Condensation of a Binary Vapor Mixture

For two component mixtures we may, in fact, devise alternative procedures suitable for hand calculations. 

A conventional bubble point calculation involves the specification of the liquid mole fractions and pressure the subsequent computation of the vapor-phase mole fractions and the system temperature. For a binary system (and only for a binary system) we may specify the temperature and pressure and compute the mole fractions of both phases. Thus, our first step is to estimate the interface temperature T. The second step is to solve the equilibrium equations for the mole fractions on either side of the interface. This step is, in fact, equivalent to reading the composition of both phases from a T-x-y equilibrium diagram. 

If the liquid phase may be considered unmixed, the relative rates of condensation are given by 

We may now solve the energy balance (Eq. 15.1.12) for the interface temperature that may be compared with the previous estimate. If the two values of differ to any extent, we may use the newer value or some weighted average of the new and old values and go back to solving the interface equilibrium equations. 

The steps of this computational procedure are summarized in Algorithm 15.2. It is left as an exercise for our readers to show that this simple procedure yields appropriate numerical results when applied to the system in Example 15.1.1. 

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