One Component of Two Permeating

We consider now again two chambers, as shown in Fig. 6.6. In one chamber, there is a mixture of two gases (1) and (2) and in the other chamber there is only one component (1). We assume that the component (1) may move freely from one chamber into the other. The component (2) is restricted to stay in the left chamber. Further, thermal energy may exchange freely between the two chambers. However, manal energy may not exchange. Therefore, we have the conditions 

From these equations, we derive the conditions of equilibrium expressed in terms of the intensive variables  

We start first with a simple argument. If one component can diffuse freely through the barrier, then in both chambers the partial pressures of the component must be equal in equilibrium. Therefore, 

We could show this with similar arguments as with one component, treated in Sect. 6.6.1. We note that the total pressure is the sum of the partial pressures, i.e.. 

Here x and x 2 are the mole fractions of the component (1) and the component (2) in the left chamber. This is the desired relation between the change of the total pressure and the amount of component (2). 

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