, it is useful to consider the time evolution of the concentrations ca(i) = NA t)/V and cb (t) = IVb t)/V defined as the number of molecules per volume V of type A and B, respeclively. We imagine that the concentrations ca(1 ) and CB(t) can be determined experimentally in a time-resolved way. Since molecules can only convert into each other and are not created or destroyed, the total number of molecules N = +... 

The absorption in the collision-induced features, both from free pairs and dimers, grows in proportion to both the number of molecules per volume element and the number of collision partners. Therefore, collision-induced absorption depends on the product of the densities of the partners. When the partners are the same (H2-H2, N2-N2), the absorption depends on the square of the density. The absorption strength also increases at lower gas temperatures, since this corresponds to higher densities at a given pressure, and because the molecules are thermally distributed over fewer energy levels. The theory and spectroscopy of collision-induced absorption have been reviewed by Welsh (1972) and by Bimbaum (1985). 

Here, the concentration is in units of molecules per volume. If the concentration is inserted in mol m , it has to be multiplied with the Avogadro constant first. 

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