Measures of Composition

This book uses the term concentration to mean the molar density of a component, for example, moles of A per unit volume of the reacting mixture. In the International System of Units (SI) concentration is in moles per cubic meters where the moles are gram moles. Molarity is classically defined as moles per liter of solution and is a similar concentration measurement. Molality is classically defined as moles per kilogram of solvent (not of solution) and is thus not a standard measure of concentration. For gases at low pressure and moderate temperatures, partial pressures are sometimes used instead of concentrations since partial pressures are proportional to concentration for ideal gases. 

Other measures of composition such as mole fraction and mass fraction are less commonly used to express chemical reaction rates. Weight measurements are frequently used to prepare solutions or fill reactors. The resulting composition will have a known ratio of moles and masses of the various components, but the numerical value for concentration requires that the density be known. Good practice is to prepare solutions in mass units and then convert to standard concentration units based on the known or observed density of the solution under reaction conditions. To avoid ambiguity, modern analytical chemists frequently define both molarity and molality in weight units as moles per kilogram of solution or moles per kilogram of solvent. 

Sucrose, 342.3 g, is dissolved in one liter of water at room temperature. Calculate the composition by various measures. 

A word of caution involves the definition of mole. As indicated above, SI moles are gram moles, the mass in grams of 6.02 x 10 molecules. There is an inconsistency in the SI system of units that may cause problems when converting molar densities and molar flow rates to mass densities and mass flow rates. A point in the system with molar concentrations (i.e., molar densities) of a and b has a mass density of p = qMa + bMs, where Ma and Mb are the molecular weights of the two components. 

The resulting units on p are grams per cubic meter and must be divided by 1000 to 

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F.A. Reed, T. Batzinger, R.W. Reed, and S. Jonsson. Porosity measurement of composites using attenuation methods. Review of Progress in Quantitative Nondestructive Evaluation, 12, 1993. 

The Kellogg and DePriester charts and their subsequent extensions and generahzations use the molar average boiling points of the liquid and vapor phases to represent the composition effect. An alternative measure of composition is the convergence pressure of the system, which is defined as that pressure at which the Kvalues for aU the components in an isothermal mixture converge to unity. It is analogous to the critical point for a pure component in the sense that the two... 

Temperature is the hardest parameter to control in a fractionation system. It exhibits high process and measurement lag. Temperature can also be ambivalent as a measure of composition. Pressure changes are reflected quickly up and down the column. Temperature changes are not. It is typical to provide three-mode controllers for all temperature applications. 

Main use Measurement of composition and of trace-level impu-... 

An attempt to use the infrared spectrum of materials collected at the sea surface for a quantitative measure of composition has been made by Baier et al. [285]. They dipped a germanium crystal through the surface film, then ran an internal reflectance spectrum on the material clinging to the crystal. From the spectrum, they concluded that the bulk of the material present in the surface film was there as glycoproteins and proteoglycans. 

While the mole fraction is a natural measure of composition for solutions of metallic elements or alloys, the mole fraction of each molecule is chosen as the measure of composition in the case of solid or liquid mixtures of molecules.1 In ionic solutions cations and anions are not randomly mixed but occupy different sub-lattices. The mole fractions of the atoms are thus an inconvenient measure of composition for ionic substances. Since cations are mixed with cations and anions are mixed with anions, it is convenient for such materials to define composition in terms of ionic fractions rather than mole fractions. In a mixture of the salts AB and AC, where A is a cation and B and C are anions, the ionic fractions of B and C are defined through... 

Since dew point can be calculated from composition, direct determination of dew point for a particular hquefied petroleum gas sample is a measure of composition. It is, of course, of more direct practical value, and if small quantities of higher-molecular-weight material are present, it is preferable to use a direct... 

For solutions for which the molality is a convenient measure of composition, it has been suggested [6] that can be expressed as a polynomial in m... 

The small conversions needed in differential reactors require more accurate measurements of composition than the other reactor types. 

FIGURE 11.74 Schematic diagram of aerosol particle mass spectrometer for measurement of composition of continuous beams of volatile and semivolatile particles (graciously provided by P. Zie-mann, 1998). 

The variables that need to be controlled in chemical processing are temperature, pressure, liquid level, flow rate, flow ratio, composition, and certain physical properties whose magnitudes may be influenced by some of the other variables, for instance, viscosity, vapor pressure, refractive index, etc. When the temperature and pressure are fixed, such properties are measures of composition which may be known exactly upon calibration. Examples of control... 

There are numerous properties of materials which can be used as measures of composition, e.g. preferential adsorption of components (as in chromatography), absorption of electromagnetic waves (infra-red, ultra-violet, etc.), refractive index, pH, density, etc. In many cases, however, the property will not give a unique result if there are more than two components, e.g. there may be a number of different compositions of a particular ternary liquid mixture which will have the same refractive index or will exhibit the same infra-red radiation absorption characteristics. Other difficulties can make a particular physical property unsuitable as a measure of composition for a particular system, e.g. the dielectric constant cannot be used if water is present as the dielectric constant of water is very much greater than that of most other liquids. Instruments containing optical systems (e.g. refractometers) and/or electromechanical feedback systems (e.g. some infra-red analysers) can be sensitive to mechanical vibration. In cases where it is not practicable to measure composition directly, then indirect or inferential means of obtaining a measurement which itself is a function of composition may be employed (e.g. the use of boiling temperature in a distillation column as a measure of the liquid composition—see Section 7.3.1). 

Online measurements of composition would be very appreciated, because composition is the most important variable. Unfortunately, direct measurements of the amount of a single component can be obtained only in a few cases, and typically for gaseous system, an example being the measurement of oxygen based on its paramagnetism. In fact, liquid phase systems are usually made out of components of similar chemical structure, and these must be separated before measuring their quantity. 

Thus, online measurements of composition are usually limited to some overall property. A typical example is pH, defined as the absolute value of the logarithm of the molar concentration (or, more exactly, activity) of hydrogen ion pH can be measured by exploiting the electric potential established between two proper electrodes immersed in the sample fluid, usually a glass membrane electrode and a reference electrode [15], Notwithstanding the temperature dependence and the alkaline error (at high pH, a marked sensitivity to the effect of Na+ and of other monovalent... 

Since the SF is a ratio of ratios, any measure of composition (mole fraction, mass fraction, concentration, etc.) can be used in Equation 7.1 as long as one consistently uses the same measure for both upstream and downstream phases in contact with the membrane. Locally within a module, the ratio of compositions leaving the downstream face of a membrane equals the ratio of the transmembrane fluxes of A vs. B. Local fluxes of each component are determined by relative transmembrane driving forces and resistances acting on each component. The ratio of the feed compositions in the denominator provides a measure of the ratio of the respective driving forces for the case of a negligible downstream pressure. This form normalizes the SF to provide a measure of efficiency that is ideally independent of the feed composition. 

Since Ki is expressed as a ratio, any consistent measure of composition in the membrane and external phases may be used in Equation 7.2. When K> 1, the membrane acts as a concentrator that attracts component i from the external phase and makes it available at the membrane surface for transmembrane movement. Intermolecular forces of solvation and mixing that are responsible for the partitioning process may be entropic as well as enthalpic in origin. The balance of these forces acting between the membrane and external phase can cause either a higher or lower concentration of a given solute inside the membrane relative to the external phase. If the tendency to enter the membrane is negligible, the partition coefficient approaches zero, that is, Kj —> 0. 

If one is performing CMBs of an area in which particulate emissions from coal combustion are dominated by those from one to several plants, it is obviously desirable to use a coal component based on measurements of compositions of the particles released by those specific plants, preferably particles collected in their plumes. However, as those data are rarely available, we have placed data from as many multielement studies as possible in the library so the user can construct a component from results of the most appropriate studies that have been done. 

If the feed composition and the column pressure are constant, temperature can be used as an indirect measure of composition. When the bottom product composition is being controlled, the temperature sensor is located in the lower half of the column and when overhead composition is controlled, in the upper half of the column. The temperature sensor should be located on a tray that strongly reflects changes in composition (Figure 2.84). When two compounds of relatively close vapor pressures are to be separated, two temperatures or a temperature difference can be used instead of a single sensor. This configuration can also be used to eliminate the effects of column pressure variations. 

RBS provides a measure of composition-depth profile for elements. It uses a beam of high voltage helium ions to interact with the sample. The sample atoms recoil in a semi-classical collision, such that those ions reflected lose an amount of energy characteristic of the target atom and the amount of material traversed by the reflected ion. However, this method is not good for light elements such as H and He. 

With the use of the MCs+ technique to reduce matrix effects in SIMS, Gao et al measured the composition of InxGai.xN alloys and confirmed the validity of this technique with the RBS method [12], It was shown that the SIMS-MCs+ method can provide very accurate measurements of composition on complex structures and devices [13],... 

Investigations by DLS measurements of composite particles indicated that the original thermosensitive properties of the PNIPA network are not suppressed by the incorporation of metal particles into the network. That is, the shrinking and re-swelling of microgel is not hampered by the incorporation of metal nanoparticles into the network. The metal composite particles show similar volume transition temperature as the carrier particle at 32°C, which is in excellent agreement with previous findings on these systems as shown in Fig. 7 [64, 65], This indicates... 

In both of these schemes, the feed is flow controlled and the overhead vapor flow is adjusted for pressure control. The arrangement shown in Figure 3.14(A) is more common, with the level controller adjusting the bottom flow and the temperature controller adjusting the steam flow. Note that the temperature is an inferred measure of composition. This inferred composition control is achieved by adjusting the steam flow such that the material balance has more or less vapor removed overhead. 

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