SECTION 4 Counting Atoms

In a typical EEL spectrum, the count rate Ia (area under the excitation edge after background subtraction, for element A) is a product of the incident electron current density, J0, the number of atoms Na of element A per unit area, and oa> the total ionization cross-section per atom for the excitation of the appropriate inner-shell by the incident electrons. However, to preserve good energy resolution, an aperture is placed after the specimen which limits scattering to angles less than P and hence only a fraction of the core loss signal Ia(P) is measured. Moreover, in most... 

The meaning of a chemical formula was discussed in Chapter 5, and we learned how to interpret formulas in terms of the numbers of atoms of each element per formula unit. In this chapter, we will learn how to calculate the number of grams of each element in any given quantity of a compound from its formula and to do other calculations involving formulas. Formula masses are presented in Section 7.1, and percent composition is considered in Section 7.2. Section 7.3 discusses the mole—the basic chemical quantity of any substance. Moles can be used to count atoms, molecules, or ions and to calculate the mass of any known number of formula units of a substance. Section 7.4 shows how to use relative mass data to determine empirical formulas, and the method is extended to molecular formulas in Section 7.5. 

In the last section we saw that we can easily count things like jelly beans and mints by weighing. Exactly the same principles can be applied to counting atoms. 

To summarize, we have seen that we can count atoms by weighing if we know the average atomic mass for that type of atom. This is one of the fundamental operations in chemistry, as we will see in the next section. 

In the previous section we used atomic mass units for mass, but these are extremely small units. In the laboratory a much larger unit, the gram, is the convenient unit for mass. In this section we will learn to count atoms in samples with masses given in grams. 

All you need to do is figure the molecular weights of each reactant and product, and then incorporate the weights into the equation. Use the periodic table to find the weights of the atoms and the compound (see the section Counting by Weighing, earlier in this chapter, for the directions) and multiply those numbers by the number of moles, like this ... 

In Section 2.1 we said that you would study chemistry at the particulate level. In other words, chemists are interested in the individual particles that make up a sample of matter. In Section 2.6 we identified atoms and molecules as two of these particles. To understand the amounts of substances in a chemical change, we must know the number of particles of the different substances in the reaction. That s not an easy number to find. Literally counting atoms and molecules is not practical. The number is extremely large. 

Consideration of stereochem-iitry. The parity or handedness - R/S or chjirans - of a stcreoccnter can be obtained by considering the sequence of the Morgan numbers of die atoms, similarly to CIP. Then the number of pairwise interclianges is counted until the numbers arc in ascending order (see Section 2,8,5). 

Perhaps the most notable difference between S-N and N-O compounds is the existence of a wide range of cyclic compounds for the former. As indicated by the examples illustrated below, these range from four- to ten-membered ring systems and include cations and anions as well as neutral systems (1.14-1.18) (Sections 5.2-5.4). Interestingly, the most stable systems conform to the well known Htickel (4n -1- 2) r-electron rule. By using a simple electron-counting procedure (each S atom contributes two electrons and each N atom provides one electron to the r-system in these planar rings) it can be seen that stable entities include species with n = 1, 2 and 3. 

Students stressed that it is mueh easier to write down ehemieal equation and check whether it is balaneed with the use of models, beeause they ean eoneretely count the number of atoms on eaeh side of the ehemieal equation. [Teacher from Sehool N° 3, Section 1 ]... 

Next we count the number of lone pairs on the carbon atom. There are no lone pairs on the carbon atom. (If you are not sure how to tell that there are no lone pairs there, go back to Chapter 1 and review the section on counting lone pairs.) Now we take the sum of the attached atoms and the number of lone pairs—in this case, 3 + 0 = 3. Therefore, three hybridized orbitals are being used here. That means that we have mixed two p orbitals and one s orbital (a total of three orbitals) to get three equivalent sp orbitals. Thus, the hybridization is sp. Let s take a closer look at how this works. 

A Lewis structure shows all valence electrons and only valence electrons, so a correct count of valence electrons is essential. Recall from Section 8- that the number of valence electrons of an atom can be found from its position in the periodic table. Add the contributions from all atoms to obtain a total count of valence electrons. If the species is an anion, add one electron for each negative charge if the species is a cation, subtract one electron for each positive charge. 

Functions and partly also constants for nonbonded interactions within single molecules (intramolecular interactions) have been taken over in many cases from investigations of interactions between different molecules (intermolecular interactions) (7,3). The derivation of parameters for nonbonded interactions presents further difficulties, e.g. the problem of the anisotropy of such interactions (8, 23) and parameter correlations (Section 2.4.). There is no agreement on the question whether pairs of atoms separated by a chain of only three bonds should be counted as nonbonded interactions. Some authors include these pairs,... 

Despite its smaller cross section, the other nuclear reaction used for deuterium analysis, the (2H,p) reaction, can be made extremely sensitive, as Myers (1987) has shown. The key is that the proton is emitted with such high energy, 15 MeV, that the detector can be mounted behind the sample wafer (Fig. 1) ensuring a very low background count rate and hence good sensitivity. Myers measured deuterium amounts as low as 1012 atoms/cm2 in his study of deuterium uptake by Si02. However, the depth resolution of this measurement was poor, l jum. 

---