Molar basis

Since we are explicitly interested in the difference in the sizes of solvent and solute molecules, it is more appropriate to express the values of AU on a per unit volume basis rather than on a molar basis. Accordingly, in Eq. (8.41) we replace the total number of sites N by the total volume of the mixture V and write... 

Acrylate and methacrylate polymerizations are accompanied by the Hberation of a considerable amount of heat and a substantial decrease in volume. Both of these factors strongly influence most manufacturing processes. Excess heat must be dissipated to avoid uncontrolled exothermic polymerizations. In general, the percentage of shrinkage decreases as the size of the alcohol substituent increases on a molar basis, the shrinkage is relatively constant (77). 

P-Endorphin. A peptide corresponding to the 31 C-terminal amino acids of P-LPH was first discovered in camel pituitary tissue (10). This substance is P-endorphin, which exerts a potent analgesic effect by binding to cell surface receptors in the central nervous system. The sequence of P-endorphin is well conserved across species for the first 25 N-terminal amino acids. Opiates derived from plant sources, eg, heroin, morphine, opium, etc, exert their actions by interacting with the P-endorphin receptor. On a molar basis, this peptide has approximately five times the potency of morphine. Both P-endorphin and ACTH ate cosecreted from the pituitary gland. Whereas the physiologic importance of P-endorphin release into the systemic circulation is not certain, this molecule clearly has been shown to be an important neurotransmitter within the central nervous system. Endorphin has been invaluable as a research tool, but has not been clinically useful due to the avadabihty of plant-derived opiates. 

The optimum modulus occurs at about a 2 1 weight ratio of OTOS to OBTS. Similar optimums have been observed with other accelerator combinations. The examples shown in Figure 4 are calculated from regression equations developed from designed experiments in a black-filled natural mbber compound. On a molar basis, the synergistic accelerator complex appears to consist of two dithiocarbamate ligands and one mercaptobenzothiazole moiety, as shown in stmcture (15) (14). 

For optimum disinfection in swimming pools, the pH is maintained in the 7.2 to 7.6 range where HOCl represents 69—47% of the FAC. By contrast, the HOBr fraction varies from 97 to 93%. Nevertheless, the bactericidal effectiveness of HOCl is greater than that of HOBr below pH 8 on a molar basis (8). However, above pH 8 the superiority of HOCl is overcome by the fact that the concentration of C10 exceeds that of HOCl above pH 7.5, whereas the concentration of HOBr stiU exceeds that of BrO up to pH 8.7. Hypochlorous acid is a better viricide than HOBr, but HOBr is more effective against certain algae (9). 

The same chemical mechanisms and driving forces presented for phenol-formaldehyde resins apply to resorcinol resins. Resorcinol reacts readily with formaldehyde to produce resins (Fig. 2) which harden at ambient temperatures if formaldehyde is added. The initial condensation reaction, in which A-stage liquid resins are formed, leads to the formation of linear condensates only when the resorcinol/formaldehyde molar ratio is approximately 1 1 [119]. This reflects the reactivity of the two main reactive sites (positions 4 and 6) of resorcinol [120]. However, reaction with the remaining reactive but sterically hindered site (2-positiori) between the hydroxyl functions also occurs [119]. In relation to the weights of resorcinol-formaldehyde condensates which are isolated and on a molar basis, the proportion of 4- plus 6-linkages relative to 2-linkages is 10.5 1. However, it must be noted that the first-mentioned pair represents two condensa-... 

The condensation reaction of resorcinol with formaldehyde, on an equal molar basis and under identical conditions, also proceeds at a rate which is approximately 10 to 15 times faster than that of the equivalent phenol-formaldehyde system [16-18,123]. The high reactivity of the resorcinol-formaldehyde system renders it impossible to have these adhesives in resol form. Therefore, only resorcinol-formaldehyde novolaks, i.e. resins not containing methylol groups can be produced. All the resorcinol nuclei are linked together through methylene... 

It is more common to express chemical quantities on a molar basis, and Eq. (5-31) becomes... 

The relative amounts of the individual components (or species) making up a mixture or solution can be expressed in a variety of ways, depending upon the system at hand. A volumetric, mass, or molar basis may be employed to represent the compositions of multicomponent systems. 

Molar Basis. The mole fraction (x.) of a component i in a multicomponent mixture is defined as... 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

For a nonreactive system, the material balance may be done either on a mass or on a molar basis. 

In an extensive study by Read et al. [93], 10 anionic surfactants were evaluated for their ability to remove pyritic sulfur and ash from ultrafine Illinois no. 5 coal by flotation processes. The authors observed that of the commercially available surfactants, sodium dodecyl sulfate was the most effective on either a weight or a molar basis, followed by a linear AOS (average molweight 272) and alkylpolyethoxylated sulfonates. Of the noncommercial surfactants tested, -(E -b-dodecene-b-suIfonate (f0) was the most effective and better than any commercial surfactant on a dosage/recovery basis. 

The gas phase mass transfer coefficient for the absorption of ammonia into water from a mixture of composition NHj 20%, N2 73%, Hj 7% is found experimentally to be 0.030 m/s. What would you expect the transfer coefficient to be for a mixture of composition NH3 5%, N2 60%, Hj 35% All compositions are given on a molar basis. The total pressure and temperature are die same in both cases. The transfer coefficients are based on a steady-state film model and the effective film thickness may be assumed constant. Neglect the solubility of Ny and Hi in water. 

The main reason for this is that the polymer molecules are extremely large compared with those of the solvent. To take an extreme example, consider 78 g of benzene injected into a perfectly crosslinked tractor tyre. On a molar basis, this is an extremely dilute solution one molecule of solute in one mole of solvent. Yet, because of the extreme difference in size between the two types of molecule involved, the behaviour of such a system is nothing like that of a dilute solution. 

Similar expressions can be written for third-order reactions. A reaction whose rate is proportional to [A] and to [B] is said to be first order in A and in B, second order overall. A reaction rate can be measured in terms of any reactant or product, but the rates so determined are not necessarily the same. For example, if the stoichiometry of a reaction is2A-)-B—>C- -D then, on a molar basis, A must disappear twice as fast as B, so that —d[A]/dt and -d[B]/dr are not equal but the former is twice as large as the latter. 

A feed stream containing 40 mole percent p-xylene and 60 mole percent chlorine was fed to the reactor. The results of one experiment in a batch reactor gave the following results on a molar basis ... 

This example expresses all the performance measures on a molar basis. The mass yield of l,4-dimethyl-2,3-dichlorobenzene sounds a bit better. It is 0.541 lb of the desired product per pound of xylene charged. 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

In this article, all numerical comparisons of relative sweetness are given on a molar basis. 

Wine and by-products Cinnamic acid derivatives, anthocyanins and flavanols dominate (10 to 20 J,M gallic acid equivalents) Oil-in-water emulsion (dressing model) Red wine yields better protection, but phenols in white and rose wine seem more efficient on a molar basis Sanchez-Moreno et al., 2000... 

The mature domain contains a very high percentage of the aromatic amino acids phenylalanine and tyrosine (>10% on a molar basis). 

The Mg content of hydrothermally altered volcanic rocks is reflected by the extent of seawater-volcanic rock interaction at elevated temperatures, because it has been experimentally and thermodynamically determined that nearly all of the Mg in seawater transfer to volcanic rocks, owing to the reaction of the cycled seawater with volcanic rocks at elevated temperatures (Bischoff and Dickson, 1975 Mottl and Holland, 1978 Wolery, 1979 Hajash and Chandler, 1981 Reed, 1983 Seyfried, 1987). It has been shown that the CaO content of hydrothermally altered midoceanic ridge basalt is inversely correlated with the MgO content with a slope of approximately — 1 on a molar basis (Mottl, 1983). This indicates that Ca of basalt is removed to seawater and Mg is taken up from seawater by the formation of chlorite and smectite during the seawater-basalt interaction. This type of reaction is simply written as ... 

Chemical production rates are often expressed on a molar basis but can be easily converted to mass flow quantities (kg/s). The mass balance equation can then be expressed as... 

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