A Pseudomonas aeruginosa culture has a maximum specific growth rate μmax = 0.8 h^-1 on glucose. In a chemostat, what dilution rate D will prevent washout?
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AGreater than 0.8 h^-1
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BLess than 0.8 h^-1
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CEqual to 0.8 h^-1
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D1.6 h^-1
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EExactly zero
Answer
Correct Answer: Less than 0.8 h^-1
Explanation
Introduction / Context:In a chemostat, steady state requires that the net specific growth rate equals the dilution rate (μ = D). If D exceeds the culture’s μ at the operating conditions, biomass cannot keep up with outflow and washout occurs. Choosing D relative to μmax is a basic control decision.
Given Data / Assumptions:
- μmax = 0.8 h^-1 for Pseudomonas aeruginosa on the stated medium.
- Operating substrate concentration supports μ ≤ μmax.
- No cell retention device.
Concept / Approach:To avoid washout, set D < μ at the achieved substrate level. Since μ cannot exceed μmax, a safe guideline is D < μmax, with margin for disturbances and maintenance requirements.
Step-by-Step Solution:
At steady state: μ = D.Washout threshold: D ≥ μ → at limiting case, D = μmax is risky.Therefore, to prevent washout: choose D < 0.8 h^-1.Additional safety margin (e.g., 0.6–0.7 h^-1) is common in practice.Verification / Alternative check:Chemostat theory predicts X → 0 as D approaches μmax from below if substrate is limiting and any perturbation pushes μ < D.
Why Other Options Are Wrong:
- D > 0.8: guarantees washout.
- D = 0.8: marginal; susceptible to washout.
- D = 1.6: far above μmax; immediate washout.
- D = 0: not a chemostat (becomes batch).
Common Pitfalls:Ignoring that μ depends on substrate; operating too close to μmax reduces robustness to fluctuations.
Final Answer:Less than 0.8 h^-1