Molar substitution

Substituting molar fractions X and molalities m for activities in the solid and in the liquid phase, respectively, we obtain... 

Strictly speaking, the letters in brackets represent activities, but we will usually follow the practice of substituting molar concentrations for activities in most calculations. Thus, if some participating species A is a solute, [A] is the concentration of A in moles per liter. If A is a gas, [A] in Equation 18-12 is replaced by p, the partial pressure of A in atmospheres. If A is a pure liquid, a pure solid, or the solvent, its activity is unity, and no term for A is included in the equation. The rationale for these assumptions is the same as that de.scribed in Section 9B-2, which deals with equilibrium-constant expressions. 

Substitute molarity into the equation for osmotic pressure to solve for x. 71 = MRT... 

We call this relationship the equilibrium-constant expression (or merely the equilibrium expression) for the reaction. The constant K, the equilibrium constant, is the numerical value obtained when we substitute molar equilibrium concentrations... 

Substituting molar volumes of elementary links for ratios of their molar masses to density of polymer and substituting Dual expression (t ) to Eqrration (6), get ... 

HEC is available in a wide range of viscosities (from 10 to 100,000 mPa s (=cP) in 2% aqueous solution at ambient temperature). It is soluble in cold and hot water or some mixtures of water and water-miscible organic solvents. The nonionic chemical structure and its solubility in both cold and hot water are the main advantages for the utilization of HEC. HPC has a thermal gel point like MC and it is thermoplastic. Because of its high level of substitution (molar substitution about 4) and its remarkable hydrophobic character it is soluble in a number of organic solvents as well as water. 

The high reactivity of the 5-position in 1.3-selenazoles toward electrophilic substitution was also observed on azocoupling. By reacting molar quantities of an aqueous solution of a diazonium salt with an ethanolic solution of a 2-arylamino selenazole. for example, the corresponding 2-arylamino-5 azoselenazoles are formed in a smooth reaction (100). They deposit from the deeply colored solution and form intenselv red-colored compounds after their recrystallization from a suitable solvent (Scheme 36l. 

The second molar equivalent of the alkyllithium adds to the alkylcopper to give a neg atively charged dialkyl substituted derivative of copper(I) called a dialkylcuprate It is formed as its lithium salt a lithium dialkylcuprate... 

Substituting the molarity and volume of titrant for moles, and rearranging gives... 

As in osmotic pressure experiments, polymer concentations are usually expressed in mass volume units rather than in the volume fraction units indicated by the Einstein equation. For dilute solutions, however, Eq. (8.100) shows that

partial molar volume of the polymer in solution, and M is the molecular weight of the polymer. Substituting this relationship for (pin Eq. (9.9)gives... 

Alkaline Catalysts, Resoles. Resole-type phenoHc resins are produced with a molar ratio of formaldehyde to phenol of 1.2 1 to 3.0 1. For substituted phenols, the ratio is usually 1.2 1 to 1.8 1. Common alkaline catalysts are NaOH, Ca(OH)2, and Ba(OH)2. Whereas novolak resins and strong acid catalysis result in a limited number of stmctures and properties, resoles cover a much wider spectmm. Resoles may be soHds or Hquids, water-soluble or -insoluble, alkaline or neutral, slowly curing or highly reactive. In the first step, the phenolate anion is formed by delocali2ation of the negative charge to the ortho and para positions. 

Nucleophilic Substitution Route. Commercial synthesis of poly(arylethersulfone)s is accompHshed almost exclusively via the nucleophilic substitution polycondensation route. This synthesis route, discovered at Union Carbide in the early 1960s (3,4), involves reaction of the bisphenol of choice with 4,4 -dichlorodiphenylsulfone in a dipolar aprotic solvent in the presence of an alkaUbase. Examples of dipolar aprotic solvents include A/-methyl-2-pyrrohdinone (NMP), dimethyl acetamide (DMAc), sulfolane, and dimethyl sulfoxide (DMSO). Examples of suitable bases are sodium hydroxide, potassium hydroxide, and potassium carbonate. In the case of polysulfone (PSE) synthesis, the reaction is a two-step process in which the dialkah metal salt of bisphenol A (1) is first formed in situ from bisphenol A [80-05-7] by reaction with the base (eg, two molar equivalents of NaOH),... 

The substitution of HPC is defined by the MS. Molar substitutions higher than approximately 3.5 are needed for solubiUty in water and organic solvents. 

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

Isothiazole has an absorption maximum in ethanol solution at 244 nm, with a molar absorptivity of 5200. This absorption occurs at a longer wavelength than with pyrazole or isoxazole, the displacement being due to the presence of the sulfur atom. A series of approximate additive wavelength shifts has been drawn up in Table 11 and this should enable prediction of UV maxima of isothiazoles with reasonable accuracy, even for multiply substituted compounds. The longest wavelength band results from a electronic... 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

Triazole has been prepared by the oxidation of substituted 1,2,4-triazoles, by the treatment of urazole with phosphorus pentasulfide, by heating equimolar quantities of formyl-hydrazine and formamide, by removal of the amino function of 4-amino-l,2,4-triazole, by oxidation of l,2,4-triazole-3(5)-thiol with hydrogen peroxide, by decarboxylation of 1,2,4-triazole-3(5)-carboxylic acid, by heating hydrazine salts with form-amide,by rapidly distilling hydrazine hydrate mixed with two molar equivalents of formamide, i by heating N,N -diformyl-hydrazine with excess ammonia in an autoclave at 200° for 24 hours, and by the reaction of 1,3,5-triazine and hydrazine monohydrochloride. ... 

Note that the brackets, [ ], refer to the concentration of the species. K,p is the solubility product constant hence [Cu " ] and [OH] are equal to the molar concentrations of copper and hydroxyl ions, respectively. The K p is commonly used in determining suitable precipitation reactions for removal of ionic species from solution. In the same example, the pH for removal of copper to any specified concentration can be determined by substituting the molar concentration into the following equation ... 

If an excess of butyllithium (2 5 1 molar ratio) is used during metalation, a mixture of butylated naphthyllithium compounds is formed Reactions of this mixture with electrophiles give a mixture ot 6 and 7-butyl-substituted hexa-fluoronaphthalene derivatives in respective ratios of 4 1 [38] (equation 16)... 

Diaminoquinoline also reacts with aldehydes in nitromethane. In a molar ratio of 1 1 it gave 2-substituted 106, and in a molar ratio of 1 2,1,2-disubstituted imidazo[4,5-/]quinolines 107 were formed (85IJC372, 82MI4). 

Biimidazole and bibenzimidazole with [(ri -2-RC3H )Pd(p-Cl)]2 (R = H, Me) taken in the 2 1 molar ratio in the presence of methanolic potassium hydroxide give complexes of the type 146 (83JCS(D)1729) and with [(ti -2-RC3H ) Pd(Mc2C0) ](C10 ) - 147. When the ratio of 2,2 -biimidazole or 2,2 -bibenz-imidazole and [(Ti -2-RC3H )Pd(p-Cl)]2 (R = H, Me) is 1 1, the homo-tetranuclear species 148 result. Heterotetranuclear palladium(II)-rhodium(I) complexes 149 (L2 = cod) follow from [(TiLcod)Rh(Hbim)] and [(ri -2-R-C3H )Pd(acac)]. They are readily carbonylated with complete substitution of... 

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