Rty

where Y is the total distance of diffusion. Because P = PA + PB = constant, it follows that dP = dPA + dPB = 0 and therefore dPA = ~dPB. Substituting this expression into equation 10 gives

In other words, in the case of diffusion of ideal gases, the diffusivities of each individual component are identical.

Diffusion of Gas A Through a Stagnant Layer of Gas B.

Consider water evaporating from an open flask into the air, as shown in Figure 2. In this case, water vapor A is diffusing through a stagnant layer of air B at the top of the water surface. We know that air is only slightly absorbed by water, whereas water vapor does escape from the water's surface through the still air layer and into the bulk stream outside the flask. Therefore

and the general equation 9 becomes (by rearranging)

When dealing with a dilute system at constant temperature T and pressure P, Dab can be considered constant, and thus integration of equation 14 gives

Na RTY ""VP - PA1 By introducing the concept of logarithmic mean value

i mln

V - pA1, we can rewrite equation 15 as

When the difference between PA1 and PA2 is small, say P ~ PAJP — Pa2> < 1-5, using an arithmetic mean Pm instead of a logarithmic mean introduces an error of less than 1.5%, and equation 16 becomes

Furthermore, when the partial pressure of the diffusing matter is low compared to the total pressure, thenP — PA1 P - PA2 P and Pm P, and equation 17 becomes

Pai Pbi

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