Counting formula

The counting formula for the Kekule structures of triangular benzenoids is rather simple 135... 

For nanoribbons, the counting formulas for 6- and 10-membered circuits are given in terms of the -numbers of polyphenanthrenes (note that K(2h) = Ar( )ph)... 

While this equation is certainly valid for ensemble of molecules all subjected to a hypothetical identical time-dependent environment, the validity of this equation for a SM is far from being obvious. In fact, as we discuss below, we can expect this equation to be valid only under certain conditions. By using Eq. (4.17) the probability of recording n photons in time interval (0, T) is given by the classical counting formula [68]... 

When a polycyclic graph G is considered, obtaining the number of spanning trees is rather involved. One needs first to compute the Laplacian spectrum, and then to use it in the following counting formula, based on the matrix-tree theorem, in order to get the number of spanning trees of G (Mohar, 1989) ... 

It is evident that the cycle-edge incidence matrix is the transpose of the edge-cycle incidence matrix. This matrix is presented because it is used in the counting formula for spanning trees of graphs (see Section 2.20). 

Organic chemists have devised a number of shortcuts to speed the writing of structural formulas Sometimes we leave out unshared electron pairs but only when we are sure enough m our ability to count electrons to know when they are present and when they re not We ve already mentioned representing covalent bonds by dashes In condensed structural formulas we leave out some many or all of the covalent bonds and use sub scripts to indicate the number of identical groups attached to a particular atom These successive levels of simplification are illustrated as shown for isopropyl alcohol ( rub bmg alcohol )... 

The general molecular formula for an alkene is Cr,H2n Ethylene is C2H4 propene IS C3H6 Counting the carbons and hydrogens of the compound shown (CsHie) reveals that it too corresponds to CnH2n... 

The circle m a hexagon symbol was first suggested by the British chemist Sir Robert Robinson to represent what he called the aromatic sextet —the six delocalized TT electrons of the three double bonds Robinson s symbol is a convenient time saving shorthand device but Kekule type formulas are better for counting and keeping track of electrons especially m chemical reactions... 

A halogen substituent Irke hydrogen rs monovalent and when present rn a molec ular formula rs treated as rf rt were hydrogen for counting purposes... 

PSS uses the following formulae (22,23) to calculate plate count, asymmetry, and resolution. PSS uses test conditions that conform to the ISO/EN 13885 and DIN 55672 requirements for SEC sample testing. 

The following formula is used to calculate the plate count ... 

Problem 6.3 Diazepam, marketed as an antianxiety medication under the name Valium, has three rings, eight double bonds, and the formula C]6H/CIN20. How many hydrogens does diazepam have (Calculate the answer don t count hydrogens in the structure.)... 

Molar mass is important when we need to know the number of atoms in a sample. It would be impossible to count out 6 X ID23 atoms of an element, but it is very easy to measure out a mass equal to the molar mass of the element in grams. Each of the samples shown in Fig. E.2 was obtained in this way each sample contains the same number of atoms of the element (6.022 X 1023), but the masses vary because the masses of the atoms are different (Fig. E.4). The same rule applies to compounds. Flence, if we measure out 58.44 g of sodium chloride, we obtain a sample that contains 1.000 mol NaCl formula units (Fig. E.5). 

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