Partial pressure of a species

The partial pressure of a species in an ideal-gas mixture is equivalent to the mole fraction. Thus... 

We will complete our discussion of chemical potential by using Equation IV. 17 to obtain the logarithmic term in concentration that is found for fij in a liquid phase. First, it should be pointed out that Equation IV. 17 has no concentration term per se for the chemical potential of species j in a gas phase. However, the partial pressure of a species in a gas phase is really analogous to the concentration of a species in a liquid e.g., PjV = rijRT for gaseous species/ (Eq. IV.15), and concentration means number/volume and equals n/V, which equals P/RT. 

Raoult s law states that the partial pressure of a species in the vapor phase is proportional to the mole fraction of the species in the liquid phase. The constant of proportionality is the vapor pressure of the pure species. Mathematically, this expressed as... 

The equations above have been the basis of most atmospheric aqueous-phase chemistry models that include mass transport limitations [e.g., Pandis and Seinfeld (1989)]. These equations simply state that the partial pressure of a species in the cloud interstitial air changes due to mass transport to and from the cloud droplets (incorporating both gas and interfacial mass transport limitations). The aqueous-phase concentrations are changing also due to aqueous-phase reactions that may be limited by aqueous-phase diffusion included in the factor Q. 

If you have a rigid container containing a mixture of gases, the partial pressure of a species is simply the pressure the gas would have if that one species occupied the entire volume of the container. 

Activity ak- ti-v9-te (1530) n. A quantity which measures the parent or effective concentration (or, for a gas, partial pressure) of a species and which takes into account interparticle interactions which produce non-ideal behavior. At low concentrations (or pressures) activity is essentially equal to concentration (or pressure). 

Numerical values of equilibrium constants can be calculated if the partial pressures of products and reactants at equilibrium are known. Sometimes you will be given equilibrium partial pressures directly (Example 12.3). At other times you will be given the original partial pressures and the equilibrium partial pressure of one species (Example 12.4). In that case, the calculation of K is a bit more difficult, because you have to calculate the equilibrium partial pressures of all the species. 

The equilibrium constant for a chemical system can be used to calculate the partial pressures of the species present at equilibrium. In the simplest case, one equilibrium pressure can be calculated, knowing all the others. Consider, for example, the system... 

More commonly K is used to determine the equilibrium partial pressures of all species, reactants, and products, knowing their original pressures. To do this, you follow what amounts to a four-step path. 

Express the equilibrium partial pressures of all species in terms of a single unknown, x. To do this, apply the principle mentioned earlier The changes in partial pressures of reactants and products are related through tite coefficients of the balanced equation. To keep track of these values, make an equilibrium table, like the one illustrated in Example 12.4. 

We will see functions like the one occurring under the logarithm operator quite often. For efficiency, this is generally written as In(Products)/(Reactants), where (Products) and (Reactants) denote the partial pressures of the species relative to the standard state pressure raised to a power that is equal to the stoichiometric coefficients. Kp is the equilibrium constant in terms of pressures. Since all pressures are in the same units, Rp is dimensionless. Note that in some literature there may be a combination of some power of P with Kp to obtain an equilibrium constant with pressure units. In this case. 

Derivation of the Langmuir Equation— Adsorption of a Single Species. The kinetic approach to deriving a mathematical expression for the Langmuir isotherm assumes that the rate of adsorption on the surface is proportional to the product of the partial pressure of the adsorbate in the gas phase and the fraction of the surface that is bare. (Adsorption may occur only when a gas phase molecule strikes an uncovered site.) If the fraction of the surface covered by an adsorbed gas A is denoted by 0Ay the fraction that is bare will be 1 — 0A if no other species are adsorbed. If the partial pressure of A in the gas phase is PA, the rate of adsorption is given by... 

In initial rate studies no products need be present in the feed, and the terms in the rate expression involving the partial pressures of these species may be omitted under appropriate experimental conditions. The use of stoichiometric ratios of reactants may also cause a simplification of the rate expression. If one considers a reversible bimolecular surface reaction between species A and ,... 

Mass spectrometry techniques are the most usual and versatile methods for analysis of the gas [90], Here the effusing vapour is ionized by an ionization source and the product analyzed with a mass spectrometer. The different vapour species are identified and the partial pressures of all species determined. The partial pressure of species i of a compound or a solution with a specific composition is at a specific temperature ... 

It is found by experiment that rates almost always have power-law dependences on the densities (such as concentration, density on a surface, or partial pressure) of chemical species. For example, our first example of the homogeneous reaction of cyclopropane to propylene exhibits a rate of decomposition that can be written as... 

A multicomponent mixture flows through a tube, which is selectively permeable for species A, which is one of the components in the mixture (Fig. 3.21). Assume steady flow. Assume that the flux of A out of the tube depends on the internal partial pressure of A, K. Futher, assume that the flow conditions are such that the system may be modeled as a plug flow, for which there are no radial gradients. Assume that there may be homogeneous chemical reaction, with the molar volumetric chemical-production rates given as m. ... 

Several methods are commonly used to specify the abundance of substances in the atmosphere. For gaseous constituents common practice is to specify abundances as mixing ratios, or equivalently as mole fractions of the species in air. This quantity is simply the ratio of the partial pressure of a substance to the total pressure. The advantage of this unit is that it is independent of pressure and temperature, and for an atmospheric component that is well mixed, the mixing ratio will be constant as the pressure or temperature changes. Common units for specifying mixing ratios are parts... 

Step 1 Set up a table with columns labeled by the species taking part in the reaction. In the first row, show the initial molar concentrations or partial pressures of each species. 

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