Mass Relations in Chemical Formulas

As you will see shortly, the formula of a compound can be used to determine the mass percents of the elements present. Conversely, if the percentages of the elements are known, the simplest formula can be determined. Knowing the molar mass of a molecular compound, it is possible to go one step further and find the molecular formula. In this section we will consider how these three types of calculations are carried out. 

Click Coached Problems for a self-study module on percent composition. 

The percent composition of a compound is specified by citing the mass percents of the elements present. For example, in a 100-g sample of water there are 11.19 g of hydrogen and 88.81 g of oxygen. Hence the percentages of the two elements are 

Knowing the formula of a compound, Fe203 you can readily calculate the mass percents of its constituent elements. It is convenient to start with one mole of compound (Example 3.4a). The formula of a compound can also be used in a straightforward way to find the mass of an element in a known mass of the compound (Example 3.4b). 

Metallic iron is most often extracted from hematite ore, which consists of iron(III) oxide mixed with impurities such as silicon dioxide, Si02. 

Q What are the mass percents of iron and oxygen in iron(III) oxide  

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The general topic of this chapter is stoichiometry (stoy-key-OM-e-tree), the study of mass relations in chemistry. Whether dealing with atomic masses (Section 3.1), molar masses (Section 3.2), chemical formulas (Section 3.3), or chemical reactions (Section 3.4), you will be answering some very practical questions that ask how much or how many—." For example—... 

A chemical formula tells the numbers and the kinds of atoms that make up a molecule of a compound. Because each atom is an entity with a characteristic mass, a formula also provides a means for computing the relative weights of each kind of atom in a compound. Calculations based on the numbers and masses of atoms in a compound, or the numbers and masses of molecules participating in a reaction, are designated stoichiometric calculations. These weight relationships are important because, although we may think of atoms and molecules in terms of their interactions as structural units, we often must deal with them in the lab in terms of their masses—with the analytical balance. In this chapter, we consider the Stoichiometry of chemical formulas. In following chapters, we look at the stoichiometric relations involved in reactions and in solutions. 

The mole is associated with a specific chemical entity as defined by its chemical formula [15], Its structural formula, isotopic composition, isomeric form, crystal structure, or chirality may have to be given in order to completely specify the entity of interest. The achievable uncertainty of amount-of-substance measurement is limited by that of its apparent molar mass. This consideration affects not only measurements on entities with variable molar mass, but those on pure substances. It is related to the traditional and important concern about purity. 

The concentration of the various species in a multi-component mixture may be expressed in numerous ways. In this book the equations are formulated in terms of mass fluxes, thus mass concentrations are used. However, the equations could as well be formulated in terms of molar fluxes, and molar concentrations as usually applied in basic textbooks in Chemical Engineering (e.g., [11] [169] [13]). The mass concentration, pc, is the mass of species c per unit of volume of solution. The species c mass density relates to the familiar molar concentration by the simple formula Cc = is the molecular... 

Some of the most difficult structural problems in the indole alkaloid field are associated with the bisindole alkaloids of the vobtusine type. Since 1955, vobtusine has been isolated on numerous occasions, often in large quantities, from the Apocynaceae species Callichilia, Conopharyngia, Rejoua, and Voacanga A correct molecular formula could only be determined by high-resolution mass spectrometry. In 1966 a partial structure was proposed for the alkaloid and later in the same year a complete structure was put forward. An unambiguous structural proof is, however, still lacking. The difficulty arises from the complete resistance of the alkaloid and its derivatives to cleavage, in contrast, for example, to the dimers of the voacamine and vinblastine types. Non-cleavable dimers occur also in calabash-curare but in these cases chemical correlation with cleavable alkaloids has been possible (see Section 2, p. 209). To date no bisindole alkaloid related to vobtusine has been found which can be split into monomeric units. 

It is remarkable that no empirical mixture parameters and no experimental data are required to use the equation. The only parameters in the Flory-Huggins equation are the hard core volumes V, which are a pme-component property, and the atomic or group contribution values are found in standard compilations. Since the v/s are significant in the FH equation only in terms of their ratios, pure-liquid molar volumes are often used for V in place of hard core volumes. For solutions of polymers of the same chemical formula, molecular masses are legitimate substitutes for V , for the same reason. Thus the volume fractions ( ) can be substituted by mass fractions W . Either volume fraction or mass fraction is directly related to laboratory data. To avoid mole fractions, the activity tti from Equations (4.368) and (4.369) can be used to calculate by / = aj. ... 

Figure 3.4 Summary of the mass-mole-number relationships for compounds. Moles of a compound are related to grams of the compound through the molar mass (jtt in g/mol) and to the number of molecules (or formula units) through Avogadro s number (6.022 XICF molecules/mol). To find the number of molecules (or formula units) in a given mass, or vice versa, convert the information to moles first. With the chemical formula, you can calculate mass-mole-number information about each component element.

We use chemical formulas to relate the masses of substances to the numbers of atoms, molecules, or ions contained in the substances, a relationship that leads to the crucially important concept of the moie, defined as 6.022 x 10 objects (atoms, molecules, ions, etc.). 

Chemical formulas and chemical equations both have a quantitative significance in that the subscripts in formulas and the coefficients in equations represent precise quantities. The formula H2O indicates that a molecule of this substance (water) contains exactly two atoms of hydrogen and one atom of oxygen. Similarly, the coefficients in a balanced chemical equation indicate the relative quantities of reactants and products. But how do we relate the numbers of atoms or molecules to the amounts we measure in the laboratory Although we cannot directly count atoms or molecules, we can indirectly determine their numbers if we know their masses. Therefore, before we can pursue the quantitative aspects of chemical formulas and equations, we must examine the masses of atoms and molecules. 

Cellulose was defined as a chemical substance related to polysaccharides in 1838 thanks to the works of French chemist Anselme Payen, who isolated it from plant matter and determined its chemical formula (Payen, 1838). Cellulose is the most abundant organic matter on Earth. Total resources of cellulose in nature reach one trillion tons (Klemm et al., 2005). Moreover, being renewable in nature, a mass of this biopolymer increases by approximately 100 billion tons annually as a result of photobiosynthesis (Field et al., 1998). Cellulose is present in all plants and algae cellulose of the tunicin type forms the shells of certain marine creatures, and it is also synthesized by some microorganisms, for example, Gluconacetobacter xylinus. 

When a new molecule is synthesized, an elemental analysis is routinely performed to help verify its identity. This test, which measures the mass percentage of each element in the compound, is also Ifequendy done as part of the process of identifying any substance whose composition is unknown. The mass percentages describe the compound s composition, and so they must be related to its chemical formula. But the data obtained from elemental analysis describe the composition in terms of the mass of each element, whereas the formula describes the composition in terms of the number of atoms of each element. So these are two different representations of very similar information, and the molar masses of the elements provide a connection between them. The process of obtaining the empirical formula of a compound from its percent composition by mass is best illustrated by an example. 

Chemical formulas indicate the relative number of each kind of element in a compoimd. These numbers are based on atoms or moles. By using molar masses, we can use the information in a chemical formula to determine the relative masses of each kind of element in a compoimd. We can then relate the mass of a sample of a compound to the masses of the elements contained in the compound. 

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