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The problem describes a vertical flash drum used to separate a water/methanol mixture at a rate of 10 kmol/hr. It provides the following information:

- The vapor stream at the outlet has a methanol composition of 0.6.
- The flow rate ratio of the outlet liquid stream to the outlet vapor stream is 1 (i.e., \( L/V = 1 \)).
- We need to determine the composition of the outlet liquid stream and the feed stream.

### Solution Approach

Let:
- \( F \) represent the feed flow rate (10 kmol/hr),
- \( L \) be the liquid flow rate,
- \( V \) be the vapor flow rate, 
- \( x_A \) be the mole fraction of methanol in the liquid phase,
- \( y_A \) be the mole fraction of methanol in the vapor phase, and
- \( z_A \) be the mole fraction of methanol in the feed stream.

From the problem, we know:
- \( y_A = 0.6 \),
- \( L/V = 1 \), implying \( L = V \), and
- Total feed, \( F = L + V = 10 \).

So, \( L = V = 5 \) kmol/hr.

### Step 1: Mass Balance
The overall methanol balance for the system can be expressed as:

\[
F \cdot z_A = L \cdot x_A + V \cdot y_A
\]

Substituting the known values:

\[
10 \cdot z_A = 5 \cdot x_A + 5 \cdot 0.6
\]

\[
10 \cdot z_A = 5 \cdot x_A + 3
\]

### Step 2: Vapor-Liquid Equilibrium (VLE)
The relationship between \( y_A \) and \( x_A \) is given by the equilibrium data in the graph provided in the problem, where the equilibrium curve plots \( y_A \) vs. \( x_A \). From the graph, when \( y_A = 0.6 \), the corresponding \( x_A \) (the liquid composition) can be approximated as:

\[
x_A \approx 0.38
\]

### Step 3: Solve for \( z_A \) (Feed Composition)
Now, substitute \( x_A = 0.38 \) into the mass balance equation:

\[
10 \cdot z_A = 5 \cdot 0.38 + 3
\]

\[
10 \cdot z_A = 1.9 + 3
\]

\[
10 \cdot z_A = 4.9
\]

\[
z_A = 0.49
\]

### Final Results:
- The composition of the liquid stream \( x_A \) is approximately **0.38**.
- The composition of the feed stream \( z_A \) is approximately **0.49**.

Would you like further clarification on this solution?

### Related Questions:
1. What is the effect of changing the \( L/V \) ratio on the liquid composition?
2. How would the vapor composition change if the feed flow rate increased?
3. What role does the equilibrium curve play in determining phase compositions?
4. How can the process efficiency be improved in a flash drum?
5. What happens if the feed composition of methanol is less than 0.49?

### Tip:
When dealing with separation processes like a flash drum, always remember to perform a mass balance and consider phase equilibria to ensure accurate compositions.

A vertical flash drum is used to separate 10 kmol/hr of a water/methanol mixture. The composition of vapor stream at the outlet is 0.6 methanol. Assuming the ratio of the flow rate of the outlet liquid stream over the flow rate of the outlet vapor stream equals 1 (L/V=1), what is the composition of the outlet liquid stream as well as the feed stream?

Solve a flash drum separation problem involving a water/methanol mixture. Learn how to use mass balance and vapor-liquid equilibrium (VLE) concepts to find the liquid and feed compositions for a system processing 10 kmol/hr. Includes step-by-step calculations and explanations suitable for chemical engineering students.

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