Two aqueous NaOH streams are combined. Stream A is 26% NaOH by mole. Stream B is 69% NaOH by mole. The product (combined) stream has a flow rate of 125 lbmole/h and is 57% NaOH by mole. Determine the flow rate of stream A and stream B (lbmole/h).
Two aqueous NaOH streams are combined. Stream A is 26% NaOH by mole. Stream B is 69% NaOH by mole. The product (combined) stream has a flow rate of 125 lbmole/h and is 57% NaOH by mole. Determine the flow rate of stream A and stream B (lbmole/h).
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![### Problem Statement:
Two aqueous NaOH streams are combined. Stream A is 26% NaOH by mole. Stream B is 69% NaOH by mole. The product (combined) stream has a flow rate of 125 lbmole/h and is 57% NaOH by mole.
**Objective:**
Determine the flow rate of stream A and stream B (lbmole/h).
### Explanation:
To solve this problem, you need to set up a material balance equation for the NaOH components and the total flow rate. Follow these steps:
1. **Define Variables:**
- Let \( F_A \) be the flow rate of Stream A (in lbmole/h).
- Let \( F_B \) be the flow rate of Stream B (in lbmole/h).
2. **Given Information:**
- Stream A: 26% NaOH by mole (\( x_A = 0.26 \))
- Stream B: 69% NaOH by mole (\( x_B = 0.69 \))
- Combined Stream: 125 lbmole/h, 57% NaOH by mole (\( x_C = 0.57 \))
3. **Total Flow Rate Balance:**
\[
F_A + F_B = 125 \ \text{lbmole/h}
\]
4. **NaOH Component Balance:**
\[
0.26 F_A + 0.69 F_B = 0.57 \times 125
\]
5. **Solving the Equations:**
From the NaOH balance equation:
\[
0.26 F_A + 0.69 F_B = 71.25
\]
Using the total flow rate balance:
\[
F_A + F_B = 125
\]
You can use these two equations to solve for \( F_A \) and \( F_B \).
### Solution:
This section can be used to show the detailed mathematical steps for solving the equations to find \( F_A \) and \( F_B \).
**Step-by-Step Solution:**
1. Isolate \( F_B \) from the total flow rate balance equation:
\[
F_B = 125 - F_A
\]
2. Substitute \( F_B \) in the NaOH component balance equation:
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10115ea5-5f0e-4fb5-b400-8bf897ed7680%2Fcc58acd3-32d9-4cc3-87e7-06a8d04c954b%2Frliu84_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Two aqueous NaOH streams are combined. Stream A is 26% NaOH by mole. Stream B is 69% NaOH by mole. The product (combined) stream has a flow rate of 125 lbmole/h and is 57% NaOH by mole.
**Objective:**
Determine the flow rate of stream A and stream B (lbmole/h).
### Explanation:
To solve this problem, you need to set up a material balance equation for the NaOH components and the total flow rate. Follow these steps:
1. **Define Variables:**
- Let \( F_A \) be the flow rate of Stream A (in lbmole/h).
- Let \( F_B \) be the flow rate of Stream B (in lbmole/h).
2. **Given Information:**
- Stream A: 26% NaOH by mole (\( x_A = 0.26 \))
- Stream B: 69% NaOH by mole (\( x_B = 0.69 \))
- Combined Stream: 125 lbmole/h, 57% NaOH by mole (\( x_C = 0.57 \))
3. **Total Flow Rate Balance:**
\[
F_A + F_B = 125 \ \text{lbmole/h}
\]
4. **NaOH Component Balance:**
\[
0.26 F_A + 0.69 F_B = 0.57 \times 125
\]
5. **Solving the Equations:**
From the NaOH balance equation:
\[
0.26 F_A + 0.69 F_B = 71.25
\]
Using the total flow rate balance:
\[
F_A + F_B = 125
\]
You can use these two equations to solve for \( F_A \) and \( F_B \).
### Solution:
This section can be used to show the detailed mathematical steps for solving the equations to find \( F_A \) and \( F_B \).
**Step-by-Step Solution:**
1. Isolate \( F_B \) from the total flow rate balance equation:
\[
F_B = 125 - F_A
\]
2. Substitute \( F_B \) in the NaOH component balance equation:
\[
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