The maximum cell concentration (g $l^{-1}$) expected in a bioreactor with initial cell concentration of $1.75$ g $l^{-1}$ and an initial glucose concentration of $125$ g $l^{-1}$ is ($Y_{x/s} = 0.6$ g cell/g substrate) _________
Bioreactor Maximum Cell Concentration Calculation
To determine the maximum cell concentration ($X_{max}$) expected in the bioreactor, we use the concept of biomass yield from the substrate.
Yield Calculation Principle
The amount of cells produced is directly proportional to the amount of substrate consumed. The yield coefficient ($Y_{x/s}$) relates cell mass produced to substrate consumed.
The formula connecting initial and final cell and substrate concentrations is:
$X - X_0 = Y_{x/s} \times (S_0 - S)$
Where:
- $X$ = Final cell concentration (g $l^{-1}$)
- $X_0$ = Initial cell concentration (g $l^{-1}$)
- $Y_{x/s}$ = Yield coefficient (g cell / g substrate)
- $S_0$ = Initial substrate concentration (g $l^{-1}$)
- $S$ = Final substrate concentration (g $l^{-1}$)
Maximum Cell Concentration Estimate
Assuming the substrate is completely consumed ($S \approx 0$), the maximum cell concentration ($X_{max}$) can be estimated by rearranging the formula:
$X_{max} \approx X_0 + (Y_{x/s} \times S_0)$
Applying Given Values
Substitute the given values into the formula:
- $X_0 = 1.75$ g $l^{-1}$
- $S_0 = 125$ g $l^{-1}$
- $Y_{x/s} = 0.6$ g cell/g substrate
Calculation:
$X_{max} \approx 1.75 \text{ g } l^{-1} + (0.6 \text{ g cell/g substrate} \times 125 \text{ g } l^{-1})$
$X_{max} \approx 1.75 + 75$
$X_{max} \approx 76.75 \text{ g } l^{-1}$
The calculated maximum cell concentration is approximately $76.75$ g $l^{-1}$. This value falls within the expected range.
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 ________ $\text{g L}^{-1}$.
