Mass fraction, definition

Equation (4-49) is merely a special case of Eq. (4-48) however, Eq. (4-50) is a vital new relation. Known as the summahility equation, it provides for the calculation of solution properties from partial properties. Thus, a solution property apportioned according to the recipe of Eq. (4-47) may be recovered simply by adding the properties attributed to the individual species, each weighted oy its mole fraction in solution. The equations for partial molar properties are also valid for partial specific properties, in which case m replaces n and the x, are mass fractions. Equation (4-47) applied to the definitions of Eqs. (4-11) through (4-13) yields the partial-property relations ... 

Definitions Following the practice presented under Gas-Separation Membranes, distillation notation is used. Literature articles often use mass fraction instead of mole fraction, but the substitution of one to the other is easily made. 

For mixtures of substances, it is convenient to express compositions in ntole fractions or mass fractions. A process stream seldom consists of a single component. It may also contain two or more phases, or a mixture of one or more solutes in a liquid solvent. The following definitions are often used to represent the composition of component A in a mixture of components. 

Fig. 2. shows CNO abundance variation with temperature. Abundances are expressed in mass fractions as before and were determined from non-LTE model fits to e.g. Nil 3995 A, CII 4267 A, Oil 4367 A. Nitrogen shows an increase with increasing temperature, whereas oxygen implies a subtle decrease with increasing temperature and carbon does not display a definite trend... 

Note that if the mass fractions are used to define the composition vector, then by definition... 

Let Yrj denote the mass fractions of the K chemical species describing the reacting flow. By definition, KYa—. Assuming that the chemical species are numbered such that the major species (e.g., reactants) appear first,2 followed by the minor species (e.g., products), we can define a linear transformation by... 

Note that by definition XK — 1 and thus Xp is the cumulative mass fraction of the first P species. The inverse transformation corresponding to Eq. (93) is... 

Since effects of radioactive decay on the molar mass can be neglected, q>bas Sr can be replaced with an excellent precision by expressed through equation (1.3.2) as a function of mass fractions / and concentrations CSr requires... 

It is a common practice to describe mass dependent isotope fractionation processes by a single linear curve on a three-isotope-plot (Matsuhisa et al. 1978). The resulting straight lines are referred to as terrestrial mass fractionation lines and deviations from it are used as indicating nonmass-dependent isotope effects. The three-isotope-plot is based on the approximation of a power law function to linear format. To describe how far a sample plots off the mass-dependent fractionation line, a new term has been introduced A 0, A Mg, A S, etc. Several definitions of A have been introduced in the literature, which have been discussed by Assonov and Bren-ninkmeijer (2005). The simplest definition is given by ... 

Spectral analysis shows quite clearly that the various types of atoms are exactly the same on Earth as in the sky, in my own hand or in the hand of Orion. Stars are material objects, in the baryonic sense of the term. All astrophysical objects, apart from a noteworthy fraction of the dark-matter haloes, all stars and gaseous clouds are undoubtedly composed of atoms. However, the relative proportions of these atoms vary from one place to another. The term abundance is traditionally used to describe the quantity of a particular element relative to the quantity of hydrogen. Apart from this purely astronomical definition, the global criterion of metallicity has been defined with a view to chemical differentiation of various media. Astronomers abuse the term metaT by applying it to all elements heavier than helium. They reserve the letter Z for the mass fraction of elements above helium in a given sample, i.e. the percentage of metals by mass contained in 1 g of the matter under consideration. (Note that the same symbol is used for the atomic number, i.e. the number of protons in the nucleus. The context should distinguish which is intended.)... 

Note 2 Any molar-mass average can be defined in terms of mass fractions or mole fractions. In this document only a few of the important molar-mass averages are given in terms of the mass fractions, Wi, of the species with molar mass M. These definitions are most closely related to the experimental determination of molar-mass averages. 

OH. That is, it is the mass fraction of the species of two OH groups minus one oxygen. This is because in Reaction 2-79 two OH groups minus one oxygen would form one molecular H2O. This definition of OH would lead to (H20t) = (H20m) + (OH) in terms of mass fraction or wt%. The definition of mole fraction of OH is, however, the mole fraction of OH per se, not the mole fraction of 20H - O. In terms of mole fraction, [H20(] = [H20m] + [OH]/2. 

Working with multicomponent mixtures requires quantifying the amounts of various chemical constituents that comprise the mixture. In the conservation equations a mass fraction will be the most appropriate measure, since mass is a conserved quantity. By definition, the mass fraction is... 

This expression states that the product of the mean mass fraction and the overall mass flow rate must equal the integral over the channel width of the local mass flow rate of species ft. An analogous definition for the energy flow was used to define a mean temperature in the Graetz problem (Section 4.10). In nondimensional terms,... 

Based on the Sherwood number definition and the solutions for a range of inlet velocities, evaluate the mass fraction of TMG at the surface. 

Since there is not a continuously differentiable relationship between the inlet and outlet flows, the Gauss divergence theorem (i.e., the V- operation) has no practical application. Recall that, by definition, the surface unit vector n is directed outward. The sign of the mass-fraction difference in Eq. 16.68 is set by recognizing that the inlet flow velocity is opposite the direction of n, and vice versa for the exit. The overall mass-continuity equation,... 

For conversions lower than xgei the average molar mass of the polymer exhibits a continuous increase. The first two moments of the molar mass distribution are the number-average molar mass, Mn, and the mass-average molar mass, Mw, respectively. Mn is defined in terms of the number contribution of every species to the whole population. The weight factor used to define this average is the molar fraction. Mw is defined in terms of the mass contribution of every species to the whole mass, so that the mass fraction is the weight factor used in its definition. 

The current methods available for testing food derived from modern biotechnology, e. g. for the content of genetically modified food, provide results in internal, not easily convertible units. This makes compliance with legal limits, which are usually given as mass fractions, difficult or even impossible. In order to improve this unsatisfactory situation, a definition of the measurands and standardization of all details of the evaluation procedure is proposed. Such measures... 

The boundaries of trace analysis are described by the definition of trace element in the IUPAC Compendium of Chemical Terminology, 2nd edition Any element having an average concentration of less than about 100 parts per million atoms and less than 100pg g As analytical techniques have become more sophisticated and detection capabilities have improved, this upper boundary of the definition of trace is now so far away from the capabilities of analysis in a number of fields that new terms such as ultratrace analysis have entered common parlance. There is no agreement, however, on the range of ultratrace analysis, and this term has no rigorous definition. In the literature, the term is used to define the presence of elements at mass fractions less than 10 6 and 10 8 (1 pg g 1 and 0.01 pg g ) ... 

Hie chemical reaction rate is usually dependent on the molar concentrations of the reactants and not on their mass fractions, because it depends on the chance of collision of molecules. However, here the definition of in terms of mass fractions is preferred, because it can readily be incorporated into mass balances. A definition in terms of moles or molar concentrations might invite the use of mole balances instead of mass balances. Since, contrary to conservation of mass, there is no such thing as conservation of moles (because one molecule might divide into several molecules, or several might condense into one), the use of mole balances is strongly dissuaded. More information concerning the definition of conversion can be found elsewhere [2]. 

A commonly used expression for this number is Sh = 2.0 - - 0.55Re/ Scp where Rcp = d u —u /i/ is the particle Reynolds number and Scp is the fuel vapor Schmidt number. In this definition v is the carrier phase kinematic viscosity. In Eq. (8.2), one important parameter is the Spalding number Bm = Ypx f)/(1 — Yfx) where Ypx is the fuel mass fraction at the droplet surface, calculated from the fuel vapor partial pressure at the interface ppx which is evaluated from the Clausius-Clapeyron relation ... 

The two streams leaving the settler are in equilibrium with each other—that is, the ratio of the penicillin mass fractions in the two phases equals the value of K corresponding to the pH of the aqueous phase (= 2.1 in Unit 1). The impurities in the feed broth remain in the aqueous phase. The raffinate (by definition, the product stream containing the feed-solution solvent) leav-... 

Remember that implicit constraints (equations) exist in the problem formulation because of the definition of mass fraction namely, that the sum of the mass fractions in each stream must be unity ... 

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