91Ó°ÊÓ

A saturated-liquid mixture of benzene and toluene containing 50 mol% benzene is distillated in an apparatus consisting of a still pot, one theoretical plate, and a total condenser. The still pot is equivalent to one equilibrium stage, and the pressure is 101 kPa. The still is supposed to produce a distillate containing 75 mol% benzene. For each of the following procedures, calculate, if possible, the number of moles of distillate per 100 moles of feed. Assume a relative volatility of 2.5. (a) No reflux with feed to the still pot. 4: (b) Feed to the still pot, reflux ratio LID = 3. ' (c) Feed to the plate with a reflux ratio of 3. (d) Feed to the plate with a reflux ratio of 3. However, in this case, a partial condenser is employed. (e) Part (b) using minimum reflux. R (f) Part (b) using total reflux

Step by step solution

01

Understanding the Problem

We have a mixture of benzene and toluene with 50 mol% benzene. The goal is to produce a distillate with 75 mol% benzene using a distillation process, which includes different scenarios such as no reflux, reflux with different feed strategies, and special conditions like partial and total reflux. The relative volatility is given as 2.5, and the pressure is 101 kPa. Our task is to find the number of moles of distillate per 100 moles of feed for each scenario.

02

Calculating Distillate without Reflux

For no reflux (Case a), calculate the distillate composition using the equilibrium stage (still pot and one theoretical plate) calculation with the basis of an equimolar mixture and relative volatility:For an equimolar mixture:\[ x_1 = 0.5, \ Z = x_1 \cdot \left( \frac{\alpha - 1}{\alpha} \right) + x_1, \ \text{where}\ \alpha = 2.5. \]Calculate the amount of benzene in the distillate fraction and thus the distillate moles per 100 moles.

03

Calculating Distillate with Reflux Ratio L/D = 3 in Still Pot

For a reflux ratio (Case b), the reflux enhances the separation process, leading to:\[ \frac{D}{F} = \frac{x_d - x_b}{R + 1 - (R - 1) \frac{1}{\alpha}} . \]Calculate using given reflux ratio of 3, purity targets, and solve for moles of distillate, D, from feed F.

04

Applying Reflux at Plate with Reflux Ratio L/D = 3

For Case (c) with feed at the plate and reflux ratio of 3, we have:\[ y = x (R + 1)\left(\frac{\alpha}{\alpha - (R + 1)}\right) \]Substitute the known values to find moles of distillate per 100 moles of feed, considering the feed tray interaction.

05

Using Partial Condenser and Reflux at Plate with Ratio of 3

In Case (d), when a partial condenser is used, assume a similar distillation column balance:\[ x_d = y \text{ from the partial condenser equation.} \]Using the McCabe-Thiele method draw or simulate the operates lines to solve this with provided distillation efficiencies.

06

Calculating with Minimum Reflux Ratio in Still

For the minimum reflux case (Case e), determine the minimum reflux ratio using the formula based on the composition difference off the rectifying line to the feed composition point and solve the column equations for \( \left( \frac{D}{F} \right) \).

07

Solution Using Total Reflux for Comparison

In total reflux scenario (Case f), no product is withdrawn:\[ R = \infty : \ \text{all vapor returns}\to\ \text{liquid, so maximum separation is achieved and}.\ \frac{D}{F} = 0 \]This case checks the full separation without changing moles into distillate from feed terms.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Relative Volatility

Relative volatility is a key parameter in the distillation process, especially when separating two components like benzene and toluene. It measures how easily one component can be separated from another based on their respective volatilities.
When you have a relative volatility greater than 1, it indicates that one of the components is more volatile, meaning it can be more readily vaporized and separated from the other. In our exercise, the relative volatility is given as 2.5.
This suggests that benzene vaporizes easier than toluene, facilitating the separation process in the distillation setup. Relative volatility simplifies the calculations needed to determine the composition of the distillate, as it provides a ratio that can be applied to equilibrium equations.

Reflux Ratio

The reflux ratio, denoted as L/D, is the ratio of the liquid returned to the distillation column to the amount of distillate taken off. It is a crucial aspect of controlling the efficiency and effectiveness of the distillation process.
In distillation, having a higher reflux ratio often means better purity and separation, as more of the condensed vapor is returned to the column, enhancing the separation of components.
In scenarios like Case (b) and (c) of our exercise, a reflux ratio of 3 is employed. This means that for each mole of distillate collected, 3 moles are returned as liquid. Finding the right reflux ratio is essential as it influences the energy consumption and efficiency of the distillation process.

• A high reflux ratio leads to high purity but increases operation costs.
• A low reflux ratio may reduce costs but compromises on purity.

Equilibrium Stage

An equilibrium stage in a distillation process refers to the establishment of vapor-liquid equilibrium between the two phases. Each equilibrium stage represents a theoretical plate where the composition of the vapor phase and the liquid phase reach equilibrium due to repeated vaporization and condensation.
Our distillation process includes a still pot and one theoretical plate, which effectively means two equilibrium stages. These stages are crucial because they define how many times the components are separated and come into contact during the process.
It is at these stages that the separation of benzene and toluene occurs based on their relative volatilities. More equilibrium stages usually mean better separation but may also increase equipment size and operation complexity.

Benzene and Toluene Separation

Separation of benzene and toluene is a common distillation challenge as both are volatile organic compounds with similar boiling points. However, their separation is feasible due to differences in their relative volatilities.
In our exercise, we start with a 50% benzene and 50% toluene mixture, and aim to achieve a distillate that contains 75% benzene. This operation involves manipulating variables like feed strategy, reflux ratio, and potential use of additional equipment like partial condensers.
The goal is to optimize the setup to produce a distillate of the desired composition while managing energy efficiency and process economics. Different approaches to distillation, such as total reflux or minimum reflux, demonstrate alternative ways to achieve the targeted separation, each with its own trade-offs.