Question 4.11: A dilute solution of glucose enters a continuous fermentatio...
A dilute solution of glucose enters a continuous fermentation process, where yeast cells convert it to ethanol and carbon dioxide. The aqueous stream entering the reactor is at 25°C and contains 5 wt-% glucose. Assuming this glucose is fully converted to ethanol and carbon dioxide, and that the product stream leaves the reactor at 35°C, estimate the amount of heat added or removed per kg of ethanol produced. Assume that the carbon dioxide remains dissolved in the product stream.
For this constant pressure process with no shaft work, the heat effect is simply equal to the enthalpy change from the feed stream to the product stream. The fermentation reaction is:
C _6 H _{12} O _6(a q) \rightarrow 2 C _2 H _5 OH (a q)+2 CO _2(a q)
The standard enthalpy of reaction at 298 K obtained using the heats of formation in dilute aqueous solution from Table C.5 is:
\Delta H_{298}^{\circ}=(2)(-288.3)+(2)(-413.8)-(-1262.2)=-142.0 kJ \cdot mol ^{-1}
One kg of ethanol is 1/(0.046069 kg·mol^{−1}) = 21.71 mol ethanol. Each mole of glucose produces two moles of ethanol, so 10.85 mol of reaction must occur to produce 1 kg of ethanol. The standard enthalpy of reaction per kg ethanol is then (10.85)(−142.0) = −1541 kJ·kg^{−1} . The mass of glucose required to produce 1 kg ethanol is 10.85 mol \times 0.18016 kg·mol^{−1} = 1.955 kg glucose. If the feed stream is 5 wt-% glucose, then the total mass of solution fed to the reactor per kg ethanol produced is 1.955/0.05 = 39.11 kg. Assuming that the product stream has the specific heat of water, about 4.184 kJ·kg^{−1}·K^{−1} , then the enthalpy change per kg ethanol for heating the product stream from 25°C to 35°C is:
4.184 kJ \cdot kg ^{-1} \cdot K ^{-1} \times 10 K \times 39.11 kg =1636 kJ
Adding this to the heat of reaction per kg ethanol gives the total enthalpy change from feed to product, which is also the total heat effect:
Q=\Delta H=-154 l +1636=95 kJ \cdot( kg \text { ethanol })^{-1}
This estimate leads to the conclusion that a small amount of heat must be added to the reactor because the reaction exothermicity is not quite sufficient to heat the feed stream to the product temperature. In an actual process, the glucose would not be fully converted to ethanol. Some fraction of the glucose must be directed to other products of cellular metabolism. This means that somewhat more than 1.955 kg glucose will be needed per kg of ethanol produced. The heat release from other reactions may be somewhat higher or lower than that for the production of ethanol, which would change the estimate. If some of the CO_{2} leaves the reactor as a gas, then the heat requirement will be slightly higher because the enthalpy of CO_{2} (g) is higher than that of aqueous CO_{2} .