Negative deviation

Figure 4-6. Representation of vapor-liquid equilibria for a binary system showing strong negative deviations from Raoult s law.

Figure 7 shows a fit of the UNIQUAC equation to the iso-baric data of Nakanishi et al. (1967) for the methanol-diethyl-amine system this system also exhibits strong negative deviations from Raoult s law. The UNIQUAC equation correctly re-... 

The negative deviations from the limiting law are reproduced by the HNC and DHLL + B2 equations but not by the MS approximation. 

At larger bond lengths, the true potential is "softer" than the harmonie potential, and eventually reaehes its asymptote whieh lies at the dissoeiation energy Dg above its minimum. This negative deviation of the true V(R) from 1/2 k(R-Rg)2 eauses the true vibrational energy levels to lie below the harmonie predietions. 

Calibration curves showing positive and negative deviations from Beer s law. 

For small concentrations of analyte, Pstray is significantly smaller than Pq and Py, and the absorbance is unaffected by the stray radiation. At higher concentrations of analyte, however, Pstray is no longer significantly smaller than Py and the absorbance is smaller than expected. The result is a negative deviation from Beer s law. 

If the molecular species in the liquid tend to form complexes, the system will have negative deviations and activity coefficients less than unity, eg, the system chloroform—ethyl acetate. In a2eotropic and extractive distillation (see Distillation, azeotropic and extractive) and in Hquid-Hquid extraction, nonideal Hquid behavior is used to enhance component separation (see Extraction, liquid—liquid). An extensive discussion on the selection of nonideal addition agents is available (17). 

To force the naturally more volatile component i overhead, the solvent should either behave essentially ideally with component j and cause positive deviations from Raoult s Law for component i (7 1 and 7 > 1), or behave essentially ideally with component i and cause negative deviations from... 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

This example clearly shows good distribution because of a negative deviation from Raonlt s lawin the extract layer. The activity coefficient of acetone is less than 1.0 in the chloroform layer. However, there is another problem because acetone and chloroform reach a maximum-boiling-point azeotrope composition and cannot be separated completely by distillation at atmospheric pressure. 

A higher-boiling solvent, e.g., 1,1,2-trichloroethane, can be used which still gives acetone a negative deviation from Raonlt s law =... 

In Example 1 the solute, acetone, contains a ketone carbonyl group which is a hydrogen acceptor, i.e., solute class 5 according to Table 15-4. This solute is to be extracted from water with chloroform solvent which contains a hydrogen donor group, i.e., solvent class 4. The solute class 5 and solvent class 4 interaction in Table 15-4 is shown to give a negative deviation from Raonlt s law. 

A negative deviation reduces the activity of the solute in the solvent, which enhances the liqnid-hqnid partition ratio but also leads to maximnm-boihng-point azeotropes. Among other classes of solvents shown in Table 15-4 that suppress the escaping tendency of a ketone are classes 1 and 2, i.e., phenohcs and acids. 

Other approaches to account for various effects have been developed. Negative deviations from Raoult s law (i.e., y < 1) are frequently... 

We developed a sensor for determination of content of phosphorars in metallurgical melts. In quality of ion conductor used orthophosphate of calcium which pressed in tablets 010 mm. Tablets (mass 1-2 g) annealed at a temperature 400°C during 7-10 h. Tablets melts then in a quartz tube and placed the alloy of iron containing 1 mass % P. Control of sensor lead on Fe - P melts. Information on activities (effective concentration) of phosphorars in Fe - P melts was received. It is set that the isotherm of activity of phosphorars shows negative deviations from the Raouls law. Comparison them with reliable literary inforiuation showed that they agree between itself. Thus, reliable data on activities (effective concentration) of phosphorars in metallic melts it is possible to received by created electrochemical sensor for express determination. 

These equations are ealled the moment equations, beeause we are effeetively taking moments of the data about a point to measure the dispersion over the whole set of data. Note that in the varianee, the positive and negative deviates when squared do not eaneel eaeh other out but provide a powerful measure of dispersion whieh... 

We are now in a position to examine the relative accuracies of a variety of different model chemistries by considering their performance on the G2 molecule set. The following table lists the mean absolute deviation from experiment, the standard deviation and the largest positive and negative deviations from experiment for each model chemistry. The table is divided into two parts the first section lists results for single model chemistries, and the remaining sections present results derived from... 

It is interesting to note that our derivation of the viscosity function Eq. (7) was not restricted within TP-TLCP systems. The negative deviation flow behav-... 

A distinct viscosity reduction occurs as a small quantity of TLCP is added to a thermoplastic matrix. This negative deviation effect from the log-additivity rule was ex-... 

Figure 8-6. Acetone (1)-Chloroform (2) system at 50°C. Azeotrope formed by negative deviations from Raoult s Law (dashed lines). Data of Sesonke, dissertation. University of Delaware, used by permission. Smith, B.D., Design of Equilibrium Stage Processes, McGraw-Hill New York (1963), all rights reserved.

Figure 5.10 shows a plot of Vm/Vm versus pressure for methane at 25°C. Up to about 150 atm, methane shows a steadily increasing negative deviation from ideality, as might be expected on the basis of attractive forces. At 150 atm, Vm is only about 70% of V ,. 

These equations suggest that a plot of M vs conversion should be linear. A positive deviation from the line predicted by eq. 16 indicates incomplete usage of transfer agent (T) while a negative deviation indicates that other sources of polymer chains are significant (e.g. the initiator). 

Deviations in which the observed vapor pressure are smaller than predicted for ideal solution behavior are also observed. Figure 6.8 gives the vapor pressure of. (CHjCF XiN +. viCHCfi at T — 283.15 K, an example of such behavior,10 This system is said to exhibit negative deviations from Raoult s law. 

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