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.51 What would be the sucrose concentration in the input feed for the output to be 45 kg biomass h−1?
Chemostat Culture: Sucrose Concentration Calculation for 45 kg Biomass Output
Chemostat cultures maintain steady-state conditions where biomass output depends on feed flow rate, dilution rate, and yield coefficients derived from initial data. The query provides initial conditions to compute biomass yield on substrate (YX/S), which remains constant, allowing calculation of the new input sucrose concentration (Sin,new) for a target biomass productivity of 45 kg h-1.
🎯 Key Parameters
Given Data:
- Working volume V = 60 m³
- Dilution rate D = 0.55 h-1
- Steady-state biomass X = 4.5 kg m-3
- Residual sucrose S = 2.0 kg m-3
- Initial feed Sin = 10.0 kg m-3
Step 1: Feed flow rate F = D × V = 0.55 × 60 = 33 m³ h-1
Step 2: Initial biomass productivity = F × X = 33 × 4.5 = 148.5 kg h-1
Step 3: Biomass yield YX/S = X / (Sin – S) = 4.5 / (10.0 – 2.0) = 0.5625 kg biomass per kg sucrose
⚙️ Target Calculation
Target biomass productivity = 45 kg h-1
- New biomass concentration Xnew = 45 / 33 ≈ 1.3636 kg m-3
- Sucrose consumed = Xnew / YX/S ≈ 1.3636 / 0.5625 ≈ 2.424 kg m-3
- New feed concentration Sin,new = S + sucrose consumed = 2.0 + 2.424 = 4.424 kg m-3
Closest option: (B) 4.425 kg m-3 ✅
📊 Option Analysis
| Option | Sin,new (kg m-3) | Xnew (kg m-3) | Productivity (kg h-1) | Status |
|---|---|---|---|---|
| (A) | 3.225 | 0.694 | 22.9 | ❌ Too Low |
| (B) | 4.425 | 1.363 | 45.0 | ✅ CORRECT |
| (C) | 5.115 | 1.786 | 58.9 | ❌ Too High |
| (D) | 6.525 | 2.588 | 85.4 | ❌ Too High |
🎓 Key Chemostat Principles
- Steady-state: μ = D (growth rate equals dilution rate)
- Mass balance: Biomass productivity = F × X
- Yield constant: YX/S remains same across conditions
- Substrate balance: Sin – S = X / YX/S
Target Keywords: chemostat sucrose concentration, biomass output 45 kg h, dilution rate 0.55 h⁻¹, biochemical engineering
✅ Final Answer: Option (B) 4.425 kg m⁻³
