Equilibrium involving pressures

Since capillary tubing is involved in osmotic experiments, there are several points pertaining to this feature that should be noted. First, tubes that are carefully matched in diameter should be used so that no correction for surface tension effects need be considered. Next it should be appreciated that an equilibrium osmotic pressure can develop in a capillary tube with a minimum flow of solvent, and therefore the measured value of II applies to the solution as prepared. The pressure, of course, is independent of the cross-sectional area of the liquid column, but if too much solvent transfer were involved, then the effects of dilution would also have to be considered. Now let us examine the practical units that are used to express the concentration of solutions in these experiments. 

In Chap. 8 we saw how the equilibrium osmotic pressure of a solution is related to AG for the mixing process whereby the solution is formed. Any difference in the concentration of the solution involves a change in AG j, ... 

Reaction quotient (Q) An expression with the same form as Kbut involving arbitrary rather than equilibrium partial pressures, 333-334 Reaction rate The ratio of the change in concentration of a species divided by the time interval over which the change occurs, 285 catalysis for, 305-307 collision model, 298-300 concentration and, 287-292,314q constant, 288 enzymes, 306-307 egression, 288... 

When studying heterogeneous equilibria involving clathrates, one is faced with peculiar difficulties owing to the hysteresis effects mentioned in the introduction the solute in a clathrate crystal of hydroquinone, for instance, will not come to thermodynamic equilibrium with the vapor in which it is placed. Consequently it is impossible, or at least very difficult, to measure the equilibrium vapor pressure of the solute in a clathrate by placing some crystals in a tensometer (cf. the experiments of Wynne-Jones and Anderson,58 and those of Leech and Richards reported by Powell33). 

Binary (vapor + liquid) equilibria studies involve the determination of / as a function of composition. the mole fraction in the liquid phase. Of special interest is the dependence of/ on composition in the limit of infinite dilution. In the examples which follow, equilibrium vapor pressures, p,. are measured and described. These vapor pressures can be corrected to vapor fugacities using the techniques described in the previous section. As stated earlier, at the low pressures involved in most experiments, the difference between p, and / is very small, and we will ignore it unless a specific application requires a differentiation between the two. 

The equilibrium oxygen pressure over the series of iron oxides at 1100°C is shown in the figure, (a) What phases are involved (b) What does the sloping part of the plot indicate (c) Write equations for each of the formation reactions taking place, (d) Estimate the value of the reaction Gibbs energy, AGr per mole of product, at 1100°C for each reaction. The value of AGr for the formation of... 

The procedure developed by Joris and Kalitventzeff (1987) aims to classify the variables and measurements involved in any type of plant model. The system of equations that represents plant operation involves state variables (temperature, pressure, partial molar flowrates of components, extents of reactions), measurements, and link variables (those that relate certain measurements to state variables). This system is made up of material and energy balances, liquid-vapor equilibrium relationships, pressure equality equations, link equations, etc. 

For first-order reactions then, there is no compressibility term in the expression for In k, no matter what concentration scale is used. For higher order reactions involving molar concentrations, Eq. (22) could be applied when accurate rate data are available. Whether Eq. (27) should be applied depends on the method used for obtaining the data. If a spectrophotometric determination of the relative decrease in [A] is used, a relative measure of (d In k/dp)T is obtained from Eq. (27). If an absolute determination of [A] can be made at various times, Eq. (24) can be used directly, and k and (d In k/dp)T can be immediately obtained. The situation is easily generalized to higher order kinetics. In some cases, where AVf < 0 and the method of measurement detects [A] but not [X ], there may be a slight displacement of the quasi-equilibrium with pressure which leads to different initial concentrations of A. When AVf can be determined from Eq. (22), it may appear pressure-dependent, i.e.,... 

Mass transfer in polymeric solutions by molecular diffusion is a comparatively slow process, and in extraction equipment where mass transfer occurs through a thin wiped film, inordinately large equipment surface areas are often required in order to obtain substantial rates of mass transfer. In commercial practice when this situation occurs, the required surface areas may, instead, be obtained by either one of two methods, both of which involve reducing the pressure in the extraction zone. In one approach the extraction pressure is fixed at a value which is less than the equilibrium partial pressure of the monomer or solvent in the polymeric solution fed to the extraction zone. In these circumstances gas bubbles... 

The BET method (Brunauer, Emmett and Teller, 1938) with N2 as the adsorbate, is by far the most common method of measuring the surface areas of Fe oxides. Various commerical instruments are available for these measurements. The method involves measuring the extent of adsorption of N2 (at the boiling temperature of liquid N2 - 77 K) on the outgassed solid as a function of the relative pressure, p/po. he. the adsorption isotherm p is the partial pressure of the adsorbate and po is its equilibrium vapour pressure. The following linear relationship exists between the amount adsorbed, v, (cm g ) and the relative vapour pressure, p/po, ... 

It is important to remember the significance of irv. It refers specifically to the equilibrium between two surface states. There is a danger of confusing ttv with the equilibrium spreading pressure ire, introduced in Chapter 6. The latter is the pressure of the equilibrium film that exists in the presence of excess bulk material on the surface. It is the equilibrium spreading pressure that is involved in the modification of Young s equation (Equation (6.49)), for which a bulk phase is present on the substrate. For tetradecanol at 15°C, the equilibrium spreading pressure is about 4.5 10 2 N m so ire and irv are very different from one another. 

We can generalize from this example and say that, for any chemical equilibrium involving a different number of moles of gas on each side of the balanced equation, the equilibrium position will always shift with an increase in total pressure toward the side with the smaller number of gaseous moles the value ofXp will remain unchanged. 

Other perturbations have been demonstrated. The pressure,, jump, similar to the T-jump in principle, is attractive for organic reactions where Joule heating may be impractical both because of the solvent being used and because concentrations might have to be measured by conductivity. Large (104—105 kPa) pressures are needed to perturb equilibrium constants. One approach involves pressurizing a liquid solution until a membrane ruptures and drops the pressure to ambient. Electric field perturbations affect some reactions and have also been used (2), but infrequendy. 

Figure A.l. displays the various forms of writing equilibrium constants involving pressure, concentration, molality, mole fractions and fugacity etc - for a general reaction of the form ...

Equilibrium — A system has reached equilibrium when the properties of the system (such as volume, pressure, color, composition, etc.) no longer change with time. For a chemical equilibrium (involving one or more reversible chemical reactions), the forward and reverse directions of each reaction proceed at equal rates and the system has reached a state of minimum -> Gibbs energy. See also -> reversibility. 

Figure 4.1b is a typical illustration of the Donnan equilibrium [1], A membrane impermeable to macroions (P" ) but permeable to small ions (M+, X ) and solvent molecules (S) divides a solution into two regions. The situation is a common one in colloid science, and the fact that the equilibrium salt concentration in region II (the simple electrolyte solution), [X ]n, is greater than that in region I (the region occupied by the macroions), [X ]I( has been used in countless dialysis experiments. It is also well known [2] that equilibrium involves the establishment of not only a pressure difference but also an electrical potential difference across the membrane and that, in the simple case where the mobile ions behave as ideal solutes, the equilibrium condition is expressed as... 

Consider the conditions of equilibrium involving the chemical potentials for two phases at specified temperature and pressure. Show that a double tangent... 

The equilibrium involving ReFg, irFg, ReF-y and (irF ) occurs in the condensed phase at ordinary temperatures. Because ReFg and IrFg are each in equilibrium with appreciable pressures of the vapors [14,15]) at room temperature, hG° for equation (3) can be taken as approximately equal to AG° for equation (8) ... 

We now cite the types of experimental data in the literature, by which an analysis of surface adsorption effects is carried out. One common experiment involves measuring adsorption isotherms. By weighing or by volumetric techniques one determines as a function of equilibrium gas pressure the amount of gas held on a given surface at a specified temperature. Usually this quantity varies sigmoidally with rising pressure P, as sketched in Fig. 5.2.1 for a variety of temperatures 7). By standard methods that rely on the Brunauer, Emmett, Teller isotherm equa-tion one can determine the point on the isotherms at which monolayer coverage of the surface is complete it is usually is located fairly close to the knee of the isotherm. From the cross sectional area of the adsorbate molecules and from the amount needed for monolayer coverage one may then ascertain more or less quantitatively the surface area of the adsorbent. As-... 

Calculate the equilibrium partial pressures of all species involved in a gas-phase chemical or gas-solid reaction from the initial pressure(s) of the reactants (Section 14.5, Problems 27-32). 

---