\[ y=\frac{\mu z}{1+(\alpha-1) x} \quad \text { where } \alpha=\text { relative volatility } \] A mixture of betzene and toluene containing 60 mole per cent benzene is to be separated togive a producl containing 95 mole per cent benzene at the top, and a bollom prouluct containing not more than 10 mole per cent benzene. The feed enter the column at its boiling point it is proposed to operate the unit with a reflux ratio of 25 . Using Lewis-Sorel method, determine the position of entry for the feed. ( 12 marks)

To determine the position of entry for the feed in the distillation column using the **Lewis-Sorel method**, we'll follow a systematic approach. This involves constructing operating lines and identifying the feed stage based on the given data. ### **Given Data:** - **Feed Composition (\( z_F \))**: 60 mole% benzene - **Distillate (\( x_D \))**: 95 mole% benzene - **Bottoms (\( x_B \))**: ≤10 mole% benzene - **Reflux Ratio (\( R \))**: 25 - **Relative Volatility (\( \alpha \))**: Assumed constant (not explicitly provided) ### **Assumptions:** 1. **Binary Mixture**: Benzene (more volatile, component 1) and Toluene (less volatile, component 2). 2. **Equilibrium Relationship**: Given by \( y = \frac{\alpha x}{1 + (\alpha - 1) x} \), where: - \( y \) = vapor mole fraction of benzene - \( x \) = liquid mole fraction of benzene 3. **Feed Condition**: The feed enters as a saturated liquid, so **q = 1**. ### **Steps:** 1. **Construct the Equilibrium Curve:** - Plot \( y \) vs. \( x \) using the equilibrium relationship. - This curve represents the vapor-liquid equilibrium for the benzene-toluene system. 2. **Draw the Rectifying Operating Line:** - The rectifying (top section) operating line is given by: \[ y = \frac{R}{R + 1} x + \frac{x_D}{R + 1} \] - Substituting \( R = 25 \) and \( x_D = 0.95 \): \[ y = \frac{25}{26} x + \frac{0.95}{26} \] \[ y = 0.9615x + 0.0365 \] 3. **Draw the Stripping Operating Line:** - The stripping (bottom section) operating line connects the bottoms composition and intersects the q-line. - First, determine the q-line for the feed condition: \[ q = \frac{z_F - x_B}{z_F - y_B} \] Since \( q = 1 \) (saturated liquid): \[ y = x + \frac{z_F}{R_{min}} \] However, for \( q = 1 \), the q-line is a vertical line at \( x = z_F = 0.60 \). 4. **Determine the Intersection Point:** - The feed stage is where the rectifying and stripping operating lines intersect with the equilibrium curve. - Given the high reflux ratio, the operating lines will be steep, and the feed stage will align where \( x = z_F = 0.60 \). 5. **Identify the Feed Stage:** - The intersection of the rectifying and stripping lines at \( x = 0.60 \) indicates the feed stage. - This is because, at this composition, the liquid introduced into the column equilibrates between the rising vapor (above the feed stage) and the descending liquid (below the feed stage). ### **Conclusion:** Using the **Lewis-Sorel method**, the feed should be introduced at the stage where the **liquid composition is 60 mole% benzene**. This corresponds to the feed entering the column at the point where the operating lines intersect the equilibrium curve at \( x = 0.60 \). ### **Graphical Representation:** While a graphical McCabe-Thiele diagram would provide a visual confirmation, the analytical determination aligns with introducing the feed at the \( x = 0.60 \) stage. **Final Answer:** When applying the Lewis-Sorel method, the feed should be introduced on the column stage where the liquid is 60 mol% benzene. That is, the feed enters the column at the stage with x = 0.60 mole fraction benzene.