In an industrial process to make alcohol, bacteria, sugar, and water are fed into a bioreactor. The bacteria make alcohol, and water as well as leftover sugar. We desire to remove all the cells from the process stream so we may purify our alcohol product. The process stream enters a separator where the cellular components are separated from the rest of the stream. The entering process stream contains 30 wt% alcohol, 5 wt% sugar, 10 wt% cells, and the rest water. Two product streams, a cell-rich stream and a cell-free stream, leave the separator. The cell-rich stream is 90 wt% cells, 2.5 wt% sugar, 0.5 wt% alcohol, and 7wt% water.

Question

a) Write our species mass conservation equations for alcohol, bacteria, sugar, and water. Write a total mass conservation equation.
b) How many of the mass balance equations are linearly independent ?
c) Determine the composition of the cell-free stream.