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Let's analyze the problem step-by-step. The setup is a system involving an absorber used to dry air by passing it counter-current to sulfuric acid, with specific flow rates and concentrations noted for various streams in the process.

### Problem Breakdown and Data Extraction
1. **Stream 1**: Inlet stream of air into the absorber.
   - Flow rate = 2270 kg/min
   - Composition: 98.0 wt% Air, 2.0 wt% Water

2. **Stream 2**: Outflow of dry air from the absorber.
   - We need to calculate the details for this stream based on the absorber’s operation.

3. **Stream 4**: Effluent (discharged solution) from the absorber.
   - We are tasked with calculating the flow rate and composition here (part a).

4. **Stream 5**: Recycle stream that returns part of the solution back to the absorber.
   - We need to determine flow rate and composition for this stream (part b).

5. **Stream 6**: Make-up stream with concentrated sulfuric acid.
   - Flow rate = 518 kg/min
   - Composition: 99.0 wt% \( \text{H}_2\text{SO}_4 \), 1.0 wt% Water

6. **Stream 7**: Mixture of the recycled solution and the make-up sulfuric acid, entering the absorber.
   - Composition given as 94.0 wt% \( \text{H}_2\text{SO}_4 \), 6.0 wt% Water.
   - We need to determine the flow rate for this stream (part d).

### Solution Outline
The problem involves material balances for each component (air, \( \text{H}_2\text{SO}_4 \), and water) in the absorber and associated streams. We’ll approach each part of the question by setting up balances:

#### Part (a): Calculate the flow rate and composition of Stream 4 (effluent).
   - We will set up mass balances around the absorber for sulfuric acid and water, considering the input from Stream 1 and output in Streams 4 and 5.

#### Part (b): Calculate the flow rate and composition of Stream 5 (recycle stream).
   - Using the mass balance for water and \( \text{H}_2\text{SO}_4 \), we will determine how much of the solution is recycled versus discharged.

#### Part (c): Calculate the flow rate and composition of Stream 3.
   - This involves understanding the internal distribution within the absorber system.

#### Part (d): Calculate the flow rate of Stream 7.
   - Stream 7 is a combination of Streams 5 and 6. Given the target concentration (94.0 wt% \( \text{H}_2\text{SO}_4 \)), we will perform a mass balance to find the required flow rate.

Would you like me to proceed with detailed calculations for each part?

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### Additional Questions for Further Understanding
1. What are the steps to set up mass balances in absorption systems?
2. How do you determine the recycle ratio in a process involving a recycle stream?
3. What are common methods for calculating flow rates in counter-current absorption?
4. How can the water balance help in determining the air-drying efficiency?
5. What other compositions could affect the balance in multi-component systems like this?

### Tip
For complex processes like absorption systems with recycle, always start by identifying knowns and unknowns for each stream, and then apply component-wise mass balances systematically.

Adapted from Problem 3.25 in Duncan and Reimer. Air can be dried by bubbling through sulfuric acid. The absorber below passes air counter-current to a sulfuric acid solution. 99.0 wt% sulfuric acid is added to the recycled sulfuric acid solution to maintain a concentration of 94.0 wt% sulfuric acid in the absorber.

Calculate the following:

a. Flow rate and composition of the effluent, stream 4.
b. Flow rate and composition of the recycle, stream 5.
c. Flow rate and composition of stream 3.
d. Flow rate of stream 7.

Learn how to calculate the flow rates and compositions for streams in a sulfuric acid absorption system. This problem involves applying mass balance principles for air drying in a counter-current absorber system, suitable for college-level engineering students.

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