Partial pressure-composition relations

Consider a liquid or solid solution of several components in equilibrium with its vapour. For the ith component we have 

At temperatures at which the vapour pressure is sufficiently small the vapour phase may be expected to approximate fairly closely to a perfect gas mixture. Thus 

It follows that the equilibria of solutions can always be discussed thermodynamically in terms of the partial pressures in the saturated vapour (or the fugacities if the vapour phase is imperfect). Consider, for example, the reaction of NO2 with water as in nitric acid manu- 

Therefore the difficulty in the study of solutions arises when we wish to relate the composition of the gas phase with the composition of the solution with which it is in contact. In general, the partial pressure of any component of the vapour may be expected to be a function of temperature, together with its mole fraction in solution and also the mole fractions of all other species (or rather a function of N — 1 mole fractions if there are N substances in solution). Thus 

The simplest possible relationship of this kind is where Pi is directly proportional to Xi and is independent of all other mole fractions  

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The changes in reaction rates that lead to equilibrium are associated with changes in the concentrations in moles per liter (page 168) of reactants and products. The same information can also be given by other measures of composition. For gases, the partial pressure is related to the concentration in a simple way (page 15) ... 

An ideal gas obeys Dalton s law that is, the total pressure is the sum of the partial pressures of the components. An ideal solution obeys Raoult s law that is, the partial pressure of the ith component in a solution is equal to the mole fraction of that component in the solution times the vapor pressure of pure component i. Use these relationships to relate the mole fraction of component 1 in the equilibrium vapor to its mole fraction in a two-component solution and relate the result to the ideal case of the copolymer composition equation. 

In order to allow integration of countercurrent relations like Eq. (23-93), point values of the mass-transfer coefficients and eqiiilibrium data are needed, over ranges of partial pressure and liquid-phase compositions. The same data are needed for the design of stirred tank performance. Then the conditions vary with time instead of position. Because of limited solubihty, gas/liquid reactions in stirred tanks usually are operated in semibatch fashion, with the liquid phase charged at once, then the gas phase introduced gradually over a period of time. CSTR operation rarely is feasible with such systems. 

The supply composition of MEK is related to its partial pressure via Dalton s law ... 

Dalton s Law relates composition of the vapor phase to the pressure and temperature well below the critical pressure, that is, total pressure of a system is the sum of its component s partial pressure ... 

In other words, the partial pressure of a gas in a mixture is equal to its mole fraction multiplied by die total pressure. This relation is commonly used to calculate partial pressures of gases in a mixture when the total pressure and the composition of the mixture are known (Example 5.9). 

To find how AG changes with composition, we need to know how the molar Gibbs free energy of each substance varies with its partial pressure, if it is a gas, or with its concentration, if it is a solute. We have already seen (in Section 8.3) that the molar Gibbs free energy of an ideal gas J is related to its partial pressure, P(, by... 

The voltage measured will now appear to drift as the composition range of the nonstoichiometric oxide is crossed. The voltage will become constant above and below the composition range of the oxide. Note that this is closely related to the variation of oxygen partial pressure over a nonstoichiometric oxide (see Sections 7.3, 7.4). 

What about the upper curve Glad you asked (sigh.). The composition in the vapor is also related to Dalton s Law of Partial Pressures. For an ideal gas... 

The voltage of MCFCs varies with the composition of the reactant gases. The effect of reactant gas partial pressure, however, is somewhat difficult to analyze. One reason involves the water gas shift reaction at the anode due to the presence of CO. The other reason is related to the consumption of both CO2 and O2 at the cathode. Data (55,64,65,66) show that increasing the reactant gas utilization generally decreases cell performance. 

As reactant gases are consumed in an operating cell, the cell voltage decreases in response to the polarization (i.e., activation, concentration) and to the changing gas composition (see discussion in Section 2). These effects are related to the partial pressures of the reactant gases. 

Fig. 3.8 Relation between temperature, oxygen partial pressure, and oxygen non-stoichiometry, y, for the starting composition (ZnO)]8.3(MnO)26.8(Fe203)54.9. y denotes the weight gain from the standard composition.

First, we discuss the phase relation from the viewpoint of the phase rule. Because Mn- Zn ferrite is composed of four elements (Mn, Zn, Fe, O), the freedom F in the phase rule is expressed as f = 6 — p. Considering one solid phase with a spinel structure (see Section 2.5 and Ref. 3), equilibrated with the oxygen (partial) pressure Po., we get the relation F = 4. The starting compounds for the preparation of Mn-Zn ferrite are ZnO, MnO, and Fe2O3, in the molar ratio a / 3 — (a -I- j6). This mixture is heated at fixed temperature and partial oxygen pressure, and the product obtained has the composition Zn Mn Fcj Under conditions of fixed temperature, fixed oxygen... 

In contrast to the pressure of an ideal gas, the fugacity is not only a function of the amount of substance and temperature, but also of the composition (types and amounts of gaseous compounds present) of the gaseous system and of die total pressure. The fugacitiy of a gaseous compound is, however, closely related to its partial pressure. To account for the nonideality of the gas, one can relate these terms by using a fugacity coefficient, 0ig ... 

Raoult s and Dalton s equations both represent the partial pressure of a component in a gas mixture. In the case of Raoult s equation, the gas must be in equilibrium with a liquid. These equations may be combined by eliminating partial pressure. The resulting equation relates the compositions of the gas and liquid phases in equilibrium to the pressure and temperature at which the gas-liquid equilibrium exists. 

The isomerization of the olefin prior to its hydroformylation has been the explanation of this question (3) and the formation of isomeric aldehydes was related to the presence of isomeric free olefins during the hydroformylation. This explanation, however, is being questioned in the literature. The formation of (+) (S) -4-methylhexanal with an optical yield of more than 98% by hydroformylation of (+) (S)-3-methyl-l-pentene (2, 6) is inconsistent with the olefin isomerization explanation. Another inconsistency has been the constance of the hydroformylation product composition and the contemporary absence of isomeric olefins throughout the whole reaction in hydroformylation experiments carried out with 4-methyl-1-pentene and 1-pentene under high carbon monoxide partial pressure. The data reported in Ref. 4 on the isomeric composition of the hydroformylation products of 1-pentene under high carbon monoxide pressure at different olefin conversions have recently been checked. The ratio of n-hexanal 2-methylpentanal 2-ethylbutanal was constant throughout the reaction and equal to 82 15.5 2.5 at 100°C and 90 atm carbon monoxide. 

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