Concentration types mole fractions

Values in roman type are based on concentrations expressed in mol dm . Values in italics are based on concentrations expressed in mole fractions. The difference (b)-(a) refers to the replacement reaction... 

Alloys of lead and thallium have a structure based upon cubic closest packing from 0 to about 87-5 atomic percent thallium. The variation of the lattice constant with composition gives strong indication that ordered structures PbTl, and PbTl, exist. In the intermediate ranges, solid solutions of the types Pb(Pb,Tl)a and Pb(Pb,Tl)TlB exist. Interpretation of interatomic distances indicates that thallium atoms present in low concentration in lead assume the same valence as lead, about 2-14, and that the valence of thallium increases with increase in the mole fraction of thallium present, having the same value, about 2-50, in PbTls and PbTl, as in pure thallium. A theory of the structure of the alloys is presented which explains the observed phase diagram,... 

The results are presented as plots of DP against mole fraction of isobutene. With methyl chloride, methylene dichloride, or vinyl chloride as diluent the DP rises very steeply to a sharp peak with increasing monomer concentration, and then falls off in a curve of exponential type (Figure 4). With ethyl chloride there is apparently no maximum, the... 

The paddle mill was used to study the effect of surfactant type on a solvent-aqueous-surfactant extraction scheme for the recovery of bitumen from Athabasca tar sand. n the experiments of Figures 4,5 and 6, bitumen recovered from the surface phases was measured as a function of the mole fraction of ethylene oxide in the surfactant and as a function of the extraction step in which the surfactant was added. The results are reported as the % of the total bitumen present in the surface fraction. The amount of surfactant used was that required to give a final aqueous concentration of 0.02% (w/v), but in different sets of experiments the surfactant was added at various stages in the process. 

Although units of weight percent and mole fraction can be applied to all types of solutions, the most common concentration terms are molarity or molality. If water is the solvent, the solution is called an aqueous solution. 

This type of graph has some interesting properties and must be used carefully. First of all, it should be noted that pure phases of the three components correspond to each apex of the triangle and that concentrations should be in either mole fractions or percentages. From this it is easy to see which concentration axis refers to any particular com-... 

Fig. 8. Gas temperature and CO and C02 mole fractions (a) multipoint radial concentration collocation, type I conditions (b) gas temperatures at the radial temperature collocation point.

In gas-phase chemistry it is straightforward to specify the concentrations of all of the chemical species, such as by a single array of the species mole fractions, which sums to unity. The situation can be much more complex in heterogeneous reactions. For example, there may be multiple, distinct solid phases, or different types of surfaces or materials all present simultaneously. The formalism that we describe is a very general and systematic way to account for the different groupings and normalization constraints among many col-... 

Cdg Concentration of D in gas phase, moles/volume Cdp Concentration of D in crystallite phase, moles/zeolite pore volume Deff Effective diffusion coefficient, (length) 2/time F Volumetric feed rate to reactor, volume/time H Henry s law-type constant relating gas phase mole fraction to crystallite phase mole fraction... 

The parameters of the Michaelis-Menten type kinetics were calculated for the reactions and are summarized in Table II. The apparent Michaelis constant values (Km) are rather large, indicating that the concentration of the complex at the equilibrium state is not high, unlike ordinary enzymatic reactions. The ratio of kJKm against the second-order rate constant with sulfuric acid (k2) can be considered to be an indication of the rate enhancement. The ratio increased with increasing mole fraction of the vinyl alcohol repeating unit in the copolymer and with... 

Patterson, Wilhelm, and others13 have proposed an explanation for this behavior. They suggest that a random contribution to C m is present of the type we observed in Figures 17.5, 17.6, and for the (oxane + cyclohexane) system as shown in Figure 17.8. This contribution would be negative and approximately parabolic in shape. In addition, a nonrandom contribution is present that is nonparabolic in form and concave upwards with the major contribution in the mid-mole fraction range. This contribution results from concentration fluctuations in the solution. The sum of these two contributions... 

The data obtained in these equilibrium studies have been treated quantitatively by Carmichael and Heffel (53) and by Brown and Slusarczuk (33), who evaluated the equilibrium data in terms of cyclization constants. The latter are identical with ring-chain constants of the type of Eq. (29) where the concentrations are expressed in mole fractions of building units. Table XI... 

The overall reaction rate has a temperature dependence governed by the specific reaction rate k(T) and a concentration dependence that is expressed in terms of several concentration-based properties depending on the suitability for the particular reaction type mole or mass concentration, component vapor partial pressure, component activity, and mole or mass fraction. For example, if the dependence is expressed in terms of molar concentrations for components A(Ca) and B(Cb), the overall reaction rate can be written as... 

These multiples of the unit one are not part of the SI and ISO recommends that these symbols should never be used. They are also frequently used as units of concentration without a clear indication of the type of fraction implied (e.g. mole fraction, mass fraction or volume fraction). To avoid ambiguity they should only be used in a context where the meaning of the quantity is carefully defined. Even then, the use of an appropriate SI unit ratio may be preferred. 

In a binary mixture of solvents Si and S2, a cation M with a coordination number k and charge z forms k+ ) cations of the type [M(Si)i(S2)a - ]" with i = 0.. .k, differently solvated in the first solvation shell. These differently solvated species have been called solvatomers [254]. For example, with octahedrally coordinated cations k = 6), k + + 2 = solvatomers are to be expected (including three cisitrans isomeric solvatomers with i = 2, 3, or 4). In favourable cases, the concentrations of all solvatomers have been obtained as a function of the solvent mole fraction by NMR measurements [254]. 

The pressure/area isotherm for a cholesterol monolayer is of a very noncompressible liquid condensed type (Ries, 1976). The compressibility of a cholesterol monolayer is increased only slightly on the introduction of low concentrations of Azone (X = 0.2) but if the mole fraction of Azone in the film is increased to 0.4 and above, the compressibility increases dramatically and the film can be classed as liquid expanded. Another feature of these higher Azone concentrations is a small kink in the isotherm at approximately 32 mN m. This pressure is equal to the collapse pressure of a pure Azone monolayer found by these workers, and the kink in the Azone/cholesterol isotherm may be due to squeeze-out of Azone (Schuckler and Lee, 1991). 

Fig.l shows several types of breakthrough curves obtained for IPA-TCE -Y-type zeolite system. For this system, reversal of the order of breakthrough (turn over) occurred twice at concentrations of 0.25 and 0.75 mole fractions of IP A, respectively. When the mole fractions were 0.25 and 0.75, the mixture of two components behaved as if it was a single component system as shown in Fig.2 (B) and (D). For other azeotropic mixture systems, the turnover occurred only once. The breakthrough curves for other systems always showed so-called constant pattern behavior for the whole concentration range.

Table 15 Various properties related to hydrogen bonds in urea-water mixtures, gives the mole fraction of urea, and itx gives the number of hydrogen bonds around molecules of the type X. T y gives the life time (in fs) for hydrogen bonds between molecules x and y, with x being the donor and y the acceptor. The two entries for each concentration shows the results for the two different models for urea. All results are from ref. 52...

Because the concentration of a solution is so variable, we need two ways to indicate how much solute is in a particular solution. There are several ways to measure the concentration of a solution, including molarity, molality, and mole fraction. The type of measurements you use will often depend upon the situation or on the calculations that you want to be able to carry out. 

Figure 3.3 The different types of excess isotherms. Plots of the surface excess concentration, r (mmol/g), with n total number of mole of components 1 and 2, versus the mole fraction (except Figure 3.3-11, plot of (mg/g) versus weight fraction, wi). (I) 1,2-Dichloroethane (1) and benzene (2) on alumina gel at 25°C. (II) Benzene (1) and n-heptane on (a) alumina gel, (b) silica gel at 25°C. (Ill) Ethanol (1) and water (2) on charcoal at 25°C. (IV) Benzene (1) and ethanol (2) on charcoal at 25°C. (V) 1,2-Dichloroethane (1) and benzene (2) on charcoal at 25°C. Reproduced from G. Schay, Surf. Coll. Sci, 2 (1969) 155 (Figs. 1 to 5), with kind permission of Springer Science and Business Media.

Classically, the plot of the surface excess of one component of a binary mixture versus its concentration (mole fraction) in the mixture can belong to one of five different types, as illustrated in Figure 3.3. In type I, the plot has a maximum arormd X = 0.5. In type II, there is still a maximum, but it takes place at a lower mole fraction. In type III, the curve has an inflection point but does not intersect the concentration axis, and the maximxmi occurs at a low value of the mole fraction. 

A discussion of the thermodynamics and kinetics of solubility hrst requires a discussion of the method hy which solubility is reported. The solubility of a substance may be dehned in many different types of units, each of which represents an expression of the quantity of solute dissolved in a solution at a given temperature. Solutions are said to be saturated if the solvent has dissolved the maximal amount of solute permissible at a particular temperature, and clearly an unsaturated solution is one for which the concentration is less than the saturated concentration. Under certain conditions, metastable solutions that are supersaturated can be prepared, where the concentration exceeds that of a saturated solution. The most commonly encountered units in pharmaceutical applications are molarity, normality, molality, mole fraction, and weight or volume percentages. 

An indication of whether or not the above condition for ideality is met is obtained from the vapor pressure of the solution. At a given temperature, the vapor pressure of a pure liquid is a measure of the ability of molecules to escape from the liquid to the gas phase. By studying the vapor pressure of a solution as a function of its composition at constant temperature one may assess the solution s ideality or its degree of departure from ideality. For an ideal solution, the tendency of molecule A to escape is proportional to its mole fraction, that is, to its concentration expressed in terms of the fraction of molecules which are of type A. The proportionality constant must be the vapor pressure of pure component A because this vapor pressure is reached when the mole fraction is unity. This result is Raoult s law, which is expressed mathematically as... 

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