Single-Stage Mass and Energy Balances

If a feed stream with mole rate F separates in an eqnilibrium stage into a vapor product with mole rate V and a liquid product with mole rate L, then by overall material balance, 

A component material balance on either component is written as 

A total enthalpy balance on the equilibrium stage is written as 

Looking back at Equations 5.23, 5.24, 5.25, and 5.26, it can be seen that the rates of F, L, and V obey the lever rule with respect to compositions and enthalpies. If, for instance, F is considered a pivot point, the product of vapor rate V times compositional line segment ZT equals the product of liquid rate L times compositional line segment XZ. Similar relations apply to enthalpy line segments HpH and hHp and also to line segments FV and LF. Also, points V and L could be selected as the pivot points instead of point F. 

The above concepts amount to a graphical representation of the overall material, component material, and enthalpy balances around an equilibrium stage. A column solution may be developed by applying these graphical rules on an enthalpy-composition diagram. 

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