Additivity laws

In order to draw the property - composition diagram, coordinates are usually chosen so that the ideal system values correspond with the additive law regarding concentration [313]. It is known, for instance, that in an ideal system, molar volume changes additively with the concentration, and is expressed in molar fractions or molar percentages, whereas specific volume changes linearly with the concentration, and is expressed in mass fractions or mass percentages. 

Fig. 59 shows, schematically, possible property variations for a hypothetical binary system composed of components A and B. Variation of the values of the property in accordance with the additive law indicates that the system s behavior is close to that of an ideal system. 

The differences between two (free and with the bound target) sensor states are detected when they possess different values of anisotropy, rf of free and rb of bound state (Fig. la). Their fractional contributions depend also on the relative intensities of correspondent forms. Since the additivity law is valid only for the intensities, the parameters derived in anisotropy sensing appear to be weighted by fractional intensities of these forms, Ft and Fb ... 

The heat of fusion AHf (obtained from the area under the DSC melting curve) and percentage crystallinity calculated from AHf is found to be linearly dependent on butadiene content, and independent of the polymer architecture. This is shown in Figure 3. Also, the density of the block copolymers was found to be linearly dependent on butadiene content (see Figure 4). The linear additivity of density (specific volume) has been observed by other workers for incompatible block copolymers of styrene and butadiene indicating that very little change in density from that of pure components has occurred on forming the block copolymers.(32) While the above statement is somewhat plausible, these workers have utilized the small positive deviation from the linear additivity law to estimate the thickness of the boundary in SB block copolymers.(32)... 

This formula defines the Einstein addition law for parallel velocities. It shows that, no matter how closely P and (3 approach unity f3" can never exceed unity. In this sense c can be considered to be the ultimate speed allowed by special relativity. 

Food additives law (EU), 12 36-37 Food additive suppliers, 12 70 Food analysis... 

The additivity law can also be expressed with the polarization ratio ... 

The emission anisotropy r0(A) at a wavelength of excitation X results from the addition of contributions from the JLa and b excited states with fractional contributions fa(X) and fh(X), respectively. According to the additivity law of emission anisotropies, ro(X) is given by... 

Wiedemann s additivity law physchem The law that the mass (or specific) magnetic... 

It is remarkable that the predicted modulus from Equation 14 is higher in value than the one predicted by a simple linear additivity law due to the reinforcing effect of the heteropolymer couplings. 

According to P. Pascal,0 fluorine is diamagnetic the specific magnetic susceptibility is —3447 X10 j and the atomic susceptibilitv calculated from the additive law of mixtures for organic compounds is —63X10-1. Ionic fluorine is univalent and negative. The decomposition voltage required to separate this element from its compounds is 1 75 volts.7 The ionic velocity (transport number) 8 of fluorine ions at 18° is 46 6, and 52-5 at 25° with a temp, coeff. of 0 0238. 

The rotation of polarized light.—Rotation of polarized light7 is additive for soln. of mixtures of salts which do not form double salts, and there is a marked deviation from the additive law for mixtures known to form double salts. 

When a mixture containing compounds with known spectra is analysed, it is possible to determine the mixture s composition. According to the additivity law (equation (11.10)), the spectrum of the mixture corresponds to the weighted superposition of each of the individual constituents. The following section recalls the classical calculation method. It is rarely used as such because it is typically incorporated into software. 

Given a mixture of three components a, b and c in solution (with concentrations Ca, Cb, Cc), it is possible to measure the absorbance of this solution at three different wavelengths A1 A2 and A3, giving Au A2 and A3. Since the absorption coefficients of the three components at each of these wavelengths is known (9 values in total, from e to c) it is possible to write the following system of simultaneous equations using the additivity law (it is assumed that the optical path is 1 cm) ... 

If cells are constructed by making different combinations of half-cells, then the cell emf values obey an additive law. It is therefore convenient to combine half-cells with a single reference half-cell and thus obtain a series of related emf values compared to the reference half-cell taken as zero. 

In what follows when discussing the general properties of the chemical kinetic equations, we will assume that the additional laws of conservation (if there are any) have b en discovered and the respective values of x are included in the matrix A as additional rows. 

In this case we assume the absence of any additional laws of conservation arising in the case when a linear system has autonomous groups of substances (see Sect. 5.1). 

In numerical calculations of adsorption energies, however, expression (7) is mostly used. It is assumed that the two last terms of Eq. (11) are counterbalanced by the contribution of the repulsion forces (see Sec. IV,4). Expression (7) gives the interaction energy between two atoms. In order to evaluate the adsorption energy, the interaction energies of the adsorbed atom with all individual atoms of the adsorbent should be calculated and added together. This addition is allowed, as the dispersion forces are, at a first approximation, additive. If a molecule instead of an atom is adsorbed, the summation should be made for all atoms of the molecule. In the latter case we may sometimes expect deviations from the additive law. Many molecules show different polarizabilities in different directions. If the position of an adsorbed molecule is fixed, the angles of its various axes of polarizability with respect to the surface enter into the calculations (25). If, however, the molecule rotates freely, which is often the case in physical adsorption, this correction is not necessary. 

There are, however, many systems in which deviations occur from a simple additive law for conductance. The system of CdClj and KCI is a case in point (full line in Fig. 5.53). A minimum in the conductivity curve is observed. What is the significance of this minimum ... 

The associated variance Pq is thus taken into account from the addition law as follows ... 

The theoretical density of mineralorganic-material-filled thermoplast compositions can be calculated by the additiveness law ... 

During recent years the application of the methods of x-ray and electron diffraction to the determination of the structure of molecules has permitted interatomic distances of a large number of bonds to be obtained and attempts have been made to find simple additive laws which will describe the observed data. In the case of ionic crystals the suggestion was made that each ion could be regarded as a small sphere, which just touch each other in the crystal. To each ion, therefore, there may be ascribed an ionic radius which is maintained by the ion in 1 crystals of a particular type, for example, in which the coordination number of the ion remains the same. For different coordination numbers of a particular ion, it is necessary to give different ionic radii. 

Statistical (follow certain addition laws) Examples of each can be found in Young and Lovell, ... 

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