Mass Balance Calculation on a Triangular Diagram
One kilogram of a binary mixture containing 50 wt % of species A and 50 wt % of species B is mixed with two kilograms of a ternary mixture containing 15 wt % of A, 5 wt % of B, and 80 wt % of species C.
a. What is the composition of the final mixture (assuming there is no liquid-liquid phase splitting)?
b. Plot the compositions of the two initial mixtures and the final mixture on a triangular diagram.
a. The mass balance on each species is
A: 0.5 × 1 + 0.15 × 2 = 0.8 kg
B: 0.5 × 1 + 0.05 × 2 = 0.6 kg
C: 0.0 × 1 + 0.80 × 2 = 1.7 kg
Since, from an overall mass balance, there are 3 kg in the final mixture, the final composition is
A: 0.8/3 = 0.267 weight fraction or 26.7 wt %
B: 0.6/3 = 0.200 weight fraction or 20.0 wt %
C: 1.6/3 = 0.533 weight fraction or 53.3 wt %
b. The two feed compositions and the final mixture composition are plotted on the accompanying triangular diagram.
Comment
The final mixture composition is on a straight line connecting the two feed compositions. This is another example of the lever rule, and is merely a result of the mass balances being linear equations. Note also that the composition of the final mixture is found at two-thirds of the distance from the first feed to the second feed in accordance with their relative amounts. This graphical linear relation between the two feeds and the final mixture is the opposite case to that of a single feed that splits into two equilibrium streams, which is the case in liquid-liquid extraction.
