Temperature, convenience

Since the interposition of a barrier layer diminishes the effective contact between reactants, the nucleation step in solid + solid reactions is Usually completed very rapidly at temperatures conveniently used in studies of the bulk reaction and, accordingly, the rate processes are often deceleratory throughout. In addition to the progressive diminution in rate... 

Pentane and toluene were selected as SCF solvents because these hydrocarbons have critical temperatures convenient to the desired operating temperatures for processing petroleum residua and coal liquids, respectively. 

The metalorganic precursor compounds that have been most commonly used to grow thin films of semiconductors and related materials are listed below in Table I, along with the currently available vapor pressure data. These precursors are typically pyrophoric liquids or high-vapor-pressure solids. The simple metal alkyls (methyl and ethyl derivatives) are the most often employed for the growth of III-V compound semiconductors since they have reasonably high vapor pressures and can be readily delivered using a H2 carrier gas and precursor source temperatures conveniently near room temperature. 

Consider the reaction C02(g) + H2(g) - CO(g) + H20(flr) at 25°C. This is a reaction commonly encountered in the chemical industry (the water-gas-shift reaction), though it takes place only at temperatures well above 25°C. However, the data used are for 25°C, and the initial step in any calculation of thermal effects concerned with this reaction is to evaluate the standard heat of reaction at 25°C. Since the reaction is actually carried out entirely in the gas phase at high temperature, convenience dictates that the standard states of all products and reactants at 25°C be taken as the ideal-gas state at 1 bar or l(atm), even though water cannot actually exist as a gas at these conditions. The pertinent formation reactions are... 

In solution, the complexes 11 lose dinitrogen slowly at room temperature (convenient rates are obtained at 60°) to give the alkylidene complexes, 12 (eq. 31) (37J. Since carbenes are two-... 

Reaction of Metals on Water or Dilute Acid. Electropositive metals, such as the alkali metals and alkaline earth metals, are so chemically reactive that they rapidly displace hydrogen from water or dilute acid at room temperature. Convenient laboratory methods employ sodium amalgam or calcium with water, or zinc with hydrochloric acid ... 

We assume that a decomposition reaction exhibiting product inhibition depends upon temperature and reaction time in such a way that two energies of activation, E and E, can be defined, both constant from some very low conversion to the highest conversion of interest. E = energy of activation calculated from values of fraction unconverted (X) at constant conversion and variable time and temperature. E is calculated at constant reaction time and variable conversion and temperature. Also we define r = EE and Xx = fraction unconverted at T = Tx and t = fi, where tx and Tx are reaction times and temperatures conveniently chosen in the range of the known data. 

Since the reaction is actually carried out entirely in the gas phase at high temperature, convenience dictates that the standard states of all products and reactants at 298.15 K (25°C) be taken as the ideal-gas state at I bar, even though water camiot actually exist as a gas at these conditions. 

Low viscosity reduced volatility good pot life ambient cure temperature convenient mix ratios good toughness... 

However, if the liquid solution contains a noncondensable component, the normalization shown in Equation (13) cannot be applied to that component since a pure, supercritical liquid is a physical impossibility. Sometimes it is convenient to introduce the concept of a pure, hypothetical supercritical liquid and to evaluate its properties by extrapolation provided that the component in question is not excessively above its critical temperature, this concept is useful, as discussed later. We refer to those hypothetical liquids as condensable components whenever they follow the convention of Equation (13). However, for a highly supercritical component (e.g., H2 or N2 at room temperature) the concept of a hypothetical liquid is of little use since the extrapolation of pure-liquid properties in this case is so excessive as to lose physical significance. 

The pressure at which standard-state fugacities are most conveniently evaluated is suggested by considerations based on the Gibbs-Duhem equation which says that at constant temperature and pressure... 

The maximum concentration atltainable under such conditions is termed the solubility of the substance at the specific temperature used in the experiment, since solubility generally increases with rising temperature. Solubility is usually expressed in grams per 100 g of solvent, or grams per 100 g of solution. Sometimes, for practical convenience, it may be expressed in grams per 100 ml of solvent or solution. 

The sulphonic acids are usually prepared by the action of sulphuric acid upon a compound. The concentration of the acid and the temperature of reaction are varied according to the reactivity of the compound. Often oleum is used or even chiorosulphonic acid. Alternatively sulphur trioxide complexed to pyridine or dioxan can be used with reactive substrates. Aminosulphonic acids such as sulphanilic and naphthionic acids are most conveniently prepared by heating the sulphate of the amine at ISO C. 

The above equation is valid at low pressures where the assumptions hold. However, at typical reservoir temperatures and pressures, the assumptions are no longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the ideal gas law. In practice, it is convenient to represent the behaviour of these real gases by introducing a correction factor known as the gas deviation factor, (also called the dimensionless compressibility factor, or z-factor) into the ideal gas law ... 

As stated in the introduction to the previous chapter, adsorption is described phenomenologically in terms of an empirical adsorption function n = f(P, T) where n is the amount adsorbed. As a matter of experimental convenience, one usually determines the adsorption isotherm n = fr(P), in a detailed study, this is done for several temperatures. Figure XVII-1 displays some of the extensive data of Drain and Morrison [1]. It is fairly common in physical adsorption systems for the low-pressure data to suggest that a limiting adsorption is being reached, as in Fig. XVII-la, but for continued further adsorption to occur at pressures approaching the saturation or condensation pressure (which would be close to 1 atm for N2 at 75 K), as in Fig. XVII-Ih. 

There are an infinite number of other integrating factors X with corresponding fiinctions ( ) the new quantities T and. S are chosen for convenience.. S is, of course, the entropy and T, a fiinction of 0 only, is the absolute temperature , which will turn out to be the ideal-gas temperature, 0jg. The constant C is just a scale factor detennining the size of the degree. 

In experimental work it is usually most convenient to regard temperature and pressure as die independent variables, and for this reason the tenn partial molar quantity (denoted by a bar above the quantity) is always restricted to the derivative with respect to Uj holding T, p, and all the other n.j constant. (Thus iX = [right-hand side of equation (A2.1.44) it is apparent that the chemical potential... 

On the other hand, in the theoretical calculations of statistical mechanics, it is frequently more convenient to use volume as an independent variable, so it is important to preserve the general importance of the chemical potential as something more than a quantity GTwhose usefulness is restricted to conditions of constant temperature and pressure. 

It is convenient to define a relative activity a. in tenns of the standard states of the reactants and products at the same temperature and pressure, where Aj = fi, =... 

These are the same states as in Figure Bl.l 1.8, but attention is now drawn to the populations of the four spin states, each reduced by subtracting the 25% population that would exist at very low field, or alternatively at infinite temperature. The figures above each level are these relative differences, in convenient units. The intensity of any one transition, i.e. of the relevant peak in the doublet, is proportional to the difference of these differences, and is therefore proportionally relative to unity for any transition at Boltzmaim equilibrium, and 4 for any transition. 

The Boltzmann constant is ks and T the absolute temperature. — is the Dirac delta function. Below we assume for convenience (equation (5)) that the delta function is narrow, but not infinitely narrow. The random force has a zero mean and no correlation in time. For simplicity we further set the friction to be a scalar which is independent of time or coordinates. 

Hite s treatment is based on equations (5.18) and (5.19) which describe the dusty gas model at the limit of bulk diffusion control and high permeability. Since temperature Is assumed constant, partial pressures are proportional to concentrations, and it is convenient to replace p by cRT, when the flux equations become... 

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