Matter quantitative

To view matters quantitatively, one looks again at Equations (3.57) and (3.58) ... 

First, it is cmcial to verify whether the steps we visualized were elementary steps, which have the minimum height determined by the crystal structure and molecular size. To discuss this matter quantitatively, we presumed two cases. The first is where we could fully visualize all steps that existed on the ice crystal surface. The... 

The physics of X-ray refraction are analogous to the well known refraction of light by optical lenses and prisms, governed by Snell s law. The special feature is the deflection at very small angles of few minutes of arc, as the refractive index of X-rays in matter is nearly one. Due to the density differences at inner surfaces most of the incident X-rays are deflected [1]. As the scattered intensity of refraction is proportional to the specific surface of a sample, a reference standard gives a quantitative measure for analytical determinations. 

As a practical matter elimination can always be made to occur quantitatively Strong bases especially bulky ones such as tert butoxide ion react even with primary alkyl halides by an E2 process at elevated temperatures The more difficult task is to find condifions fhaf promofe subsfifufion In general fhe besf approach is fo choose condi lions lhal favor fhe 8 2 mechanism—an unhindered subslrale a good nucleophile lhal IS nol slrongly basic and fhe lowesl praclical lemperalure consislenl wilh reasonable reaclion rales... 

The time is perhaps not yet ripe, however, for introducing this kind of correction into calculations of pore size distribution the analyses, whether based on classical thermodynamics or statistical mechanics are being applied to systems containing relatively small numbers of molecules where, as stressed by Everett and Haynes, the properties of matter must exhibit wide fluctuations. A fuller quantitative assessment of the situation in very fine capillaries must await the development of a thermodynamics of small systems. Meanwhile, enough is known to justify the conclusion that, at the lower end of the mesopore range, the calculated value of r is almost certain to be too low by many per cent. 

Analytical chemistry is often described as the area of chemistry responsible for characterizing the composition of matter, both qualitatively (what is present) and quantitatively (how much is present). This description is misleading. After all, almost all chemists routinely make qualitative or quantitative measurements. The argument has been made that analytical chemistry is not a separate branch of chemistry, but simply the application of chemical knowledge. In fact, you probably have performed quantitative and qualitative analyses in other chemistry courses. For example, many introductory courses in chemistry include qualitative schemes for identifying inorganic ions and quantitative analyses involving titrations. 

An analysis, particularly a quantitative analysis, is usually performed on several replicate samples. How do we report the result for such an experiment when results for the replicates are scattered around a central value To complicate matters further, the analysis of each replicate usually requires multiple measurements that, themselves, are scattered around a central value. 

Since the 0 s are fractions, the logarithms in Eq. (8.38) are less than unity and AGj is negative for all concentrations. In the case of athermal mixtures entropy considerations alone are sufficient to account for polymer-solvent miscibility at all concentrations. Exactly the same is true for ideal solutions. As a matter of fact, it is possible to regard the expressions for AS and AGj for ideal solutions as special cases of Eqs. (8.37) and (8.38) for the situation where n happens to equal unity. The following example compares values for ASj for ideal and Flory-Huggins solutions to examine quantitatively the effect of variations in n on the entropy of mixing. 

During the nineteenth century the growth of thermodynamics and the development of the kinetic theory marked the beginning of an era in which the physical sciences were given a quantitative foundation. In the laboratory, extensive researches were carried out to determine the effects of pressure and temperature on the rates of chemical reactions and to measure the physical properties of matter. Work on the critical properties of carbon dioxide and on the continuity of state by van der Waals provided the stimulus for accurate measurements on the compressibiUty of gases and Hquids at what, in 1885, was a surprisingly high pressure of 300 MPa (- 3,000 atmor 43,500 psi). This pressure was not exceeded until about 1912. 

Analytical methods aie utilised by all branches of the chemical iadustry. Sometimes the goal is the quaUtative deterniiaation of elemental and molecular constituents of a selected specimen of matter othertimes the goal is the quantitative measurement of the fractional distribution of those constituents and sometimes it is to monitor a process stream or a static system. Information concerning the various iadividual analytical methods may be found ia separate articles dispersed alphabetically throughout the Eniyclopedia. The articles ate iatroductions to topics each of which is the subject of numerous books and other pubhcations. 

Quantitative Relationship of Conductivity and Antistatic Action. Assuming that an antistatic finish forms a continuous layer, the conductance it contributes to the fiber is proportional to the volume or weight and specific conductance of the finish. As long as the assumption of continuity is fulfilled it does not matter whether the finish surrounds fine or coarse fibers. Assuming a cylindrical filament of length 1 cm and radius r, denoting the thickness of the finish layer as Ar and the specific conductance of the finish k, the conductance R of the finish layer is given by the equation (84) ... 

Impurities in bromine may be deterrnined quantitatively (54). Weighing the residue after evaporation of a bromine sample yields the total nonvolatile matter. After removing the bromine, chloride ion may be deterrnined by titration with mercuric nitrate, and iodide ion by titration with thiosulfate water and organic compounds may be detected by infrared spectroscopy sulfur may be deterrnined turbidimetricaHy as barium sulfate and heavy metals may be deterrnined colorimetricaHy after conversion to sulfides. 

Static sampling systems are defined as those that do not have an active air-moving component, such as the pump, to pull a sample to the collection medium. This type of sampling system has been used for over 100 years. Examples include the lead peroxide candle used to detect the presence of SO2 in the atmosphere and the dust-fall bucket and trays or slides coated with a viscous material used to detect particulate matter. This type of system suffers from inability to quantify the amount of pollutant present over a short period of time, i.e., less than 1 week. The potentially desirable characteristics of a static sampling system have led to further developments in this type of technology to provide quantitative information on pollutant concentrations over a fked period of time. Static sampling systems have been developed for use in the occupational environment and are also used to measure the exposure levels in the general community, e.g., radon gas in residences. 

Ellipsometry can be sensitive to layers of matter only one atom thick. For example, oxidation of freshly cleaved single-crystal graphite can be monitored from the first monolayer and up. The best thicknesses for the ellipsometric study of thin films are between about 1 nm and 1000 nm. Although the spectra become complicated, films thicker than even 1 pm can be studied. Flat planar materials are optimum, but surface and interfacial roughness can be quantitatively determined if the roughness scale is smaller than about 100 nm. Thus ellipsometry is ideal for the investigation of interfacial surfaces in optical coatings and semiconductor struc-... 

However, the spatial resolution of AES is mueh greater than that of XPS and ean approaeh approximately 25 nm. This makes AES a powerful technique for constructing high-resolution maps showing the distribution of chemical species across a surface. Because of the small analysis area, it is an easy matter to combine AES with inert gas sputtering to construct depth profiles showing the distribution of chemical species as a function of distance away from the surface and into the bulk of the solid. Quantitative analysis can be done using sensitivity factors and an equation similar to Eq. 17. 

A bulk sample is the last choice and the least desirable. It should be submitted "for laboratory use only" if there is a possibility of contamination by other matter. The type of bulk sample submitted to the laboratory should be cross-referenced to the appropriate air samples. A reported bulk sample analysis for quartz (or cristobalite) will be semi-quantitative in nature because (1) The XRD analysis procedure requires a thin layer deposition for an accurate analysis. (2) The error for bulk samples analyzed by XRD is unknown because the particle size of nonrespirable bulk samples varies from sample to sample. 

These are the characteristics which need to be specified and their achievement controlled, assured, improved, managed, and demonstrated. These are the characteristics which form the subject matter of the specified requirements referred to in ISO 9000. When the value of these characteristics is quantified or qualified they are termed quality requirements or requirements for quality. ISO 8402 1994 defines requirements for quality as an expression of the needs or their translation into a set of quantitatively or qualitatively stated requirements for the characteristics of an entity to enable its realization and examination. While rather verbose, this definition removes the confusion over quality requirements and technical requirements. (An additional definition is provided in Appendix A.) Technical requirements for a product or service are quality requirements. The requirements of ISO 9000 are quality system requirements. 

The central role of the concept of polarity in chemistry arises from the electrical nature of matter. In the context of solution chemistry, solvent polarity is the ability of a solvent to stabilize (by solvation) charges or dipoles. " We have already seen that the physical quantities e (dielectric constant) and p (dipole moment) are quantitative measures of properties that must be related to the qualitative concept of... 

The quantitative determination of cineol has been fully dealt with in Vol. I. of this work under Eucalyptus Oil, hut as this body occurs in various other oils, and its determination is a matter of considerable importance, details of its estimation are also dealt with here. 

This observation is important in the study of the chiral recognition mechanism in this system. This may be a practical matter when determining the trace amount of one enantiomer in the presence of its dominant antipode. The smaller peak is always desired to be eluted first for best quantitation. 

The results of one of Lavoisier s quantitative experiments are shown in Table A the data are taken directly from Lavoisier. If you add up the masses of reactants and products (expressed in arbitrary units), you find them to be the same, 510. As Lavoisier put it, "In all of the operations of men and nature, nothing is created. An equal quantity of matter exists before and after the experiment."... 

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