Calculations counting atoms

In this chapter, you will learn how chemists count atoms by organizing large numbers of them into convenient, measurable groups. You will learn how these groups relate the number of atoms in a substance to its mass. Using your calculator and the periodic table, you will learn how to convert between the mass of a substance and the number of atoms it contains. 

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. 

The situation is similar in counting atoms, but much more difficult. Individual atoms cannot be seen to be counted, nor can they be weighed in the ordinary manner. Still, if the mass of 1 atom can be determined (in amu, for example) the number of atoms in a mole can be calculated. Historically, what chemists have done in effect is to weigh very large numbers of atoms of different elements where the ratio of atoms of the elements is known they have gotten the ratio of the masses of individual atoms from the ratio of the mass of the different elements and the relative numbers of atoms of the elements. 

In the arithmetic of chemistry, a lot of calculations come down to counting atoms and molecules. The international unit for the amount of substance isn t the kilogram (which is used for mass), it s the mole. Chemists need to think in terms of numbers of particles, and this is what the mole allows. The mole is a very large number 6.022 x 1023. It is the number of carbon-12 atoms in exactly 12.00 grams of that isotope. It is such an important number in chemistry that it has its own special name, Avogadro s number, named after Amadeo Avogadro (1776-1856), one of the most famous early scientists. 

The mole is often referred to as a chemist s unit of quantity. Counting atoms is a difficult process and beyond the scope of most calculators, but measuring the mass of a sample is easy when we can relate the number of atoms in a sample to its mass. This is the unique purpose of the mole. A mole of any substance is its molecular formula weight expressed in grams. Avogadro s number s a universal constant that states the number of molecules in a mole Nq = 6.023 x 10 molecules/mole. One mole (abbreviated mol) of any element (chemical compound) has the same number of chemical particles as one mole of another element (chemical compound). In other words, 1 mole of any compound contains 6.02 x 10 molecules. Review the following problem using the mole concept. 

The Slater-type functions (STF) with the radial part in the form (8.3) and integer n can be used as the basis functions in Hartree-Fock-Roothaan calculations of atomic waveftmctions. The radial dependence of the atomic orbitals is an expansion in the radial Slater-type basis functions ipimp whose indices are I, running over s,p, symmetries, and p counting serially over basis-set members for a given s3Tnmetry ... 

Each combination of four atoms (A, B. C. and D) is characterized by two parameters, e and e.. As for the CICC, is a parameter that depends on atomic properties and on distances, and is calculated by Eq. (27), with r, again being the sum of bond lengths between atoms on the path with the minimum number of bond counts. However c is now a geometric parameter (dependent on the conformation)... 

HyperChem quantum mechanics calculations must start with the number of electrons (N) and how many of them have alpha spins (the remaining electrons have beta spins). HyperChem obtains this information from the charge and spin multiplicity that you specify in the Semi-empirical Options dialog box or Ab Initio Options dialog box. N is then computed by counting the electrons (valence electrons in semi-empirical methods and all electrons in fll) mitio method) associated with each (assumed neutral) atom and... 

To conclude Chapter 6, let us connect it with Chapter 4 through a simple calculation involving the intensity of cobalt Ka as measured by counting 1 square centimeter over a 1-second interval. The measured intensity for massive cobalt corresponds to about 500,000 counts. By means of Equations 6-7 and 6-9, we calculate from this number a value of 23 counts for AI (Equation 6-9) for a monolayer of cobalt atoms. The measured value from Table 4-4 is 15 counts. The good agreement shows that absorption effects may be calculated with confidence. 

The potential usefulness of x-ray emission spectrography for trace analysis is implicit in the results of approximate calculations presented in Chapter 4. Thus, it was estimated that the intensity of cobalt Ka generated under practicable conditions in a monolayer (area, 1 sq cm) of cobalt atoms might give 133 counts per second (4.16). Such a sample weighs 0.2 pg. 

The 8V + 6 valence electron rule has been completely substantiated by the calculated four-membered species in Table 2 [7], Boldyrev, Wang, and their collaborators presented experimental and theoretical evidence of aromaticity in the Al/ [19] Ga/" [20], In " [20] and isoelectronic heterosystems, XAl [21], The Al/" unit (14e) was found to be square planar and to possess two n electrons, thus conforming to the (An + 2)n electron counting rule for aromaticity. The n electron counting rule would be more powerful if we could predict the number of n electrons of metal atomic rings in an unequivocal manner. Our SN+6 electron rule only requires the number of valence electrons in Al/, which is easy to count. 

Here, Wj is the number of neighboring atoms at the distance d,. Because the atoms separated by more than twice the shortest interatomic distance cannot be counted as neighboring, the summation is Hmited only to the interatomic distances less than twice dg. Without this limitation, calculation of the parame-... 

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