[SunilNagpal]

A microorganism grows in a continuous ‘chemostat’ culture of 60 m3 working volume with sucrose as the growth limiting nutrient at dilution rate, D = 0.55 h-1. The steady state biomass concentration is 4.5 Kg dry biomass m-3 and the residual sucrose concentration is 2.0 Kg m-3. The sucrose concentration in the incoming feed medium is 10.0 Kg m-3.

What would be the yield Y X/S (Kg biomass/Kg substrate)?

Options:


0.562


0.462


0.362


0.162

Answer:

There are two ways to arrive at the solution to this question:

a) Look at the units of the quantity you need to find out:
The units as we can see are: Kg biomass/Kg substrate

Now given the fact that we need to arrive at this unit, we will need 'weight of biomass in numerator'. So, it means that the concentration of biomass shall be our numerator (i.e  4.5 Kg dry biomass m-3). Now we need to get rid of the m-3 in our numerator and also get the Kg substrate in denominator. So it means that in denominator, we shall need some concentration of substrate (Kg substrate m-3). Given the fact that we have two substrate concentrations, decision is about choosing the denominator. At this juncture, one should know the meaning of Yield:

Yield is : Biomass that you get out of the culture / Substrate you use

So, here, Biomass we are getting is 'Steady state concentration' and substrate we are using is 'Initial concentration - Final Concentration of substrate' i.e 10 - 2 = 8 Kg substrate m-3

So this gives us our denominator: 8 kg substrate m-3.

Hence our Yield should be 4.5 Kg biomass m-3/8 Kg substrate m-3 = 0.562 Kg biomass / Kg substrate

b) Keep in mind the formula for finding the steady state biomass concentration in a chemostat:

x = Y(si - so) where Y is yield, si is input stream substrate conc., So is output stream substrate conc. at steady state.

So, here x=4.5kgm-3
Si is 10kg m-3
So is 2Kg m-3

Hence Y is 4.5/10-2 = 4.5/8 = 0.562 Kg biomass/Kg substrate


Try solving 51st question of GATE BT 2011 now. In case it is not solvable, let me know.

Best wishes
Sunil