When negligible

This displays the facts that the field inside a dielectric is not simply that which is applied externally (but is modified by intervening polarized molecules), and that the medium may contain k kinds of oscillators each with its own proper frequency vq. In the case of a single oscillator, the same in all the N molecules per gram-molecule, and when negligible compared with vl, we have (20), from (18) and (19) ... 

At low pressures, it is often permissible to neglect nonidealities of the vapor phase. If these nonidealities are not negligible, they can have the effect of introducing a nonrandom trend into the plotted residuals similar to that introduced by systematic error. Experience here has shown that application of vapor-phase corrections for nonidealities gives a better representation of the data by the model, oven when these corrections... 

Wlien is very short, which is almost always true with nuclei having/> 1/2, the dipolar contribution to relaxation will be negligible and, hence, there will be no contributions to the integral from either NOE or saturation. However, resonances more than about 1 kHz wide may lose intensify simply because part of the FID will be lost before it can be digitized, and resonances more than 10 kHz wide may be lost altogether. It is also hard to correct for minor baseline distortions when the peaks themselves are very broad. 

When the non-adiabatic coupling terms x and x are considered negligibly small and dropped from Eq. (B.15), we get the uncoupled approximate Schrbdinger equation... 

For vei y small vibronic coupling, the quadratic terms in the power series expansion of the electronic Hamiltonian in normal coordinates (see Appendix E) may be considered to be negligible, and hence the potential energy surface has rotational symmetry but shows no separate minima at the bottom of the moat. In this case, the pair of vibronic levels Aj and A2 in < 3 become degenerate by accident, and the D3/, quantum numbers (vi,V2,/2) may be used to label the vibronic levels of the X3 molecule. When the coupling of the... 

The amount of halic(I) acid formed when the halogen reacts reversibly with water decreases from chlorine to iodine and the concentration of iodic(I) acid in a saturated solution of iodine is negligible. However the equilibrium... 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

Fig. II, 56, 6 is a simple distillation head when this is fitted into a flask with a ground glass socket, the assembly is virtually a distillation flask. The bottom cone is usually 19, 24 or 29 the side cone is generafly B19 but may be 24 the thermometer socket is 14. For many purposes, a thermometer is fitted into a one-hole rubber stopper of correct taper and then inserted into the 14 socket the area of rubber which is exposed to the action of the organic vapour is relatively so small that the amount of contamination thus introduced is negligible. If, however, all rubber stoppers must be absent because of the highly corrosive character of the vapour, a thermometer with a 14 cone is employed. It is important to have the thermometer of the same glass as the distillation head, otherwise difficulties may arise owing to the different expansion coefficients of the two kinds of glass.

Equip a 1-litre three-necked flask with a powerful mechanical stirrer, a separatory funnel with stem extending to the bottom of the flask, and a thermometer. Cool the flask in a mixture of ice and salt. Place a solution of 95 g. of A.R. sodium nitrite in 375 ml. of water in the flask and stir. When the temperature has fallen to 0° (or slightly below) introduce slowly from the separatory funnel a mixture of 25 ml. of water, 62 5 g. (34 ml.) of concentrated sulphuric acid and 110 g. (135 ml.) of n-amyl alcohol, which has previously been cooled to 0°. The rate of addition must be controlled so that the temperature is maintained at 1° the addition takes 45-60 minutes. AUow the mixture to stand for 1 5 hours and then filter from the precipitated sodium sulphate (1). Separate the upper yellow n-amyl nitrite layer, wash it with a solution containing 1 g. of sodium bicarbonate and 12 5 g. of sodium chloride in 50 ml. of water, and dry it with 5-7 g. of anhydrous magnesium sulphate. The resulting crude n-amyl nitrite (107 g.) is satisfactory for many purposes (2). Upon distillation, it passes over largely at 104° with negligible decomposition. The b.p. under reduced pressure is 29°/40 mm. 

The density determination may be carried out at the temperature of the laboratory. The liquid should stand for at least one hour and a thermometer placed either in the liquid (if practicable) or in its immediate vicinity. It is usually better to conduct the measurement at a temperature of 20° or 25° throughout this volume a standard temperature of 20° will be adopted. To determine the density of a liquid at 20°, a clean, corked test-tube containing about 5 ml. of toe liquid is immersed for about three-quarters of its length in a water thermostat at 20° for about 2 hours. An empty test-tube and a shallow beaker (e.g., a Baco beaker) are also supported in the thermostat so that only the rims protrude above the surface of the water the pycnometer is supported by its capillary arms on the rim of the test-tube, and the small crucible is placed in the beaker, which is covered with a clock glass. When the liquid has acquired the temperature of the thermostat, the small crucible is removed, charged with the liquid, the pycnometer rapidly filled and adjusted to the mark. With practice, the whole operation can be completed in about half a minute. The error introduced if the temperature of the laboratory differs by as much as 10° from that of the thermostat does not exceed 1 mg. if the temperature of the laboratory is adjusted so that it does not differ by more than 1-2° from 20°, the error is negligible. The weight of the empty pycnometer and also filled with distilled (preferably conductivity) water at 20° should also be determined. The density of the liquid can then be computed. 

The differenee in these two results (parts a. and b.) will beeome negligible at large values of Z when the perturbation beeomes less signifieant as in the ease of Z = 1. 

Nuclei have many times more mass than electrons. During a very small period of time when the movement of heavy nuclei is negligible, electrons are moving so fast that their distribution is smooth. This leads to the approximation that the electron distribution is dependent only on the fixed positions of nuclei and not on their velocities. This approximation allows two simplifications... 

Electric current ampere A Magnitude of the current that, when flowing through each of two straight parallel conductors of infinite length, of negligible cross-section, separated by 1 meter in a vacuum, results in a force between the two wires of 2 X 10 newton per meter of length. 

The cryoscopic constant Kj gives the depression of the melting point AT (in degrees Celsius) produced when 1 mol of solute is dissolved in 1000 g of a solvent. It is applicable only to dilute solutions for which the number of moles of solute is negligible in comparison with the number of moles of solvent. It is often used for molecular weight determinations. 

The molecules in an adsorbed layer interact not only with the solid, hut also with their neighbours within the layer. The effect is negligible when the fractional coverage 0 of the surface is small and the adsorbed molecules are therefore far apart, but it becomes increasingly significant as the monolayer becomes more and more crowded. A densely occupied monolayer will act in some degree as an extension of the solid, and will be able to attract further molecules from the gas phase in the manner already described, though more... 

A second criticism is that the model restricts attention to the forces between the adsorbent and the adsorbate molecules—the vertical interactions—and neglects the forces between an adsorbate molecule and its neighbours in the same layer—the horizontal interactions. From the nature of intermolecular forces (p. 5) it is certain that these adsorbate-adsorbate interactions must be far from negligible when a layer is approaching completion and the average separation of the molecules is therefore small in relation to their size. 

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

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