A culture of Rhizobium is grown in a chemostat (100 m3 bioreactor).
The feed contains 12 g/L sucrose.
Ks for the organism is 0.2 g/L and
μmax = 0.3 h-1.
Q.49 If Yx/s = 0.4 g/g for the above culture and
steady state cell concentration in the bioreactor is 4 g/L,
the resulting substrate concentration will be
Options:
(A) 2 g/L
(B) 8 g/L
(C) 4 g/L
(D) 6 g/L
Calculation of Substrate Concentration in a Chemostat Using Biomass Yield Coefficient
In continuous culture systems such as chemostats, the steady-state substrate
concentration depends on the biomass yield coefficient and the amount of biomass
formed. This numerical demonstrates how to calculate residual substrate
concentration using a simple substrate mass balance.
Question Overview
- Bioreactor volume = 100 m3
- Feed substrate concentration (S0) = 12 g/L
- Biomass yield coefficient (Yx/s) = 0.4 g/g
- Steady-state biomass concentration (X) = 4 g/L
Key Concept
Biomass yield coefficient is defined as:
Yx/s = Biomass formed / Substrate consumed
Therefore:
Substrate consumed = X / Yx/s
At steady state:
S = S0 − (X / Yx/s)
Step 1: Calculate Substrate Consumed
Substrate consumed = 4 / 0.4
= 10 g/L
Step 2: Calculate Steady-State Substrate Concentration
S = 12 − 10
S = 2 g/L
Correct Answer
Option (A): 2 g/L
Important Exam Tips
- Always apply substrate mass balance in chemostat problems.
- Yield coefficient links biomass formed to substrate consumed.
- Formula to remember: S = S0 − X / Yx/s
Conclusion
For a chemostat with feed substrate concentration of
12 g/L and biomass concentration of
4 g/L, the steady-state substrate concentration
is 2 g/L when the yield coefficient
Yx/s is 0.4 g/g.
Hence, Option (A) is the correct answer.
