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 12.00 wt% molasses and the remainder white sugar. A second round of crystallization reduces the molasses content to 1.40 wt% molasses. A plant wishes to produce a brown sugar ideal for baking that contains 6.50 wt% molasses. In order to acheive this concentration of molasses, a plant feeds once-crystallized brown sugar into a recrystallizer. Some of this feed is diverted into a bypass stream that rejoins the sugar that leaves the crystallizer. Pure molasses leaves the crystallizer as an outlet stream. This process is described by the flow chart. m, g/min *, g molasses/g y, g white sugar/g Crystallizer m, g/min x g molasses/g y, & white sugar/g m, g/min *, g molasses/g y, & white sugar/g mg/min x, g molasses/g yg g white sugar/g m. g/min Ag molasses/g yg white sugar/g mg molasses/min x1 = x2 = x3 = 0.1200 g molasses/g X5 = 0.0140 g molasses/g X6 = 0.0650 g molasses/g y = y2 = y; = 0.8800 g white sugar/g Ys = 0.9860 g white sugar/g yo = 0.9350 g white sugar/g Write the material balance equations for the species around the elements of the process. Put your responses in terms of numeric mass fractions and the mass flow rate variables. Do not include units in your responses. Open the hint panel for an identical flow chart you can view while writing the equations. First, write the mass balances for molasses and white sugar around the point where the bypass stream splits off from the crystallizer feed in terms of m, m2, and mz. molasses entering bypass point = molasses leaving bypass point molasses entering bypass point = molasses leaving bypass point = white sugar entering bypass point = white sugar leaving bypass point white sugar entering bypass point = white sugar leaving bypass point = Write the mass balances for molasses and white sugar around the crystallizer in terms of me, me, and ms. molasses entering crystallizer = molasses leaving crystallizer molasses entering crystallizer = molasses leaving crystallizer = white sugar entering crystallizer = white sugar leaving crystallizer white sugar entering crystallizer = white sugar leaving crystallizer Write the mass balances for molasses and white sugar around the mixing point of the bypass and crystallizer product streams in terms of ms.mns, and molasses entering mixing point = molasses leaving mixing point molasses entering mixing point molasses leaving mixing point = white sugar entering mixing point white sugar leaving mixing point white sugar entering mixing point white sugar leaving mixing point = Write the mass balances for molasses and white sugar around the entire process in terms of mi, *114, and me molasses entering process = molasses leaving process molasses entering process molasses leaving process white sugar entering process = white sugar leaving process white sugar entering process white sugar leaving process If the plant wishes to produce 450.0 g/min of brown sugar today, what is the feed rate, mi? = g/min What is the flow rate of pure molasses from the crystallizer, 4? What is the fraction of the feed that bypasses the crystallizer! Mg ANI
