Brown sugar is a mixture of white sugar and molasses. Unrefined brown sugar cont

Question

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 14.00 wt% molasses and the remainder white sugar. A second round of crystalization reduces the molasses content to 1.40 wt% molasses. A plant wishes to produce a brown sugar ideal for baking that contains 4.00 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. This process is described by the flow chart below.

Explanation / Answer

overall balance over the spliiting pt.

m1 = m2 + m3

mass balance over molasses

m1* 0.14 = m2*0.14 + m3*0.14

mass balance over sugar

m1*0.86 = m2*0.86 + m3*0.86

balance over the crystallizer unit

m2 = m4 + m5

mass balance over mollases

m2*0.14 = m4*g +m5*0.014

mass balance over sugar

m2*0.86 = m4*0.986

balance over the entire system

m1 = m4 + m6

mass balance over molasses

m1*0.14 = m4*g + m6*0.04

mass balance over white sugar

m1*0.86 = m6*0.96

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