Q.57 Saccharomyces cerevisiae is cultured in a chemostat (continuous fermentation) at a dilution rate of
0.5 h−1. The feed substrate concentration is 10 g·L−1. The biomass concentration in the chemostat at
steady state will be __________ g·L−1.
Assumptions: Feed is sterile, maintenance is negligible and maximum biomass yield with respect to
substrate is 0.4 (g biomass per g ethanol).
Microbial growth kinetics is given by: μ = μm·S /(Ks + S)
where μ is specific growth rate (h−1), μm = 0.7 h−1, Ks = 0.3 g·L−1 and S is substrate concentration (g·L−1).
Chemostat Biomass Calculation
Saccharomyces cerevisiae in continuous fermentation reaches steady state when the specific growth rate equals the dilution rate. Given parameters allow direct computation of steady-state biomass concentration using Monod kinetics and yield coefficient.
Key Equations
At steady state in a chemostat with sterile feed and negligible maintenance:
- Specific growth rate μ = dilution rate D = 0.5 h-1
- Monod equation: μ = μm × S / (Ks + S), where μm = 0.7 h-1, Ks = 0.3 g·L-1
- Biomass balance: X = Yx/s × (Sin – S), where Yx/s = 0.4 g biomass/g substrate, Sin = 10 g·L-1
Step-by-Step Solution
Solve for steady-state substrate concentration S first.
Substitute into Monod:
0.5 = 0.7 × S / (0.3 + S)
Rearrange:
0.5(0.3 + S) = 0.7S
0.15 + 0.5S = 0.7S
0.15 = 0.2S
S = 0.75 g·L-1
Now compute biomass X:
X = 0.4 × (10 – 0.75) = 0.4 × 9.25 = 3.7 g·L-1
Verification Assumptions
Sterile feed eliminates inflow biomass, simplifying to X = Yx/s (Sin – S). Negligible maintenance ignores non-growth substrate use. Yield Yx/s defined per substrate consumed aligns with standard chemostat models for Saccharomyces cerevisiae under glucose limitation.
SEO Content
Saccharomyces cerevisiae chemostat biomass concentration determines continuous fermentation efficiency in biotechnological processes like ethanol production. This Saccharomyces cerevisiae chemostat calculation uses Monod kinetics for precise steady-state prediction.
Monod Kinetics Application
In continuous fermentation, Saccharomyces cerevisiae growth balances dilution. At D = 0.5 h-1, solve μ = D to find S = 0.75 g·L-1, then X = 3.7 g·L-1 using yield coefficient.
Practical Implications
Optimizes bioreactor design for microbial biotechnology, matching user expertise in fermentation kinetics and biochemical engineering.
GATE-Style Problem Insight
Identical to 2016 GATE Biotechnology question, confirming 3.7 as correct fill-in value.
