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Let's solve this problem step-by-step to determine the percentage of acetic acid (A) in the process feed that is recovered in the distillate stream.

### Given Information

1. **Process Stages**:
   - **Liquid-Liquid Extraction**: Acetic acid (A) is extracted from water (W) into hexanol (H).
   - **Distillation**: The hexanol-rich extract is fed into a distillation column.

2. **Feed to Extraction Vessel**:
   - Composition: **18% acetic acid** and **82% water**.

3. **Extraction Outcome**:
   - The water-rich stream leaving the vessel contains **1.0% acetic acid**.

4. **Distillation Column**:
   - The hexanol-rich extract goes into the column.
   - Distillate Composition: **96% acetic acid** and **4% hexanol**.
   - Bottom Stream Composition: **98% hexanol** and **2% acetic acid**.
   - **95% of hexanol** fed to the extraction vessel is recovered.

5. **Mass Information**:
   - For every **100 kg** of distillate, we have the given composition.

### Problem Requirement
We need to calculate the percentage of acetic acid in the process feed that is recovered in the **distillate stream**.

### Step-by-Step Analysis

#### 1. Mass Balance on Acetic Acid in Liquid-Liquid Extraction

The feed mixture to the extraction vessel is **18% acetic acid and 82% water**. 

- Let’s assume the **feed flow rate** to the extraction vessel is **100 kg**.
- **Acetic acid in the feed** = \( 100 \times 0.18 = 18 \, \text{kg} \)
- **Water in the feed** = \( 100 \times 0.82 = 82 \, \text{kg} \)

After the extraction, the water-rich stream leaving the vessel contains **1.0% acetic acid**. 

- Let’s denote the mass of the water-rich stream as \( W_{\text{out}} \).
- The acetic acid in this stream is **1%** of \( W_{\text{out}} \).

For a mass balance on acetic acid in the **liquid-liquid extraction** stage:

\[
18 = A_{\text{extract}} + 0.01 \times W_{\text{out}}
\]

Where \( A_{\text{extract}} \) is the mass of acetic acid that goes into the hexanol-rich extract. This \( A_{\text{extract}} \) is subsequently fed to the distillation column.

#### 2. Distillation Column Mass Balance

The **hexanol-rich extract** from the liquid-liquid extraction vessel is fed into a distillation column. The distillation column separates the mixture into:

- **Distillate**: **96% acetic acid** and **4% hexanol**
- **Bottoms Stream**: **98% hexanol** and **2% acetic acid**

For every **100 kg** of distillate, there is **96 kg** of acetic acid.

#### 3. Acetic Acid Recovery Calculation

We need to determine the percentage of acetic acid in the **process feed** that ends up in the **distillate stream**.

- Let \( A_{\text{dist}} \) be the mass of acetic acid in the distillate.
- From the distillation, we know that the distillate contains **96%** acetic acid.
  
If we have **100 kg** of distillate, then:

\[
A_{\text{dist}} = 100 \times 0.96 = 96 \, \text{kg}
\]

To determine the percentage recovery of acetic acid:

\[
\text{Percentage Recovery} = \left( \frac{A_{\text{dist}}}{A_{\text{feed}}} \right) \times 100\%
\]

Where:

- \( A_{\text{feed}} = 18 \, \text{kg} \) (initial amount of acetic acid in the feed)

\[
\text{Percentage Recovery} = \left( \frac{96}{18} \right) \times 100\% = 533.33\%
\]

However, this value seems incorrect since it exceeds 100%, indicating there may be an issue with interpretation or mass assumptions. Let's clarify calculations?

Relative_questions

In a two-stage process, acetic acid (A) is extracted from water (W) into hexanol (H) in a liquid-liquid extraction vessel and the extract is subsequently separated by distillation. Assume that water is completely insoluble in hexanol. A mixture containing 18% acetic acid and 82% water is fed to a liquid-liquid extraction vessel. Pure hexanol is fed to the column to extract the acetic acid. The water rich stream leaving the vessel contains 1.0% acetic acid. The hexanol-rich extract from the vessel is fed to a distillation column. The composition of the distillate is 96% acetic acid and 4% hexanol. The bottoms stream contains 98.0% hexanol and recovers 95% of the hexanol fed to the liquid-liquid extraction vessel. For every 100 kg of distillate, calculate the percentage of acetic acid in the process feed that is recovered in the distillate stream.

Solve a two-stage chemical process problem involving acetic acid recovery. Learn how to calculate the percentage of acetic acid recovered using mass balance equations and percentage recovery formulas. Includes detailed steps on liquid-liquid extraction and distillation. Ideal for chemical engineering students.

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