Molecular diffusion coefficient in air

Figure 18.9 Molecular diffusion coefficients in air, Dla, at 25°C for different molecules plotted as a function of (a) their liquid molar volume, V(, (calculated as ratio of molar mass M, to liquid density, p,L), and (b) their molar mass, Mh Data from references reviewed by Fuller et al. (1966) plotted on double-logarithmic scale.

Illustrative Example 18.2 Estimating Molecular Diffusivity in Air Problem Estimate the molecular diffusion coefficient in air, >,a, ofCFC-12 (see Illustrative Example 18.1) at 25°C (a) from the mean molecular velocity and the mean free path, (b) from the molar mass, (c) from the molar volume, (d) from the combined molar mass and molar volume relationship by Fuller (Eq. 18-44), (e) from the molecular diffusivity of methane. 

P 18.5 Temperature and Pressure Dependence of the Molecular Diffusion Coefficient in Air... 

Table 24.5 Characteristic Data of Chemical Tracers Used for the Gas Exchange Experiment Nondimensional Henry s Law Constant, Ki3/vi, Molecular Diffusion Coefficient in Air, Dia, and Water, Diw, Octanol-Water Partition Coefficient, Kiow, All valid for 4°C (Data from Cirpka et al., 1993)...

M-L -T ) across the stagnant air layer according to Pick s law would be defined by the molecular diffusion coefficient in air, D, the concentration gradient and the thickness of the film,... 

Equation [2-32] reduces to Eq. [2-29] when 8W/D is much greater than 8JDaH, and to Eq. [2-31] when it is much less. Note that the molecular diffusion coefficient for molecules in air (DJ is approximately 104 times greater than the corresponding molecular diffusion coefficient in water (Dw), whereas the air film thickness, 8a, is generally much less than 104 times the water film thickness, 8W. 

Transport in the subsurface environment is slow compared with the other environmental media. Contaminants may move only tens of meters per year by advection, contrasting sharply with surface waters, which travel this far in minutes or hours, and air, which may travel this far in seconds (as discussed in the next chapter). Similarly, Fickian transport coefficients are rarely higher than thousandths of a square centimeter per second and are often no larger than a fraction of the molecular diffusion coefficient in free water. Many organic compounds that would rapidly volatilize into the atmosphere from surface waters may reside in groundwaters for decades or longer. 

The notation is explained in Fig. 1-16, and Dg and DL are the molecular diffusion coefficients for air and for seawater, respectively. The flux is maintained by the concentration differences across the molecular diffusion layers. The flux is directed from the ocean into the atmosphere when the concentration in seawater is greater than that at the interface the flux is directed from the atmosphere into the ocean when the concentration difference is negative. If the exchanging gas obeys Henry s law, the concentrations at the gas-liquid interface are connected by... 

Estimate the volumetric mass transfer coefficient in a Taylor flow capillary with an internal diameter of 1 mm and a volumetric gas flow of Vq = 2.71 cm min and a volumetric liquid flow of = 2.0 cm min Use the simphfied model presented in Equation 7.27 and compare the values with those predicted with the empirical model Equation 7.14. Use the physical properties for air and water presented in Example 7.1. The molecular diffusion coefficient in the liquid phase is approximated with = 10 m s . ... 

In addition to the theoretical and semiempirical methods for estimating molecular diffusivities in air, several empirical methods, based on regressions of measured diffusivities and other parameters, like molecular weight and molar volume, are available. These methods provide easily calculated estimates when the property data required to apply the more rigorous semiempirical methods are not available. Molecular weight is an excellent parameter for empirical correlations because it is easily determined from the chemical formula and is an important parameter in the theoretical model. Diffusion coefficients in air can be expected to have power-law dependence on molecular... 

Tybsre m is the total mass of analyte collected, D the molecular diffusion coefficient, A the area of the diffusion channel, L the diffusion path length, C the analyte concentration in the air, and Tt the sampling time. In deriving equation (8.7) it was assumed t. that the sorbent is effective sink for the analyte and,... 

The data available on the molecular diffusion coefficient of organic vapors in air are meager, but they indicate (in accordance with approximate theory) an inverse proportionality to the square root of molecular weight. The rate of mass transfer by molecular diffusion will be proportional to the diffusion coefficient and to the SVC, itself proportional to vapor pressure times molecular weight (M). We should expect, therefore, under standard conditions of ventilation, that the rate of loss will be proportional to vapor pressure X The ratio of observed rate to... 

A schematic representation of the boundary layers for momentum, heat and mass near the air—water interface. The velocity of the water and the size of eddies in the water decrease as the air—water interface is approached. The larger eddies have greater velocity, which is indicated here by the length of the arrow in the eddy. Because random molecular motions of momentum, heat and mass are characterized by molecular diffusion coefficients of different magnitude (0.01 cm s for momentum, 0.001 cm s for heat and lO cm s for mass), there are three different distances from the wall where molecular motions become as important as eddy motions for transport. The scales are called the viscous (momentum), thermal (heat) and diffusive (molecular) boundary layers near the interface. 

Values for Da and D can also be estimated in terms of reference values for water in air and oxygen in water (Dx = Dref[MWref/MWx] ). The exponents have been estimated from experimental observations. It is now possible to estimate evaporation rates under static conditions by first estimating molecular diffusion coefficients, deriving values for the partial transfer velocities and calculating fctot-The data summarized in Table 4.6 use some laboratory observations listed in Tables 4.3-4.5 to evaluate this model. Reasonable agreement is observed between the calculated and observed values, considering possibilities for experimental error and uncertainties in the values for Henry s law constant, and so on. 

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