Question

A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is 0.5 g biomass / g substrate. The initial concentrations of biomass and substrate are 2 g L\(^{-1}\) and 200 g L\(^{-1}\), respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is _________ g L\(^{-1}\).

Hint:

The maximum biomass concentration in a batch culture can be calculated by multiplying the apparent growth yield by the initial concentration of the substrate.

Answer 1

Correct Answer: 102

The maximum biomass concentration that can be achieved is determined by the maximum amount of substrate available and the apparent growth yield. The maximum biomass concentration is given by: \[ X_{\text{max}} = Y_{\text{X/S}} \times S_{\text{initial}}, \] where:
- \( Y_{\text{X/S}} = 0.5 \, \text{g biomass/g substrate} \) is the apparent growth yield,
- \( S_{\text{initial}} = 200 \, \text{g L}^{-1} \) is the initial concentration of substrate.
Substituting the values into the equation: \[ X_{\text{max}} = 0.5 \times 200 = 100 \, \text{g L}^{-1}. \] Thus, the maximum biomass concentration that can be achieved is 100 g L\(^{-1}\).