Atomic masses Stoichiometry

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—... 

This is a critical chapter in your study of chemistry. Our goal is to help you master the mole concept. You will learn about balancing equations and the mole/mass relationships (stoichiometry) inherent in these balanced equations. You will learn, given amounts of reactants, how to determine which one limits the amount of product formed. You will also learn how to determine the empirical and molecular formulas of compounds. All of these will depend on the mole concept. Make sure that you can use your calculator correctly. If you are unsure about setting up problems, refer back to Chapter 1 of this book and go through Section 1-4, on using the Unit Conversion Method. Review how to find atomic masses on the periodic table. Practice, Practice, Practice. 

Strategy. Before we start, we need to know (i) what is the electrode reaction. Next, we need to determine (ii) the number of moles (or fractions thereof) of charge which flows through the cell. This is Faraday s first law in action. Knowing the number of moles, we then invoke Faraday s second law and decide from the reaction stoichiometry (iii) how many moles of metal are formed. Finally (iv), now knowing the number of moles of metal, we can calculate the mass of metal from the known atomic mass. The following procedure is therefore adopted ... 

In introductory chemistry courses, much emphasis is necessarily placed on the concept of stoichiometry, that is, the fact that elements combine in certain definite proportions by weight, proportions that reflect their valences and atomic masses. For much of the chemistry of the main group elements and organic compounds, this concept works extremely well, but in transition metal chemistry in particular it is common for ions of more than one oxidation state to form with comparable ease, and sometimes to occur together in the same ionic solid. The presence of more highly oxidized cations... 

While the concept of atom economy is simple, unlike the E factor it does not take into account the actual yield or stoichiometry (actual masses or molar excesses)... 

For a reaction in which the stoichiometric relation between analyte and product is not 1 1, we must use the correct stoichiometry in formulating the gravimetric factor. For example, an unknown containing Mg2+ (atomic mass = 24.305 0) can be analyzed gravimetrically to produce magnesium pyrophosphate (Mg2P207. FM 222.553). The gravimetric factor would be... 

The mole can be realized in a similar way but, of course, there are millions of different types of mole. It is more appropriate to speak of realizing a mole and this can be done by measuring a specified entity and making use of chemical stoichiometry and atomic mass values to relate the measured property to mass, as defined in the definition of the mole, i.e., Mx = Nx/An = m/ M, where Mx = number of moles of entity X Nx = number of entities of X An = Avogadro s number m = mass of X M = atomic mass of X. 

Historically, the fluoride complexes are most important. Aristid Von Grosse (1934) used K2PaF7 in his determination of the atomic mass of Pa in 1931. Colourless crystals of this and other complexes MPaFe, M2PaFv, and MsPaFg (M = K, Rb, Cs) can be obtained by changing the stoichiometry, e.g. ... 

In this chapter we will consider the quantities of materials consumed and produced in chemical reactions. This area of study is called chemical stoichiometry. To understand chemical stoichiometry, you must first understand the concept of relative atomic masses. 

The conversion factor for converting between mass and amount in moles is the molar mass of the substance. The molar mass is the sum of atomic masses from the periodic table for the atoms in a substance. Skills Toolkit 3 shows how to use the molar mass of each substance involved in a stoichiometry problem. Notice that the problem is a three-step process. The mass in grams of the given substance is converted into moles. Next, the mole ratio is used to convert into moles of the desired substance. Finally, this amount in moles is converted into grams. 

Elemental analysis is important in establishing the purity and identity of a known compound, or the empirical (stoichiometric) formulae of a new one. Elemental composition is usually quoted as percent by mass, from which the stoichiometry can be determined from atomic mass (RAM) values. Consider a compound (X) with the following composition by mass ... 

In chemically reacting mixture 0 (for several reacting constituents at least) due to chemical reactions among reacting constituents. The reactions are described by stoichiometry. Here we follow Bowen [14, 30, 31], see also [12, 48, 65], using non-orthogonal bases (see Appendix A.4) therefore, we use upper or lower indices for contravariant or covariant components. In stoichiometry, we assume that each constituent is composed of atomic substances (atoms—often chemical elements) in definite proportions. The constituent a = 1,..., n is characterized by a positive constant— the molar mass M , which is therefore a linear combination of atomic masses of atomic substances a = 1,2,..., z... 

Critical parameters that allowed this important progress evolved around discrete, reproducible features exhibited by each atomic element such as well-defined (a) atomic masses, (b) reactivities, (c) valency, (d) stoichiometries, (e) mass-combining ratios, and (f) bonding directionalities. These intrinsic elemental properties, inherent in all atom-based elemental stmctures. 

Stoichiometry is built on an understanding of atomic masses (Section 2.4) and on a fundamental principle, the law of conservation of mass The total mass of all substances presetit after a chemical reaction is the same as the total ma b e the reaction. The French nobleman and scientist Antoine Lavoisier (Figure 3.1 ) discovered this important chemical law in the late 1700s. In a chemistry text published in 1789, Lavoisier stated the law in this eloquent way "We may lay it down as an incontestable axiom that, in all the operations of art and nature, nothing is created an equal quantity of matter exists both before and after the experiment."... 

In the furnace, a mass balance must hold. Due to the equilibrium, we consider atomic mass balance for the hydrogen, carbon, and oxygen based on the stoichiometry of the two reactions. Next, we define the equilibrium constants for the two reactions, and we also use the correlations from the literature where, as in previous examples. Pi is the partial pressure of component i given in atm while t is in K ... 

Assigning values of the relative masses of the atoms of chemical elements allowed chemistry to develop into a physical science. The concepts of relative atomic mass and the law of conservation of mass allowed quantitative chemistry (stoichiometry) to develop. Aristotle wrote, Mathematics is the study of quantity and Descartes wrote, Mathematics is the science of order and measurement. The deepest philosophical and scientific mysteries are often those that we take for granted. It is quite possible that you have never reflected on the fact that chemists uses mathematics to describe and explain the physical world. Mathematical concepts, such as differential equations and logarithms, that were developed for purely abstract reasons turn out to explain real chemical phenomena. Their utility (usefulness), as physicist Eugene Wigner once wrote,... 

In earlier chapters, we discovered the importance of atomic masses in matters relating to stoichiometry. To understand certain physical and chemical properties, we need to know something about atomic sizes. In this section we describe atomic radius, the first of a group of atomic properties that we will examine in this chapter. 

As was suggested in the preceding discussion, most of the arene complexes isolated by metal-atom techniques are benzene derivatives. However, heterocyclic ligands are also known to act as 5- or 6-electron donors in transition-metal 7r-complexes (79), and it has proved possible to isolate heterocyclic complexes via the metal-atom route. Bis(2,6-di-methylpyridine)Cr(O) was prepared by cocondensation of Cr atoms with the ligand at 77 K (79). The red-brown product was isolated in only 2% yield the stoichiometry was confirmed by mass spectrometry, and the structure determined by X-ray crystal-structure analysis, which supported a sandwich formulation. 

Sections 2- and 3- describe how to use the relationships among atoms, moles, and masses to answer how much questions about individual substances. Combining these ideas with the concept of a balanced chemical equation lets us answer how much questions about chemical reactions. The study of the amounts of materials consumed and produced in chemical reactions is called stoichiometry. 

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