Liquids solutions

It is a common practice to try to relate the activity coefficients of ions with the composition and dielectric constant under certain conditions of temperature. The most indicated theory is that of Debye-Huckel, for dilute solutions. This theory is not valid when the concentrations are high. 

We will not make the deduction, and details can be found in Hill s book. According to this theory, the rate constant for a bimolecular reaction would be given by  

Ya and ys = activity coefficients of A and B, respectively AB = activity coefficient of the activated complex. 

In general, these activity coefficients are not thermodynamically known and can be determined by analogy with the existing data for the compounds, with the exception 

This ionic Strength depends on the concentration of the reactants and the charge of the respective ions. Usually, it can be expressed by the following equation  

A hypothetical free energy of hydration of AG = -65 2kcal/mol has been derived for the PHi ion from its gas-phase proton affinity and the aqueous pKg value of PH3 [16]. 

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It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

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. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

It was pointed out that a bimolecular reaction can be accelerated by a catalyst just from a concentration effect. As an illustrative calculation, assume that A and B react in the gas phase with 1 1 stoichiometry and according to a bimolecular rate law, with the second-order rate constant k equal to 10 1 mol" see" at 0°C. Now, assuming that an equimolar mixture of the gases is condensed to a liquid film on a catalyst surface and the rate constant in the condensed liquid solution is taken to be the same as for the gas phase reaction, calculate the ratio of half times for reaction in the gas phase and on the catalyst surface at 0°C. Assume further that the density of the liquid phase is 1000 times that of the gas phase. 

Kirkwood J G 1935 Statistical mechanics of fluid mixtures J. Chem. Phys. 3 300 Kirkwood J G 1936 Statistical mechanics of liquid solutions Chem. Rev. 19 275... 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

A reactive species in liquid solution is subject to pemianent random collisions with solvent molecules that lead to statistical fluctuations of position, momentum and internal energy of the solute. The situation can be described by a reaction coordinate X coupled to a huge number of solvent bath modes. If there is a reaction... 

Instead of concentrating on the diffiisioii limit of reaction rates in liquid solution, it can be histnictive to consider die dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily hivestigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. 

In liquid solution. Brownian motion theory provides the relation between diffiision and friction coefficient... 

Figure A3.6.11. Viscosity dependence of transmission coefficient of the rate of cyclohexane chair-boat inversion in liquid solution (data from [100]).

Typical singlet lifetimes are measured in nanoseconds while triplet lifetimes of organic molecules in rigid solutions are usually measured in milliseconds or even seconds. In liquid media where drfifiision is rapid the triplet states are usually quenched, often by tire nearly iibiqitoiis molecular oxygen. Because of that, phosphorescence is seldom observed in liquid solutions. In the spectroscopy of molecules the tenn fluorescence is now usually used to refer to emission from an excited singlet state and phosphorescence to emission from a triplet state, regardless of the actual lifetimes. 

Closs G L and Forbes M D E 1991 EPR spectroscopy of electron spin polarized biradicals in liquid solutions. Technique, spectral simulation, scope and limitations J. Phys. Chem. 95 1924-33... 

Grolier J-P E 1994 Heat capacity of organic liquids Solution Calorimetry, Experimental Thermodynamics vol IV, ed K N Marsh and PAG O Hare (Oxford Blackwell)... 

The fonnation of clusters in the gas phase involves condensation of the vapour of the constituents, with the exception of the electrospray source [6], where ion-solvent clusters are produced directly from a liquid solution. For rare gas or molecular clusters, supersonic beams are used to initiate cluster fonnation. For nonvolatile materials, the vapours can be produced in one of several ways including laser vaporization, thennal evaporation and sputtering. 

Figure C 1.5.5. Time-dependent fluorescence signals observed from liquid solutions of rhodamine 6G by confocal fluorescence microscopy. Data were obtained with 514.5 mn excitation and detected tlirough a 540-580 nm...

Heath J R and LeGoues F K 1993 A liquid solution synthesis of single crystal germanium quantum wires Chem. Phys. Lett. 208 263... 

Heath J R 1992 A liquid solution phase synthesis of crystalline silicon Science 258 1131... 

Because of the high rate of emission of alpha particles and the element being specifically absorbed on bone the surface and collected in the liver, plutonium, as well as all of the other transuranium elements except neptunium, are radiological poisons and must be handled with very special equipment and precautions. Plutonium is a very dangerous radiological hazard. Precautions must also be taken to prevent the unintentional formulation of a critical mass. Plutonium in liquid solution is more likely to become critical than solid plutonium. The shape of the mass must also be considered where criticality is concerned. 

A stream of a liquid solution can be broken up into a spray of fine drops from which, under the action of aligned nozzles (skimmers) and vacuum regions, the solvent is removed to leave a beam of solute molecules, ready for ionization. The collimation of the initial spray into a linearly directed assembly of droplets, which become clusters and then single molecules, gives rise to the term particle beam interface. 

Some solids inlet systems are also suitable for liquids (solutions) if the sample is first evaporated at low temperatures to leave a residual solid analyte, which must then be vaporized at higher temperatures. 

We define Fj to be the mole fraction of component 1 in the vapor phase and fi to be its mole fraction in the liquid solution. Here pj and p2 are the vapor pressures of components 1 and 2 in equihbrium with an ideal solution and Pi° and p2° are the vapor pressures of the two pure liquids. By Dalton s law, Plot Pi P2 Pi/Ptot these are ideal gases and p is propor-... 

Vapor pressure lowering. Equation (8.20) shows that for any component in a binary liquid solution aj = Pj/Pi°. For an ideal solution, this becomes... 

Liquid solutions are often most easily dealt with through properties that measure their deviations, not from ideal gas behavior, but from ideal solution behavior. Thus the mathematical formaUsm of excess properties is analogous to that of the residual properties. 

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