Solutions terms defined

Here the permeability of the membrane to the solute is defined in terms of reflection coefficients aQ and for osmosis and filtration respectively. When (To = 1, then perfect semi-permeabihty results. in Eq. (4) is the diffusive permeabihty of the membrane, while (Cj) is the average composition of the solute in the membrane. 

As just pointed out, the acidity or basicity of a solution can be described in terms of its H+ concentration. In 1909, Suren Sorensen (1868-1939), a biochemist working at the Carlsherg Brewery in Copenhagen, proposed an alternative method of specifying the acidity of a solution. He defined a term called pH (for power of the hydrogen ion ) ... 

Recall that from the perspective of thermodynamics, every concentration is measured relative to a defined standard concentration. For any gas, the defined standard is 1 bar pressure for any solute in aqueous solution, the defined standard is 1 M. We treat the concentration terms in equilibrium constant expressions in this same way. 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

Historically, an ideal solution was defined in terms of a liquid-vapor or solid-vapor equilibrium in which each component in the vapor phase obeys Raoult s law. 

The terms defined above are perhaps illustrated by using the example of the simple assay which we have mentioned before. The assay in Box 1.3 is laid out in the style of a SOP. This particular section of the operating procedure describes the assay itself but there would also be other sections in the procedure dealing with safety issues, the preparation and storage of the solutions used for extraction and dilution, the glassware required and a specification of the instrumentation to be used. 

The pH scale, which is logarithmic, is used to define the acidity or alkalinity of a solution (i.e. in terms of the concentration of hydrogen ions (Hconc) in solutions (Bond 1987)). To a first approximation, the pH of a solution is defined as — logio[Hconc]- A neutral solution at room temperature (RT) has a pH of 7. Acids have pH values less than this. 

Maximum recoveries can be significantly affected by permeation losses. Control of permeation losses must be achieved through the proper choice of membrane type. A membrane with high rejection of most organics must be selected. The membrane rejection (R) for a solute is defined in terms of the permeate solute concentration (Cp) and feed solute concentration (CF) ... 

Rather than write hydronium ion concentrations in molarity, it s more convenient to express them on a logarithmic scale known as the pH scale. The term pH is derived from the French puissance d hydrogene ("power of hydrogen") and refers to the power of 10 (the exponent) used to express the molar H30+ concentration. The pH of a solution is defined as the negative base-10 logarithm (log) of the molar hydronium ion concentration ... 

The molality scale is useful for experiments in which physical measurements (freezing point, boiling point, vapor pressure, osmotic pressure, etc.) are made over a wide range of temperatures. The molality of a given solution, which is determined solely by the masses of solution components, is independent of temperature. In contrast, the molar concentration (or the normality) of a solution is defined in terms of volume it may vary appreciably as the temperature is changed, because of the temperature-dependence of the volume. As a point of interest, in dilute aqueous solutions (less than 0.1M), the molality is very close numerically to the molarity. 

The second strategy we mention in this rapid survey replaces the QM description of the solvent-solvent and solute-solvent with a semiclassical description. There is a large variety of semiclassical descriptions for the interactions involving solvent molecules, but we limit ourselves to recall the (1,6,12) site formulation, the most diffuse. The interaction is composed of three terms defined in the formula by the inverse power of the corresponding interaction term (1 stays for coulombic interaction, 6 for dispersion and 12 for repulsion). Interactions are allowed for sites belonging to different molecules and are all of two-body character (in other words all the three- and many-body interactions appearing in the cluster expansion of the Hss and HMS terms of the Hamiltonian (1.1)... 

By comparing Equation (3.149) with Equation (3.156) we can see a direct parallelism between the first two terms of V° (i.e. excluding the overlap) and the covalent coupling Vcc. As a matter of fact the parallelism becomes equivalence when the donor and acceptor units coincide with the previous A and B chromophores of the Harcourt model and their transition densities are dominated by a single excitation. This parallelism allows the combination of the VIEF term defined in Equation (3.150) with the Trp of the Harcourt model in order to get an effective coupling in solution,... 

A key feature of Li electrodes in electrolyte solutions, which is critical for their use as anodes in rechargeable batteries, is their cycling efficiency. In general, this term defines what percentage of Li deposited electrochemically remains electrically active and can thus be dissolved electrochemically. We can define Li cycling efficiency (LiCE.) per cycle as... 

This equation indicates that the ApK term defined at a specified a value reflects the fi%e H -ion concentration ratio between the Donnan phase and the bulk solution phase. 

Reproducing the in and out of plane scattering restricted the solution to the Ni-terminated octopolar model uniquely, plus the following symmetry-related atomic relaxations in each atomic layer p (p=0 for the apex layer of atoms). Note that 3 of the 4 atoms in layer p of the unit cell have symmetry-related vertical displacements s, whereas the independent atom has vertical displacement (see Fig. 10). Likewise, 5pj defines a radial displacement of symmetry-related atoms away from the in-plane position of the apex atom (see Fig. 10). The Pp,s terms define the possible rotational displacements. Detailed fitting reveals that all 5pj and pp terms are negligible except 6i=0.117 0.015A. 

The simplest treatment, which might be regarded as a reasonable approximation when the solute makes a contribution to the nonlinearity that is much larger than that of the solvent, is to neglect the first term in eqn (7.11) and assume that the refractive indices and dielectric constant occurring in the field factors are simply the measured values for the solution as a whole. The composition of the solution is defined in terms of the weight fraction of the solute and to obtain the 7Vi values the measured density is required. The unapproximated eqn (7.11) becomes. 

The concentration of a solution is defined as the number of moles of the solute in one litre or one cubic decimetre of solution. The unit of concentration is mol dm Solute is the term used for the substance which is dissolved. For more information on solution terms, see Unit 4.6. 

The acidity of aqueous solutions is frequently described in terms of the pH scale. Acids (Box 3.3) give rise to hydrogen ions (H+) in solution and the pH value of such a solution is defined ... 

It may be noted that in an ideal solution where all ions are completely noninteracting (a situation realized only under conditions of high dilution), the activity coefficient term would equal unity, and then K would be equal to Kc-The ionic strength of a solution is defined as ... 

The pH of a solution is defined in terms of the negative logarithm (to base 10) of the hydrogen ion activity (a ) by the following expression ... 

Some liquid mixtures obey Raoult s law, but most of the solutions deviate from this. Thus, the name ideal liquid solutions is defined for solutions that obey Raoult s law. Similarly to real gases, real solutions that do not obey Raoult s law should also be expressed by thermodynamical equations. Since we can still measure the vapor pressure of real solutions, instead of the mole fraction XA term in Equation (164), we may write... 

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