Elemental balance

Multiply each element balance by Li, a. Lagrange multipher ... 

The coefficients a, b and c, which appear throughout these balance equations describe the extent to which these reactions occur relative to the growth reaction (ie 1 + o) and are written taken into account elemental balances for each reaction. 

In this section we will consider the energetics of exopolysaccharide production in some detail. We will see how chemostat (substrate limited) derived yield coefficients and slfbstrate elemental balances can be used to determine how the nature of the substrate influences... 

Moles of the remaining components are found using elemental balance. The method has been discussed, so now we make a balance for each element. 

K.25 The following redox reactions are important in the refining of certain elements. Balance the equations and in each case, write the name of the source compound of the element (in bold face) and the oxidation state in that compound of the element that is being extracted ... 

Chemical Chemical differences Chemical element balance... 

More detailed statistical analyses (chemical element balance, principal component analysis and factor analysis) demonstrate that soil contributes >50% to street dust, iron materials, concrete/cement and tire wear contribute 5-7% each, with smaller contributions from salt spray, de-icing salt and motor vehicle emissions (5,93-100). A list is given in Table VII of the main sources of the elements which contribute to street dust. 

Note that the elemental balances do not involve additional reaction rate terms since the elements are not changed by chemical reaction. 

If we neglect the case of nuclear reactions, this means a balance must be run over every chemical element that is present. However, when no chemical reactions are occurring in a given unit, a component rather than an element balance is run. This is then checked by running an over-all balance to determine if the total amount of material that enters each unit also leaves each unit. 

These yields are also given on the basis of 100 g of original dry coal before fractionation. The bottom line of the table shows the mass of each fraction obtained from 100 g of dry coal. For every 100 g of original dry coal an additional 100 g of extraneous material was present. Elemental balances and other evidence (]J showed this to be made up almost entirely of phenol chemically combined with the coal material, with traces present of residual solvent associated with the fractions as a result of the coal preparation and fractionation scheme. Note that with fractions A and B no solid residue was obtained. 

Watson, J. G., Chemical element balance receptor model methodology for assessing the sources of fine and total suspended particulate matter in Portland, Oregon, PhD Thesis, Oregon Graduate Center, Beaverton, Oregon, 1979. 

Equation (A) or (B) stems from the fact that the two element balances involve three quantities related to amounts of the species. These balances may be written as follows ... 

A complex reacting system is defined as one that requires more than one chemical equation to express the stoichiometric constraints contained in element balances. In such a case, the number of species usually exceeds the number of elements by more than 1. Although in some cases a proper set of chemical equations can be written by inspection, it is useful to have a universal, systematic method of generating a set for a system of any complexity, including a simple system. Such a method also ensures the correct number of equations (R), determines the number (C) and a permissible set of components, and, for convenience for a very large number of species (to avoid the tedium of hand manipulation), can be programmed for use by a computer. 

A proper set of chemical equations provides an aid in chemical book-keeping to determine composition as reaction proceeds. This is the role of chemical stoichiometry. On the one hand, it prescribes elemental balances that must be obeyed as constraints on reaction on the other hand, in prescribing these constraints, it reduces the amount of other information required (e g., from kinetics) to determine the composition. 

One of the most useful tools for design and analysis of performance is the balance equation. This type of equation is used to account for a conserved quantity, such as mass or energy, as changes occur in a specified system element balances and stoichiometry, as discussed in Section 1.4.4, constitute one form of mass balance. 

Estimation through elemental balances Anaerobic bioreactor parameters estimation [81]... 

To illustrate the application of data reconciliation to linear systems, we will consider the problem presented by Ripps (1965). Four mass flows are measured, two entering and two leaving a chemical reactor. Three elemental balances are considered ... 

Give yourself 2 points for the answer shown above, or for the coefficients 1, 9/2, 6, and 7. Give yourself 1 point if you have one or more, not all, of the elements balanced. 

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