Conversions Involving Molar Quantities

1 Moles The rate of reaction is commonly expressed in terms of molar concentration, and thus it is important to have a method for expressing molar quantities in terms of component mass fractions. It was previously shown that the molar flow rate of a component i in a mixture may be expressed in terms of z, simply in terms of the molecular weight and mass flow rate of i 

The mass flow rate may be written in terms of Zj to give 

Similar expressions may be obtained for batch systems as well. The total molar flow rate of all components in a mixture is given by 

Substitution of Equation 9.4 into this expression gives This may be expressed in terms of W vgfz) to give 

2 Concentration The molar concentration of component i, c,, is expressed in terms of the molar flow rate, n and the total volumetric flow rate of the mixture Q,ot 

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U and V respectively. Systeme International (SI) units, described in Appendix B, are used extensively but not slavishly. Chemically convenient quantities such as the gram (g), cubic centimeter (cm ), and hter (L = dm =10 cm ) are still used where useful—densities in g cm , concentrations in mol L , molar masses in g. Conversions of such quantities into their SI equivalents is trivially easy. The situation with pressure is not so simple, since the SI pascal is a very awkward unit. Throughout the text, both bar and atmosphere are used. Generally bar = 10 Pa) is used when a precisely measured pressure is involved, and atmosphere = 760 Torr = 1.01325 X 10 Pa) is used to describe casually the ambient air pressure, which is usually closer to 1 atm than to 1 bar. Standard states for all chemical substances are officially defined at a pressure of 1 bar normal boiling points for liquids are still understood to refer to 1-atm values. The conversion factors given inside the front cover will help in coping with non-SI pressures. 

We ve seen the importance of the concept of the mole when dealing with chemical reactions involving macroscopic quantities of material. But generally it is not possible to measure the number of moles in a sample directly because that would imply that we can count molecules. Molar masses provide a crucial connection and allow us to convert from masses, which can be measured easily, to numbers of moles. The mass and the number of moles are really just two different ways of expressing the same information—the amount of a substance present. The molar mass functions much like a unit conversion between them, allowing us to go from... 

The dimensions of permeabiUty become clear after rearranging equation 1 to solve for P. The permeabiUty must have dimensions of quantity of permeant (either mass or molar) times thickness ia the numerator with area times a time iaterval times pressure ia the denomiaator. Table 1 contains conversion factors for several common unit sets with the permeant quantity ia molar units. The unit nmol/(m-s-GPa) is used hereia for the permeabiUty of small molecules because this unit is SI, which is preferred ia current technical encyclopedias, and it is only a factor of 2, different from the commercial permeabihty unit, (cc(STP)-mil)/(100 in. datm). The molar character is useful for oxygen permeation, which could ultimately involve a chemical reaction, or carbon dioxide permeation, which is often related to the pressure in a beverage botde. 

Conversion of coal to benzene or hexane soluble form has been shown to consist of a series of very fast reactions followed by slower reactions (2 3). The fast initial reactions have been proposed to involve only the thermal disruption of the coal structure to produce free radical fragments. Solvents which are present interact with these fragments to stabilize them through hydrogen donation. In fact, Wiser showed that there exists a strong similarity between coal pyrolysis and liquefaction (5). Recent studies by Petrakis have shown that suspensions of coals in various solvents when heated to 450°C produce large quantities of free radicals (. 1 molar solutions ) even when subsequently measured at room temperature. The radical concentration was significantly lower in H-donor solvents (Tetralin) then in non-donor solvents (naphthalene) (6). 

This scheme differs from the various systems in use in industry and academia in that it uses the mole instead of the cc(STP) to express the quantity of matter being transported, the pascal rather than the atmosphere or the cm. Hg. to express pressure, the meter rather than the mil, the inch, or the centimeter to express length, and the second rather than the day to express time. Our experience indicates that the existing variety of unit systems leads to confusion and that calculations of related physical properties such as permeabilities, diffusion coefficients, and solubilities are easier using the SI units. More modern measurement systems which detect permeants by means of the electrical currents generated by individual atoms are easier to analyze when one uses moles rather than cc(STP) to express the amount of matter undergoing transport. Applications involving the transport of mixed permeant species are also easier to deal with on a molar basis. Conversion tables between the SI units and customary units are provided on the SRM certificate and in the appropriate standards documents (4, 5). ... 

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