110. A Continuous Stirred Tank Reactor (CSTR) is running at a dilution (D) of 0.3 ℎ−1 and the product formed is growth associated with 𝑌𝑃/𝑥 = 0.2 𝑔/𝑔. In order to obtain productivity = 1.2 𝑔𝑙−1ℎ−1 we need to have at steady state a biomass concentration of:
A. 0.8 g/l
B. 1.8 g/l
C. 0.072 g/l
D. 20 g/l

Detailed Explanation:

In a Continuous Stirred Tank Reactor (CSTR), maintaining the desired productivity is essential for process efficiency. Given the dilution rate and yield coefficient, we can calculate the required biomass concentration to achieve the target productivity.

The formula for the productivity in a growth-associated reaction is:

Productivity=YP/X×Biomass concentration×D\text{Productivity} = Y_{\text{P/X}} \times \text{Biomass concentration} \times DProductivity=YP/X​×Biomass concentration×D

Where:

• YP/X=0.2 g/gY_{\text{P/X}} = 0.2 \, \text{g/g}YP/X​=0.2g/g is the yield coefficient (product formed per unit biomass),

• D=0.3 h−1D = 0.3 \, \text{h}^{-1}D=0.3h−1 is the dilution rate, and

• The target productivity is $1.2\text{g/L}\text{h}$.

Rearranging the formula to solve for the biomass concentration:

Biomass concentration=ProductivityYP/X×D\text{Biomass concentration} = \frac{\text{Productivity}}{Y_{\text{P/X}} \times D}Biomass concentration=YP/X​×DProductivity​

Substitute the given values:

Biomass concentration=1.2 g/L h0.2 g/g×0.3 h−1=1.20.06=20 g/L\text{Biomass concentration} = \frac{1.2 \, \text{g/L} \, \text{h}}{0.2 \, \text{g/g} \times 0.3 \, \text{h}^{-1}} = \frac{1.2}{0.06} = 20 \, \text{g/L}Biomass concentration=0.2g/g×0.3h−11.2g/Lh​=0.061.2​=20g/L

Thus, the biomass concentration required at steady state to achieve a productivity of 1.2 g/L*h is 20 g/L.

Answer:

D. 20 g/l