The production of a product P from a particular gram-negative bacteria follows the Monod growth law max CsCc rg = Ks+Cs = with μmax = 1 h-¹, Ks = 0.25 g/dm³, and Yc/s 0.5 g/g. (a) The reaction is to be carried out in a batch reactor with the initial cell concentration of Cco = 0.1 g/dm³ and substrate concentration of C5o = 20 g/dm³. Cc Cco+Yc/s(Cs0 - Cs) Plot r-rs-re Cs, and C as a function of time. (b) The reaction is now to be carried out in a CSTR with Cso = 20 g/dm³ and Co = 0. What is the dilution rate at which wash-out occurs? (c) For the conditions in part (b), what is the dilution rate that will give the maximum product rate (g/h) if Y = 0.15 g/g? What are the concentrations C, C₁, C₂, and -r, at this value of D?
The production of a product P from a particular gram-negative bacteria follows the Monod growth law max CsCc rg = Ks+Cs = with μmax = 1 h-¹, Ks = 0.25 g/dm³, and Yc/s 0.5 g/g. (a) The reaction is to be carried out in a batch reactor with the initial cell concentration of Cco = 0.1 g/dm³ and substrate concentration of C5o = 20 g/dm³. Cc Cco+Yc/s(Cs0 - Cs) Plot r-rs-re Cs, and C as a function of time. (b) The reaction is now to be carried out in a CSTR with Cso = 20 g/dm³ and Co = 0. What is the dilution rate at which wash-out occurs? (c) For the conditions in part (b), what is the dilution rate that will give the maximum product rate (g/h) if Y = 0.15 g/g? What are the concentrations C, C₁, C₂, and -r, at this value of D?
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![## The Production of a Product P from Gram-Negative Bacteria: Monod Growth Law
The Monod growth law for the production of a product P from a specific gram-negative bacteria is described by the following equation:
\[ r_g = \frac{\mu_{\text{max}} C_s C_c}{K_s + C_s} \]
**Parameters:**
- \(\mu_{\text{max}} = 1 \, \text{h}^{-1}\)
- \(K_s = 0.25 \, \text{g/dm}^3\)
- \(Y_{c/s} = 0.5 \, \text{g/g}\)
### (a) Batch Reactor Conditions
- **Initial Conditions:**
- \(C_{c0} = 0.1 \, \text{g/dm}^3\) (Initial cell concentration)
- \(C_{s0} = 20 \, \text{g/dm}^3\) (Substrate concentration)
- **Equation for Cell Concentration:**
\[ C_c = C_{c0} + Y_{c/s}(C_{s0} - C_s) \]
- **Task:** Plot \(r_g\), \(-r_s\), \(-r_c\), \(C_s\), and \(C_c\) as a function of time.
### (b) Continuous Stirred-Tank Reactor (CSTR) Conditions
The reaction is proposed to be carried out in a CSTR with:
- \(C_{s0} = 20 \, \text{g/dm}^3\)
- \(C_{c0} = 0\)
**Objective:** Determine the dilution rate at which washout occurs.
### (c) Optimal Dilution Rate for Maximum Product Rate
- **Given:** \(Y_{p/c} = 0.15 \, \text{g/g}\)
**Objective:**
1. Calculate the dilution rate (D) that maximizes the product rate \((g/h)\).
2. Determine the concentrations \(C_c\), \(C_s\), \(C_p\), and \(-r_s\) at this optimal dilution rate.
This content is designed for educational purposes to aid in understanding the application of the Monod growth law in bioprocessing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ef5005f-99e9-4e7d-9469-054276644387%2F5fc5679e-44df-413e-b1ce-196addf28116%2Ftd78xob_processed.png&w=3840&q=75)
Transcribed Image Text:## The Production of a Product P from Gram-Negative Bacteria: Monod Growth Law
The Monod growth law for the production of a product P from a specific gram-negative bacteria is described by the following equation:
\[ r_g = \frac{\mu_{\text{max}} C_s C_c}{K_s + C_s} \]
**Parameters:**
- \(\mu_{\text{max}} = 1 \, \text{h}^{-1}\)
- \(K_s = 0.25 \, \text{g/dm}^3\)
- \(Y_{c/s} = 0.5 \, \text{g/g}\)
### (a) Batch Reactor Conditions
- **Initial Conditions:**
- \(C_{c0} = 0.1 \, \text{g/dm}^3\) (Initial cell concentration)
- \(C_{s0} = 20 \, \text{g/dm}^3\) (Substrate concentration)
- **Equation for Cell Concentration:**
\[ C_c = C_{c0} + Y_{c/s}(C_{s0} - C_s) \]
- **Task:** Plot \(r_g\), \(-r_s\), \(-r_c\), \(C_s\), and \(C_c\) as a function of time.
### (b) Continuous Stirred-Tank Reactor (CSTR) Conditions
The reaction is proposed to be carried out in a CSTR with:
- \(C_{s0} = 20 \, \text{g/dm}^3\)
- \(C_{c0} = 0\)
**Objective:** Determine the dilution rate at which washout occurs.
### (c) Optimal Dilution Rate for Maximum Product Rate
- **Given:** \(Y_{p/c} = 0.15 \, \text{g/g}\)
**Objective:**
1. Calculate the dilution rate (D) that maximizes the product rate \((g/h)\).
2. Determine the concentrations \(C_c\), \(C_s\), \(C_p\), and \(-r_s\) at this optimal dilution rate.
This content is designed for educational purposes to aid in understanding the application of the Monod growth law in bioprocessing.
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