Straight prediction

If the small temis in p- and higher are ignored, equation (A2.5.4) is the Taw of the rectilinear diameter as evidenced by the straight line that extends to the critical point in figure A2.5.10 this prediction is in good qualitative agreement with most experiments. However, equation (A2.5.5). which predicts a parabolic shape for the top of the coexistence curve, is unsatisfactory as we shall see in subsequent sections. 

Thus, if measured values of the left hand side of equation (6.4) are plotted against the mean pressure (pj + p2)/2, the theory predicts a straight line with slope B /pu RT and and intercept D /RT at (p +p )/2 = 0, and experiments of Carman [35] confirm that this is the case. In contrast,... 

An area of great interest in the polymer chemistry field is structure-activity relationships. In the simplest form, these can be qualitative descriptions, such as the observation that branched polymers are more biodegradable than straight-chain polymers. Computational simulations are more often directed toward the quantitative prediction of properties, such as the tensile strength of the bulk material. 

To gain some idea of the meaning of this shaded area, consider the straight line OA of slope a/q shown in Figure 25.4. The line enters the region of stable motion at P and leaves it at Q. For typical values of U (1000 V), V (6000 V), co (1.5 MHz), and r (1.0 cm). Equation 25.2 predicts that point P corresponds to an ion of m/z 451 and Q to m/z 392. Therefore, with these parameter values, all ions having m/z between 392 and 451 will be transmitted through the quadmpole. 

Figure 3.4 is a display of data which confirms the predictions of Eq. (3.46). For T and a constant-the case in these experiments—Eq. (3.46) predicts that a plot of Uj versus 1 /M should yield a straight line with an intercept proportional to 1/M(,. The elastomers on which the experiments were conducted were copolymers of isobutylene containing a small amount of isoprene. The polymers... 

The Maxwell model thus predicts a compliance which increases indefinitely with time. On rectangular coordinates this would be a straight line of slope I/77, and on log-log coordinates a straight line of unit slope, since the exponent of t is 1 in Eq. (3.69). 

What makes Eq. (8.87) especially important is that it is the equation of a straight line. It predicts that a plot of n/RTc2 versus C2 will be linear for dilute solutions and that the slope and intercept of the plot will have the following significance ... 

Initial membrane compaction is illustrated by Figure 3. Equation 1 predicts a straight-line response of J to AP, or at P. Owing to the compaction, a lower flux is observed. Once a membrane has been subjected to some pressure (P ), equation 1 is vaHd for predicting flux up to that pressure (Fig. 3, curve B). If the membrane is subsequently subjected to higher pressure (P2), the hydrauHc permeabiUty constant is changed (Fig. 3, curve D). 

Dpi is smaller than the diffusivity in a straight cylindrical pore as a result of the random orientation of the pores, which gives a longer diffusion path, and the variation in the pore diameter. Both effects are commonly accounted for by a tortuosity factor Tp such that Dp = DjlXp. In principle, predictions of the tortuosity factor can be made if the... 

Curves relating the optimum velocity to the solute diffusivity are shown in Figure 6. It is seen that the straight lines predicted by the Van Deemter equation are realized for both solutes. 

It is seen that the Van Deemter equation predicts that the total resistance to mass transfer term must also be linearly related to the reciprocal of the solute diffusivity, either in the mobile phase or the stationary phase. Furthermore, it is seen that if the value of (C) is plotted against 1/Dni, the result will be a straight line and if there is a... 

This equation is a straight line whose slope is 1/n and whose intercept is k at C = 1. Therefore, if straight line will normally be obtained. However, there are occasions, as explained later, when this is not true. The straight and the curved isotherm lines provide valuable information for predicting adsorption operations. 

To appreciate the practical value of this analysis for E, examine the experimental results relative to the predicted straight line in Figure 3-8. The agreement is excellenti... 

Sfsjl, S)s]2, El, ElcB, E2—how can you keep it all straight and predict whal will happen in any given case Will substitution or elimination occur Wil the reaction be bimolecular or unimolecular There are no rigid answers tc... 

How can you keep straight all the rules about pericyclic reactions The summary information in Tables 30.1 to 30.3 can be distilled into one mnemonic phrase that provides an easy way to predict the stereochemical outcome of any pericyclic reaction ... 

Although the biosynthetic cascade hypothesis predicts the co-occurrence of endiandric acids D (4) and A (1) in nature, the former compound was not isolated until after its total synthesis was completed in the laboratory (see Scheme 6). Our journey to endiandric acid D (4) commences with the desilylation of key intermediate 22 to give alcohol 31 in 95% yield. The endo side chain is then converted to a methyl ester by hydrolysis of the nitrile to the corresponding acid with basic hydrogen peroxide, followed by esterification with diazomethane to afford intermediate 32 in 92% overall yield. The exo side chain is then constructed by sequential bromination, cyanide displacement, ester hydrolysis (33), reduction, and olefination (4) in a straight-... 

The total vapor pressure line in Figure 6.5 for ( yic-C6HmCH3 +. Y2C-C6H12) at T = 308.15 K is reproduced as the upper line in Figure 8.13. This line is often known as the bubble-pressure curve. We will refer to it as the liquid line. The straight line relationship for this line as predicted by equation (8.16) is evident. 

Equation (10.160) predicts that a graph of Cy,m/T against T2 should be a straight line with intercept at T = 0 since... 

Figure 10.14 Graph showing the limiting behavior at low temperatures of the heat capacity of (a), krypton, a nonconductor, and (b). copper, a conductor. The straight line in (a) follows the prediction of the Debye low-temperature heat capacity equation. In (b), the heat capacity of the conduction electrons displaces the Debye straight line so that it does not go to zero at 0 K.

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