Simple Methods

There are several models available for calculating the water content of natural gas. Only a few of them will be examined here. 

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Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

A simple method to achieve this is based on the fact that for any value of R there is a maximum asymptotic value for P, say, P axi which is given as Ft tends to - c and is given by ... 

The Parachor is a parameter used to determine the interfacial tension. It can be estimated by a simple method proposed by Quayle in 1953 ... 

Calculation of the conditions of hydrate formation is generally accomplished by software employing the Parrish and Prausnitz (1972) model. It is difficult to predict the conditions by a simple method. 

Pemberton J E, Bryant M A, Sobooinski R L and Joa S L 1992 A simple method for determination of orientation of adsorbed organios of low symmetry using surfaoe-enhanoed Raman soattering J. Rhys. Chem. 96 3776-82... 

Cyclic voltammetry provides a simple method for investigating the reversibility of an electrode reaction (table Bl.28.1). The reversibility of a reaction closely depends upon the rate of electron transfer being sufficiently high to maintain the surface concentrations close to those demanded by the electrode potential through the Nemst equation. Therefore, when the scan rate is increased, a reversible reaction may be transfomied to an irreversible one if the rate of electron transfer is slow. For a reversible reaction at a planar electrode, the peak current density, fp, is given by... 

A simple method of improvmg the effieieney of test partiele insertion [106. 107. 108 and 109] involves dividing die simulation box into small eubie regions, and identifying those whieh would make a negligible eontribution to the Widom fonnula, due to overlap with one or more atoms. These eubes are exeluded from the sampling, and a eorreetion applied afterwards for the eonsequent bias. 

The mean field teclmique is one of the most robust and simple methods used to handle larger molecules in gas and liquid enviromnents [M, 134. 135 and 136]. The basic premise of all mean-field methods is that the fiill wavefiinction represents N very weakly coupled modes (2 ) and can be approximated as... 

Jayaram, B., Beveridge, D. L. A simple method to estimate free energy from molecular simulation Renormalization on the unit interval. J. Phys. Chem. 94 (1990) 7288-7293... 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

Bashin A A and K Namboodiri 1987. A Simple Method for the Calculation of Hydration Enthalpies c Polar Molecules with Arbitrary Shapes. Journal of Physical Chemistry 91 6003-6012. 

The source of carbon dioxide. The main requirement of the carbon dioxide supply is that it shall be air-free. It is, however, almost impossible to generate carbon dioxide, by any fairly simple method, so that it is completely free from air. Nevertheless, it is possible to obtain the gas sufficiently pure so that no serious error is introduced into the determination. 

Two simple methods for the semi-micro estimation of halogens are available, (a) the Carius method, and (b) the Parr bomb method. It should be emphasised that there are other methods available for these estimations on the true micro scale, but they do not lend themselves, by virtue of the balances, apparatus and manipulation required, to semi-micro work, or to the intermittent usage which class-work necessarily entails. 

The Arndt-Eistert reaction is a comparatively simple method for converting an acid Into its next higher homologue or to a derivative of the homologous acid, such as an amide or an ester. The overall yield is generally good. The reaction... 

Now distil the filtrate A) and collect the distillate as long as it is acid to litmus. Should any solid separate out in the distilhng flask during the distUlation, add more water to dissolve it. Set aside the residue B) in the flask. Identify the volatile acid in the distihate. A simple method is to just neutralise it with sodium hydroxide solution, evaporate to dryness and convert the residual sodium salt into the S-benzyl-iao-thiuTonium salt (Section 111,85,5). 

A simple method for predicting electronic state crossing transitions is Fermi s golden rule. It is based on the electromagnetic interaction between states and is derived from perturbation theory. Fermi s golden rule states that the reaction rate can be computed from the first-order transition matrix and the density of states at the transition frequency p as follows ... 

Arelatively simple method for alleviating some of the nonphysical behaviors caused by imposing a nonbonded cutoff is to use a potential switching function (equation 14). 

It is often important in practice to know when a process has changed sufficiently so that steps may be taken to remedy the situation. Such problems arise in quality control where one must, often quickly, decide whether observed changes are due to simple chance fluctuations or to actual changes in the amount of a constituent in successive production lots, mistakes of employees, etc. Control charts provide a useful and simple method for dealing with such problems. 

Sketching an Acid—Base Titration Curve To evaluate the relationship between an equivalence point and an end point, we only need to construct a reasonable approximation to the titration curve. In this section we demonstrate a simple method for sketching any acid-base titration curve. Our goal is to sketch the titration curve quickly, using as few calculations as possible. 

This experiment demonstrates the chemical limitations to Beer s law using the NO2-N2O4 equilibrium as an example. Blanco, M. Iturriaga, H. Maspoch, S. et al. A Simple Method for Spectrophotometric Determination of Two-Components with Overlapped Spectra, /. Chem. Educ. 1989, 66, 178-180. 

Weber, P. L. Buck, D. R. Capillary Electrophoresis A Past and Simple Method for the Determination of the Amino Acid Composition of Proteins, /. Chem. Educ. 1994, 71, 609-612. This experiment describes a method for determining the amino acid composition of cyctochrome c and lysozyme. The proteins are hydrolyzed in acid, and an internal standard of a-aminoadipic acid is added. Derivatization with naphthalene-2,3-dicarboxaldehyde gives derivatives that absorb at 420 nm. Separation is by MEKC using a buffer solution of 50 mM SDS in 20 mM sodium borate. 

Figure 10.13 shows such plots of z versus D/X, where D is r for random coils, R for spheres and disks, and L for rods. More detailed theories permit these curves to be extended to larger values of than is justified by consideration of Eq. (10.97) alone. In the following example we illustrate an application of this simple method for estimating particle dimensions. 

Rapid Approximate Design Procedure. Several simplified approximations to the rigorous solutions have been developed over the years (57—60), but they aU. remain too compHcated for practical use. A simple method proposed in 1989 (61,62) uses a correction factor accounting for the effect of axial dispersion, which is defined as (57)... 

The use of flame retardants came about because of concern over the flammabiUty of synthetic polymers (plastics). A simple method of assessing the potential contribution of polymers to a fire is to examine the heats of combustion, which for common polymers vary by only about a factor of two (1). Heats of combustion correlate with the chemical nature of a polymer whether the polymer is synthetic or natural. Concern over flammabiUty should arise via a proper risk assessment which takes into account not only the flammabiUty of the material, but also the environment in which it is used. 

The best approach is to have a computer program check a series of pressure drops and see how energy requirements decrease as surface increases. If this Option is not available, the following simple method can be used to obtain specification sheet values. Start with a pressure drop of 6.9 kPa (1 psi), and anolv three correction factors, F and F, as follows. 

On the other hand, wet chlorination of refinery slimes has proven to be a rapid and simple method of obtaining high extractions of selenium from slimes. A simple wet chlorination flow sheet is shown in Figure 3. Slimes chlorination per se is not a simple deselenization operation, but rather a process wherein virtually all the constituents of slimes which form soluble chlorides report as a complex solution of mixed chlorides. Thus the use of wet chlorination requires a complete change in the process to recover the metal values in slimes. The first plant to use wet chlorination of slimes was started by Kennecott (Salt Lake City, Utah) in 1995. 

A number of substances, such as the most commonly used sulfur dioxide, can reduce selenous acid solution to an elemental selenium precipitate. This precipitation separates the selenium from most elements and serves as a basis for gravimetry. In a solution containing both selenous and teUurous acids, the selenium may be quantitatively separated from the latter by performing the reduction in a solution which is 8 to 9.5 W with respect to hydrochloric acid. When selenic acid may also be present, the addition of hydroxylamine hydrochloride is recommended along with the sulfur dioxide. A simple method for the separation and deterrnination of selenium(IV) and molybdenum(VI) in mixtures, based on selective precipitation with potassium thiocarbonate, has been developed (69). 

Ash is a measure of residual sodium acetate. A simple method consists of dissolving the PVA in water, diluting to a known concentration of about 0.5 wt %, and measuring the electrical conductivity of the solution at 30°C. The amount of sodium acetate is estabUshed by comparing the result to a cahbration curve. A more lengthy method involves the extraction of the PVA with methanol using a Soxhlet extractor. The methanol is evaporated and water is added. The solution is titrated using hydrochloric acid in order to determine the amount of sodium acetate. 

Alcohols. The direct synthesis of esters by dehydrogenation or oxidative hydrogenation of alcohols offers a simple method for the preparation of certain types of esters, such as ethyl acetate (96—98) ... 

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