Quantitative Calculations

L exposure would produce 1 ML of adsorbates if the sticking coefficient were unity. Note that a quantitative calculation of the exposure per surface atom depends on the molecular weight of the gas molecules and on the actual density of surface atoms, but the approximations inlierent in the definition of tire Langmuir are often inconsequential. [Pg.294]

Wlrile tire Bms fonnula can be used to locate tire spectral position of tire excitonic state, tliere is no equivalent a priori description of the spectral widtli of tliis state. These bandwidtlis have been attributed to a combination of effects, including inlromogeneous broadening arising from size dispersion, optical dephasing from exciton-surface and exciton-phonon scattering, and fast lifetimes resulting from surface localization 1167, 168, 170, 1711. Due to tire complex nature of tliese line shapes, tliere have been few quantitative calculations of absorjDtion spectra. This situation is in contrast witli tliat of metal nanoparticles, where a more quantitative level of prediction is possible. [Pg.2910]

Quantitative Calculations In precipitation gravimetry the relationship between the analyte and the precipitate is determined by the stoichiometry of the relevant reactions. As discussed in Section 2C, gravimetric calculations can be simplified by applying the principle of conservation of mass. The following example demonstrates the application of this approach to the direct analysis of a single analyte. [Pg.250]

Quantitative Calculations The result of a quantitative analysis by particulate gravimetry is just the ratio, using appropriate units, of the amount of analyte to the amount of sample. [Pg.264]

Quantitative Calculations The stoichiometry of complexation reactions is given by the conservation of electron pairs between the ligand, which is an electron-pair donor, and the metal, which is an electron-pair acceptor (see Section 2C) thus... [Pg.328]

Quantitative Calculations The absolute amount of analyte in a coulometric analysis is determined by applying Faraday s law (equation 11.23) with the total charge during the electrolysis given by equation 11.24 or equation 11.25. Example 11.8 shows the calculations for a typical coulometric analysis. [Pg.504]

Quantitative Calculations In a quantitative analysis, the height or area of an analyte s chromatographic peak is used to determine its concentration. Although peak height is easy to measure, its utility is limited by the inverse relationship between the height and width of a chromatographic peak. Unless chromatographic conditions are carefully controlled to maintain a constant column efficiency, variations in... [Pg.572]

Quantitative Calculations Quantitative analyses are often easier to conduct with HPLC than GC because injections are made with a fixed-volume injection loop instead of a syringe. As a result, variations in the amount of injected sample are minimized, and quantitative measurements can be made using external standards and a normal calibration curve. [Pg.586]

The science of reaction kinetics between molecular species in a homogeneous gas phase was one of the earliest helds to be developed, and a quantitative calculation of tire rates of chemical reactions was considerably advatrced by the development of the collision theoty of gases. According to this approach the rate at which the classic reaction... [Pg.45]

ISS involves simple principles of classical physics and is one of the simplest spectroscopy for quantitative calculations. Under most standard instrumental operating conditions there is essentially no dependency on the chemical bonding or matrix of the sample. Several workers have discussed quantitative aspects of ISS and ele-ihental relative sensitivities. These have been compiled with comparative measurements of sensitivity obtained from several different laboratories and are shown in... [Pg.519]

One criterion of aromaticity is the ring current, which is indicated by a chemical shift difference between protons, in the plane of the conjugated system and those above or below the plane. The chemical shifts of two isomeric hydrocarbons are given below. In qualitative terms, which appears to be more aromatic (Because the chemical shift depends on the geometric relationship to the ring current, a quantitative calculation would be necessary to confirm the correctness of this qualitative impression.) Does Hiickel MO theory predict a difference in the aromaticity of these two compounds ... [Pg.545]

Values of kH olki3. o tend to fall in the range 0.5 to 6. The direction of the effect, whether normal or inverse, can often be accounted for by combining a model of the transition state with vibrational frequencies, although quantitative calculation is not reliable. Because of the difficulty in applying rigorous theory to the solvent isotope effect, a phenomenological approach has been developed. We define <[), to be the ratio of D to H in site 1 of a reactant relative to the ratio of D to H in a solvent site. That is. [Pg.300]

Rank tlie results qualitatively on a basis of severity of consequences or perhaps quantitative calculations. [Pg.514]

Several points are worth noting about these formulae. Firstly, the concentrations follow an Arrhenius law except for the constitutional def t, however in no case is the activation energy a single point defect formation energy. Secondly, in a quantitative calculation the activation energy should include a temperature dependence of the formation energies and their formation entropies. The latter will appear as a preexponential factor, for example, the first equation becomes... [Pg.343]

Quantites calcul es comme indique ci-dessus pour les champs de gaz d couverts, avec un degre raisonnablement elev6 de certitude, qui sugg re leur existence probable. [Pg.41]

In general, if K is a very small number, the equilibrium mixture will contain mostly unreacted starting materials for all practical purposes, the forward reaction does not go. Conversely, a large K implies a reaction that, at least in principle, is feasible products should be formed in high yield. Frequently, K has an intermediate value, in which case you must make quantitative calculations concerning the direction or extent of reaction. [Pg.333]

The equation for a chemical reaction speaks in terms of molecules or of moles. It contains the basis for stoichiometric calculations. However, in the laboratory a chemist measures amounts in such units as grams and milliliters. The first step in any quantitative calculation, then, is to convert the measured amounts to moles. In mole units, the balanced reaction connects quantities of reactants and products. Finally, the result is expressed in the desired units (which may not necessarily be the same as the original units). [Pg.225]

Although this approach permits a greater qualitative understanding of the mass-transfer mechanisms that govern the transfer between two phases, it still does not permit quantitative calculations to be made, because the thickness L and the concentration cL are unknown and the total surface area of the bubbles is not included in the model. [Pg.340]

In Chapter 10, we will make quantitative calculations of U- U0 and the other thermodynamic properties for a gas, based on the molecular parameters of the molecules such as mass, bond angles, bond lengths, fundamental vibrational frequencies, and electronic energy levels and degeneracies. [Pg.17]

In equation (1.17), S is entropy, k is a constant known as the Boltzmann constant, and W is the thermodynamic probability. In Chapter 10 we will see how to calculate W. For now, it is sufficient to know that it is equal to the number of arrangements or microstates that a molecule can be in for a particular macrostate. Macrostates with many microstates are those of high probability. Hence, the name thermodynamic probability for W. But macrostates with many microstates are states of high disorder. Thus, on a molecular basis, W, and hence 5, is a measure of the disorder in the system. We will wait for the second law of thermodynamics to make quantitative calculations of AS, the change in S, at which time we will verify the relationship between entropy and disorder. For example, we will show that... [Pg.18]

The considerations presented above were based on the specific assumption that the catalytic reaction of the serine proteases involves mechanism a of Fig. 7.2. However, one can argue that the relevant mechanism is mechanism b (the so-called charge-relay mechanism ). In principle the proper procedure, in case of uncertainty about the actual mechanism, is to perform the calculations for the different alternative mechanisms and to find out which of the calculated activation barriers reproduces the observed one. This procedure, however, can be used with confidence only if the calculations are sufficiently reliable. Fortunately, in many cases one can judge the feasibility of different mechanisms without fully quantitative calculations by a simple conceptual consideration based on the EVB philosophy. To see this point let us consider the feasibility of the charge-relay mechanism (mechanism b) as an alternative to mechanism a. Starting from Fig. 7.2 we note that the energetics of route b can be obtained from the difference between the activation barriers of route b and route a by... [Pg.182]

Here, i, the van t Hoff i factor, is determined experimentally. In a very dilute solution (less than about 10 3 mol-I. ), when all ions are independent, i = 2 for MX salts such as NaCl, i = 3 for MX2 salts such as CaCl2, and so on. For dilute nonelectrolyte solutions, i =l. The i factor is so unreliable, however that it is best to confine quantitative calculations of freezing-point depression to nonelectrolyte solutions. Even these solutions must be dilute enough to be approximately ideal. [Pg.454]

There are two principal methods available for the quantum mechanical treatment of molecular structure, the valence bond method and the molecular orbital method. In this paper we shall make use of the latter, since it is simpler in form and is more easily adapted to quantitative calculations.3 We accordingly consider each electron... [Pg.195]

It has become recognized during recent years that the color of dyes is associated with the resonance of electric charge from atom to atom of the dye molecule.2,3> 4 6 6 Because of the complexity of the problem, however, it has not been easy to expand this idea into a theory of color permitting the rough quantitative calculation of the frequencies and intensities of the absorption bands of dyes. I have now developed a theory of this nature the theory and some of the results of its application are described briefly in the following paragraphs. [Pg.751]

Quantitative calculations can be made on the basis of the assumption that the density of levels in energy for the conduction band is given by the simple expression for the free electron in a box, and the interaction energy e of a dsp hybrid conduction electron and the atomic moment can be calculated from the spectroscopic values of the energy of interaction of electrons in the isolated atom. The results of this calculation for iron are discussed in the following section. [Pg.761]

Rough quantitative calculations of the energy of interaction of the electron pairs and the phonon can be made with use of the force constants for the bonds19 and the changes in the position of the minimum in the potential functions for a bond, as given by the foregoing values of the change in effective radius. [Pg.827]

Motes occupy the centrai position of this flowchart because the mote is the unit that chemists use in almost all chemical calculations. When you set out to solve a chemical problem, first interpret the question on the atomic/molecular level. The second part of chemical problem solving often involves quantitative calculations, which usually require working with moles. [Pg.100]

The problem requires quantitative calculation, because it asks for the number of moles and the number of atoms of Hg present in the plume sample. [Pg.100]

To use the ideal gas equation for quantitative calculations, we must express each quantity in appropriate units. The ideal gas equation holds only when temperature is expressed using an absolute scale. We will always use the Kelvin scale, applying the conversion introduced in Chapter E 7 (K) = T(° C) + 273.15. Typical laboratory pressures are expressed in atmospheres, and typical laboratory volumes are expressed in liters. For this choice of... [Pg.287]

This is a simple quantitative calculation, so we apply the seven-step method in condensed form. We are asked to determine the change in temperature, A 7 , that accompanies a heat flow. Thermal energy is added to each substance, so we expect an increase in temperature for each case. A diagram similar to Figure summarizes the process ... [Pg.364]

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