Chemical equations quantitative information

One of the limitations of dimensional similitude is that it shows no direct quantitative information on the detailed mechanisms of the various rate processes. Employing the basic laws of physical and chemical rate processes to mathematically describe the operation of the system can avert this shortcoming. The resulting mathematical model consists of a set of differential equations that are too complex to solve by analytical methods. Instead, numerical methods using a computerized simulation model can readily be used to obtain a solution of the mathematical model. 

The balanced equation represents a chemical reaction. It not only identifies the reactants and the products, but also gives quantitative information on the ratios of all substances involved in the reaction (Section 8.1). 

As you already know, the chemical equation provides a variety of qualitative and quantitative information essential for the calculation of the combining weights (mass) of materials involved in a chemical process. Take, for example, the combustion of heptane as shown below. What can we learn from this equation ... 

A chemical equation for a reaction must be balanced before useful quantitative information can be obtained about the reaction. Balancing an equation ensures that the same number of atoms of each element appear on both sides of the equation. Many chemical equations can be balanced by trial and error, although some will involve more trial than others. 

A balanced equation contains a wealth of quantitative information relating individual chemical entities, amounts of chemical entities, and masses of substances. It is essential for all calculations involving amounts of reactants and products if you know the number of moles of one substance, the balanced equation tells you the number of moles of all the others in the reaction. 

For many purposes this equation is too general for example, when there is some physical or chemical knowledge or suspicion of the qualitative form of the electronic structure. In these cases the solutions of the Hartree-Fock equations are often required simply to confirm this knowledge and to provide quantitative information about the energetics and distributions of the electrons. 

A number of chemical processes can be represented by stepwise solutions of equation (5), by choosing particular pathways (or reaction coordinates ) in the laboratory space of the classical PCB. In actual calculations, a finitedimensional manifold defined by selected electronic diabatic functions may suffice to obtain qualitative and semi-quantitative information. (The reader is referred to Refs. [10-13] for specific examples.) We refer to this as the quantum-classical (QC) model. The classical PCB can be used to localize possible reaction events by manipulating charges in laboratory space. 

We use the quantitative information inherent in chemical formulas and equations together with the mole concept to predict the amounts of substances consumed or produced in chemical reactions. 

It is not possible to count individual atoms or molecules, but we can indirectly determine their numbers if we know their masses. So, if we are to calculate amounts of reactants needed to obtain a given amount of product, or otherwise extrapolate quantitative information from a chemical equation or formula, we need to know more about the masses of atoms and molecules. 

QUANTITATIVE INFORMATION FROM BALANCED EQUATIONS AND LIMITING REACTANTS (SECTIONS 3.6 AND 3.7) The mole concept can be used to calculate the relative quantities of reactants and products in chemical reactions. The coefficients in a balanced equation give the relative numbers of moles of the reactants and products. To calculate the number of grams of a product from the number of grams of a reactant, first convert grams of reactant to moles of reactant. Then use the coefficients in the balanced equation to convert the nmnber of moles of reactant to moles of product Finally, convert moles of product to grams of product... 

To illustrate some of the quantitative information that may be obtained from chemical equations, consider the calcination of limestone (calcium carbonate, CaCOj) to make quicklime (CaO) for water treatment (Figure 5.4) ... 

Chemical equations are very useful in doing quantitative chemical work. The arrow in a balanced chemical equation is like an equal sign. And the chemical equation as a whole is similar to an algebraic equation in that it expresses an equality. Let s examine some of the quantitative information revealed by a chemical equation. 

Intsrprsting ChGmical Equations This representation of the reaction of hydrogen and chlorine to yield hydrogen chloride shows several ways to interpret the quantitative information of a chemical reaction. ... 

We have seen that a chemical equation provides useful quantitative information about a chemical reaction. However, there is also important information that is not provided by a chemical equation. For instance, an equation gives no indication of whether a reaction will actually occur. 

What quantitative information is revealed by a chemical equation ... 

Chemical equations also can provide quantitative information, which means that it is possible to tell how much of a reactant or a product is involved. To do that, we assume that each symbol and formula present in the equation represents exactly one atom, one molecule, or one formula unit of the element or compound. It is possible to then indicate two or more atoms, molecules, or formula units by placing coefficients in front of each of the symbols or formulas, such that the number of total atoms of each element is the same on both sides. Such an equation is said to be balanced. Using our water formation example, the following represents a balanced equation ... 

The kinetic chemical mass transfer coefficient for dissolution of immobile packets of nonaqueous phase liquids (NAPLs) in porous media is relevant to the subject of pore water leaching of surface soils. Equation 15.8 defines the mass transfer coefficient for NAPL dissolution, used to describe the transfer of chemicals from the immobile phase due to downward percolating porewaters. Much quantitative information on the subject of NAPL leaching in groundwater has been produced in the last two decades and is the subject of Part 2 of Chapter 15 titled Mass Transfer Coefficients in Porewater Adjacent to Nonaqueous Liquids and Particles the following is a review of the contents of that section pertaining to NAPL dissolution in ground water. 

If there are specific data germane to the assumption of dose-additivity (e g., if two compounds arc present at the same site and it is known that the combination is five times more toxic than the sum of the toxicitics for the two compounds), then tire development of the hazard index should be modified accordingly. The reader can refer to the EPA (1986b) mi.xiure guidelines for discussion of a hazjird index equation that incorporates quantitative interaction data. If data on chemical interactions are available, but arc not adequate to support a quantitative assessment, note the information in the assumptions being documented for the risk assessment. 

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