A bioreactor is used to ferment grain to alcohol. This reaction is carried out i

Question

A bioreactor is used to ferment grain to alcohol. This reaction is carried out in batch by the yeast Saccharomyces cerevisiae which can digest glucose (C_6H_12O_6) from plants to form ethanol (C_2H_5OH) according to the following reaction: C_6H_12O_6 righrarrow 2C_2H_5OH + 2CO_2 The reactor is initially filled with an aqueous solution containing only water and glucose. Express the final amounts of each species ( nH_2O, nC_6H_12O_6, nC_2H_5OH and nCO_2 ) in terms of the initial amounts and the extent of reaction (Xi). The reactor is initially filled with an aqueous solution containing 200 kmol water and 3.00 kmol glucose. When the reaction is complete, an analysis of the product reveals that 1.75 kmol of glucose remain. What is the extent of reaction (Xi) and the final amounts of each species ( nH_2O, nC_6H_12O_6, nC_2H_5OH and nCO_2 )? What is the fractional conversion of glucose?

Explanation / Answer

a)
Let initial amount be a and extent of reaction be E
C6H12O6 ---> 2C2H5OH + 2CO2
   a                                                                 (initial)
-E                          +2E               +2E            (change)
a-E                         2E                 2E            (final)
n(H2O) = it will not change. It will be same as initial concentration
n(C6H12O6 ) = a-E
n(C2H5OH ) = 2E
n(CO2) = 2E
b)
glucose remaining = a-E
1.75 Kmol = 3 kmol - E
E= 1.25 Kmol
n(H2O) = 200 kmol
n(C6H12O6 ) = 1.75 kmol
n(C2H5OH ) = 2E = 2*1.25 kmol = 2.5 Kmol
n(CO2) = 2E = 2*1.25 kmol = 2.5 Kmol
c)
fractional conversion = E*100/a
                                              = 1.25*100 / 3
                                              =41.7 %

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