Water, volume, molar

The pressure dependence of equilibrium constants in this work are estimated with Eq. 2.29, which requires knowledge of the partial molar volumes and compressibilities for ions, water, and solid phases. For ions and water, molar volumes and compressibilities are known as a function of temperature (Table B.8 Eqs. 3.14 to 3.19). Molar volumes for solid phases are also known (Table B.9) unfortunately, the isothermal compressibilities for many solid phases are lacking (Millero 1983 Krumgalz et al. 1999). 

In 1981, Helfrich [7] studied the effect of the external osmotic pressure on egg yolk phosphatidylcholine (EPC) giant vesicles by adding 15 mM of salt or glucose in the external medium of the vesicles. The vesicle radius appears to decrease linearly with time according to the law d /dt = -aPAc, where P is the membrane permeability coefficient to water, a, is the water molar volume, and Ac, the difference of molar concentrations. The water permeability coefficient for EPC bilayers was found to be 41 pms . ... 

Herein Pa and Pb are the micelle - water partition coefficients of A and B, respectively, defined as ratios of the concentrations in the micellar and aqueous phase [S] is the concentration of surfactant V. ai,s is fhe molar volume of the micellised surfactant and k and k , are the second-order rate constants for the reaction in the micellar pseudophase and in the aqueous phase, respectively. The appearance of the molar volume of the surfactant in this equation is somewhat alarming. It is difficult to identify the volume of the micellar pseudophase that can be regarded as the potential reaction volume. Moreover, the reactants are often not homogeneously distributed throughout the micelle and... 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Component 1 is the solute, while component 2 is water. The molar volume of the solute in mVkmole is at the solute normal boiling point, while the viscosity of water in Pa sec is at the temperature of the system resulting in a diffusivity in mVsec. The average error is about 9 percent when tested on 36 experimental systems. 

Tyn-Calus This correlation requires data in the form of molar volumes and parachors = ViCp (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from each other. Quale has compiled values of fj for many chemicals. Group contribution methods are available for estimation purposes (Reid et al.). The following suggestions were made by Reid et al. The correlation is constrained to cases in which fig < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, dimerization of the solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are = 37.4 cmVmol and yn = 105.2 cm g Vs mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8 Ig. 

If the volume fraction of methanol in the original mixture was (a), then the volume fraction of water would be (1-a). The molar volume of a substance is the ratio of the molecular weight to the density and thus the molar concentration of methanol and... 

Consider Ni exposed to Oj/HjO vapour mixtures. Possible oxidation products are NiO and Ni (OH)2, but the large molar volume of Ni (OH)2, (24 cm compared with that of Ni, 6.6 cm ) means that the hydroxide is not likely to form as a continuous film. From thermodynamic data, Ni (OH)2 is the stable species in pure water vapour, and in all Oj/HjO vapour mixtures in which O2 is present in measurable quantities, and certainly if the partial pressure of O2 is greater than the dissociation pressure of NiO. But the actual reaction product is determined by kinetics, not by thermodynamics, and because the mechanism of hydroxide formation is more complex than oxide formation, Ni (OH)2 is only expected to form in the later stages of the oxidation at the NiO/gas interface. As it does so, cation vacancies are formed in the oxide according to... 

What is the molar volume of water under each of the following conditions ... 

Plot an appropriate volume unit vs. mole fraction of acetic acid. Determine the partial molar volumes of water and acetic acid at X2 = 0, 1, and several intermediate compositions (at least three). Plot V and V2 as a function of. Y2. 

The expression applies up to a molality of approximately m = 1.10 molkg-1. What are the partial molar volumes of (a) the MgSC>4 and (b) the water when m = 0.050 moleskg-1 ... 

The apparent and partial molar volumes of aggregated sodium octyl, decyl, dodecyl, and tetradecyl sulfate molecules have been studied in detail by Vass et al. [144] from densities measured by a vibrating capillary densitometer in normal and 99.85% heavy water at 25°C and by Vass [130] from density, small-angle scattering, and positron annihilation measurements. 

There may be more than a thousandfold increase in volume when liquids or solids react to form a gas. The molar volumes of gases are close to 25 L-mol 1 under normal conditions (room temperature and pressure), whereas liquids and solids occupy only about a few tens of milliliters per mole. The molar volume of liquid water, for instance, is only 18 mL-mol 1. In other words, 1 mol of gas molecules at 25°C and 1 atm occupies as much as 1000 times the volume of 1 mol of molecules in a typical liquid or solid. 

If applied pressure P is increased from condition 1 to 2, then a(pyjpj) = V (Pi — PSi/RT, where molar volume is V, the gas constant is R and temperature is T. From this, e.g., for water, a 1000-fold increase in P only approximately doubles saturated vapor pressure p. For hydrocarbons, p could be doubled by a lower pressure increase, in the order of 150 times or so however for moderate pressures, a tenfold increase in P even here only increases p by some 5%. Hence, for most practical situations, vapor pressure of a liquid can be considered as independent of applied pressure. Vapor-free liquid may need chemical potential represented differently (possibly by work done). 

The apparent molar volume of interfacial water in AOT-reversed micelles is lower and its refractive index is greater than that of pure water. These findings, together with other experimental evidence, emphasize that these water molecnles are destructured, immobilized, and polarized by the ionic head of AOT [2,84,89]. In particular, it has been reported that the... 

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