Brown sugar is a mixture of white sugar and molasses. Unrefined brown sugar contains a large portion of molasses. After one round of crystallization of this unrefined sugar, the brown sugar product contains 11.00 wt% molasses and the remainder white sugar. A second round of crystalization reduces the molasses content to 1.20 wt% molasses. A plant wishes to produce a brown sugar ideal for baking that contains 5.00 wt% molasses. In order to acheive this concentration of molasses, a plant feeds once-crystallized brown sugar into a recrystalizer. Some of this feed is diverted into a bypass stream that rejoins the sugar that leaves the crystalizer. Pure molasses leaves the crystalizer as a bypass stream.
Write the material balance equations for the species around the elements listed below. In the answer blank to the left of the equal sign, enter in an expression for the mass of the species entering the given element. In the answer blank to the right of the equal sign, enter in an expression for the mass of the species leaving the given element.
1. If the plant wishes to produce 450.0 g/min of brown sugar today, what is the feed rate, m1?
2. What is the flow rate of pure molasses from the crystallizer, m4?
3. What is the fraction of the feed that bypasses the crystallizer?