Closed system with reactions

Simple dynamical systems have proved valuable as models of certain classes of physical systems in many branches of science and engineering. In mechanics and electrical engineering Duffing s and van der Pol s equations have played important roles and in physical chemistry and chemical engineering much has been learned from the study of simple, even artificially simple, systems. In calling them simple we mean to imply that their formulation is as elementary as possible their behaviour may be far from simple. Models should have the two characteristics of feasibility and actuality. By the first we mean that a favourable case can be made for the proposed reaction, perhaps by some further elaboration of mechanism but within the framework of accepted kinetic principles. Thus irreversible reactions are acceptable provided that they can be obtained as the limit of a consistent reversible set. By actuality we mean that they are set in an actual context, as taking place in a stirred tank, on a catalytic surface or in a porous medium. It is not usually necessary to assume the reaction to take place in a closed system with certain components held constant presumably by being in excess. 

Figure 2. pK for equilibrium between Ca-beidellite and kaolinite plotted as a function of Na content of Sierra Nevada spring waters. Arrow ABC is the path of water evolution calculated for the reaction from Na0 62Ca038 plagioclase to kaolinite in a closed system with an initial dissolved C02 of 0.0006 moles per liter. Arrow ABD is the expected path if evolution is also controlled by the two-phase equilibrium kaolinite-montmorillonite... 

This form of the fundamental equation applies at each stage of the reaction. The rate of change of G with extent of reaction for a closed system with a single reaction at constant T and P is given by... 

In a closed system this reaction may be reversible. The rest of the N02 reacts with the oxide, if oxygen is present... 

This reactor is used with solid or liquid catalysts and with liquid reactants, or for gas/liquid reactions in the presence of solid catalysts. Batch reactors are also frequently used, as closed systems with circulation of the gas, for reactions of gases catalysed by solids. Nowadays, relatively few detailed kinetic studies are performed using batch reactors. A common use of these reactors is for the rapid screening of catalysts particularily in high pressure/high temperature reactions. 

The last two hypothetical examples are correct only if the groundwater behaves as a closed system with regard to its 14C 12C ratio. Table 11.2 presents 14C data of basalt aquifers in Hawaii of mainly pre-bomb age, as reflected in the low tritium concentrations. The waters are seen to contain up to 100 mg HC03/1 and have 14C values exceeding 91 pmc in seven out of eight reported pre-bomb cases. It seems, thus, that little or no 14C was lost due to reaction with rocks, and little or no dead carbon (i.e., devoid of 14C) was added by interactions with aquifer rocks, a fact reflected also in the low HCO3 concentration. 

All polymerizations were conducted in a stirred, closed system, with oxygen at atmospheric pressure as the gas phase. Oxygen absorption was measured by an oxygen buret, which formed an integral part of the system. Depending on the reactivity of the diamine used, the reactions were run at room temperature or at slightly elevated temperatures (up to 90 °C.) in pyridine, dimethyl acetamide, hexamethyl phosphortriamide, or mixtures of these. 

Fig. 5.8. Hydrogenation of methylacetylene in a static closed system with various metals as catalysts. Left Pressure drop as a function of time. Right Selectivity to propene as a function of conversion (100% conversion corresponds with the reaction to propene [15]).

In a closed system with a circulating air pump, connect a calcium chloride drying tube and an aerator inserted in a 300-mL reaction vessel so that air passed through the treated preparation contained in the reaction vessel evaporates any metallic mercury present. In a similar manner, treat 100 mL of the Test Solution and 100 mL of water (reagent blank), and determine the maximum absorbances at the same wavelength. The absorbance of the solution from the Test Solution does not exceed that of the solution from the Standard Solution. 

For many routine reactions involving Grignard reagents in diethyl ether, the solvent vapour forms a protective blanket over the solution (cf. Ref. [5]), and drying tubes are adequate to exclude moisture. Nevertheless, the use of closed systems with inert atmospheres is recommended even for preparative work, and for physicochemical studies, where traces of alkoxides may have significant effects, it may be necessary to employ vacuum line techniques, rigorously purified atmospheres in glove boxes, and the like. The cheapest form of inert atmosphere is white spot ... 

In practice, conditions in a reactor are usually quite different than the ideal requirements used in the definition of reaction rates. Normally, a reactor is not a closed system with uniform temperature, pressure, and composition. These ideal conditions can rarely if ever be met even in experimental reactors designed for the measurement of reaction rates. In fact, reaction rates cannot be measured directly in a closed system. In a closed system, the composition of the system varies with time and the rate is then inferred or calculated from these measurements. 

The characteristic feature of CM chondrules is the coexistence of roughly equal amounts of high-temperature anhydrous silicates (olivine and pyroxene) and low-temperature hydrous clay minerals. It is generally believed that the clay minerals were formed by aqueous alteration of the high-temperature phases, either in space or in the parent body. Figure 7 shows that the phyllosilicate matrix is systematically enriched in the heavy isotopes of oxygen, relative to the whole rock. The tie-lines between whole-rock compositions and matrix compositions have slopes of —0.7, implying that the water reservoir had a composition with more positive than the silicate reservoir. Clayton and Mayeda (1999) showed that the observed patterns can be accounted for with a simple closed-system hydration reaction at temperatures near 0°C,... 

Tablets made with equivalent amounts of NaHCOs and tartaric acid were stored at 70° C. In a closed system, a reaction between the NaHCOs and the tartaric acid occurred. When the tablets were stored as an open system, the weight loss was concluded to be a decarboxylation of the NaHCOs. ...

The temperature is increased to 620 °C at a increasing rate of lOK/min and this temperature is kept for 2h. When the zeolite is completely dry, the temperature of the reactor is reduced to 520 K (247 °C), and a N2 gas stream saturated with SiCLt is passed again into the reactor (5 L/h). The temperature is now adjusted to the reaction-required value (7r), which is kept for about 40 min. Afterward, the SiCl4 stream is stopped, and the system is blown for another 15 min, then cooled to room temperature. The product is washed with distilled water until no CP is present. The final product is dried at 400 K (127 °C), and if NH4+-type zeolite is required, the product is subject to exchange with 1 mol/L aq. NH4C1 at room temperature several times. The dealumination degree is closely correlated with reaction temperature (Tu) (Table 6.6). 

The dissolved species composition of most deep, confined groundwater and of some deep unconfined groundwater may remain constant for periods of years or even thousands of years. Such constancy suggests that reactions involving those species have come to thermodynamic equilibrium. When this is the case, the water/rock system involved can be considered a closed system with respect to those species and their controlling reactions in a thermodynamic sense (the system is open to the flow of energy, but closed to the flow of matter remember that equilibrium is the time-invariant state of a closed system). For these conditions equilibrium concepts can be used to explain concentrations of the aqueous species involved. 

Caution this transformation produces nitrogen gas. The reaction system should be vented. Do not run in a closed system This reaction may also be run with diethyl ether ) A suspension of the hydrazone (20.0 g, 43.2 mmol) in methyl /ert-butylcther (MTBE 400 mL) was treated with a solution of MeLi as a complex with LiBr (1.5 M in fT O, 86.3 mL, 0.13 mol) at room temperature for 1 h, cooled to 0 °C, and quenched with water (500 mL). The reaction was extracted with MTBE (1 L), the organic layer was dried (MgSO4), and the solvent was removed in vacuo to give 12.0 g (99%) of the alkene as a white solid. 

For closed systems with chemical reactions, the enthalpy varies due to changes in both composition and temperature. We usually select a reference state at some... 

The rates of reactions may be measured when the concentrations adjust to sudden changes in pressure. This is often combined with conductivity measurements. The value of AF needed depends on AE , but typically a value of 10 MPa is used. Normally, P-jumps are generated by forcing water into a fixed volume until a membrane (made of brass foil, 0.1 mm thick) ruptures, permitting the pressure to drop to the ambient value in about 50 ps. There is no upper limit for F-jumps on an acceptable time scale. A variable-pressure version has been demonstrated. The key feature was a closed system with a large reservoir pressurized to the desired final pressure and with a smaller... 

As a consequence of the conservation of the mass of the elements, the following holds for a closed system with several components in which a chemical reaction is taking place ... 

To an oxyhemoglobin solution (2.5 ml.) which was equilibrated with ak, 10 /xmoles of catechol and about 100 /xgrams of metapyrocatechase were added in a closed system. The reactions were carried out in a... 

To a metapyrocatechase solution in 0.05Af potassium phosphate buffer, pH 7.5 (approximately 2.5 ml.), which was equilibrated with air 5 /xmoles of catechol were added in a closed system. The reactions were carried out in a cuvette with a 0.5-cm. light path at 24 °C. The cuvette was filled with reaction mixture and covered with a glass plate to avoid contact with air. The product formed was directly determined spectrophotometrically at 430 m/x. 

An oxidizing decomposition reaction and an explosion differ mainly in the reaction rate. Explosion processes proceed so fast that the combustion energy becomes visible in form of a flame. The wanning of the environment due to heat radiation will lead to a pressure rise in closed systems with all possible damaging consequences. 

A useful way to depict how highly energetic polymerization reactions are is the computation of their adiabatic temperature rise. Adiabatic temperature rise, is defined as the maximum temperature rise achieved during an exothermic chemical reaction when all heat generated by the reaction is adsorbed by the reacting mass in a closed system with... 

Molar balance in open and closed systems with chemical reaction... 

Molar balance in open and closed systems with chemical reaction S3 By substituting the expression of the rate G, in Equation 4.1, we obtain ... 

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