Solution deviations

Schmidder and Henderson282 have studied several solvents and metals, using the jellium model for the metal and the MSA for the solution. Deviations of the Parsons-Zobel plot from linearity in the experimental results72,286-288 at the highest concentration have been attributed to the onset of ion-specific adsorption. However, data at other electrode charges... 

Typical standard curves for a technical grade of parathion are shown in Figure 3. Beer s law is followed within the range 10 to 400 micrograms of parathion per milliliter of dyed solution. Deviation becomes apparent outside this range, under the conditions of test. 

The frequency at the minimum of this curve is called TOF by the authors. TOF varies with the temperature as shown in Fig. 1.55.6. The extrapolated intersection of the two linear portions identifies the collapse temperature. The predicted Tc by TOF for 10 % sucrose, 10 % trehalose, 10 % sorbitol and 11 % Azactam solution deviates from observations by a freeze-drying microscope (Table 1, from [1.126]) to slightly lower temperatures, the differences are -3 °C, -1.4 °C, 2.2 °C and 0.7 °C. 

See also Developer solutions Deviations, for polymethine dyes,... 

In the colorimetric estimation of p-phenethylbiguanide the plot of readings against concentration is found ipIO) to be a straight line at concentrations less than 10 W. Above this concentration, p-phenethylbi-guanide in solution deviates sharply from Beer s Law. It may be concluded that in the low concentration range over which Beers Law is valid, the compound exists in the monomeric state in aqueous solution. 

As engineers, we need some approximate values not only for design purposes but also to have a sense of the parameter s magnitude. Thus, to go one step further in our analysis, we would like to answer the question what is the practical limit above which the two solutions deviate considerably, or in other words what should be limit of the pressure drop in the reactor in order to assume that its effect is negligible. ... 

The set of equations (3.7-3.9) shows that the sign and magnitude of the second virial coefficient provides information on how the behaviour of the macromolecular solution deviates from that of the thermodynamically ideal state, thus reflecting the nature and intensity of the inter-molecular pair interactions (both biopolymer-biopolymer and biopolymer-solvent) (Prigogine and Defay, 1954 Tanford, 1961 Ogston 1962 ... 

With regard to their viscosity, nitrocellulose solutions demonstrate the typical properties of lyophilic colloids. The action of pressure, temperature and concentration causes anomalies to appear indicating that these solutions deviate from the... 

Most solutions deviate from Raoult s lav/. The curved lines in Fig. 1 represent positive deviations, with f ff > x. The ratio /i//]° is called activity, and... 

A plot of 2 vs. -t2 for symmetrical systems (i.e., ii vo) is shown in Fig. 1 for a series of values of the heat lerm, It shows how the partial vapor pressure of a component of a binary solution deviates positively from Raoult s law more and mure as the components become more unlike in their molecular attractive forces. Second, the place of T in die equation shows that tlic deviation is less die higher the temperature. Third, when the heat term becomes sufficiently large, there are three values of U2 for the same value of ay. This is like the three roots of the van der Waals equation, and corresponds to two liquid phases in equilibrium with each other. The criterion is diat at the critical point the first and second partial differentials of a-i and a are all zero. 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

In real solution, on the other hand, the vapour pressure of a solute deviates from Raoult s law. 

Few liquid mixtures are actually ideal over their entire composition range. Figure 33.2 illustrates two cases where the vapour pressure of liquid mixtures (solutions) deviate from Raoult s Law (Frame 32 and this frame, equations (33.3) and (33.4)) (positively A/B or negatively C/D) over the composition range but shows (see caption to figure) the end composition members (both representing cases of dilute solutions) do follow Raoult s Law for a limited, small, composition range. 

A letterpress printing ink is a dispersion of pigment particles in a polymer solution. Deviation from ideality is assured by the presence of polymers of high molecular weight dissolved in solvents of differing polarity so as to disperse particles of differing polarity, shape, and size. 

Non-ideal solutions deviate as a rule from Raoult s law. One can however still retain the form of the equation derived for ideal solutions if, instead of the mole fraction xa, the activity aa is used ... 

Like gases, solutions can also be thought of as ideal. Raoult s law only works for ideal solutions. Ideal solutions are described as those solutions that follow Raoult s law. Solutions that deviate from Raoult s law are nonideal. What makes a solution deviate from ideal behavior The main reason is intermolecular attractions between solute and solvent. When the attraction between solute and solvent is very strong, the particles attract each other a great deal. This makes it more difficult for solute particles to enter the vapor phase. As a result, fewer particles will enter that state and the vapor pressure will be lower than expected. Remember, Raoult s law operates on the assumption that the reason for a decrease in the number of particles leaving the solution is that fewer can be on the surface in order to leave. If, in addition to this, the solute particles are also holding more tightly to the solvent particles, then fewer will leave the surface than expected. The most ideal solutions are those where the solvent and solute are chemically similar. 

Ideal solutions behave in accord with Raoult s Law, which relates the partial pressure of a solute vapor to the mole fraction of soiute in solution and the saturated vapor pressure of pure solute. Deviations from ideality can be accomodated by use of the activity coefficient such that... 

Liquid-liquid solutions obeying this form of Raoult s law are said to be ideal. However, as with solutions containing nonvolatile solutes, deviations from Raoult s law are often observed. These can be positive or negative, as shown in Fig. 17.11. 

In a Tafel plot, the logarithm of the current is plotted against t], as illustrated in Figure 1. Note that the slope is equal to —ccnF/2.2RT and the intercept corresponds to logj o. From these values, k° can be determined with Eq. 11. Tafel plots are often employed in corrosion studies, since k° is usually small and the condition Co(0, t) Si Cq can be accomplished by simply stirring the solution. Deviations from the idealized Tafel behavior are seen at large t], where Cq(0,/) becomes significantly smaller than Cq. 

Consider the variation of the solution of a transient heat transfer problem with time at a specified nodal point. Both the numerical and actual (exact) solutions coincide at the beginning of the first time step, as expected, but the numerical. solution deviates from the exact. solution as the time t increases. The difference between the two solutions at t Ar is due to the approximation at the first time step only and is called the local discretization error. One would expect the situation to get worse with each step since the second step uses the erroneous result of the first step a,s its starting point and adds a second local discretization error on top of it, as shown... 

Berry 1992). As with PBG, the ratios K jK2 and K2fK2 are roughly 10, but the ratio Xi/ribend was found to be only around 7, much less than for PBG. The behavior of these PBZT solutions deviates from theoretical expectations in other respects as well. Although molecular modeling indicates that the PBZT molecule should be quite flexible, with kp around 21.5 nm (Farmer et al. 1993), both intrinsic viscosity measurements (Berry 1989) and... 

The lowest-energy solutions deviating from spherieal symmetry are the 2p-orbitals. Using Eqs (7.44), (7.45) and the f = 1 spherical harmonics, we find three degenerate eigenfunctions ... 

Easy recognition of the two peaks over a wide range of relative concentrations is possible for Rs = l and this is essentially the practical minimum resolution desirable. It is usually stated that R = 1 corresponds to a peak purity of about 98% however, this is correct only for equal concentrations of the two solutes. As the ratio of relative concentrations of the two solutes deviates from 1, the recovery of the lower concentration solute at a given level of purity becomes poorer. 

Thus in the case of strong electrolytes the deviations are important even in very dilute solutions, and this is evidently related to the long range of action of electrostatic forces. On the other hand in some solutions, such as chlorobenzene + bromobenzene, where the two molecules are of closely similar chemical structure, the solutions deviate very little from ideality over the whole concentration range. Solutions which remain ideal at all concentrations are called perfect solutions. We shall return in the next paragraph to a consideration of the conditions which must be satisfied for a solution to be perfect. 

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