Question

Plant cells are cultured in a bioreactor using sucrose as the carbon source and ammonia as the nitrogen source. The vessel is sparged with air. Elemental analysis of the plant cells gives a molecular formula of CH1.63O0.80N0.13 with negligible ash. Yield measurements show that 0.52 g of plant cells is produced per g of sugar consumed. If 10 kg of the plant cell is needed, (a) how much sugar is consumed per hour, and (b) at what rate must oxygen be provided to the reactor in units of mol/min?

Answer 1

a) 0.52 grams of plant cells are produced by 1 grams of sugar. Hence, to find the sugar needed for making 10 kg = 10000 grams of plant, we use the formula:

Hence, 19.231 kg of sugar needs to be consumed. Let t be the time required to make 10kg plant. Hence, the amount of sugar consumed per hour becomes 19.231/t kg per hour.

b) The elemental composition of plant cells is:

Hence, the molecular weight of plant will be:

Now, the aim is to produce 10kg of plant. Hence, the moles of plant that need to be produced are:

Now from the formula, we know that 0.80 moles of O are required for generating 1 mole of plant. Hence, to generate 354 moles of plant, we will require:

But these are the moles of atomic oxygen. 1 mole of molecular oxygen has two moles of atomic oxygen. Hence, the number of moles of molecular oxygen needed are:

Thus, 141.6 moles of molecular oxygen are needed for this purpose. Let T be the time required to generate 10kg plant. Hence, the amount of molecular oxygen needed per minute becomes 141.6/T moles/min.