Understanding Specific Substrate Consumption Rate Unit
The specific substrate consumption rate quantifies how efficiently a microbial culture consumes a substrate relative to its own biomass. In simpler terms, it measures the amount of substrate consumed per unit of biomass per unit of time.
Deriving the Unit
Let's break down the components:
- Substrate Consumption: Measured in mass units, typically grams (g).
- Rate: Implies consumption over time, typically hours (h). So, a substrate consumption rate might be expressed as g/h.
- Specific Rate: The term 'specific' indicates normalization by the amount of biomass present. Biomass is also measured in mass units, typically grams (g).
Therefore, the unit for specific substrate consumption rate is derived as:
$ \frac{\text{Mass of Substrate}}{\text{Mass of Biomass} \cdot \text{Time}} $Substituting the common units:
$ \frac{g}{g \cdot h} $Evaluating the Options
Based on the derivation:
- Option 1 ($\frac{g}{L \cdot h}$) represents the volumetric substrate consumption rate (mass per volume per time).
- Option 2 ($\frac{g}{h}$) represents the total substrate consumption rate (mass per time).
- Option 3 ($\frac{g}{g \cdot h}$) correctly represents the specific substrate consumption rate (mass of substrate per mass of biomass per time).
- Option 4 ($\frac{gmoles}{L \cdot h}$) represents the molar volumetric substrate consumption rate.
Thus, the correct unit for specific substrate consumption rate in a growing culture is $\frac{g}{g \cdot h}$.
Important Questions from Kinetics of Cell Growth Substrate Utilization and Product Formation
If the rate at which $E. coli$ divides is $0.5 \text{ h}^{-1}$, then its doubling time is _______________ h.
- Which of the following factors can affect the growth of a microbial culture in a batch cultivation process?
Let $y(t)$ be a bacterial population whose growth is given by
$ \frac{dy}{dt} = \lambda(y + 2) $
where $ \lambda $ is the growth rate constant. If $y(0) = 1$ and $y(1) = 4$, then the value of $ \lambda $ is
If the doubling time of a bacterial population is 3 hours, then its average specific growth rate during this period is _________ $h^{-1}$.
(Round off to two decimal places)
- A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is $0.5 \frac{\text{g biomass}}{\text{g substrate}}$. The initial concentrations of biomass and substrate are $2 \text{ g L}^{-1}$ and $200 \text{ g L}^{-1}$, respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is ________ $\text{g L}^{-1}$.
