Relative Masses of Atoms and Molecules

The chemist knows that atoms and molecules react in definite proportions. Unfortunately, he or she cannot conveniently count the number of atoms or molecules that participate in a reaction. But since the chemist has determined their relative masses, he or she can describe fiieir reactions on the basis of the relative masses of atoms and molecules reacting, instead of the number of atoms and molecules reacting. For example, in the reaction... 

For thousands of years, people have heated rocks and distilled plant juices to extract materials. Over the past two centuries, chemists have learnt more and more about how to get materials from rocks, from the air and the sea, and from plants. They have also found out the right conditions to allow these materials to react together to make new substances, such as dyes, plastics and medicines. When we make a new substance it is important to mix the reactants in the correct proportions to ensure that none is wasted. In order to do this we need to know about the relative masses of atoms and molecules and how these are used in chemical calculations. 

How do chemists use the mole and molar masses to count numbers and relative numbers of atoms and molecules Relate your answer to the techniques you used to count rice, nuts, and washers. 

The mass spectrometer serves for the exact determination of the masses of atoms and molecules as well as for the registration of the mass spectra from particle mixtures to mass and relative proportion. The first ion trap detector was developed in 1919 by F.W. Aston. 

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. 

Formula mass The sum of the atomic masses of all the atoms in a formula unit of a compound. Although the average masses of atoms and molecules may be expressed in atomic mass units (amu or u), formula mass is generally viewed as being relative and without units. 

Avogadro recognized the significance of this principle for the determination of atomic weights as his papers title makes clear Essay on a Manner of Determining the Relative Masses of the Elementary Molecules, and the Proportions in which They Enter into these Compounds. 

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. 

Thus, the main relativistic effects are (1) the radical contraction and energetic stabilization of the s and p orbitals which in turn induce the radial expansion and energetic destabilization of the outer d and f orbitals, and (2) the well-known spin-orbit splitting. These effects will be pronounced upon going from As to Sb to Bi. Associated with effect (1), it is interesting to note that the Bi atom has a tendency to form compounds in which Bi is trivalent with the 6s 6p valence configuration. For this tendency of the 6s electron pair to remain formally unoxidized in bismuth compounds (i.e. core-like nature of the 6s electrons), the term inert pair effect or nonhybridization effect has been often used for a reasonable explanation. In this context, the relatively inert 4s pair of the As atom (compared with the 5s pair of Sb) may be ascribed to the stabilization due to the d-block contraction , rather than effect (1) . On the other hand, effect (2) plays an important role in the electronic and spectroscopic properties of atoms and molecules especially in the open-shell states. It not only splits the electronic states but also mixes the states which would not mix in the absence of spin-orbit interaction. As an example, it was calculated that even the ground state ( 2 " ) of Bij is 25% contaminated by Hg. In the Pauli Hamiltonian approximation there is one more relativistic effect called the Dawin term. This will tend to counteract partially the mass-velocity effect. 

Similarly, physics has developed to its present state through the concepts of mass and weight and the application of them as a means to measure forces. In any practical sense a force can only be quantified by measuring its effect relative to a mass that has itself been quantified. In the basic principles of Newtonian mechanics, a force is equal to the product of mass and acceleration (F = ma). Newtonian mechanics, however, is not sufficient to describe the small structure of atoms and molecules. This is the realm of quantum mechanics, of which Newtonian mechanics is a subset. 

The lowest-order effect of relativity on energetics of atoms and molecules—and hence usually the largest—is the spin-free relativistic effect (also called scalar relativity), which is dominated by the one-electron relativistic effect. For light atoms, this effect is relatively easily evaluated with the mass-velocity and Darwin operators of the Pauli Hamiltonian, or by direct perturbation theory. For heavier atoms, the Douglas-Kroll-Hess method or the NESC le method provide descriptions of the spin-independent relativistic effect that are satisfactory for all but the highest accuracy. 

The size distribution of the clusters produced in the cluster source is quite smooth, containing no information about the clusters except their composition. To obtain information about, for example, the relative stability of clusters, it is often useful to heat the clusters. Hot clusters will evaporate atoms and molecules, preferably until a more stable cluster composition is reached that resists further evaporation. This causes an increase in abundance of the particularly stable species (i.e., enhancing the corresponding peak in the mass spectrum, then commonly termed fragmentation spectrum ). Using sufficiently high laser fluences (=50 /iJ/mm ), the clusters can be heated and ionized simultaneously with one laser pulse. 

Individual atoms are far too small to be weighed on a balance. However, as you will soon see, it is possible to determine quite accurately the relative masses of different atoms and molecules. Indeed, it is possible to go a step further and calculate the actual masses of these tiny building blocks of matter. 

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