Mass proportions

When component and mixture concentrations of any species i are known, mass proportions can be calculated from the lever rule ... 

We have shown that the vector mesons in the CFL phase have masses of the order of the color superconductive gap, A. On the other hand the solitons have masses proportional to F%/A and hence should play no role for the physics of the CFL phase at large chemical potential. We have noted that the product of the soliton mass and the vector meson mass is independent of the gap. This behavior reflects a form of electromagnetic duality in the sense of Montonen and Olive [29], We have predicted that the nucleon mass times the vector meson mass scales as the square of the pion decay constant at any nonzero chemical potential. In the presence of two or more scales provided by the underlying theory the spectrum of massive states shows very different behaviors which cannot be obtained by assuming a naive dimensional analysis. 

An example of a binary eutectic system AB is shown in Figure 15.3a where the eutectic is the mixture of components that has the lowest crystallisation temperature in the system. When a melt at X is cooled along XZ, crystals, theoretically of pure B, will start to be deposited at point Y. On further cooling, more crystals of pure component B will be deposited until, at the eutectic point E, the system solidifies completely. At Z, the crystals C are of pure B and the liquid L is a mixture of A and B where the mass proportion of solid phase (crystal) to liquid phase (residual melt) is given by ratio of the lengths LZ to CZ a relationship known as the lever arm rule. Mixtures represented by points above AE perform in a similar way, although here the crystals are of pure A. A liquid of the eutectic composition, cooled to the eutectic temperature, crystallises with unchanged composition and continues to deposit crystals until the whole system solidifies. Whilst a eutectic has a fixed composition, it is not a chemical compound, but is simply a physical mixture of the individual components, as may often be visible under a low-power microscope. 

FIGURE 6.7 Representation of the migration behavior of cationic, anionic, and neutral analytes in CZE with sufficiently strong EOF to detect all analytes at the cathodic end of the capillary (panel A) and related electropherogram (panel B). Molecular masses proportional to the symbol size. 

Percent by Mass proportion of the mass of each element in a compound expressed as a percent or proportion of solute mass as total mass of solution Perfect Gas see Ideal Gas Period a horizontal row in the periodic table Permanent Hardness condition of water when magnesium and calcium are combined with chlorides and sulfates rather than carbonates, cannot be removed by heating Petrochemical chemicals derived from oil or natural gas... 

We also assume that the material added contributes to both melt and solid in mass proportions y and (1 - y)... 

MASS PROPORTION Fe203 / CaO IN CALCIUM CONTAINING CLAY FIRING COLOUR... 

The thermal time constant of a reactor characterizes the dynamics of the evolution of the reactor temperature. In fact, since it contains the ratio of the mass proportional to volume with the dimension L3 to the heat exchange area with the dimension L2, it varies non-linearly with the reactor scale, as is explained in Section 2.4. Some values of the time constant obtained with normalized stainless steel reactors [1] are summarized in Table 9.3. The variation by a factor of about 7, over the range considered here, is critical during scale-up. The heating or cooling times are often expressed as the half-life, the time required for the temperature difference to be divided by two ... 

Mass fraction (x) The mass proportion of gas and/or vapour in the mixture ... 

In this chapter, you have learned about the relationships among the number of particles in a substance, the amount of a substance in moles, and the mass of a substance. Given the mass of any substance, you can now determine how many moles and particles make it up. In the next chapter, you will explore the mole concept further. You will learn how the mass proportions of elements in compounds relate to their formulas... 

Taking into account the mass proportions of HjO and CO2 we find the equilibrium value to be 32 bar and the carbonate content of the ocean to be 1.1 g-ion/1. As Garrels and Mackenzie point out, the chemical activity of such an ocean-atmosphere system would have been frightful. 

Figure 16.8 Mass proportions of trace element transported as dissolved and particulate forms in the Solimoes River at Manacapuru, in the Negro River at Paricatuba (Manaus), and in the Amazon River at Obidos.

This study consists in verifying the coherence of a few commonly used analysis methods of nitrogen adsorption-desorption isotherms. These methods were tested on model samples obtained by mechanically mixing two micro- and mesoporous solids respectively with known mass proportions. Although the individual analysis methods may lead to discrepancies in the interpretation of the isotherms, their systematic comparison allows drawing a coherent picture of the porous texture. 

Two materials have been used a mesoporous alumina (Pural SCC30 - Condea) and a microporous amorphous Si-Ti co-gel. Five mixtures were prepared by mixing these materials in various mass proportions. The nomenclature of samples is given as X(y), y is the weight percentage of microporous material. 

Walter M. J., Sisson T. W., and PresnaU D. C. (1995) A mass proportion method for calculating melting reactions and application to melting of model upper mantle Iherzolite. Earth Planet. Sci. Lett. 135, 77—90. 

From the molecular weights of 806 for glyceryl tri-palmitate and of 56.1 for potassium hydroxide, the mass proportions are ... 

Constant mass proportions were originally determined by analysing the compound copper carbonate, CuCOa, in the 1790s. We now know that no matter how the copper carbonate is prepared it always contained atoms of copper, carbon, and oxygen in the proportions 1 1 3. 

The PhEur 2005 and USPNF 23 (Suppl. 1) describe copovidone as a copolymer of l-ethenylpyrrolidin-2-one and ethenyl acetate in the mass proportion of 3 2. 

Now let s suppose you analyzed 500.0 g of sucrose isolated from a sample of sugar cane. The analysis is shown in Table 3-5. Note in Column 2 that the percent by mass values equal those in Column 2 in Table 3-4. According to the law of definite proportions, samples of a compound from any source must have the same mass proportions. Conversely, compounds with different mass proportions must be different compounds. Thus, you can conclude that samples of sucrose always will be composed of 42.2% carbon, 6.50% hydrogen, and 51.30% oxygen. 

This statement needs some qualification. As explained in the next section, many elements have several isotopes, which are species whose atoms have almost identical chemical properties but different masses. Natural variation in isotope abundance leads to small variations in the mass proportions of elements in a compound, and larger variations can be induced by artificial isotopic enrichment. 

Leaves, with a mass C/N ratio of 45, are to be blended with sludge from a wastewater treatment plant with a C/N ratio of 7.5. Determine the mass proportions of each component in order to achieve an optimum (for sludge management) blended C/N ratio in the 22-26 range. Assume that the following conditions apply ... 

Our study of stochiometry has shown that substances react in definite mole and mass proportions. Using previously discussed gas laws, we can show that gases also react in simple, definite proportions by volume. For example, one volume of hydrogen always combines (reacts) with one volume of chlorine to form two volumes of hydrogen chloride, if all volumes are measured at the same temperature and pressure... 

When identification is done, the mass fraction of the substance in the material can be studied. Detection by FID and some forms of MS allow reaching a mass proportional response and establishing a quantified link between signal, mass of product and impurity. ECD allows the presence of heteroatoms, e.g. halogens, to be revealed. HPLC may reveal the presence of a substance that is not accessible by GC. Atomic spectrometry, as used for the purity of inorganic substances, can help to determine the amount of metal in an organo-metallic substance and the presence of some metals or metalloids. 

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