Water vapor concentration expressions

For the system described in problem 3.3 develop a general expression for computing the water vapor concentration profile through the stagnant air film. 

During the daytime, a transpiring and photosynthesizing plant community as a whole can have a net vertical flux density of CO2 (/coz) downward toward it and a net vertical flux density of water vapor (71W) upward away from it into the turbulent air above the canopy. These flux densities are expressed per unit area of the ground or, equivalently, per unit area of the (horizontal) plant canopy. Each of the flux densities depends on the appropriate gradient. The vertical flux density of water vapor, for example, depends on the rate of change of water vapor concentration in the turbulent air, c, with respect to distance, z, above the vegetation ... 

Futerko and Hsing presented a thermodynamic model for water vapor uptake in perfluorosulfonic acid membranes.The following expression was used for the membrane—internal water activity, a, which was borrowed from the standard Flory—Huggins theory of concentrated polymer solutions ... 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

In this expression Ac describes the difference between the concentration of water vapor at the water surface and that at the desiccant surface Ac = cw - cdes. Since cdes < cw, Ac may be replaced by cw, which in turn equals pM/RT, where p and M are the vapor pressure and molecular weight, respectively, of water. With this substitution the expression for dQldt becomes A(DIAx)(pMIRT). The ratio DlAx has units length time 1, so we identify it as the reciprocal of the transport resistance. Note that r increases as the effective value of Ax increases and the effective value of D decreases. Thus l/r is the only unknown in the expression dQldt = A(Mr) pMIRT) and can be calculated from the measured rate of weight increase with different monolayers present. ... 

First consider the removal of pure water from an initial or feed solution of concentration x1 expressed as mole fraction of salt. Because the removal of water will change the concentration of the solution and since, to fulfill the condition of reversibility, the water vapor removed must at all times be in equilibrium with salt solution, a differential treatment is indicated. Write Equation 1 in the form... 

Equation (2.79) expresses the driving force in pervaporation in terms of the vapor pressure. The driving force could equally well have been expressed in terms of concentration differences, as in Equation (2.83). However, in practice, the vapor pressure expression provides much more useful results and clearly shows the connection between pervaporation and gas separation, Equation (2.60). Also, the gas phase coefficient, is much less dependent on temperature than P L. The reliability of Equation (2.79) has been amply demonstrated experimentally [17,18], Figure 2.13, for example, shows data for the pervaporation of water as a function of permeate pressure. As the permeate pressure (p,e) increases, the water flux falls, reaching zero flux when the permeate pressure is equal to the feed-liquid vapor pressure (pIsal) at the temperature of the experiment. The straight lines in Figure 2.13 indicate that the permeability coefficient d f ) of water in silicone rubber is constant, as expected in this and similar systems in which the membrane material is a rubbery polymer and the permeant swells the polymer only moderately. 

Equation 3.2.6 gives the concentration of water vapor in the inlet air as function of tjw, yiw, and Ahyw, where the subscript, w, means wet bulb. The equations are in functional notation to indicate that these data may be available in tables, graphs or equations. The wet-bulb temperature, tiw, will be discussed later. Equation 3.2.7 expresses the mole fraction of water vapor in the exit air in terms of the vapor pressure at saturation. The air leaving the tower is assumed to be 90% saturated, a value recommended by Walas [12]. 

The concentration of water vapor in air is called the humidity of the air. However, humidity may be expressed in several ways. To understand the interrelationships among temperature, vapor pressure, heat energy, and humidity, one may consult psychrometric charts that are found in most chemical engineering handbooks (15-17). Charts may be differentiated for certain conditions of temperature and pressure. For example, charts are designated for low, medium and high temperature as well as for conditions of pressure. A particularly lucid discussion of the use of the psychrometric chart may be found in Ref. 18. 

The relative humidity ( ) may be expressed as the ratio of the actual concentration of water vapor in the air to the saturation concentration of water vapor in the air under the... 

Experiments show that as long as some liquid water is in the container, the pressure of water vapor at 25°C is 0.03126 atm. The position of this equilibrium is not affected by the amount of liquid water present, and therefore liquid water should not appear in the mass action law. Recall that for a gas or solute, a ratio of pressures or concentrations appears in the law of mass action. This ratio is equal to 1 when the gas or solute is in its reference state (1 atm or 1 M). For a pure liquid appearing in an equilibrium chemical equation, the convention is to take that pure liquid as the reference state, so the liquid water contributes only a factor of 1 to the equilibrium expression and can thus be entirely omitted. We postpone justification of this rule to Section 14.3. 

The water flux, J, which is normally expressed as kg (or L) m h is proportional to the water vapor pressure gradient, Apm, between the feed-membrane and strip-membrane interfaces, and the membrane mass transfer co-efficient K, [Eq. (3)]. The vapor pressure gradient between the two interfaces depends on the water activity, a, in the bulk feed and strip streams, and the extent to which concentration polarization reduces that activity at each interface. Whilst can be estimated using established diffusional transport equations, it is more difficult to estimate values for the water vapor pressure at the membrane wall for use in Eq. (3). However, an overall approach using the vapor pressures of the bulk solutions and semi-empirical correlations that take account of the different conditions near the membrane wall can be used to estimate J. 

Feed-side and strip-side concentration polarization result in a reduction in the driving force for mass transfer. There is a decrease in water activity at the feed-membrane interface and an increase at the strip-membrane interface. This results in a reduction in the water vapor pressure gradient across the membrane. The feed side and strip side mass transfer co-efficients, Kf and K, respectively, can be expressed in terms of the solute diffusion co-efficient in the boundary layer, D, ... 

The acetone concentration in an effluent air stream is to be reduced from 1% mole to 0.05% mole by scrubbing with water in a countercurrent absorber. Assuming Henry s law holds at these concentrations, and that it may be expressed as T = 2.45X, where X and Y are equilibrium acetone mole fractions in the liquid and gas, calculate the minimum water rate required for an air-acetone mixture rate of 100 kmol/h. How many equilibrium stages would be required if the water rate is twice the minimum What is the concentration of acetone in the water leaving the absorber Assume water vapor in the gas and air dissolved in the water are negligible. Solve this problem graphically. 

Air is ma.de up primarily of N2, O2, and Ar, which comprise 99.9% of dry air. There is a variable amount of water vapor, and many minor and trace gaseous components, as well as aerosol and particulate species. Table 26.1 lists some atmospheric gaseous components of environmental interest, along with representative concentrations in the troposphere. Typically, gaseous concentrations are expressed as mixing ratios, that is, volume/volume concentrations. A 1-ppm concentration represents 1 volume in 10 volumes of air. Such mixing ratios are independent of temperature and pressure. Environmental effects, though, may be quantitatively related to mass concentrations, and concentrations may be reported as mass per unit volume, usually mg/m of air, under specific conditions of temperature and pressure. Aerosols and particulates are reported in this way. 

Weiss and co-workers reported solubilities for He, " He, Ne, Ar, Kr as well as for O2 and N2 as a function of temperature and salinity for fresh and ocean waters (Table 1 Weiss 1970, 1971 Weiss and Kyser 1978). As this fundamental piece of work was strongly motivated by practical oceanographic research, the noble gas solubilities were expressed in the form of equilibrium concentrations with moist atmospheric air. For the atmosphere, it is justified to assume that its major elemental composition remains constant over the relevant time scales controlling gas exchange. Hence the gas partial pressure pi can be expressed by the total atmospheric pressure ptot corrected for water vapor content, Cw(T), and the volume or mole fraction Zi of the gas i in dry air (Ozima and Podosek 1983). 

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