Approximate linear relationship

With the addition of increasing amounts of electrolyte this variance decreases and an approximate linear relationship between internal and external pH exists in a 1 Af electrolyte solution. The cell-0 concentration is dependent on the internal pH, and the rate of reaction of a fiber-reactive dye is a function of cell-0 (6,16). Thus the higher the concentration of cell-0 the more rapid the reaction and the greater the number of potential dye fixation sites. 

In the benzene series, an approximately linear relationship has been obtained between the chemical shifts of the para-hydrogen in substituted benzenes and Hammett s a-values of the substituents. Attempts have been made, especially by Taft, ° to use the chemical shifts as a quantitative characteristic of the substituent. It is more difficult to correlate the chemical shifts of thiophenes with chemical reactivity data since few quantitative chemical data are available (cf. Section VI,A). Comparing the chemical shifts of the 5-hydrogen in 2-substituted thiophenes and the parahydrogens in substituted benzenes, it is evident that although —I—M-substituents cause similar shifts, large differences are obtained for -j-M-substituents indicating that such substituents may have different effects on the reactivity of the two aromatic systems in question. Differences also... 

The most fundamental thermodynamic approach of Rudakov (6) applies to all condensed systems. The actual linear relationship is argued to exist between enthalpy (AH) and entropy (AS) of intermolecular interaction, as reflected in an approximately linear relationship between the total enthalpy and entropy. Special attention has been given to hydrophobic interaction (89, 90) in water solutions, which makes the isokinetic behavior more pronounced and markedly changes its slope. 

At concentrations below that yielding the maximum whiteness achievable there is an approximately linear relationship between whiteness and the logarithm of the concentration... 

The actual sizes of the observed cis- and trans- couplings are influenced by the electronegativity of the substituents attached to the double bond. In general, the more electronegative the substituents, the smaller the observed couplings. (There is actually an approximately linear relationship between the size of the coupling and the sum of the electronegativities of the substituents). 

There is an approximately linear relationship between Rv and spin transfer coefficients determined from electron and nuclear magnetic resonance and neutron diffraction, i.e., a contraction of the unit cell accompanies the transfer of spin from transition metal to the ligands. 

An approximately linear relationship also exists between Rv and the Fe2+ Mossbauer isomer shift, i.e., between shortening of Fe2+—X bonds and increased electron transfer to the 4s orbitals of Fe2+. 

The p -value for bromination established in methanol is also valid in a variety of other protic solvents. Linear correlations between the bromination rates of unbranched alkenes in methanol and those in a 70-30 methanol-water mixture (M70) [(22) Barbier and Dubois, 1968], in pure water [(23) Bienvenue-Goetz and Dubois, 1968] and in acetic acid [(24) Ruasse and Zhang, 1984) are observed. An approximately linear relationship (25) between... 

These QSPR (quantitative structure-property relationship) plots display the usual approximately linear relationships similar to those of the alkyl and chlorinated aromatic hydrocarbons. 

Approximately linear relationships between the calculated Ano+ values (kJ/mol) and a- or a -constants, or values of total charge on the NO group of complex q+N0 were found for the 3- and 4-substituted pyridines (81) ... 

Figure 2.6. The approximate linear relationship between (Miedema 1973) and the electronegativity r) (Pauling scale) as illustrated by de Boer et al. (1988).

A key criterion for the evaluation of a promising area is the approximately linear relationship between the area of the depletion zone and the amount of gold contained in the deposit (Fig. 3). 

CSD on Rosin-Rammler Chart. lognogn/RjVlog p. Figure 1 shows some examples of CSD on R-R chart. As mentioned above, R based on Equation 4 does not obey the R-R s expression except for Rn at j=l and Rn, Rw at j=. Nevertheless, as can be seen from Figure 1, it was found that there exists an approximate linear relationship between R and p (or L) on R-R graph paper in the... 

It is seen that an approximately linear relationship exists between the retention volume of each alkane and Its carbon number and that the smaller molecule exhibits the greatest retention. This is a direct result of the exclusion properties of the silica gel support. The fact that the data, taken at the two different temperatures, fall on the same straight line confirms that little or no partition is taking place and that the difference In retention between the Individual solutes is entirely related to their molecular size. 

Figure 11.8 Approximately linear relationship between solvation free energy and solvent-accessible surface area for linear and branched alkanes. A best fit line passing through zero has a slope of...

For a given set of flow parameters, the strained flame speed is taken as the fluid velocity at the minimum in the profile just upstream of the flame. Law and collaborators developed an analysis that uses a series of variously strained flames to predict strain-free laminar burning velocities [238,438,448]. As the strain rate is decreased, the strained flame speed decreases and the flame itself moves farther from the symmetry plane. There is an approximately linear relationship between the strained flame speed and the strain rate. Thus, after measuring the velocity profiles (e.g., by laser-dopler velocimetry) for a number of different strain rates, the strain-free burning velocity can be determined by extrapolating the burning velocity to zero strain. 

A plot of the reject ratio as a function of the sunt, C. yields an approximately linear relationship. Thin f used to indicate a reject rate for a particular system. The line dient for the 35-mm (1.4-in.] cyclone is, not surprisingly, i steeper than for the 60-mm (2.4-in.) cyclone (Fig. 6). 

The influence of exchangeable monovalent cations on the framework vibrations for the hydrated zeolites Linde A and X has been investigated. An approximately linear relationship is found between the frequency of some absorption bands and the inverse of the sum of the cation and framework oxygen ionic radii. It is proposed that the shift in framework vibrations is largely caused by those cations which are strongly interacting with the zeolite framework. Thus the linear relationship indicates that these monovalent cations are all similarly sited in the zeolite lattice. This is consistent with the presently available x-ray analyses on some of these zeolites. Since Rb + and Cs + are only partially exchangeable in both Linde A and Linde X, these cations deviate from this linear relationship. 

There is an approximately linear relationship between the CTL intensity and the concentration of the combustible vapors, ranging over more than two orders of concentration... 

Hydrophobic binding. The hydrophobic effect can have both enthalpic and entropic components, although the classical hydrophobic effect is entropic in origin (Section 1.9.1). Studies on the associations between planar aromatic molecules show an approximately linear relationship between the interaction energy and their mutual contact surface area with slope 64 dyn cm-1, very close to the macroscopic surface tension of water (72 dyn cm-1). Hence, in the absence of specific host or guest interactions with the solvent the hydrophobic effect can be calculated solely from the energy required to create a free surface of 1 A2 which amounts to 7.2 X 10 12 J or 0.43 kjA 2 mol. ... 

It is now evident why the formation of the alkylvanadates is insensitive to the pKa of the parent alcohol. The electron density about vanadate is close to optimal, so small changes arising from variation in the ability of the ligand to donate or withdraw electrons are relatively unimportant components of complexation of the alcohols. It would be expected, and is also observed, that both resonance and inductive effects are small for the reaction of vanadate with phenols [4], Considering that the pKa values of the various substituted phenols are considerably lower than 15, an approximately linear relationship (Figure 9.3) between the pKa of the aryl-vanadate and the pKa of the ligand would be expected and can be predicted from the observations of alkylvanadates. There are only minor differences that arise because of resonance electron donation and withdrawal. 

Using the results of 12 iPP/EP blends, 4 iPP/EP block copolymers and 1 pure EP copolymer [13, 14], the Xe chemical shift of Xe absorbed in EP can be correlated to the chemical composition of EP, i.e., the ethylene fraction. Figure 12.9 shows an approximately linear relationship between the Xe chemical shift and the weight fraction ethylene in the EP copolymer. The values for the pure components PE (ethylene content = 1) and iPP (ethylene content = 0) are included. Of course, this also implies that a linear relationship exists between the Xe chemical shift and the density of the EP copolymer. 

For large times in Figure 5, an approximately linear relationship exists between log (i) and t, which is consistent with the equation... 

Fig. 2.8 shows that the logarithm of maximum rates (Eq. 2.16) spanning 12 order of magnitude for intraprotein ET reaction as a function of the edge-to edge distance generates an approximate linear relationship with p = 1.4 A-l (Moser and Dutton, 1992). A similar... 

---