Quantitative Calculations from Chemical Equations

Chemistry is a quantitative science, and it is important to know how to do some of the basic chemical calculations early in a beginning chemistry course. Among the most important of these are the calculations of the quantities of substances consumed or produced in a chemical reaction. Such calculations are classified as stoichiometry. Heat is normally evolved or taken up in the course of a chemical reaction. The calculation of the quantity of heat involved in a reaction falls in the branch of chemistry called thermodiemistry. 

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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... 

The term titrimetric analysis refers to quantitative chemical analysis carried out by determining the volume of a solution of accurately known concentration which is required to react quantitatively with a measured volume of a solution of the substance to be determined. The solution of accurately known strength is called the standard solution, see Section 10.3. The weight of the substance to be determined is calculated from the volume of the standard solution used and the chemical equation and relative molecular masses of the reacting compounds. 

In this case, as in all others, a calculation should be made at the conclusion of the experiment of the percentage of the theoretical yield which has been obtained, keeping in mind the following considerations. According to the chemical equation one mole of alcohol (46) should be used for one mole of potassium bromide (119). Actually, however, in the case of organic reactions, which as a rule do not proceed quantitatively, one of the components is used in excess, in keeping with the law of mass action (pp. 142,143), and its choice is often determined by economic considerations. Thus, for example, 1 kg. of potassium bromide costs about 6s., and 1 kg. of duty-free alcohol, Is. 2d. The price of a mole of KBr (119 x 6s.) is therefore to that of a mole of alcohol (95 per cent) (46 x Is. 2d.) approximately as 14 1. From the economic standpoint it is therefore advisable to use the cheaper alcohol in excess in order that as much as possible of the dearer bromine compound may be con-... 

As the styrene process shows, it is not generally feasible to operate a reactor with a conversion per pass equal to the equilibrium conversion. The rate of a chemical reaction decreases as equilibrium is approached, so that the equilibrium conversion can only be attained if either the reactor is very large or the reaction unusually fast. The size of reactor required to give any particular conversion, which of course cannot exceed the maximum conversion predicted from the equilibrium constant, is calculated from the kinetics of the reaction. For this purpose we need quantitative data on the rate of reaction, and the rate equations which describe the kinetics are considered in the following section. 

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. 

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 more quantitative interpretation of chemical shift data cannot be made at present, with few exceptions, such as the calculations of ring current shifts. The theory of chemical shifts is by and large inadequate to deal with the subtleties of the observed changes. A priori calculations remain grossly inaccurate, because the large number of parameters contained in the equations cannot be derived from any experimental measurement. Even calculations of ring current shifts involve iterative fitting of these parameters to known crystal structure data. The view of molecular structure derived from a study of chemical shifts thus reveals a wealth of detail blurred in its essentials. 

Thermogravimetry is an attractive experimental technique for investigations of the thermal reactions of a wide range of initially solid or liquid substances, under controlled conditions of temperature and atmosphere. TG measurements probably provide more accurate kinetic (m, t, T) values than most other alternative laboratory methods available for the wide range of rate processes that involve a mass loss. The popularity of the method is due to the versatility and reliability of the apparatus, which provides results rapidly and is capable of automation. However, there have been relatively few critical studies of the accuracy, reproducibility, reliability, etc. of TG data based on quantitative comparisons with measurements made for the same reaction by alternative techniques, such as DTA, DSC, and EGA. One such comparison is by Brown et al. (69,70). This study of kinetic results obtained by different experimental methods contrasts with the often-reported use of multiple mathematical methods to calculate, from the same data, the kinetic model, rate equation g(a) = kt (29), the Arrhenius parameters, etc. In practice, the use of complementary kinetic observations, based on different measurable parameters of the chemical change occurring, provides a more secure foundation for kinetic data interpretation and formulation of a mechanism than multiple kinetic analyses based on a single set of experimental data. 

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. 

When we know the balanced chemical equation for a reaction, we can determine the mole and mass relationships between the reactants and products. Then we use molar masses to calculate the quantities of substances used or produced in a particular reaction. We do much the same thing at home when we use a recipe to make a cake or add the right quantity of water to make soup. In the manufacturing of chemical compounds, side reactions decrease the percent of product obtained. From the actual amount of product, we can determine the percent yield for a reaction. Knowing how to determine the quantitative results of a chemical reaction is essential to chemists, engineers, pharmacists, respiratory therapists, and other scientists and health professionals. 

Figure 6 Intensity dependence of the infrared laser chemical steady state rate constant over many orders of magnitude in a doubly logarithmic presentation (including prediction of ionization), (a) Semiquantitative prediction. Depending on the molecule, typical ranges of Iq would be 0.1 to 10 W cm with /o = 1 W cm being a good intermediate, (b) Quantitative calculation for a reaction similar to the prototype reaction (equation 1) of CF3I with / c 1 MW cm being a typical condition. The full point.s are calculated from the nonlinear case B/C master equation model of this reference and include all ranges n < 1, n = 1, and n > 1 that have now been found experimentally. Ionization is predicted to occur at intensities where rate.s exceed about 10 -10 s , . see (a) ...

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. 

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