Numbers, approximate, calculation

Radiation heat flux is strongly time dependent, because both the flame surface area and the distance between the flame and intercepting surfaces vary during the eourse of a flash fire. The path of this curve ean be approximated by calculating the radiation heat flux at a sufficient number of discrete points in time. 

Calculate the approximate number of ATP molecules that can be obtained from the oxidation of cAl 1-heptadecenoic acid to COg and water. 

Approximate number of stages = Hp calculated in (5) divide by H/stage calculated previously = No. stages... 

During the last decade MO-theory became by far the most well developed quantum mechanical method for numerical calculations on molecules. Small molecules, mainly diatomics, or highly symmetric structures were treated most accurately. Now applicability and limitations of the independent particle, or Hartree-Fock (H. F.), approximation in calculations of molecular properties are well understood. An impressive number of molecular calculations including electron correlation is available today. Around the equilibrium geometries of molecules, electron-pair theories were found to be the most economical for actual calculations of correlation effects ). Unfortunately, accurate calculations as mentioned above are beyond the present computational possibilities for larger molecular structures. Therefore approximations have to be introduced in the investigation of problems of chemical interest. Consequently the reliability of calculated results has to be checked carefully for every kind of application. Three types of approximations are of interest in connection with this article. 

It exhibits a single oxidation process (Ea = + 0.59 V, vs. SCE) affected by some adsorption problems. These adsorption phenomena, which typically affect the electrochemical response of these derivatives, sometimes make it difficult to ascertain by controlled potential coulometry the effective number of electrons involved in the oxidation step. In this case, the (approximate) number of electrons involved per molecule of dendrimer, nd, can be roughly calculated by comparing the cyclic voltammetric responses of the dendrimer with that of the ferrocene monomer using the following empirical equation.27,40... 

The simple theory of electronegativity fails in this discussion because it is based merely on electron transfer energies and determines only the approximate number of electrons transferred, and it does not consider the interactions which take place after transfer. Several calculations in the alkali halides of the cohesive energy (24), the elastic constants (24), the equilibrium spacing (24), and the NMR chemical shift 17, 18, 22) and its pressure dependence (15) have assumed complete ionicity. Because these calculations based on complete ionicity agree remarkably well with the experimental data, we are not surprised that the electronegativity concept of covalency fails completely for the alkali iodide isomer shifts. 

Note It is very helpful to read out the Pm+i/Pm ratio from a mass spectmm to calculate the approximate number of carbon atoms. Provided no other element contributing to M+1 is present, an M+1 intensity of 15 %, for example, indicates the presence of 14 carbons. (For the risk of overestimation due to autoprotonation cf. Chap. 7.2.1)... 

For example for a box with four cells containing four balls, there is only one configuration and VF = 1, S = 0. When the box expands further to 64 cells, W = 64 /(60 4 ) = 635,376 and S/k = 13.36. When the box expands further to a very large number m, we use Stirling s approximation to calculate the number of combinations ... 

We can calculate the approximate number of amino acid residues in a simple protein containing no other... 

For gases, n = e 1 is an excellent approximation. The easiest approach to condensed phases maintains this approximation, where calculations of the molecular first-order and response properties are performed for the isolated molecule, while accounting for the effect of intermolecular interactions through the number density N = Aa/Vm, and therefore by taking appropriate values of Vm. This rough, often at best qualitative, approach is somewhat relaxed by employing expansions of the birefringence constant with the density, that is in inverse powers of Vm. This introduces the appropriate virial coefficients [15,16]... 

Mathematical formulae for determining approximately numbers and densities of states have been used extensively in the calculations of rates of ionic decompositions. The classical approximation, which was employed in the pioneering studies [500, 720], is now recognised as giving serious errors in the calculated rates [883]. Some of the more accurate formulae have been evaluated by comparing their results with those obtained by direct or exact counting of states [306, 308]. It was found [306, 308] that a particular formula used most commonly in mass... 

The Hohenberg-Kohn-Sham density functional theory provides the common formal framework for various computational methods. Since each of the methods in use involves approximations, the calculated properties are not exact. Nevertheless, these methods proved to be very useful in chemistry and materials science. The huge and ever growing number of applications (see Figure 2-1) speaks for itself. Frequently,... 

Previous studies have shown that there is a correlation between the enthalpy of hydration of alkanes and their accessible surface area [30,31] or related magnitudes. Moreover, relationships between the hydration numbers calculated from discrete simulations for hydrocarbons and both the free energy and enthalpy of hydration of these molecules have also been reported [32] and have been often used to evaluate solvation enthalpies. Analysis of our results, illustrates the existence of a linear relationship between A//n eie and the surface of the van der Waals cavity,. SVw, defined in MST computations for the calculation of the non-electrostatic contributions (Figure 4-1). In contrast, no relationship was found for the electrostatic component of the hydration enthalpy (A//eie data not shown). Clearly, in a first approximation, one can assume that the electrostatic interactions between solute and solvent can be decoupled from the interactions formed between uncharged solutes and solvent molecules. 

The above example illustrates how an approximate hand calculation can be carried out to obtain the effectiveness factor for a single reaction in a multicomponent reaction mixture. It has of course been necessary to make a number of assumptions. One... 

The level of radioactivity in a single-stranded DNA is taken as an indication of SSBs. Calculation of the approximate number of breaks requires reference to the molecular size of the cellular genome and comparison with the known number of breaks induced in genomes of specific sizes by X-ray and UV-irradiation of known dosage (see Collins, 1977). 

The quantitative interpretation of the dielectric relaxation times is still not on a satisfactory basis. The earliest attempt in this direction was made on the basis of an ion-oriented hydration sheath, for the formation of which a calculated number of hydrogen-bonds must be broken. This breakage changes the equilibrium of species in the liquid, and statistical relationships connect the proportion of bonds broken, the equilibrium populations, and the relaxation time. From the observed shift of relaxation time one can calculate the number of molecules in the sheath, and show that for temperatures between 276 and 298 K it is approximately the same as the number calculated from the depression of the static permittivity (comparison in Figure 4 of ref. 54). This treatment is open to criticism on the following grounds ... 

At the same conditions of density and temperature, the smallest cation (Na" ") has larger dynamic hydration number than K" " and Rb", as found experimentally from correlations of conductance measurements. The trend holds at all subcritical conditions. This behavior is opposite to that of static coordination numbers calculated from time-averaged radial distribution functions, which give increasing coordination numbers when the ionic radius increases. Another interesting feature of the hydration numbers is given by their temperature dependence. For all ions at 573 K, dynamic hydration numbers (even when lower than their corresponding coordination numbers) are approximately the same as they are at ambient conditions. The same characteristic is observed at supercritical conditions, as illustrated in Table 12. 

It is not sufficient even for an approximate calculation to know the form of the function L for a limited range of temperature (see p. 407). The value of the constant C depends to a considerable extent on the form of the function L at very low temperatures. For the calculation of C it is therefore necessary to know the values of the specific heats at very low temperatures. These have recently been determined in Nemst s laboratory for a number of solid substances, but unfortunately almost exclusively for substances which volatilise only at very high temperatures. Iodine is apparently the only substance whose vapour pressure and specific heats at low temperatures are both known. In this case the vapour pressure constant c can therefore be calculated with a certain degree of approximation. The calculation is as follows ... 

Your teacher will tell you the approximate number of small beads in 1 g. Knowing that number, calculate the mass of 200 small beads. Record the mass that you have calculated. 

The average molecular mass of an amino acid is 110 g/mol. Calculate the approximate number of amino acids in a protein that has a molecular mass of 36 500 g/mol. 

Milled seed ( 0.4%) is added. The ideal amount of seed is calculated to provide the approximate number of 5-10 micron particles that will double in size during essentially all growth (see Chapter 5). 

---