Volume VI

We define a partial molar volume Vi such that V = riiVi -I- U2V2... 

Component 1 is the solute, while component 2 is the solvent. Units of T, P, and V are °R, psia, and cmVgmole, respectively. Diffusivity is then in ftVhr. The molar volumes Vi and Vo at the normal boiling point... 

Carl Shipb Marvel, Editor in-Chief. no pages. Volume VI. 

For the case depicted in Fig. 4.22, the pressure along the isentrope at the volume Vi corresponding to a Hugoniot state (P, FJ is given by... 

It is important to realize that all static phases will contribute to retention and, as a result, a number of different distribution coefficients will control the retention of the solute. Nevertheless, the situation can be simplified to some extent. The static interstitial volume (Vi(s)) and the pore volume fraction (Vp(i)) will contain mobile... 

As [M], [W] and [MW] were defined in moles per milliliter then the volume (vi) after mixing will be... 

Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

Now, the maximum sample volume (Vi) that can be placed on the column that would restrict the increase to less than 5% has been shown to be. 

Assuming the peak variance is increased by 5% due to the sample volume, (Vi) will... 

Jones, A.G., 1997. Attrition and Breakage. In Crystallization Manual. (Harwell Separation Processes Service, AEA Technology), Volume VI, Part III, 100 pp. 

A large number of experiments [22,68-71] have shown that the specific volume, vi, and specific entropy, Sh, of the high-pressure hexagonal phase of PE are closer to the corresponding values v , and s , of the melt than they are to those of the orthorhombic phase, and s. For instance, at 500 MPa, the ratio of entropies of the orthorhombic-hexagonal and hexagonal-melt transi-... 

The required relief area. A], for a volume V] = 1 cu m obtained from the nomograms. The same reduced explosion pressure, P,.ed, and same static activation pressure, Psiau of the relief device are the same for both volumes Vi and V2, and therefore constant. WTien the mechanical strength of the vessel, is changed, the maximum volume and height will change with the hazard class, St-1, St-2, or St-3. 

Examples.—(1) If a mol of gas expands isothermally and reversibly from volume Vi to volume V2 the diminution of free energy is ... 

Now suppose we have the gases Gb G2,. . G in the amounts specified at the beginning of this section, all at the same temperature T, separately confined in vessels of volumes Vi, V2,. . V , respectively. If we add together the free energies of the separate gases, the sum may be called the free energy of tlic unmixed gases. Thus ... 

For a discussion of representative examples, see J. B. Ott and J. R. Goates, Temperature Measurement With Application to Phase Equilibria Studies," Chapter 6 of Physical Methods of Chemistry, Volume VI, Determination of Thermodynamic Properties, B. W. Rossiter and R. C. Baetzold, Editors, John Wiley Sons, New York, 1992. 

Bemasconi, C. F. In Investigation of Rates and Mechanisms of Reactions, Parts I and II Volume VI, Techniques of Chemistry Weissberger, A., Ed. 4th Ed. Wiley-Interscience New York, 1981. 

As already stated any sample placed on a column will have a finite volume, and the variance of the injected sample will contribute directly to the final peak variance. It follows that the maximum volume of sample that can be placed on the column must be limited, or the column efficiency will be seriously reduced. Consider a volume Vi, injected onto a column. Normal LC injections will start initially as a rectangular distribution and the variance of the eluted peak will be the sum of the variances of the injected sample plus the normal variance of the eluted peak. 

Let a volume (Vi) be injected onto a column resulting in a rectangular distribution of sample at the front of the column. According to the principle of the Summation of Variances, the variance of the final peak will be the sum of the variances of the sample volume plus the normal variance of a peak for a small sample. 

The analyst can calculate the maximum sample volume (Vi) in a simple manner from the efficiency of a peak eluted close to the dead volume and the dimensions of the column. 

To determine the band dispersion that results from a significant, but moderate, sample volume overload the summation of variances can be used. However, when the sample volume becomes excessive, the band dispersion that results becomes equivalent to the sample volume itself. In figure 10, two solutes are depicted that are eluted from a column under conditions of no overload. If the dispersion from the excessive sample volume just allows the peaks to touch at the base, the peak separation in milliliters of mobile phase passed through the column will be equivalent to the sample volume (Vi) plus half the base width of both peaks. It is assumed in figure 10 that the efficiency of each peak is the same and in most cases this will be true. If there is some significant difference, an average value of the efficiencies of the two peaks can be taken. 

In this model of non-ideal reactor mixing, a fraction, fi, of the volumetric feed rate, F, completely by-passes the mixing in the reactor. In addition, a fraction, f2, of the reactor volume, V, exists as dead space. F3 is the volumetric rate of exchange between the perfectly mixed volume Vi and the dead zone volume V2 of the reactor. 

Figure 5. A schematic representation of superposed steady-state reservoirs of constant volumes Vi (fractional crystallization is omitted in this schema). At steady-state, Vi/xi=V2/x2=..., where x is the residence time. This is analogous to the law of radioactive equilibrium between nuclides 1 and 2 Ni/Ti=N2/T2=...A further interest of this simple model is to show that residence times by definition depend on the volume of the reservoirs.

Fig. 5.7(a) Vomeronasal pump (vasomotor activation and control of VN fluid contents) reciprocal compression/relaxation of lumenal and vascular volumes, vi/ve = internal/ external simus vessels, (a) Fluid intake — lumen expanded/vessels relaxed — pressure drops, (b) Fluid expulsion — lumen compressed/vessels expanded — pressure rise (from Schilling, 1970). 

The purpose of this compilation is to tabulate the densities of compounds, hence only minimal description of experimental methods used to measure the density of liquids or solids appears. Detailed descriptions of methods for density determination of solids, liquids and gases, along with appropriate density reference standards, appear in a chapter by Davis and Koch in Physical Methods of Chemistry, Volume VI, Determination of Thermodynamic Properties [86-ros/bae],... 

Lewis, E. S. (Editor), Investigation of Rates and Mechanisms of Reactions, Third Edition, Volume VI, Part I of Techniques of Chemistry, Wiley, New York, 1974. 

Volume VI. Preparation and Assay of Enzymes (Continued) Preparation and Assay of Substrates Special Techniques... 

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