Elementary amount

The fact above can be stated differently. Instead of saying that a substance is made up of countable particles, one might say that there is a smallest possible portion of substance, an elementary amount (of substance) t. The following is valid for this elementary amount ... 

In this case, N is the particle number, r is the elementary amount of substance that we already used in Sect. 1.4, and is the Boltzmann constant (a natural constant just as R and t). Accordingly, we obtain for pressure according to the (modified) gas law ... 

Elementary amount (of substance), quantum of amount (of substance) (15, 16)... 

Amount of substance mole mol Amount of substance which contains as many specified entities as there are atoms of car-bon-12 in exactly 0.012 kg of that nuclide. The elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. 

Mole. The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. 

Injection of Water or Steam at the Gas Turbine Compressor Exit. Steam injection or water injection has been often used to augment the power generated from the turbine as seen in Figure 2-42. Steam can be generated from the exhaust gases of the gas turbine. The HRSG for such a unit is very elementary as the pressures are low. This technique augments power and also increases the turbine efficiency. The amount of steam is limited to about... 

Alkyl fluorides have been prepared by reaction between elementary fluorine and the paraffins, by the addition of hydrogen fluoride to olefins, by the reaction of alkyl halides with mercurous fluoride, with mercuric fluoride, with silver fluoride, or with potassium fluoride under pressure. The procedure used is based on that of Hoffmann involving interaction at atmospheric pressure of anhydrous potassium fluoride with an alkyl halide in the presence of ethylene glycol as a solvent for the inorganic fluoride a small amount of olefin accompanies the alkyl fluoride produced and is readily removed by treatment with bromine-potassium bromide solution. Methods for the preparation of alkyl monofluorides have been reviewed. ... 

In the second approach, a value for is not assumed but a relationship for dip/dT is determined from semi-empirical expressions for the amount of cooling air that is required in an (elementary) turbine blade row. One such relationship, derived in Ref. [5], gives... 

Let us assume that A P is an elementary reaction and that it is spontaneous and essentially irreversible. Irreversibility is easily assumed if the rate of P conversion to A is very slow or the concentration of P (expressed as [P]) is negligible under the conditions chosen. The velocity, v, or rate, of the reaction A P is the amount of P formed or the amount of A consumed per unit time, t. That is. 

In view of the enthalpy and activation energy (see Section II, B, 1) of the decomposition of arylpentazoles the activation energy for the reversal of the decomposition, the 1,3-addition of elementary nitrogen to arylazides, can be estimated to be 25-30 kcal/mole, an amount which does not exclude the reaction. To ascertain whether the decomposition of arylpentazoles is a reversible reaction, p-ethoxyphenylazide-[j8-N ] (see Section II, B, 3) adsorbed on charcoal was exposed to unlabeled nitrogen (45-50°, 380 atm, 100 hr), but the anticipated exchange of between the reactants was not detected. ... 

The mole is the amount of substance which contains as many elementary units as there are atoms in 0.012 kilogram of carbon-12. The elementary unit must be specified and may be an atom, a molecule, an ion, a radical, an electron or other particle or a specified group of such particles. ... 

Discussion. This gravimetric determination depends upon the separation and weighing as elementary selenium or tellurium (or as tellurium dioxide). Alkali selenites and selenious acid are reduced in hydrochloric acid solution with sulphur dioxide, hydroxylammonium chloride, hydrazinium sulphate or hydrazine hydrate. Alkali selenates and selenic acid are not reduced by sulphur dioxide alone, but are readily reduced by a saturated solution of sulphur dioxide in concentrated hydrochloric acid. In working with selenium it must be remembered that appreciable amounts of the element may be lost on warming strong hydrochloric acid solutions of its compounds if dilute acid solutions (concentration <6M) are heated at temperatures below 100 °C the loss is negligible. 

The use of even the very simple models for isothermal operation described in Section IV,B requires a substantial amount of information regarding the elementary iate processes occurring in a gas-liquid-particle operation, as discussed in Section IV,A. While a considerable amount of information of this kind is available in the chemical engineering literature, it is widely scattered. It will be attempted in this section to present a comprehensive review of this information in order to facilitate its use. It is hoped that this review will be of value not only to those chemical engineers directly interested in the practical applications of gas-liquid-particle operations, but also, by pointing to the several areas characterized by very limited information, to those interested in research in this field. 

Assuming that the reaction probability of all the elementary processes is equal in the reaction of 1,4-DCB crystals, the calculated yields of unreacted 1,4-DCB, cyclophane, and oligomer by simulation, should be 1.8, 37.7, and 60.5% by weight, respectively. Furthermore, if all the photoexcited species of the monocyclic dimer are assumed to be converted into cyclophane, these yields should become 6.9, 65.6 and 27.5%. It is, therefore, rather surprising that in an extreme case of the experiment the yield of cyclophane is more than 90% while the amount of unreacted 1,4-DCB is less than 2%. One plausible mechanism to explain this result is that the first formation of cyclophane induces the successive formation of cyclophane so as to enhance its final yield. If such an induction mechanism plays an appreciable role, an optically active cyclophane zone may be formed, at least in a micro spot surrounding the first molecule of cyclophane, as illustrated in Scheme 13. The assumption of an induction mechanism was verified later in the photoreaction of 7 OMe crystals (see p. 151). 

The undoubtedly structure-sensitive reaction NO -r CO has a rate that varies with rhodium surface structure. A temperature-programmed analysis (Fig. 10.8) gives a good impression of the individual reaction steps CO and NO adsorbed in relatively similar amounts on Rh(lll) and Rh(lOO) give rise to the evolution of CO, CO2, and N2, whereas desorption of NO is not observed at these coverages. Hence, the TPRS experiment of Fig. 10.8 suggests the following elementary steps ... 

One of the regions of the USSR that suffered most from pesticide use was Uzbekistan, where a large amount of work took place in the 1960s without even elementary knowledge, and with chronic and mass violations of existing regulations and standards [A49]. 

A mole of a substance is the number of elementary particles (atoms, molecules) found in the mass (in grams) of that substance that corresponds to its atomic or molecular weight. In molar volumes, which amount to 22.4 L for gases and are different from solid to solid, there are always the same number of atoms or molecules. This "magic number", Avogadro s number, is 6.022xl023 mol-1. 

Water — not an element, but elementary for.life. For this reason, when astronomers suspect life on distant worlds, they search for water. In this respect, the Earth is paradise. 71% of the surface is covered with water with a volume of 1.386 million km3. This equates to a cube with an edge length of 1110 km, which is almost equivalent to one third of the diameter of the moon. This amount would be plentiful if life on land were not dependent on fresh water. Sea water, with approxi-... 

Many individual finite state automata are joined together to form a regular array in one, two, or more dimensions this entire array is the cellular automaton. The CA evolve, as all cells in this array update their state synchronously. Into each cell is fed a small amount of input provided by its neighbors. Taking account of this input, the cell then generates some output, which determines the next state of the cell in deciding what its output should be, each cell consults its state, which consists of one piece, or a few pieces, of information stored within it. In the most elementary of automata, the state of the cell that comprises this finite state automaton is very simple, perhaps just... 

The BET approach is essentially an extension of the Langmuir approach. Van der Waals forces are regarded as the dominant forces, and the adsorption of all layers is regarded as physical, not chemical. One sets the rates of adsorption and desorption equal to one another, as in the Langmuir case in addition, one requires that the rates of adsorption and desorption be identical for each and every molecular layer. That is, the rate of condensation on the bare surface is equal to the rate of evaporation of molecules in the first layer. The rate of evaporation from the second layer is equal to the rate of condensation on top of the first layer, etc. One then sums over the layers to determine the total amount of adsorbed material. The derivation also assumes that the heat of adsorption of each layer other than the first is equal to the heat of condensation of the bulk adsorbate material (i.e., van der Waals forces of the adsorbent are transmitted only to the first layer). If it is assumed that a very large or effectively infinite number of layers can be adsorbed, the following result is arrived at after a number of relatively elementary mathematical operations... 

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