Pure liquids

1 Pure Liquids. - Iwahashi et studied the dynamical dimer structure and liquid structure of fatty acids in their binary liquid mixture. Celebre et alP investigated the planarity of styrene in the liquid phase. The NMR data are consistent with the ring fragment, averaged over the ring-ene rotation, planar, while the ene fragment is not. 

Vilfan and Yuk discussed the nuclear spin relaxation resulting from molecular translational dilfusion of a liquid crystal in the isotropic phase confined to spherical microcavities. Their analysis can be also applied to other fluids in porous media. Nilsson et used high-resolution NMR and high-resolution diffusion-ordered spectroscopy (DOSY) for the characterization of selected Port wine samples of different ages with the aim of identifying changes in composition. 

The application of FST to pure liquids is rather trivial. However, we include it here for the sake of completeness. We find from Equation 1.46 that for a single component (1), 

The extreme limit of high density of s is the pure liquid. Normally, the liquids of interest are either at room temperature and 1 atm pressure or along the liquid-vapor coexistence equilibrium line. Let l and g be the liquid and the gaseous phases of a pure component s at equilibrium. The Gibbs energy of 

Knowing the densities s of in the two phases at equilibrium, gives us only the difference in the solvation Gibbs energies of s in two phases. However, in many cases, especially near the triple point, the density of the gaseous phase is quite low, in which case we may assume that AG/ 0 and therefore relation (7.106) reduces to 

When evaluating other thermodynamic quantities of solvation from data along the equilibrium line, care must be exercised to distinguish between derivatives at constant pressure and derivatives along the equilibrium line. The connection between the two is 

we use straight derivatives to indicate differentiation along the equilibrium line. The two derivatives of AG on the rhs of equation (7.108) are identified as the solvation entropy and the solvation volume, respectively thus, 

Usually, data are available to evaluate both of the straight derivatives in equation (7.108). This is not sufficient, however, to compute both AS / and A V/. Fortunately, A V/ may be obtained directly from data on molar volume and compressibility of the pure liquid. For the pure system s we have 

This chapter will be given over to atomic and molecular liquids. A pure molecular liquid is a liquid comprising only one type of non-dissociated molecules. The study of liquids is more difficult than that of gases and solids because they are in an intermediary state, structurally speaking. Indeed, as is the case with solids, we can imagine that in liquids (and this is confirmed by X-ray diffraction), the interactions between molecules are sufficiently powerful to impose a sort of order within a short distance of the molecules. However, the forces involved in these interactions are sufficiently weak for the molecules to have relative mobility and therefore for there to be disorder (no form of order) when they are far apart, as is the case with gases. 

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

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For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

However, if the liquid solution contains a noncondensable component, the normalization shown in Equation (13) cannot be applied to that component since a pure, supercritical liquid is a physical impossibility. Sometimes it is convenient to introduce the concept of a pure, hypothetical supercritical liquid and to evaluate its properties by extrapolation provided that the component in question is not excessively above its critical temperature, this concept is useful, as discussed later. We refer to those hypothetical liquids as condensable components whenever they follow the convention of Equation (13). However, for a highly supercritical component (e.g., H2 or N2 at room temperature) the concept of a hypothetical liquid is of little use since the extrapolation of pure-liquid properties in this case is so excessive as to lose physical significance. 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

We find that the standard-state fugacity fV is the fugacity of pure liquid i at the temperature of the solution and at the reference pressure P. ... 

Chapter 3 discusses calculation of fugacity coefficient < ). Chapter 4 discusses calculation of adjusted activity coefficient Y fugacity of the pure liquid f9 [Equation (24)], and Henry s constant H. 

For condensable components, we use the symmetric normaliza-L as x - 1 therefore, the quantity in brackets is the fugacity of pure liquid i at system temperature and pressure. 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

For pure liquids the standard-stare fugacity is represented... 

Figure 1 gives an enthalpy-concentration diagram for ethanol(1)-water(2) at 1 atm. (The reference enthalpy is defined as that of the pure liquid at 0°C and 1 atm.) In this case both components are condensables. The liquid-phase enthalpy of mixing... 

Enthalpies are referred to zero enthalpies of the pure liquids. at 1.013 bars and 273.2 K. 

Appendix C-2 gives constants for the zero-pressure, pure-liquid, standard-state fugacity equation for condensable components and constants for the hypothetical liquid standard-state fugacity equation for noncondensable components... 

The constants in Equation (5) are not the same as those in Equation (4). Using this saturation pressure, the pure-liquid reference fugacity at zero pressure is then calculated from the equation... 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

The partial fugacity of component i in the liquid phase is expressed as a function of the total fugacity of this same component in the pure liquid state, according to the following relation ... 

C , = average specific heat of the pure liquid between... 

The surface tension of a pure liquid should and does come out to be the same irrespective of the method used, although difficulties in the mathematical treatment of complex phenomena can lead to apparent discrepancies. In the case of solutions, however, dynamic methods, including detachment ones, often tend... 

We have considered the surface tension behavior of several types of systems, and now it is desirable to discuss in slightly more detail the very important case of aqueous mixtures. If the surface tensions of the separate pure liquids differ appreciably, as in the case of alcohol-water mixtures, then the addition of small amounts of the second component generally results in a marked decrease in surface tension from that of the pure water. The case of ethanol and water is shown in Fig. III-9c. As seen in Section III-5, this effect may be accounted for in terms of selective adsorption of the alcohol at the interface. Dilute aqueous solutions of organic substances can be treated with a semiempirical equation attributed to von Szyszkowski [89,90]... 

Adsorption may occur from the vapor phase rather than from the solution phase. Thus Fig. Ill-16 shows the surface tension lowering when water was exposed for various hydrocarbon vapors is the saturation pressure, that is, the vapor pressure of the pure liquid hydrocarbon. The activity of the hydrocarbon is given by its vapor pressure, and the Gibbs equation takes the form... 

A complication now arises. The surface tensions of A and B in Eq. IV-2 are those for the pure liquids. However, when two substances are in contact, they will become mutually saturated, so that 7a will change to 7a(B) and 7b to 7B(A). That is, the convention will be used that a given phase is saturated with respect to that substance or phase whose symbol follows in parentheses. The corresponding spreading coefficient is then written 5b(A)/a(B)-... 

This method suffers from two disadvantages. Since it measures 7 or changes in 7 rather than t directly, temperature drifts or adventitious impurities can alter 7 and be mistakenly attributed to changes in film pressure. Second, while ensuring that zero contact angle is seldom a problem in the case of pure liquids, it may be with film-covered surfaces as film material may adsorb on the slide. This problem can be a serious one roughening the plate may help, and some of the literature on techniques is summarized by Gaines [69]. On the other hand, the equipment for the Wilhelmy slide method is simple and inexpensive and can be just as accurate as the film balance described below. 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

The discussion so far has been confined to systems in which the solute species are dilute, so that adsorption was not accompanied by any significant change in the activity of the solvent. In the case of adsorption from binary liquid mixtures, where the complete range of concentration, from pure liquid A to pure liquid B, is available, a more elaborate analysis is needed. The terms solute and solvent are no longer meaningful, but it is nonetheless convenient to cast the equations around one of the components, arbitrarily designated here as component 2. 

It is quite clear, first of all, that since emulsions present a large interfacial area, any reduction in interfacial tension must reduce the driving force toward coalescence and should promote stability. We have here, then, a simple thermodynamic basis for the role of emulsifying agents. Harkins [17] mentions, as an example, the case of the system paraffin oil-water. With pure liquids, the inter-facial tension was 41 dyn/cm, and this was reduced to 31 dyn/cm on making the aqueous phase 0.00 IM in oleic acid, under which conditions a reasonably stable emulsion could be formed. On neutralization by 0.001 M sodium hydroxide, the interfacial tension fell to 7.2 dyn/cm, and if also made O.OOIM in sodium chloride, it became less than 0.01 dyn/cm. With olive oil in place of the paraffin oil, the final interfacial tension was 0.002 dyn/cm. These last systems emulsified spontaneously—that is, on combining the oil and water phases, no agitation was needed for emulsification to occur. 

The adsorbed state often seems to resemble liquid adsorbate, as in the approach of the heat of adsorption to the heat of condensation in the multilayer region. For this reason, a common choice for the standard state of free adsorbate is the pure liquid. We now have... 

The integral heat of adsorption Qi may be measured calorimetrically by determining directly the heat evolution when the desired amount of adsorbate is admitted to the clean solid surface. Alternatively, it may be more convenient to measure the heat of immersion of the solid in pure liquid adsorbate. Immersion of clean solid gives the integral heat of adsorption at P = Pq, that is, Qi(Po) or qi(Po), whereas immersion of solid previously equilibrated with adsorbate at pressure P gives the difference [qi(Po) differential heat of adsorption q may be obtained from the slope of the Qi-n plot, or by measuring the heat evolved as small increments of adsorbate are added [123]. 

Hardouin F and Levelut A M 1980 X-ray study of reentrant polymorphism N-S -N-S in a pure liquid orystal oompound J.Physlque4 41-56... 

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