A process for the microbial synthesis of $1,3-$propanediol $(C_3{H}_8{O}_2)$ uses an anaerobic

fermenter with a selected strain of $K.$ pneumoniae to convert glycerol $(C_3{H}_8{O}_3)$ to $1,3-$

propanediol and acetic acid $(C_2{H}_4{O}_2).$ All other byproducts are of negligible concentration. The

fermentation and cell growth equation can be written:

$68C_3{H}_8{O}_3+3N{H}_{3}3C_4{H}_7{O}_{2}N+49C_3{H}_8{O}_2+15C_2{H}_4{O}_2+15C{O}_2+40H_{2}O$

The continuous fermentation process is set up at $37C$ and atmospheric pressure. Anaerobic

conditions are maintained by sparging the fermentation broth with $N_2$ at a flowrate of $500$

litres per minute. The medium, containing ammonia, is fed at $500kg$ per hour, and has a

composition of $14\%(\frac{w}{w})$ glycerol. Suppression of the side reactions is achieved by excess

glycerol, so the liquid product contains $3\%(\frac{w}{w})$ unreacted glycerol.

$2$a$.$ Draw a process diagram. List all your assumptions necessary to write a material

balance.

$2$b$.$ List your unknowns.

$2$d$.$ Compute the molar rate of glycerol consumption by $K.$ pneumoniae in the fermenter.

The molecular weight of glycerol is $92gmo{l}^{-1}.$

$2$f$.$ Estimate the flowrate $V$ and composition of the offgas stream.