Partial pressures pressure-volume changes

Keep in mind that, as long as temperature remains constant, pressure-volume changes do not change the value of K. Rather, these changes alter the partial pressures of the gaseous substances. In Sample Exercise 15.8, we calculated Kp = 2.79 X 10 for... 

Previous studies of the effect of pressure on reactions of electrons have been done mainly in polar solvents. In water, electron reaction rates typically change at most by 30% for a 6-kbar pressure change (Hentz et al., 1972). However, the reaction of electrons with benzene in liquid ammonia is accelerated considerably by pressure the volume change for this reaction is -71 cc/mole (B6 ddeker et al., 1969). Studies of this type have been used to provide information on the partial molar volume of the electron in polar solvents. 

Example Partial Molar Volume. Consider a binary liquid mixture (A and B) at constant temperature and pressure. The volume change due to a differential change of the composition is... 

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

The temperature change is also small so that the exponential term can be taken as unity. The molar flow G can be assumed to be constant between A and B and the C02 conversion is proportional to the change in C02 partial pressure, dp. The volume of the section of bed is Adi so that the rate of C02 conversion, dX, is therefore ... 

Chao and Seader assume that the partial molar volumes are independent of composition this assumption is equivalent to saying that at constant temperature and pressure there is no volume change upon mixing the pure liquid components, be they real or hypothetical. The term on the right-hand side of Eq. (46) is assumed to be zero for all temperatures, pressures, and compositions. This assumption is very poor near critical conditions, and is undoubtedly the main reason for the poor performance of the Chao-Seader correlation in the critical region. 

Since Ag is a function of pressure, it follows that, under certain conditions, a change in pressure may produce immiscibility in a completely miscible system, or, conversely, such a change may produce complete miscibility in a partially immiscible system. The effect of pressure on miscibility in binary liquid mixtures is closely connected with the volume change on mixing, as indicated by the exact relation... 

The expression for K involving the concentrations of the species involved is found to be independent of volume. This implies that any change of pressure is not going to change the final state of equilibrium. The same result can be obtained by taking into consideration the alternative expression involving the partial pressures. If the pressure on the system is increased to n times its original value then all the partial pressures will be increased in the same proportion. This obviously implies that the equilibrium is independent of the pressure. The effect of some other factors on this reaction may now be considered. One such factor can be the addition of substances. For example, on addition of more A2, the partial pressure of A2 in the reactor would increase momentarily from pAl to some value, p A/. It has already been seen that... 

As a consequence, a change in overall volume or total gas pressure will have no effect on the position of equilibrium. In the equilibrium constant expression, the two partial pressures in the numerator will be affected to exactly the same degree as the two partial pressures in the denominator, and Qp will continue to equal Kp. 

Alternatively, we may redefine the rate of reaction in terms of the rate of change of the partial pressure of a substance. If density is constant, this is analogous to the use of -dc,/dt (equation 2.2-10), and hence is restricted to this case, usually for a constant-volume BR. 

For the mechanistic interpretation of activation volume data for nonsymmetrical electron-transfer reactions, it is essential to have information on the overall volume change that can occur during such a process. This can be calculated from the partial molar volumes of reactant and product species, when these are available, or can be determined from density measurements. Efforts have in recent years focused on the electrochemical determination of reaction volume data from the pressure dependence of the redox potential. Tregloan and coworkers (139, 140) have demonstrated how such techniques can reveal information on the magnitude of intrinsic and solvational volume changes associated with electron-transfer reactions of transition... 

For many gaseous solutions, even if the gases are not ideal, the partial molar volumes of the components are equal to the molar volumes of the pure components at the same total pressure. The gases are said to obey Amagat s mle, and the volume change on mixing is zero. Under these conditions, the gaseous solution behaves ideally in the sense that it obeys the equation... 

A thermodynamic parameter (dV/dnB)T,F,n g which describes how the volume of component S in a multicomponent system depends on the change in its amount expressed in mol. Hpiland recently summarized the partial molar volumes of numerous biochemical compounds in aqueous solution. See Dalton s Law of Partial Pressures Concentrations Molecular Crowding... 

These equilibrium reactions occur with large decreases in both volume and entropy. Volume changes range from —80 to —300 cm /mol depending on the solute and pressure. These volume changes, A V, are associated with the electrostriction of the solvent around the product anion, Fei(ion), and, to some extent, with a contribution of the partial molar volume of the electron, V(e). Thus ... 

For certain liquids like cyclohexene [158], o-xylene, and m-xylene [159], the mobility increases with increasing pressure (see Fig. 11). These results provided the key to understand the two-state model of electron transport. In terms of the model, AFtr is positive for example, for o-xylene, AFtr is +21 cm /mol. Since electrostriction can only contribute a negative term, it follows that there must be a positive volume term which is the cavity volume, Fcav(e). The observed volume changes, AFtr, are the volume changes for reaction (23). These can be identified with the partial molar volume, V, of the trapped electron since the partial molar volume of the quasi-free electron, which does not perturb the liquid, is assumed to be zero. Then the partial molar volume is taken to be the sum of two terms, the cavity volume and the volume of electrostriction of the trapped electron ... 

For the semi-batch stirred tank reactor, the model was based on the following assumptions the reactor is well agitated, so no concentration differences appear in the bulk of the liquid gas-liquid and liquid-solid mass transfer resistances can prevail and finally, the liquid phase is in batch, while hydrogen is continuously fed into the reactor. The hydrogen pressure is maintained constant. The liquid and gas volumes inside the reactor vessel can be regarded as constant, since the changes of the fluid properties due to reaction are minor. The total pressure of the gas phase (P) as well as the reactor temperature were continuously monitored and stored on a PC. The partial pressure of hydrogen (pnz) was calculated from the vapour pressure of the solvent (pvp) obtained from Antoine s equation (pvpo) and Raoult s law ... 

With the aid of Eqs. (2.1), (2.7), (2.9), and (2.11), you should be able to prove to yourself that the reversible, non-pressure-volume work, dWs, is equivalent to the free energy change, dG, so that Eq. (2.60) becomes, with proper use of partial differentials. 

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