Partial pressure 417,

The partial pressure pi of substance i in a gas mixture is defined as the product of its mole fraction in the gas phase and the pressure of the phase  

the sum of the partial pressures equals the pressure of the gas phase. This statement is known as Dalton s Law. It is vahd for any gas mixture, regardless of whether or not the gas obeys the ideal gas equation. 

We can begin by converting some of the given information into units more commonly used for gases. 

we will use the value in torr and choose the corresponding value for R. We could also convert from torr to atm, of course. 

The temperature and pressure are near typical room conditions, and the volume is a little more than a half liter. So this should correspond to a small balloon filled with CO2. One gram is a pretty small mass, but seems reasonable for the gas in a small balloon. 

By using the ideal gas law, we can determine many properties of an individual gas. In many instances, however, we encounter interesting situations with more than one gas present. Our consideration of the levels of pollutants in air is an obvious example. Even if we ignore any pollutants present, clean air is already a mixture of gases. Aside fi-om the possibility of chemical reactions, how do the observed properties of a gas mixture differ from those of pure gases  

The answer to this question is actually su ested by the gas law. In particular, note that none of the terms in the gas law equation depends on the identity of the gas. Consider a sample of air, and for simplicity assume that it consists entirely of N2 and O2. Assuming that the air behaves ideally, its pressure can be expressed using the gas law  

---

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

Reactor diluents and solvents. As pointed out in Sec. 2.5, an inert diluent such as steam is sometimes needed in the reactor to lower the partial pressure of reactants in the vapor phase. Diluents are normally recycled. An example is shown in Fig. 4.5. The actual configuration used depends on the order of volatilities. 

Dalton s law of partial pressures The total pressure (P) exerted by a mixture of gases is equal to the sum of the partial pressures (p) of the components of the gas mixture. The partial pressure is defined as the pressure the gas would exert if it was contained in the same volume as that occupied by the mixture. 

For gas reactions where the gases are assumed to follow ideal behaviour this equation becomes AG° = RT]n Kp, where Kp is defined in terms of the partial pressures of reactants and products. Thus for the general reaction above,... 

The relative humidity is the ratio of the partial pressure of the water vapour in the air to the partial pressure of water vapour in the air when saturated at the same temperature. This ratio is usually expressed as a p>ercentage. 

For a substance, A, whose partial pressure is p, the values (intensities) of ions 57 and 43, for example are given as(Ji)... 

In the case of three-phase equilibria, it is also necessary to account for the solubility of hydrocarbon gases in water. This solubility is proportional to the partial pressure of the hydrocarbon or, more precisely, to its partial fugacity in the vapor phase. The relation which ties the solubility expressed in mole fraction to the fugacity is the following ... 

Improving the cetane number as well as lowering the aromatics content requires higher partial pressures as well as higher hydrogen consumption. 

Relationship between the residual aromatics content, the hydrogen partial pressure, and the chemical hydrogen consumption (for a SR gas oil). 

The corrosion rate of steel in carbonic acid is faster than in hydrochloric acid Correlations are available to predict the rate of steel corrosion for different partial pressures of CO2 and different temperatures. At high temperatures the iron carbonate forms a film of protective scale on the steel s surface, but this is easily washed away at lower temperatures (again a corrosion nomogram is available to predict the impact of the scale on the corrosion rate at various CO2 partial pressures and temperatures). 

According to Dalton s laM of partial pressures, observed experimentally at sufficiently low pressures, the pressure of a gas mixture m a given volume V is the sum of the pressures that each gas would exert alone in the same volume at the same temperature. Expressed in tenns of moles n. 

The partial pressure p- of a component in an ideal-gas mixture is thus... 

Given this experimental result, it is plausible to assume (and is easily shown by statistical mechanics) that the chemical potential of a substance with partial pressure p. in an ideal-gas mixture is equal to that in the one-component ideal gas at pressure p = p. 

In the phase equilibrium between a pure solid (or a liquid) and its vapour, the addition of other gases, as long as they are insoluble in the solid or liquid, has negligible effect on the partial pressure of the vapour. 

In electrochemical cells (to be discussed later), if a particular gas participates in a chemical reaction at an electrode, the observed electromotive force is a fiinction of the partial pressure of the reactive gas and not of the partial pressures of any other gases present. 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

If tire diffusion coefficient is independent of tire concentration, equation (C2.1.22) reduces to tire usual fonn of Pick s second law. Analytical solutions to diffusion equations for several types of boundary conditions have been derived [M]- In tlie particular situation of a steady state, tire flux is constant. Using Henry s law (c = kp) to relate tire concentration on both sides of tire membrane to tire partial pressure, tire constant flux can be written as... 

The path length is set by the experimental configuration while a is known for each transition (such as OO O J—> OO l, J 1 or OO l J—> 00 2, J 1). Thus, a measurement of zi///provides the partial pressure P of molecules produced in probed states such as OO O Jor 00 1 J. (Strictly, optical probing measures the difference in the partial pressures between the upper and lower states of the probed transition however, in practice, the lower state population is always much larger than the upper state population so that the probe senses only the lower state population in the experiment.)... 

White phosphorus is very reactive. It has an appreciable vapour pressure at room temperature and inflames in dry air at about 320 K or at even lower temperatures if finely divided. In air at room temperature it emits a faint green light called phosphorescence the reaction occurring is a complex oxidation process, but this happens only at certain partial pressures of oxygen. It is necessary, therefore, to store white phosphorus under water, unlike the less reactive red and black allotropes which do not react with air at room temperature. Both red and black phosphorus burn to form oxides when heated in air, the red form igniting at temperatures exceeding 600 K,... 

When Che diameter of the Cube is small compared with molecular mean free path lengths in che gas mixture at Che pressure and temperature of interest, molecule-wall collisions are much more frequent Chan molecule-molecule collisions, and the partial pressure gradient of each species is entirely determined by momentum transfer to Che wall by mechanism (i). As shown by Knudsen [3] it is not difficult to estimate the rate of momentum transfer in this case, and hence deduce the flux relations. 

Local average values of concentrations and partial pressures, rather chan point values, are also used in Che flux relations. However, in this case it is convenient to use interstitial local averages, based on the void volume rather than the total volume, since these are. ore closely related to the properties of bulk gases. 

---