Constant partial pressure

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... 

The effect of plasticizers and temperature on the permeabiUty of small molecules in a typical vinyUdene chloride copolymer has been studied thoroughly. The oxygen permeabiUty doubles with the addition of about 1.7 parts per hundred resin (phr) of common plasticizers, or a temperature increase of 8°C (91). The effects of temperature and plasticizer on the permeabiUty are shown in Figure 4. The moisture (water) vapor transmission rate (MVTR or WVTR) doubles with the addition of about 3.5 phr of common plasticizers (92). The dependence of the WVTR on temperature is a Htde more comphcated. WVTR is commonly reported at a constant difference in relative humidity and not at a constant partial pressure difference. WVTR is a mixed term that increases with increasing temperature because both the fundamental permeabiUty and the fundamental partial pressure at constant relative humidity increase. Carbon dioxide permeabiUty doubles with the addition of about 1.8 phr of common plasticizers, or a temperature increase of 7°C (93). 

Finally, the following remark may be in order on the situation shown in the inset of Fig. 7. The gas branch of the equilibrium f/j-ice-gas represents a constant partial pressure of methane,... 

As indicated, it is suggested that the table be constructed in symbolic form first, and numerical values substituted afterwards. If molar amounts are used, as in the table above, the results are valid whether the density is constant or not. If density is constant, molar concentrations, C , may be used in a similar manner. If both density and temperature are constant, partial pressure, pt, may be used in a similar manner. 

Figure 7.5 Variation of equilibrium oxygen partial pressure (a) equilibrium between a metal, Ag, and its oxide, Ag20, generates a fixed partial pressure of oxygen irrespective of the amount of each compound present at a constant temperature (b) the partial pressure increases with temperature (c) a series of oxides will give a succession of constant partial pressures at a fixed temperature and (d) the Mn-O system. [Data from T. B. Reed, Free Energy of Formation of Binary Compounds An Atlas of Charts for High-Temperature Chemical Calculations, M.I.T. Press, Cambridge, MA, 1971.]...

Equilibrium diagram of CaCC>3 as a function of pH at constant partial pressure of C02 aJPCOs -SxlO 4 atm b) PCOjj = 1 atm. 

Figure 11-1 Equilibrium Constants (Partial Pressures in MPa) for (a) Water Gas Shift, (b) Methane Formation, (c) Carbon Deposition (Boudouard Reaction), and (d) Methane Decomposition (J.R. Rostrup-Nielsen, in Catalysis Science and Technology, Edited by J.R. Anderson and M. Boudart, Springer-Verlag, Berlin GDR, p.l, 1984.)... 

MINTEQA2 http //www.epa.gov/ceampubl/mmedia/minteq/index.htm MINTEQA2 is an equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorbed species, and multiple solid phases under a variety of conditions including a gas phase with constant partial pressures. 

Nitrogen sensitivity (equipment constant) Partial pressure of the gas Ion current for atomic number m... 

Table 5. Effect of Temperature at Constant Partial Pressure CO and Constant Gauge...

If a cell is operated potentiometrically, then only two electrodes are required. However, if closed-circuit operation is to be employed it is necessary to measure electrode overpotentials. To measure electrode overpotentials it is necessary to use a three-electrode DC system. The system consists of a working electrode which is exposed to reaction conditions, a counter electrode (which is exposed to a constant partial pressure of oxygen in the case of an oxygen-ion conducting electrolyte), and a reference electrode. The reference electrode remains unpolarized during the measurements and may be exposed to either reaction conditions or the constant conditions of the counter electrode. A power supply is used to polarise the working and counter electrodes while the current is recorded (see Figure 3). 

Because of non-adherence of the site sorption mode to a strict Langmuir mechanism, as noted previously, Eq. (18), as well as Eqs. (20) or (20 a), must, at the quantitative level, be validated experimentally. This can be done most conveniently by varying the partial pressure of one component at various constant partial pressures of the other. Sorption data of this type have recently been reported for PMMA-C02, C2H4 at 35 °C69 70). As shown in Fig. 7, the agreement between experiment and calculation from the pure component isotherms, though not perfect, is nevertheless quite impressive. 

The simplest case is a mixture of gases with no thermodiffusion or entrainment. Under a temperature gradient, diffusion equilibrium in such a mixture is achieved for constant partial pressure of each component. 

The reactor was next flushed with nitrogen (1 atm) to remove air from the reactor which was then pressurised with hydrogen (13 bar). The reaction proceeded at a constant partial pressure of hydrogen which was taken to be the total pressure. The stirrer speed was increased to 1200 rpm and nitrobenzene (3.7 g, 0.0333 mol) was added at a constant rate of 8 mL min-1. 

Where the flux J is the flow of gas. The flux is the amount of material transported per unit time through a unit surface area and according to Eq. (9-1) is proportional to the constant partial pressure difference Ap between both sides of the membrane. The proportionality constant P is called the permeability coefficient and is the product of the diffusion coefficient D and the solubility coefficient S (or sorption constant) of the gas in the membrane ... 

This reaction lends itself nicely to an experimental demonstration of the influence of concentration on reaction velocity. When crystals of nitrogen pentoxide are left in the reaction chamber they maintain a constant partial pressure corresponding to the sub-... 

Inspection of the curves of the effectiveness factor versus the Weisz modulus for different values of Kp. s and E reveals two interesting phenomena when E > 0 (Fig. 20) [87, 88, 91]. At first, for large values of Ay i.s (10-100) effectiveness factors above unity may occur even though isothermal conditions prevail. This can be explained by the fact that the reaction rate given by eq 103 has a maximum for certain combinations of p and P2. This maximum results from the assumption that the rate is proportional to the concentration of the adsorbed reactants At and A2 which compete for adsorption sites on the active (inner) surface. When, for example, Ai is adsorbed more strongly than A2, then a raised partial pressure of Ai, at constant partial pressure of A2, will lead to a displacement of A2 from the surface, and hence to a lowered reaction rate. By a quantitative analysis, it can be shown that effectiveness factors above unity will appear whenever Kp, is greater than (E + 2)/E [91]. 

The Lambda probe is usually shaped like a sparking plug where the solid-state electrolyte forms a closed-end cylinder that it inserted into the exhaust gas. The inside of the cylinder is in contact with ambient air with a constant partial pressure of oxygen, po2,i> and the outside is in contact with the exhaust gas in which the partial pressure of oxygen, po2,2, is monitored by measuring the potential difference between the two platinum electrodes... 

Fig. 3.3-16 shows that the line width increases as the pressure of a gas increases (even by adding an inert gas at constant partial pressure of the analyte). As a result of condensation of the gas to a liquid, the entire band is reduced to one line. Solidification further reduces the band width. Since the integral intensity remains constant, the intensity of the band maximum increases, and so does the sensitivity (Schrader et al., 1981). In short Reducing the sample temperature increases the sensitivity. 

Results obtained in a constant-pressure semi-batch reactor in which synthesis gas was supplied on demand are listed in Table 5.2. The analytical accuracy is said to be within 0.002 M. [Before alcohol analysis the samples were hydrogenated to convert any residual aldehydes to the corresponding alcohols.] At the resulting constant partial pressures of CO and H2 in the reactor and with very good gas-liquid mass transfer, the CO and H2 concentrations in the liquid remain constant and the rate depends only on the propene concentration (see pseudo-orders, Section 3.3.2). 

Figure 5.11. Concentration histories of alcohol and first four successive ethoxy adducts in batch ethoxylation at constant partial pressure of ethene oxide, calculated for = 0.012 min-1 for reaction of alcohol, k2 = 0.015 min-1 for reaction of adducts (ale = alcohol 1-EO, 2-EO, 3-EO, 4-EO = first, second, third, and fourth adduct, respectively).

All steps from the second on amount to insertion of an ethoxy block between a previously inserted block and the —OH group, and so have very similar rate coefficients. Usually, the original alcohol reacts at a slighdy lower rate. If the reaction is carried out at constant partial pressure of ethene oxide, each insertion including the first is pseudo-first order in the alcohol or ethoxy alcohol reactant. With increasing reaction time in batch, successive adducts reach maximum concentrations and then decay to form higher adducts, as shown for a calculated case in Figure 5.11. The variation in yield structure with reactor space time in a continuous stirred-tank reactor is similar, but with less pronounced concentration maxima. 

Since each step consists of the same chemical event, the oxidation of a secondary carbon atom, the rate coefficients of all steps are almost the same. [With each attack the number of still unoxidized secondary carbon atoms in the molecule decreases, and so does the statistical probability of further oxidation however, for the first few products of a long-chain paraffin this effect remains minor.] At constant partial pressure of oxygen, the steps are pseudo-first order in the respective organic reactant. 

Fig. 7.—Variation of the observed first order decay constants partial pressure of NO. The gas mixtures contained O, —0.125 Torr NO2+2.5 Torr H2 , —0.20 Ton NO2+2.5 Torr H2 , —0.125 Torr NO2 + I5 Torr H2. In all cases the total pressure was made up to 30 Torr by...

Experiments were made at various partial pressures of cyclohexane and hydrogen, but at constant total pressure. Experiments were also made at constant partial pressure of hydrocarbon or hydrogen. The contact time was held constant in this latter case by holding the ratio of hydrocarbon partial pressure to feed rate constant. The rate decreased with an increase in total pressure and with an increase in either hydrocarbon or hydrogen partial pressure. An example of this data taken at 460° is shown in Tables II and III. 

Gas Flow Rate. The model can be extended to consider all five desired variables, and the restriction of a constant partial pressure of carbon dioxide can be removed by developing material balances for carbon dioxide in both the liquid and gas phases. The material balance on dissolved carbon dioxide is shown in Equation 25. Rb is the rate of production of carbon dioxide from the substrate by the methane bacteria and Rc is the rate of production of carbon dioxide from bicarbonate. The reaction of substrate and bicarbonate to produce carbon dioxide is given in Equation 28. 

Figure 4.2. Schematic representation of closed (a, b), open (c) and isolated (d) systems. In system (a) a volatile substance can be exchanged between water and the gas phase. The total quantity of matter within the system remains constant. In system (b) the water phase is closed toward the gas phase no exchange with the gas phase occurs H2CO or NH3 are treated as nonvolatile species. In the open system (c) exchange of matter with the environment occurs for example, a water in equilibrium with the atmosphere is characterized by a constant partial pressure of COaCPco )- System (d) represents an isolated system. No exchange of matter and energy occurs with the environment. (Metaphorically, the system is like a thermos bottle.)...

A very simple model showing some of the characteristics of the carbonate system of natural waters is provided by equilibrating pure water with a gas phase (e.g., the atmosphere) containing CO2 at a constant partial pressure. One may then vary the pH by the addition of strong base or strong acid, thereby keeping the solution in equilibrium with pcoi- This simple model has its coun-... 

Figure 4.14. Equilibrium composition of a solution in presence of CaC03(s) (calcite) at constant partial pressure of CO2 (Pcoz = 10" atm) at 25°C. If no acid or base is added, the equilibrium composition is indicated by the arrow.

Two varieties of calculation are possible in an open-system model, a constant partial pressure of the gas component is maintained in a closed-system model, an initial partial pressure of a component is given, for example, for a... 

IR spectroscopy was mainly used to characterize the sorbed species. The zeolite powder was pressed into self supporting wafers and analyzed in situ during all treatments (i.e., activation, sorption, reaction) by means of transmission absorption IR spectroscopy using a BRUKER IPS 88 FTIR spectrometer (resolution 4 cm" ). For the sorption experiments, an IR cell equipped with IR transparent windows which could be evacuated to pressures below 10" mbar was used [11]. The activated zeolite wafer was contacted with a constant partial pressure (0.001 mbar) of the adsorbate at 308 K until adsorption-desorption equilibrium was reached (which was monitored by time resolved IR spectroscopy). For the coadsorption experiments, the catalysts were equilibrated with 0.001 mbar of both adsorbates admitted in sequentional order. The spectra were normalized for the sample thickness by comparing the intensities of the absorption bands of the adsorbate with the integral intensity of the lattice vibration bands of the zeolite between 2090 and 1740 cm". The surface coverage was quantified by calibration with gravimetric measurements (under conditions identical to the IR spectroscopic experiments). 

Fig. 10 Friction coefficient measured in contact-mode AFM scan as a function of /i-propanol partial pressure. Filled squares are data taken at increasingly larger constant partial pressures, and open circles are those taken at decreasingly smaller constant partial pressures.

Fickian Diffusion and Linear Driving Force models are generally used to describe the transport of water vapour into the alumina particles. For isothermal adsorption of water vapour from a constant partial pressure (P ) batch adsorption system on a spherical adsorbent particle of radius Rp, the uptake profiles are given by [13] ... 

For constant partial pressure, Tf is inversely proportional to total pressure. Therefore, A T will decrease with an increase in total pressure. This translates to isothermal operation... 

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