Shorthand notation

We often designate the concentrations of the active species as well. 

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Dirac showed in 1928 dial a fourth quantum number associated with intrinsic angidar momentum appears in a relativistic treatment of the free electron, it is customary to treat spin heiiristically. In general, the wavefimction of an electron is written as the product of the usual spatial part (which corresponds to a solution of the non-relativistic Sclnodinger equation and involves oidy the Cartesian coordinates of the particle) and a spin part a, where a is either a or p. A connnon shorthand notation is often used, whereby... 

The shorthand notation in the rhs of equation (A3.6.5) is frequently referred to as the Leffler-Gnmwald operator [7]. 

A quite successful integrator for (16), which is based on the idea of operator splitting, is the PICKABACK scheme of Nettesheim et al. [19]. With the shorthand notation... 

For any sizeable system the Slater determinant can be tedious to write out, let alone the equivalent full orbital expansion, and so it is common to use a shorthand notation. Various notation systems have been devised. In one system the terms along the diagonal of the matrix are written as a single-row determinant. For the 3x3 determinant we therefore have ... 

We have used the shorthand notation for the integrals in the final expression. Note that the two-electron integrals may involve up to four different basis functions /x, v, A, a), which may in turn be located at four different centres. This has important consequences for the way in which we try to solve the equations. 

Shorthand Notation for Electrochemical Cells Although Figure 11.5 provides a useful picture of an electrochemical cell, it does not provide a convenient representation. A more useful representation is a shorthand, or schematic, notation that uses symbols to indicate the different phases present in the electrochemical cell, as well as the composition of each phase. A vertical slash ( ) indicates a phase boundary where a potential develops, and a comma (,) separates species in the same phase, or two phases where no potential develops. Shorthand cell notations begin with the anode and continue to the cathode. The electrochemical cell in Figure 11.5, for example, is described in shorthand notation as... 

What are the anodic, cathodic, and overall reactions responsible for the potential in the electrochemical cell shown here Write the shorthand notation for the electrochemical cell. 

Potentiometric electrochemical cells are constructed such that one of the half-cells provides a known reference potential, and the potential of the other half-cell indicates the analyte s concentration. By convention, the reference electrode is taken to be the anode thus, the shorthand notation for a potentiometric electrochemical cell is... 

Standard Hydrogen Electrode The standard hydrogen electrode (SHE) is rarely used for routine analytical work, but is important because it is the reference electrode used to establish standard-state potentials for other half-reactions. The SHE consists of a Pt electrode immersed in a solution in which the hydrogen ion activity is 1.00 and in which H2 gas is bubbled at a pressure of 1 atm (Figure 11.7). A conventional salt bridge connects the SHE to the indicator half-cell. The shorthand notation for the standard hydrogen electrode is... 

The saturated calomel electrode (SCE), which is constructed using an aqueous solution saturated with KCl, has a potential at 25 °C of -hO.2444 V. A typical SCE is shown in Eigure 11.8 and consists of an inner tube, packed with a paste of Hg, HgiCli, and saturated KCl, situated within a second tube filled with a saturated solution of KCl. A small hole connects the two tubes, and an asbestos fiber serves as a salt bridge to the solution in which the SCE is immersed. The stopper in the outer tube may be removed when additional saturated KCl is needed. The shorthand notation for this cell is... 

A typical Ag/AgCl electrode is shown in figure 11.9 and consists of a silver wire, the end of which is coated with a thin film of AgCl. The wire is immersed in a solution that contains the desired concentration of KCl and that is saturated with AgCl. A porous plug serves as the salt bridge. The shorthand notation for the cell is... 

Membrane Potentials Ion-selective electrodes, such as the glass pH electrode, function by using a membrane that reacts selectively with a single ion. figure 11.10 shows a generic diagram for a potentiometric electrochemical cell equipped with an ion-selective electrode. The shorthand notation for this cell is... 

Fig. 9. Partial structural formulas and shorthand notations for principal hemiceUuloses found in wood, where the sugar units ate noted as P-D-xylopyranose (Xylp), 4-Omethyl-a-D-glucopyranosyluronic acid (GlupU), a-L-arabinofuranose (Araf), P-D-glucopyranose (Glup), P-D-mannopyranose (Manp), and P-D-galactopyranose (Galp) for (a) arabino-4-O-methylglucuronoxylan from softwood, (b) 0-acetyl-galactoglucomannan from softwood, and...

Shorthand notations have been developed to avoid repetitive systematic names of unsaturated fatty acids. Eor example, linolenic or (7j -9,i7j -12-,i7j -15-octadecatrienoic acid can be represented by 18 3(9, 12, 15 ). The Greek letter A has been used to indicate presence and position of double bonds, eg a fatty acid, but it should never be used in a systematic name. An equally inappropriate but popular designation is derived by counting... 

FIGURE 11.18 Furanoses are represented by lines phosphodiesters are represented by diagonal slashes in this shorthand notation for nucleic acid structures. 

We propose, then, that chemical bonds can form if valence electrons can be shared by two atoms using partially filled orbitals. We need a shorthand notation which aids in the use of this rule. Such a shorthand notation is called a representation of the bonding. 

Equations (3-246), (3-247), and (3-248) are often abbreviated by using the shorthand notation... 

Since carbon has four bonds to fill, and because hydrogen is the most likely atom to be attached to carbon in an organic molecule, chemists invented a shorthand notation that is easier to read and draw. 

Computational strategies can be based on variational procedures using the Dirac-Frenkel time-dependent variational principle (TDVP). Introducing a shorthand notation so that... 

As a shorthand notation for indicating that a reaction is elementary, we shall include the rate constants in the stoichiometric equation. Thus, the reaction... 

These reactions could be elementary, first order, and without by-products as indicated. For example, they could represent a sequence of isomerizations. More Ukely, there will be by-products that do not influence the subsequent reaction steps and which were omitted in the shorthand notation of Equation (2.20). Thus, the first member of the set could actually be... 

Concentrations are used so frequently in chemistry that a shorthand notation for concentration is almost essential. Chemists represent the molar concentration of a species by enclosing its formula in brackets ... 

Each quantized property can be identified, or indexed, using a quantum number. These are integers that specify the values of the electron s quantized properties. Each electron in an atom has three quantum numbers that specify its three variable properties. A set of three quantum numbers is a shorthand notation that describes a particular energy,... 

A complete specification of how an atom s electrons are distributed in its orbitals is called an electron configuration. There are three common ways to represent electron configurations. One is a complete specification of quantum numbers. The second is a shorthand notation from which the quantum numbers can be inferred. The third is a diagrammatic representation of orbital energy levels and their occupancy. 

As the number of electrons In an atom Increases, a listing of all quantum numbers quickly becomes tedious. For example. Iron, with 26 electrons, would require the specification of 26 sets of 4 quantum numbers. To save time and space, chemists have devised a shorthand notation to write electron configurations. The orbital symbols (1 5, 2 p,... 

C08-0009. Determine the energy level diagram and shorthand notation for the electron configuration of the fluorine atom. 

The description of the first 10 electrons in the configuration of aluminum is identical to that of neon, so we can represent that portion as [Ne]. With this notation, the configuration of A1 becomes [Ne] 3 5" 3 p The element at the end of each row of the periodic table has a noble gas configuration. These configurations can be written in the following shorthand notation ... 

C08-0016. Determine the ground-state configurations of Mo, I, and Hg . Use shorthand notation. 

C08-0058. Write the correct ground-state electron configuration, in shorthand notation, for C, Cr, Sb, and Br. 

To avoid vriting long equations with similar terms, we introduce a convenient shorthand notation for most of the expressions considered so far. X will denote the molecules A, B, etc. and Vi the stoichiometric coefficients, which are negative for reactants and positive for products. This yields the following set of equations ... 

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