Atom ratios

The y-brass structure is adopted by a series of alloys with an electron atom ratio of 21 13, e.g. CUjZng, CugAl4., Cu3Sna. 

Reference has already been made to the high melting point, boiling point and strength of transition metals, and this has been attributed to high valency electron-atom ratios. Transition metals quite readily form alloys with each other, and with non-transition metals in some of these alloys, definite intermetallic compounds appear (for example CuZn, CoZn3, Cu3,Sng, Ag5Al3) and in these the formulae correspond to certain definite electron-atom ratios. 

Because the metal structure is locked by these atoms, the resulting compound is often much harder than the original metal, and some of the compounds are therefore of industrial importance (see under iron). Since there is a definite ratio of holes to atoms, filling of all the holes yields compounds with definite small atom-metal atom ratios in practice, all the holes are not always filled, and compounds of less definite composition non-stoichiometric compounds) are formed. 

It is extremely difficult to know values for all of these parameters precisely. Therefore, absolute quantitation is almost never attempted. The determination of relative atomic ratios is an inherently more tractable approach, however. This method is best illustrated by consideration of a binary material composed exclusively of atoms A and B that is perfectiy homogeneous up to the surface. In this case, independent equations can be developed relating the number of atoms sampled to the xps intensity for each atom as follows ... 

Therefore, the relative atomic ratio of the unknown material can be determined from... 

Equation 15 is not used direcdy for quantitation of aes data due to the same limitations discussed above for xps. Particularly troubling for aes is the inabihty to determine B for a given matrix. Thus, the analyst is left with comparing aes data from an unknown with those of known materials in an attempt to estimate relative atom ratios. This proceeds along the same lines as for xps and allows quantitation of aes data to a precision of typically better than ca 20%. 

Alternatively, the effects of valency may be felt through the decrease in stacking fault energy (SFE) of fee alloys having increasing electron to atom ratio (14). 

Plutonium occurs in natural ores in such small amounts that separation is impractical. The atomic ratio of plutonium to uranium in uranium ores is less than 1 10 however, traces of primordial plutonium-244 have been isolated from the mineral bastnasite (16). One sample contained 1 x 10 g/g ore, corresponding to a plutonium-244 [14119-34-7] Pu, terrestrial abundance of 7 x 10 to 2.8 x 10 g/g of mineral and to <10g of primordial Pu on earth. The content of plutonium-239 [15117 8-3], Pu, in uranium minerals is given in Table 2. 

Boron subhaHdes are binary compounds of boron and the halogens, where the atomic ratio of halogen to boron is less than 3. The boron monohaUdes, BCl, [20583-55-5] bromoborane(l) [19961-29-6] BBr, and iodoborane(l) [13842-56-3] BI, are unstable species that have been observed spectroscopicaHy when the respective ttihaUdes were subjected to a discharge (5). Boron dihaUde radicals have been studied, and stmctural and thermochemical data for these species ( BX2) have been deduced (5). 

The composition, properties, and size of soot particles collected from flame products vary considerably with flame conditions and growth time. Typically the C—H atomic ratio ranges from two to five and the particles consist of kregular chains or clusters of tiny spheres 10—40 nm in diameter with overall dimensions of perhaps 200 nm, although some may agglomerate further to much larger sizes. 

The results of the CHN Test are listed in Table 2. The quoted accuracy of the CHN test is 3=0.3% by weight. The hydrogen to carbon atomic ratio was... 

Fig. 15. The H/C atomic ratio versus heat-treatment temperature for samples as indicated...

Fig. 22. The capacity of the one volt plateau measured during the second cycle of several series of samples versus the H/C atomic ratio in the samples. The solid line suggests that each lithium atom binds quasi-reversibly to one hydrogen atom.

A completely different structural motif has very recently been found in the red-brown phosphide CasPg, formed by direct fusion of Ca metal and red P in the correct atom ratio in a corundum crucible at 1000 C. The structure comprises Ca + cations and Pg anions, the latter adopting a staggered ethane conformation. (Note that P+ is isolobal with C and P with H so that C2H6 = [(P+)2(P"")6] = Ps - -) The internal P-P distance is 230.1pm and the terminal P-P distances 214.9-216.9 pm, while the internal PPP angles are 104.2-106.4° and the outer angles are 103.4-103.7°. 

Bromine is substantially less abundant in crustal rocks than either fluorine or chlorine at 2.5 ppm it is forty-sixth in order of abundance being similar to Hf 2.8, Cs 2.6, U 2.3, Eu 2.1 and Sn 2.1 ppm. Like chlorine, the largest natural source of bromine is the oceans, which contain 6.5 x 10 %, i.e. 65 ppm or 65mg/l. The mass ratio Cl Br is 300 1 in the oceans, corresponding to an atomic ratio... 

The law of constant composition This tells us that a compound always contains the same elements in the same proportions by mass. If the atom ratio of the elements in a compound is fixed (postulate 3), their proportions by mass must also be fixed. 

To this point, our study of chemistry has been largely qualitative, involving very few calculations. However, chemistry is a quantitative science. Atoms of elements differ from one another not only in composition (number of protons, electrons, neutrons), but also in mass. Chemical formulas of compounds tell us not only the atom ratios in which elements are present but also the mass ratios. 

The calculations in Example 3.4 illustrate an important characteristic of formulas. In one mole of Fe203 there are two moles of Fe (111.7 g) and three moles of O (48.00 g). This is the same as the atom ratio in Fe203,2 atoms Fe 3 atoms O. In general, the subscripts in a formula represent not only the atom ratio in which the different dements are combined but also the mole ratio. 

Can you explain why the mole ratio must equal the atom ratio ... 

Strategy First (1), convert the masses of the three elements to moles. Knowing the number of moles (n) of K, Cr, and O, you can then (2) calculate the mole ratios. Finally (3), equate the mole ratio to the atom ratio, which gives you the simplest formula. 

As pointed out earlier, the mole ratio is the same as the atom ratio. To find the simplest whole-number atom ratio, multiply throughout by 2 ... 

Sometimes ifs not so easy to convert the atom ratio to simplest formula (see Problem 47 at the end of the Chapter). 

Chemical analysis always leads to the simplest formula of a compound because it gives only the simplest atom ratio of the elements. As pointed out earlier, the molecular formula is a whole-number multiple of the simplest formula. That multiple may be 1 as in H20, 2 as in H202, 3 as in CjHg, or some other integer. To find the multiple, one more piece of data is... 

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