Numerical equivalent

All three schemes, the Benson, the Laidler, and the Allen scheme, use four structure contributions for the estimation of thermochemical data of alkanes. As might be guessed, they are numerically equivalent all three schemes provide the same accuracy. This is shown below by Eqs. (7)-(10) for the interconversion of the various contributions. 

For hquid systems these surface energies expressed in mj/m are numerically equivalent to the surface tensions in mN/m(= dyn/cm). If the adhesive is phase 1 and the release coating is phase 2, then the spreading coefficient, S, of 1 on 2 is as given in equation 2. 

The optical purity is numerical equivalent to the enantiomeric excess (e.e.), which is defined as... 

Numerical Equivalance Between the Standard and the Three Adiabatic Spectral Densities... 

Figure 3. Numerical equivalence between the three representations, I, II, and III. Within the adiabatic approximation, this figure shows the numerical equivalence between the Fourier transforms of G given by Eq. (44), Gu given by Eq. (46) and Gm given by Eq. (49).

Tex is the fiber linear density expressed in g/km. N/tex, which is numerically equivalent to GPa/SG, is a unit widely used in the textile industry and very useful to characterize non-circular fibers. 

Numerous equivalent statements of the second law exist. We will begin with the following statement proposed by Clausius ... 

Many researchers refer to stems 1, 2, and 3 using their Roman numeral equivalents—that is, stems I, II, and III. These motifs are also denoted as helices I, II, and III. It should be noted at the beginning of this hammerhead ribozyme discussion that structure-function relationships, the role of various nucleobases, metal ion participation in catalysis, and other features of the system have not been completely delineated and in some cases remain controversial. Globally, the hammerhead fold appears to be similar in both solution and solid-state studies. In solution, however, the central core of the hammerhead construct appears to be highly dynamic. This may account for different experimental results among the analytical techniques used in solution and certainly explains some distinct differences seen between solution and solid-state (X-ray crystallographic) structures. 

The energy of external orbitals in real atoms (which is numerically equivalent to the first ionization potential expressed in eV) is reproduced by an empirical expression of the form ... 

The energy of the atomic orbitals in the hydrogenoid approximation is proportional to the square of the effective charge, and is (numerically) equivalent to the ionization potential... 

The activity of a perfect gas, as for any substance, is unitary, by definition, at standard state. Moreover, for a perfect gas, activity is (numerically) equivalent to pressure, at all pressures. Let us consider the relationship existing, with T held constant, between the chemical potential of component i in gaseous phase g at 1 bar (/a, 17 ) and at pressure P... 

As we saw in section 3.8.1, Raoult s law describes the properties of an ideal solution, in which the thermodynamic activity of the component is numerically equivalent to its molar concentration ... 

There are a number of other reports of difficulties in ortholithiation when further coordination sites are present molecules containing more than one strong coordinating substituent frequently require numerous equivalents of alkyUithium for lithiation . 

The many-body perturbation theory [39] [40] [41] was used to model the electronic structure of the atomic systems studied in this work. The theory developed with respect to a Hartree-Fock reference function constructed from canonical orbitals is employed. This formulation is numerically equivalent to the M ler-Plesset theory[42] [43]. 

The limit of quantification is numerically equivalent to six times the standard deviation of the measured unit when applying the analytical procedure to 20 representative blank samples. For recoveries less than 100% the limit of quantification must be corrected for the average recovery of the analyte. 

The addition of 3 % of Pigment Blue 61 already results in a significant step towards blue/red and shows almost identical incremental changes with further additions (see color locations 11,12, and 13). In addition, the bronze effect occurs which intensifies with increasing distance from the achromatic point. With Pigment Blue 15 3 in numerically equivalent increments, the hue of the black ink moves towards blue/green in the opposite direction from the achromatic point and with a negative shift (color locations 14-16). 

The actual mass of a single atom of 12C is defined as 12 daltons, one dalton being 1.661 x 10-24 g. The mass of a molecule can be given in daltons (Da) or kilodaltons (kDa). This molecular mass in daltons is numerically equivalent to the relative molecular mass (Mj) or molecular weight (MW)a and also to the molar mass (g/mol). However, it is not correct to use the dalton for the unitless quantity Mr. Masses of structures such as chromosomes, ribosomes, mitochondria, viruses, and whole cells as well as macromolecules can be given in daltons. b... 

PThe values of pK for a particular molecule are determined by titration. A typical pH dependence curve for the titration of a weak acid by a strong base is shown in figure 3.2. The concentration of the anion equals the concentration of the acid when the acid is exactly half neutralized. Note that at this point on the curve, the pH is least sensitive to the quantity of added base (or acid). Under these conditions, the solution is said to be buffered. Biochemical reactions are typically highly dependent on the pH of the solution. Therefore, it is frequently advantageous to study reactions in buffered solutions. The ideal buffer is one that has a pK numerically equivalent to the working pH. 

Figure 2. Numeric equivalents for the alkoxysilane hydrolysis cascade reaction.

Some numerical values are exact to as many significant figures as necessary, by definition. Included in this category are the numerical equivalents of prefixes used in unit definition. For example, 1 cm = 0.01 m by definition, and the units conversion factor, 1.0 x 10-2 m/cm, is exact to an infinite number of significant figures. 

Recall the numerical meaning of centi is 1 x 10 2, so we can substitute the prefix multiplier c for its numerical equivalent. We don t have to do this substitution to both sides because in trading c for its numerical equivalent, we haven t changed the value on the right side. 

Notice that our conversion factor between metric quantities has an interesting form. One side gets the prefix multiplier letter (in this case, the c ), and the other side gets the numerical equivalent of the multiplier (in this case, 1 x 10-2). Students sometimes get the number on the wrong side of the conversion factor. If you stick with the definition of the prefix multipliers given in Table 1.2, your conversion factors will always have a prefix multiplier on one side and a number on the other side. Seems fairer that way, doesn t it ... 

Measurement of Surface Energy Properties. The surface tension and surface energy of liquids are numerically equivalent. Surface energy is generally given in millijoules per... 

How can you use this relationship to relate mass and moles The periodic table tells us the average mass of a single atom in atomic mass units (u). For example, zinc has an average atomic mass of 65.39 u. One mole of an element has a mass expressed in grams numerically equivalent to the element s average atomic mass expressed in atomic mass units. One mole of zinc atoms has a mass of 65.39 g. This relationship allows chemists to use a balance to count atoms. You can use the periodic table to determine the mass of one mole of an element. 

---