Free total

The total free contribution to the second virial coeffi-F... 

The total free energy of the system is then made up of the molar free energy times the total number of moles of the liquid plus G, the surface free energy per unit area, times the total surface area. Thus... 

The excess of unchanged acetic anhydride is then hydrolysed by the addition of water, and the total free acetic acid estimated by titration with standard NaOH solution. Simultaneously a control experiment is performed identical with the above except that the alcohol is omitted. The difference in the volumes of NaOH solution required in the two experiments is equivalent to the difference in the amount of acetic add formed, i.e., to the acetic acid used in the actual acetylation. If the molecular weight of the alcohol is known, the number of hydroxyl groups can then be calculated. 

C.HsNH, + CHjCO-O-COCHa = C.R NHCOCHs -h CHjCOOH then hydrolysed with water and the total free acetic acid estimated by titration with standard NaOH solution, the result being compared with that obtained in a control or blank experiment. 

The methods described earlier for determining the total, free, or combined chlorine residual also are used in establishing the chlorine demand of a water supply. The chlorine demand is defined as the quantity of chlorine that must be added to a water supply to completely react with any substance that can be oxidized by chlorine while also maintaining the desired chlorine residual. It is determined by adding progressively greater amounts of chlorine to a set of samples drawn from the water supply and determining the total, free, or combined chlorine residual. 

For the evaporation process we mentioned above, the thermodynamic probability of the gas phase is given by the number of places a molecule can occupy in the vapor. This, in turn, is proportional to the volume of the gas (subscript g) 12- oc V In the last chapter we discussed the free volume in a liquid. The total free volume in a liquid is a measure of places for molecules to occupy in the liquid. The thermodynamic probability of a liquid (subscript 1) is thus V, oc V, frgg. Based on these ideas, the entropy of the evaporation process can be written as... 

The pulsed-plate column is typically fitted with hori2ontal perforated plates or sieve plates which occupy the entire cross section of the column. The total free area of the plate is about 20—25%. The columns ate generally operated at frequencies of 1.5 to 4 H2 with ampHtudes 0.63 to 2.5 cm. The energy dissipated by the pulsations increases both the turbulence and the interfacial areas and greatly improves the mass-transfer efficiency compared to that of an unpulsed column. Pulsed-plate columns in diameters of up to 1.0 m or mote ate widely used in the nuclear industry (139,140). 

Mvailable lime, the total free lime (ie, CaO) content in a quicklime or hydrate, is the active constituent of a lime. It provides a means of evaluating the concentration of lime. 

Gumylphenol. -Cumylphenol (PGP) or 4-(1-methyl-l-phenylethyl)phenol is produced by the alkylation of phenol with a-methylstyrene under acid catalysis. a-Methylstyrene is a by-product from the production of phenol via the cumene oxidation process. The principal by-products from the production of 4-cumylphenol result from the dimerization and intramolecular alkylation of a-methylstyrene to yield substituted indanes. 4-Cumylphenol [599-64-4] is purified by either fractional distillation or crystallization from a suitable solvent. Purification by crystallization results in the easy separation of the substituted indanes from the product and yields a soHd material which is packaged in plastic or paper bags (20 kg net weight). Purification of 4-cumylphenol by fractional distillation yields a product which is almost totally free of any dicumylphenol. The molten product resulting from purification by distillation can be flaked to yield a soHd form however, the soHd form of 4-cumylphenol sinters severely over time. PGP is best stored and transported as a molten material. 

In Section III we described an approximation to the nonpolar free energy contribution based on the concept of the solvent-accessible surface area (SASA) [see Eq. (15)]. In the SASA/PB implicit solvent model, the nonpolar free energy contribution is complemented by a macroscopic continuum electrostatic calculation based on the PB equation, thus yielding an approximation to the total free energy, AVP = A different implicit... 

For the calculation of the LDA ground-state one can proceed either via the direct" methods, i.e. via the glocal minimization of the total free energy with respect to the electronic degrees of freedom, or via the the diagonalization (for large PW basis-sets necessarily iterative diagonalization) of the KS Hamiltonian in combination with an iterative update of chai ge-density and potential. 

When a load is applied, if the product is to remain in equilibrium there must be equal force acting in the opposite direction. These balancing forces, as an example, are the reactions at the supports. For purposes of structural analysis there are several supports conditions that have been defined. The free (unsupported), simply supported, and fixed supports are the most frequently encountered. The free (unsupported) condition occurs where the edge of a body is totally free to translate or rotate in any direction. The fixed (clamped or built-in) support condition at the end of a beam or plate prevents transverse displacement and rotation. The condition can... 

It is interesting, for comparison, to apply the Flory approximation, parallel to Eq. 2, to a curved geometry. As an example, consider a star polymer with f arms and radius R. The segment volume fraction within the star can be written, tp ss fNa3/R3, so that FjtU/kT per arm can be written as v(fN)2 a3/fR3, giving rise to a total free energy per arm ... 

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