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.
Q.50 What would be the yield YX/S (kg biomass/kg substrate)?
Chemostat Basics
A chemostat maintains steady-state growth by balancing dilution rate D with specific growth rate μ, where biomass X and residual substrate S remain constant. Here, working volume is 60 m³ (unused for YX/S), D=0.55 h⁻¹, X=4.5 kg dry biomass m⁻³, S=2.0 kg m⁻³, and feed substrate S₀=10.0 kg m⁻³. Substrate consumption drives biomass formation under growth-limited conditions.
Yield Calculation
YX/S = X / (S₀ – S), derived from mass balance: biomass produced equals yield times substrate consumed.
Substitute values:
YX/S = 4.5 / (10.0 - 2.0) = 4.5 / 8.0 = 0.562 kg biomass/kg substrate
This ignores maintenance or product formation, standard for such problems.
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