Even-carbon formula

A formula is called an even—carbon formula when n and s (which necessarily have the same parity) are even integers, while is an odd-carbon formula when n and s are odd. In Table 3 (as well as in Table 3.5) it is found that the even-carbon— and odd-carbon formulas occur in alternating columns. They are characterized by n = 0, 2, 4, 6,. and n = 1, 3, 5, 7, respectively. 

Only isomeric benzenoids in Table PAH6 have the same number of a-bond edges (q) even though formulas with shift coordinates (Ad ANlc/2) of (3,2) have corresponding PAH structures with the same number of carbons and formulas with shift coordinates of (2,1) have structures with the same number of rings. Since each coordinate location (ds, Ntc) in Table PAH6 corresponds to a unique q value, the locants in Table PAH6 represent a countable infinite set as there exists a one-to-one correspondence between them and the set of all natural numbers. 

The full-drawn staircase line in Fig. 2 indicates the limit for the significant enumerations of Stojmenovic et al. [17]. In that work the separate numbers for Kekulean and non-Kekulean systems were not determined. However, it was taken into account, when the asterisks were distributed, that odd-carbon atom formulas (C HS with n and s odd) pertain to non-Kekuleans only, while even-carbon atom... 

Their data [17], which correspond to the area to the left of the staircase-line in Fig. 2, cover all benzenoids with ne < 46. All these data, linked explicitly to the appropriate C HS formulas, are quoted in a previous review [20]. Most of them, for which the classification into Kekuleans and non-Kekuleans are known, are found in our main reference [8]. A supplement of unclassified numbers is given in Table 1. Out of these numbers those for odd-carbon atom formulas give, nevertheless, the numbers of non-Kekulean benzenoid isomers (equal to the totals) hence the corresponding positions are marked with asterisks in Fig. 2 this is not the case for the even-carbon atom formulas. 

O higher members with even-carbon atom formulas ... 

In Fig. 9 the ground forms are indicated by black symbols (in the present case inscribed in circles) rhombs for even-carbon atom formulas, triangles for odd-carbon atom formulas. Higher members of the one-isomer series are identified by circles with a white rhomb or a white triangle for the even, and odd-carbon atom formulas, respectively. 

Classified numbers for constant-isomer series pertaining to even-carbon atom formulas are displayed in Table 11. These data (for h > 13) are accessible by means of Table 9 in combination with the formulas of Table 7, in accordance with the splitting of the cardinalities (27). Correspondingly, the data in Table 12... 

Table 9. Numbers of isomers, classified according to A and symmetry, for even-carbon atom formulas from Table 8 ...

Dias [53] has also observed some interesting regularities in the numbers for constant-isomer benzenoid series which combine the even-carbon atom formulas (Table 11) with the odd-carbon atom formulas (Table 12). Here we express these regularities by ... 

With practice writing structural formulas for organic molecules soon becomes rou tine and can be simplified even more For example a chain of carbon atoms can be rep resented by drawing all of the C—C bonds while omitting individual carbons The result mg structural drawings can be simplified still more by stripping away the hydrogens... 

Calcium carbonate is one of the most common filler/extenders used in the paint and coatings industry. Consumer and contractor paint formulas can include products from submicrometer size to coarse mesh sizes. The main function of calcium carbonate in paint is as a low cost extender. It is also used to improve brightness, appHcation properties, stabiHty, and exposure resistance. Coarse products help to lower gloss and sheen or even provide textured finishes. The selection of product type and particle size is deterrnined by the desired performance and cost of the coating. 

As a substance of formula (HI) should lose carbon dioxide on heating, whereas pilopic acid is stable even at 200°, it seemed probable that homo-pilopic acid is represented by (II) and pilopic acid by (IV). Jowett also showed that pilocarpine, like wopilocarpine, yields Aomopilopic acid when oxidised by permanganate.In the oxidation of the two alkaloids the two nitrogen atoms are eliminated as ammonia and methylamine. 

Compounds like the two C4M [() molecules and the three C3I I 12 molecules, which have the same formula but different structures, are called isomers, from the Greek isos + meros, meaning "made of the same parts." Isomers are compounds that have the same numbers and kinds of atoms but differ in the way the atoms are arranged. Compounds like butane and isobutane, whose atoms are connected differently, are called constitutional isomers. We ll see shortly that other kinds of isomers are also possible, even among compounds whose atoms are connected in the same order. As Table 3.2 shows, the number of possible alkane isomers increases dramatically as the number of carbon atoms increases. 

We saw in Chapter 12 that mass spectrometry gives a molecule s formula and infrared spectroscopy identifies a molecule s functional groups. Nuclear magnetic resonance spectroscopy does not replace either of these techniques rather, it complements them by "mapping" a molecule s carbon-hydrogen framework. Taken together, mass spectrometry, JR, and NMR make it possible to determine the structures of even very complex molecules. 

Benzene and related aromatic compounds were hrst isolated from the gases given off during the heating of coal in the absence of air to produce a form of carbon known as coke, used in the manufacture of steel. That benzene had the molecular formula CgHg was determined in 1825, but it took over a hundred years to prove its structure even though its correct structure was suggested in 1865. 

Cellulose and starch are macromolecules with empirical formulas that resemble hydrated carbon, CX (H2 0)y, where x and y are integers. The monomers from which these macromolecules are consfructed are sugars such as glucose and fructose. These monomers and macromolecules are the carbohydrates. Structurally, carbohydrates are very different from simple combinations of carbon and water. Even the smallest carbohydrates contain carbon chains with hydrogen atoms, OH groups, and occasional ether linkages. 

For even more convenience in representing the structures of organic compounds, particularly in printed material, line formulas are used, so-called because they are printed on one line. In line formulas, each carbon atom is written on a line adjacent to the symbols for the other elements to which it is bonded. Line formulas show the general sequence in which the carbon atoms are attached, but in order to interpret them properly, the permitted total bond orders of all the respective atoms must be kept in mind. Again referring to the compounds (a) to (e) described above, the line formulas are as follows ... 

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