Quantitative Information from Chemical Equations

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  

We could now verbalize this equation as follows Two molecules of hydrogen and one molecule of oxygen react to produce two molecules of water.  

All chemical equations can be balanced. In Section 8.2.3, we will discuss the process of how simple chemical equations may be balanced. First, we need to understand why we must balance these equations. 

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QUANTITATIVE INFORMATION FROM BALANCED EQUATIONS 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. 

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... 

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. 

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) ... 

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 ... 

The chemical engineer must have a thorough knowledge of the principles of chemical engineering to use the quantitative data obtained from fundamental. equations. Standard reference textbooks develop these principles in sufficient clarity for study purposes. Handbooks furnish information of a fundamental and an applied nature. Compilation of data can be found in the chemistry and physics handbooks in addition to the various engineering handbooks. Consult your technical librarian for a complete list of published books in this area of engineering, the Additional Selected References for each chapter at the back of the book, particularly the process-data section of Chap. 3. 

Extraction of quantitative chemical information from SECM requires a mathematical model of the interaction of the tip and substrate. Such modeling typically involves numerical solution of a reaction-diffusion equation with the boundary conditions appropriate to the interfacial kinetics. Simulation of SECM experiments is computationally much more demanding than for standard electrochemical experiments (discussed in Chapter 1.3). This is because diffusion in at least two dimensions must be considered and the discontinuity in the boundary condition between the tip metal and insulating sheath necessitates a fine mesh. 

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. 

Chemical composition analysis complementing the microstructural information obtained from EM is known as analytical EM (AEM). Important compositional variations or non-stoichiometry in a material which is seemingly phase pure or stoichiometric by the criterion of bulk diffraction techniques and compositions of surface layers can be revealed using AEM. For quantitative microanalysis a ratio method for thin crystals (Cliff and Lorimer 1975) is used, given by the equation ... 

X-variables. This leads to the presence of model residuals (E in Equations 8.19 and 8.35). The residuals of the model can be used to indicate the nature of unmodeled information in the calibration data. For process analytical spectroscopy, plots of individual sample residuals versus wavelength ( residual spectra ) can be used to provide some insight regarding chemical or physical effects that are not accounted for in the model. In cases where a sample or variable outlier is suspected in the calibration data, inspection of that sample or variable s residual can be used to help determine whether the sample or variable should be removed from the calibration data. When a model is operating on-line, the X-residuals of prediction (see Equation 8.55) can be used to determine whether the sample being analyzed is appropriate for application to a quantitative model (see Section 8.4.3). In addition, however, one could also view the prediction residual vector ep as a profile (or residual spectrum ) in order to provide some insight into the nature of the prediction sample s inappropriateness. 

An alternative, at least semi-quantitative method to follow changes in biomass composition is infrared (IR) spectroscopy [22]. From dried samples of microbial cells, IR spectra can be obtained which contain information on all major cell components. The spectra are analysed as a multi-component mixture Characteristic bands in the spectra are identified, the extinction coefficients for each component (protein, carbohydrate, lipid, and nucleic acids) at each band are determined, and the concentrations are calculated by a system of linear equations. The method gives results on all major cell components simultaneously, and is relatively quick and easy to perform, compared to the chemical analysis methods. For details see Sect. 8.4 below. 

Heterogeneously catalyzed reactions are usually studied under steady-state conditions. There are some disadvantages to this method. Kinetic equations found in steady-state experiments may be inappropriate for a quantitative description of the dynamic reactor behavior with a characteristic time of the order of or lower than the chemical response time (l/kA for a first-order reaction). For rapid transient processes the relationship between the concentrations in the fluid and solid phases is different from those in the steady-state, due to the finite rate of the adsorption-desorption processes. A second disadvantage is that these experiments do not provide information on adsorption-desorption processes and on the formation of intermediates on the surface, which is needed for the validation of kinetic models. For complex reaction systems, where a large number of rival reaction models and potential model candidates exist, this give rise to difficulties in model discrimination. 

The indirect reduction of many organic substrates, in particular alkyl and aryl halides, by means of radical anions of aromatic and heteroaromatic compounds has been the subject of numerous papers over the last 25 years [98-121]. Many issues have been addressed, ranging from the exploration of synthetic aspects to quantitative descriptions of the kinetics involved. Saveant et al. coined the expression redox catalysis for an indirect reduction, in which the homogeneous reaction is a pure electron-transfer reaction with no chemical modification of the mediator (i.e., no ligand transfer, hydrogen abstraction, or hydride shift reactions). In the following we will consider such reactions and derive the relevant kinetic equations to show the kind of kinetic information that can be extracted. 

The approach, however, is subject to four limitations. (1) The specific skeleton or functional group may not exist in the database. (2) The database may not include sufficient information to assess steric effects that can lead to nonadditivity within an available series. (3) Solvent effects, to be described in Section 3-3, are not fully taken into consideration. (4) Coupling constants are calculated from simple relationships, such as the Karplus equation (Section 4-5). Because the calculations are not quantitatively reliable, couplings generally are represented more poorly than chemical shifts by these commercial programs. Usually, the program provides a list of the compounds used to calculate chemical shifts, so that the experimentalist can judge their relevancy. Sometimes, the compound under study in fact proves to be in the database, so that the real spectrum is reproduced. If not, the experimentalist always should review the structures of the compounds used for the calculations and decide whether they are sufficiently similar to trust the calculations. 

Note that this Principle is simply a restatement of the experimental evidence which led to Table 1.2. It is a condensed statement of a very large amount of chemical information. As such it might be called a law. But this label seems pretentious in view of the lack of a quantitative definition of hardness. HSAB is not a theory, since it does not explain variations in the strength of chemical bonds. The word prefer in the HSAB Principle implies a rather modest effect. Softness is not the only factor which determines the values of A/Z° in Equation (1.1). There are many examples of very strong bonds between mismatched pairs, such as H2, formed from hard H+ and soft H. H2O, OH and 0 are all classified as hard bases, but there are great differences in their base strength, by any criterion. 

Plant uptake. Pesticide uptake by plants has not been considered in most modeling efforts. This is primarily due to an almost total lack of quantitative experimental information available to the modeler, and the presumption that the absolute mass of pesticide absorbed by the plant is small compared to the mass remaining in the system. Due to these considerations, modelers have apparently assumed that any inaccuracy in simulation of pesticide fate that results from not considering plant uptake is within the "noise" of inaccuracies produced by other assumptions about the physical, chemical, and biological processes operating in the system. While this assumption is unproven for pesticide absorption, it clearly cannot be accepted for water absorption by the plant (the U(z,t) term in Equation 4). Plant extraction of water greatly influences water flux, which affects pesticide... 

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