### 6.2 Component Mass Balances in Matrix Form

Amundson and Pontinen (1958) realized that the component mass balance equations for multicomponent distillation could be put into matrix form with one matrix for each component. To conveniently put the mass balances in matrix form, renumber the column as shown in Figure 6-2. Stage 1 is the total condenser, stage 2 is the top stage in the column, stage N-1 is the bottom stage, and the partial reboiler is listed as N. For a general stage j within the column (Figure 6-3), the mass balance for any component i is

**(6-1)**

**Figure 6-2. Distillation column for matrix analysis**

**Figure 6-3. General stage in column ...**