Ideal solutions calculating densities/concentrations

Another frequent mistake among students is to try to apply the ideal gas law to calculate the concentrations of species in condensed-matter phases (e.g., liquid or solid phases). Do not make this mistake] The ideal gas law only applies to gases. To calculate concentrations for liquid or solid species, information about the density (pj) of the liquid or solid phase is required. Both mass densities and molar densities (concentrations) as well as molar and atomic volumes may be of interest. The complexity of calculating these quantities tends to increase with the complexity of the material under consideration. In this section, we will consider three levels of increasing complexity pure materials, simple compounds or dilute solutions, and more complex materials involving mixtures of multiple phases/compounds. 

For solution scattering, solvent densities can be calculated from standard tables of buffer densities and compositions. This procedure will allow for the non-ideality of concentrated buffer solutions that are used in some X-ray scattering studies (Table 2). Macromolecular partial specific volumes v can be experimentally determined by densitometry, usually with a Paar digital density meter, to measure the density of the buffer p uff the solutions p ,p over a concentration range ... 

Solution To answer this question, we must first calculate Hq. To estimate the nucleation site density, we can calculate the molar concentration of water molecules in air using the ideal gas law as... 

This interpretation of the data was made by calcula-tionally converting each critical ejqierimental system to an ideal one in which the uranium spheres have the full crystal density (18.664 g/cm ) and the solution is a uranium-water mixture. These conversions (and all subsequent calculations) use the DTF computer code in the Sis approximation with Hansen-Rc ch cross sections. Then, two end points are calculated for the data analysis plots the first is the critical mass of a full metal sphere reflected by water the second Is the critical uranium concentration tor a metal/water mixture. An example of the results obtained at this stage of the analysis is pre-... 

The degrees of dissociation and hydration numbers calculated from vapor pressures correlate quantitatively with the properties of dilute as well as concentrated solutions of strong electrolytes. Simple mathematical relations have been provided for the concentration dependences of vapor pressure, e.m.f. of concentration cells, solution density, equivalent conductivity and diffusion coefficient. Non-ideality has thus been shown to be mainly due to solvation and incomplete dissociation. The activity coefficient corrections are, therefore, no longer necessary in physico-chemical thermodynamics and analytical chemistry. 

Calculations of departures from ideality in ionic solutions using the MSA have been published in the past by a number of authors. Effective ionic radii have been determined for the calculation of osmotic coefficients for concentrated salts [13], in solutions up to 1 mol/L [14] and for the computation of activity coefficients in ionic mixtures [15]. In these studies, for a given salt, a unique hard sphere diameter was determined for the whole concentration range. Also, thermodynamic data were fitted with the use of one linearly density-dependent parameter (a hard core size o C)., or dielectric parameter e C)), up to 2 mol/L, by least-squares refinement [16]-[18], or quite recently with a non-linearly varying cation size [19] in very concentrated electrolytes. 

As already stated, the ideal method of calibration, when it can be performed, is that of mass integration (e.g.5) sometimes also called mass-balance. That is, the instrument is calibrated directly with the particles of material under test, using the standard gravimetric and volumetric methods of an accurate balance, pipettes and flasks. A size fraction of the particles under test, preferably not exceeding some 10 1 by particle diameter to be sure that they are all measured, is diluted to a known mass concentration in electrolyte solution. The total volume, in instrument units, of the particles measured in a known volume of suspension is related to the known mass concentration and the particles immersed specific gravity (density), allowing the calibration factor to be calculated. In this way, the calibration procedure approaches an absolute reference method, as it eliminates any possible... 

At the interface between coexisting polymer solutions a central layer enriched in solvent is expected, because the two incompatible polymers avoid mutual contact. Using mean field theory extended to include excluded volume effects to describe the mixing of two polymers in a common solvent, the structure of the interface can be estimated [21]. In this approach, the polymer solution is considered a melt of ideal chains of blobs. Blobs are sequences of monomers that are correlated by excluded volume effects. Beyond a blob, no such correlations exist and the chain of blobs is ideal. The interaction between blobs of the two types of polymers is responsible for phase separation. This interaction is dependent on concentration because the blob size is dependent on concentration. The calculation [21] starts from the density of the free energy of mixing, rescaled on the relevant distance scale, that is, the blob size... 

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