Partial pressure, definition

Using partial pressures, this definition can be written as... 

The partial pressure of water vapor can be calculated as a function of the dry-bulb and wet-bulb temperatures, Eq. (12.23), and the relative humidity from its definition ... 

Henry s law States that the mass of a gas dissolved in a definite volume of liquid at constant temperature is proportional to the partial pressure of the gas. 

The definition of Kp obviously applies to tlie reaction of Eq. (4.6.1). Assuming that a K value is available or calculable, this equation may be used to detennine the partial pressures of the participating components at equilibrium. For liquid phase reactions, K is given approximately by... 

Dalton S Law of Partial Pressures. The total pressure (P) of a gaseous mixture equals the sum of the partial pressures of its components. By definition, the partial pressure of any component gas is the hypothetical pressure it would exert by occupying the entire volume (V) of the mixture at the same temperature (T). That is,... 

Thus, if the mixture of carbon dioxide and oxygen is shaken up with water, both gases will begin to pass into solution, and their partial pressures in the gas mixture will change. When the amount of each in solution stands in a definite ratio to its partial pressure, there will be equilibrium, but the amounts dissolved will not be the same as if each gas had been separately brought in contact with the same quantities of liquid under a pressure equal to its initial partial pressure in the mixture. 

Thus denoting by 0P the coverage of the promoter on the catalyst surface and by pj the partial pressures of reactants, j, of the catalytic reaction we can formulate mathematically the above definition as ... 

To express the composition of the vapor in equilibrium with the liquid phase of a binary liquid mixture, we first note that the definition of partial pressure (PA = xAP for component A) and Dalton s law (P = PA + PB) allow us to express the composition of the vapor of a mixture of liquids A and B in terms of the partial pressures of the components ... 

The activities of the various components 1,2,3. .. of an ideal solution are, according to the definition of an ideal solution, equal to their mole fractions Ni, N2,. . . . The activity, for present purposes, may be taken as the ratio of the partial pressure Pi of the constituent in the solution to the vapor pressure P of the pure constituent i in the liquid state at the same temperature. Although few solutions conform even approximately to ideal behavior at all concentrations, it may be shown that the activity of the solvent must converge to its mole fraction Ni as the concentration of the solute(s) is made sufficiently small. According to the most elementary considerations, at sufficiently high dilutions the activity 2 of the solute must become proportional to its mole fraction, provided merely that it does not dissociate in solution. In other words, the escaping tendency of the solute must be proportional to the number of solute particles present in the solution, if the solution is sufficiently dilute. This assertion is equally plausible for monomeric and polymeric solutes, although the... 

Let us consider the mechanism (85) for definiteness. The mechanism (86) yields the same result, as can be demonstrated. We denote by Poa and PH2o the partial pressures of oxygen and water vapours. If the reaction takes place in the liquid phase, the partial pressures must then be replaced by the corresponding concentrations. The surface concentrations of the chemisorbed 0 and H atoms and H02 complexes are denoted by No, Nn and Nkoi, respectively. Let N+h, N 0, N hos, N°h and N°o be the surface... 

Equilibrium constants do not have units because in the strict thermodynamic definition of the equilibrium constant, the activity of a component is used, not its concentration. The activity of a species in an ideal mixture is the ratio of its concentration or partial pressure to a standard concentration (1 M) or pressure (1 atm). Because activity is a ratio, it is unitless and the equilibrium constant involving activities is also unitless. 

Definitions for the variables and constants appearing in eqns. 1 and 2 are given in the nomenclature section at the end of this paper. The first of these equations represents a mass balance around the reactor, assuming that it operates in a differential manner. The second equation is a species balance written for the catalyst surface. The rate of elementary reaction j is represented by rj, and v j is the stoichiometric coefficient for component i in reaction j. The relationship of rj to the reactant partial pressures and surface species coverages are given by expressions of the form... 

The first method of interpreting rate of reaction in terms of partial pressure uses the verbal definition given by equation 1.4-2 for rs. By analogy with equation 4.1-3, we write the rate law (for a reactant i) as... 

Applying the definition of partial pressure for each species, p, = xtP, we have... 

Equation 2.63 is valid for any homogeneous or heterogeneous reaction. The only difference is in the definition of activities. For a species in a perfect gas-phase mixture a = pi/p°, where pi is the partial pressure of species i andp° is the standard pressure (1 bar). For a real gas-phase mixture a =f/p°, where is the fugacity of i. The fugacity concept was developed for the same reason as the activity to extend to real gases the formalism used to describe perfect gas mixtures. In the low total pressure limit (p -> 0), fi = pi. 

The energy and mass conservation equations used in the determination of the flame temperature are more conveniently written in terms of moles thus, it is best to write the partial pressure in Kp in terms of moles and the total pressure P. This conversion is accomplished through the relationship between partial pressure p and total pressure P, as given by Eq. (1.30). Substituting this expression for p, [Eq. (1.30)] in the definition of the equilibrium constant [Eq. (1.40)], one obtains... 

At pH 7, by definition pe = pe, which for this half-reaction is -tl3 75 or -t0.81 V. The choice of = 1 atm is arbitrary it represents the extreme case where O2 comprises the bulk of the atmosphere. The boimdary line equation can be redefined for other partial pressures of O2, but this causes only minor changes. For example, the lowest partial pressure at which seawater is considered to be oxic is = 0.001 atm. At this Pq, Eq. 7.45 becomes... 

Note also that selectivity becomes more complicated in systems where densities and mole numbers change. The above definition is straightforward once a suitable basis is chosen (such as moles of reactant Nao or molar flow rate Fao)> but in terms of concentrations and partial pressures one must be careful in substituting these quantities in the preceding equation. 

The number of ions i" produced from a gas in the ion source is proportional to the emission current i, to the specific ionization Sggj, to a geometry factor f representing the ionization path inside the ionization source, to the relative ionization probability RlPgaj. and to the partial pressure Pggj. This number of ions produced is, by definition, made equal to the sensitivity Egas times the partial pressure Pg ... 

N cuum technology mass spectrometer partial pressure gauges, definitions, characteristic variables, operating conditions 11/86... 

Two important ways in which heterogeneously catalyzed reactions differ from homogeneous counterparts are the definition of the rate constant k and the form of its dependence on temperature T. The heterogeneous rate equation relates the rate of decline of the concentration (or partial pressure) c of a reactant to the fraction / of the catalytic surface area that it covers when adsorbed. Thus, for a first-order reaction,... 

According to this definition f is equal to the partial pressure P, in the case of an ideal gas. The fugacity coefficient (j>- is defined by... 

At 315°C. the rate constant ki has a value of 7.0 X 1016 molecules/sec.-cm.2-atm. From the definition of kh this represents the rate of adsorption of methylcyclohexane per cm.2 of bare platinum surface at a methylcyclohexane partial pressure of 1 atm. From kinetic theory and statistical mechanics, one can calculate the number of molecules striking a unit area of surface per unit time with activation energy Ea. This is given by... 

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