Chemical formulas from experimentally determined

By this point in your study of chemistry, you have seen hundreds of chemical formulas. Have you wondered where they come from or how we know the relative numbers of atoms of each element in a compound This section describes some of the ways chemists determine chemical formulas from experimental data. 

Determining a Chemical Formula from Experimental Data 114... 

Careful analysis of Figure 4.20 indicates that six peaks in this card (43-0318) are clearly missing and three weak to medium intensity peaks have no match in the experimental pattern. The second record 49-1170, is almost a perfect match, but a hydrogen atom is missing in its chemical formula, as was determined later from neutron diffraction data. ... 

But by experimental determination the molecular refraction is found to be 48 71, which is 3-235 in excess of the value calculated from the atomic refractions. Two double bonds between carbon atoms would account for 3-414 in excess, so that it is evident that geraniol contains two such double linkages. No alcohol of the formula Cj HjgO with two double linkages can contain a ring, so that geraniol must belong to the open chain series, a conclusion entirely supported by its chemical characters. 

So far the emphasis has been on solving the crystal structure from the knowledge of the unit cell and ionic content. The motivation for this work is to provide an automated procedure to help determine or solve the crystal structure of new compounds that are synthesised in a powder form. Of course the methods developed can generate other structural topologies and perhaps a new, yet to be synthesised, crystal structure. However, the task has been to solve a particular structure and so one might extract more information from the experimental data to aid the prediction process (e.g. use of symmetry elements). Thus, the number of unwanted possible (meta)stable structures, or polymorphs, that could be generated may be reduced. In this section, the emphasis is on finding all the important polymorphs for a particular chemical formula. 

The determination of the empirical formula of a compound can be made experimentally, by determining the percentage amounts of elements present in the substance using the methods of quantitative chemical analysis. At the same time the relative molecular mass of the compound has to be measured as well. From these data the empirical formula can be determined by a simple calculation. If, for some reason, it is impossible to determine the relative molecular mass the simplest (assumed) formula only can be calculated from the results of chemical analysis the true formula might contain multiples of the atoms given in the assumed formula. 

Studies using the theory of Quantitative Structure-Activity Relationships (QSAR) are intended to suggest mathematical models capable of estimating the relevant properties of interest, especially when those cannot be experimentally determined for some reason. Such studies rely on the basic assumption that the structure of a compound completely determines its properties, which can therefore be translated into the so-called molecular descriptors. These parameters are calculated through mathematical formulae derived from several theories, such as Chemical Graph Theory, Information... 

Knowing the chemical formula and the molecular mass of a compound enables us to calculate the percent composition by mass—the percent by mass of each element in a compound. It is useful to know the percent composition by mass if, for example, we needed to verify the purity of a compound for use in a laboratory experiment. From the formula we could calculate what percent of the total mass of the compound is contributed by each element. Then, by comparing the result to the percent composition obtained experimentally for our sample, we could determine the purity of the sample. Mathematically, the percent composition is obtained by dividing the mass of each element in 1 mole of the compound by the molar mass of the compound and multiplying by 100 percent ... 

Experimental values for hc° determined by pyrolysis-combustion flow calorimetry (see below) are listed in Table 7. The elemental analysis of chars gives typical chemical formula C5H2 from which the heat of combustion of the char calculated from oxygen consumption is /ic,p° 37 kJ/g, which can be used to estimate the heat of combustion of the fuel gases of charring polymers using equation 56 if /x is known. 

Abnormal Molar Weights.— In the case of a number of substances (very commonly in the case of organic acids and hydroxy-compounds in benzene), it is found that the molar weight determined by the cryoscopic method is greater than that calculated from the usual chemical formula of the substance, by an amount exceeding the experimental error. We are therefore led to the assumption that these substances associate in solution, i.e, two or more molecules combine to... 

Magnetization measurements have been used to determine the ionic distribution in magnetic materials. The atomic moments of various ions with unpaired dor f electrons are known experimentally and theoretically. The ionic distribution in a collinear ferrimagnetic can therefore be inferred from the saturation magnetization at low temperatures. For example, the ferrospinels have tetrahedral-site moments aligned antiparallel to octahedral-site moments. Simple ferrospinels have the chemical formula FeJ JO4,... 

Percent composition establishes the relative proportions of the elements in a compound on a mass basis. A chemical formula requires these proportions to be on a mole basis, that is, in terms of numbers of atoms. Consider the following five-step approach to determining a formula from the experimentally determined percent composition of the compound 2-deoxyribose, a sugar that is a basic constituent of DNA (deoxyribonucleic acid). The mass percent composition of 2-deoxyribose is 44.77% C, 7.52% H, and 47.71% O. 

Using the freezing-point data is another experimental technique that can be used to obtain the chemical properties of a substance. In this example we were able to determine the molecular formula from the freezing-point depression and a known amount of substance dissolved in a solvent. Note that water was used as the solvent here however, other solvents can be used in freezing-point experiments. 

Given only a molecular formula (perhaps derived from an experimentally determined percentage composition and a molecular weight determination) and some chemical evidence that suggests what functional groups might be present, how might we proceed to propose a possible structure ... 

An unbalanced chemical equation is of limited use. Whenever you see an equation, you should ask yourself whether it is balanced. The principle that lies at the heart of the balancing process is that atoms are conserved in a chemical reaction. The same number of each type of atom must be found among the reactants and products. Also, remember that the identities of the reactants and products of a reaction are determined by experimental observation. For example, when liquid ethanol is burned in the presence of sufficient oxygen gas, the products will always be carbon dioxide and water. When the equation for this reaction is balanced, the identities of the reactants and products must not be changed. The formulas of the compounds must never be changed when balancing a chemical equation. That is, the subscripts in a formula cannot be changed, nor can atoms be added or subtracted from a formula. 

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