VIPSolutionsGive step-by-step solution with explanation and final answer:In chemical engineering, reactor design and reaction kinetics are fundamental concepts used to analyze how efficiently chemical reactions occur inside industrial reactors. A continuous reactor in a chemical processing plant is used to convert Reactant A into Product B through a first - order irreversible reaction. The feed stream enters the reactor with a concentration of Reactant A equal to 3 kmol/m # 3 at a volumetric flow rate of 5 m* 3/min. The reactor operates as a Continuous Stirred Tank Reactor (CSTR) with a working volume of 15 m* 3. The reaction follows first - order kinetics with a rate constant of 0.4 min™*. Using the principles of chemical engineering reactor design and mass balance, determine the outlet concentration of Reactant A and the conversion of Reactant A in the reactor.
Question:
Give step-by-step solution with explanation and final answer:
In chemical engineering, reactor design and reaction kinetics are fundamental concepts used
to analyze how efficiently chemical reactions occur inside industrial reactors. A continuous
reactor in a chemical processing plant is used to convert Reactant A into Product B through a
first - order irreversible reaction. The feed stream enters the reactor with a concentration of
Reactant A equal to 3 kmol/m # 3 at a volumetric flow rate of 5 m* 3/min. The reactor
operates as a Continuous Stirred Tank Reactor (CSTR) with a working volume of 15 m* 3. The
reaction follows first - order kinetics with a rate constant of 0.4 min™*.
Using the principles of chemical engineering reactor design and mass balance, determine the
outlet concentration of Reactant A and the conversion of Reactant A in the reactor.
This is AI generated Response.
Asked by: Francis
Created at: 2026-03-09 16:25:34
Asked by: Francis
Created at: 2026-03-09 16:25:34
Final Answer:
Rendered
Raw Text
Did you like this answer?
## Step-by-Step Solution
### **Given Data**
- **Initial concentration of A (\( C_{A} \)):** 3 kmol/m³
- **Volumetric flow rate (\( Q \)):** 5 m³/min
- **Reactor volume (\( V \)):** 15 m³
- **Rate constant (\( k \)):** .4 min⁻¹
- **Type of reactor:** CSTR (Continuous Stirred Tank Reactor)
- **Reaction order:** First order (irreversible)
---
### **1. Mass Balance for CSTR**
For a **CSTR** at steady state:
\[
\text{In} - \text{Out} + \text{Generation} =
\]
For Reactant A:
\[
Q C_{A} - Q C_{A} - r_A V =
\]
Where \( r_A \) is the rate of disappearance of A.
---
### **2. Reaction Rate Expression**
For a **first-order** reaction:
\[
r_A = k C_A
\]
---
### **3. Substitute and Rearrange**
Substitute \( r_A \) into the mass balance:
\[
Q C_{A} - Q C_{A} - k C_A V =
\]
\[
Q C_{A} = Q C_A + k C_A V
\]
\[
Q C_{A} = C_A (Q + k V)
\]
\[
C_A = \frac{Q C_{A}}{Q + kV}
\]
---
### **4. Plug in the Given Values**
- \( Q = 5 \) m³/min
- \( C_{A} = 3 \) kmol/m³
- \( k = .4 \) min⁻¹
- \( V = 15 \) m³
\[
C_A = \frac{5 \times 3}{5 + .4 \times 15}
\]
\[
C_A = \frac{15}{5 + 6}
\]
\[
C_A = \frac{15}{11}
\]
\[
C_A = 1.364 \text{ kmol/m}^3
\]
---
### **5. Calculate Conversion of A (\( X \))**
\[
X = \frac{C_{A} - C_A}{C_{A}}
\]
\[
X = \frac{3 - 1.364}{3}
\]
\[
X = \frac{1.636}{3}
\]
\[
X = .545
\]
\[
X = 54.5\%
\]
---
## **Final Answers**
### **Outlet concentration of Reactant A:**
\[
\boxed{1.36 \text{ kmol/m}^3}
\]
### **Conversion of Reactant A in the reactor:**
\[
\boxed{54.5\%}
\]
---
#### **Summary Table**
| Quantity | Value |
|---------------------------|------------------------|
| Outlet concentration (\(C_A\)) | 1.36 kmol/m³ |
| Conversion (\(X\)) | 54.5% |
Question:
give me answer without any spaces or empty values.
This is AI generated Response.
Asked by: Francis
Created at: 2026-03-09 16:32:47
Asked by: Francis
Created at: 2026-03-09 16:32:47
Final Answer:
Rendered
Raw Text
Did you like this answer?
## Step-by-Step Solution
### **Given Data**
- **Initial concentration of A (\( C_{A} \)):** 3 kmol/m³
- **Volumetric flow rate (\( Q \)):** 5 m³/min
- **Reactor volume (\( V \)):** 15 m³
- **Rate constant (\( k \)):** 0.4 min⁻¹
- **Type of reactor:** CSTR
- **Reaction order:** First order (irreversible)
### **1. Mass Balance for CSTR**
For a CSTR at steady state:
\[
Q C_{A} - Q C_{A} - r_A V = 0
\]
Where \( r_A \) is the rate of disappearance of A.
### **2. Reaction Rate Expression**
For a first-order reaction:
\[
r_A = k C_A
\]
### **3. Substitute and Rearrange**
Substituting \( r_A \):
\[
Q C_{A} = C_A (Q + k V)
\]
\[
C_A = \frac{Q C_{A}}{Q + k V}
\]
### **4. Plug in the Given Values**
\[
C_A = \frac{5 \times 3}{5 + 0.4 \times 15}
\]
\[
C_A = \frac{15}{5 + 6}
\]
\[
C_A = \frac{15}{11} \approx 1.364 \text{ kmol/m}^3
\]
### **5. Calculate Conversion of A (\( X \))**
\[
X = \frac{C_{A} - C_A}{C_{A}} = \frac{3 - 1.364}{3} \approx 0.545
\]
\[
X \approx 54.5\%
\]
## **Final Answers**
### **Outlet concentration of Reactant A:**
\[
\boxed{1.36 \text{ kmol/m}^3}
\]
### **Conversion of Reactant A in the reactor:**
\[
\boxed{54.5\%}
\]
### **Summary Table**
| Quantity | Value |
|---------------------------|------------------------|
| Outlet concentration (\(C_A\)) | 1.36 kmol/m³ |
| Conversion (\(X\)) | 54.5% |
📢 Instructions:
- Ask anything relatd to above question only.
- For new Question goto :