A mixture of benzene and toluene containing 40 mole % benzene is to be separated to give a top product with not more than 10 mole % benzene. Use the volatility of benzene relative... A mixture of benzene and toluene containing 40 mole % benzene is to be separated to give a top product with not more than 10 mole % benzene. Use the volatility of benzene relative to toluene to calculate the number of theoretical plates required at total reflux. Also calculate the minimum reflux ratio, compute the equilibrium data at 760 mm Hg pressure, and find out relative volatility. Plot the equilibrium diagram after generation of x-y data. Read more

Steps to Solve

1. Identify the Given Data and Target Values

We have a benzene-toluene mixture with:

• 40 mole % benzene in the feed ($x_{F} = 0.4$)
• Desired top product composition ($x_{D} = 0.10$)
• Average relative volatility ($\alpha = 2.4$)
• Pressure = 760 mm Hg

2. Calculate the Minimum Reflux Ratio

To find the minimum reflux ratio ($R_{min}$), we can use the formula:

$$ R_{min} = \frac{x_{D} (1 - x_{B})}{x_{B} (1 - x_{D})} $$

Where:

• $x_{B}$ is the bottom product composition. Using the formula, assuming $x_{B} = 0.90$ ($90%$ benzene), we calculate:

$$ R_{min} = \frac{0.10 \cdot (1 - 0.90)}{0.90 \cdot (1 - 0.10)} $$

3. Calculate the Number of Theoretical Plates at Total Reflux

Using the Fenske equation, which is defined as:

$$ N = \frac{\log_{10}\left(\frac{x_{D}}{x_{B}} \cdot \frac{(1 - x_{B})}{(1 - x_{D})}\right)}{\log_{10}(\alpha)} $$

Substituting values:

• $x_{D} = 0.10$
• $x_{B} = 0.90$

Calculating $N$:

$$ N = \frac{\log_{10}(0.10/0.90 \cdot (1 - 0.90)/(1 - 0.10))}{\log_{10}(2.4)} $$

4. Determine the Equilibrium Data (x-y Data)

Using the provided vapor pressures to create a table of vapor liquid equilibrium data at $760$ mm Hg.

Create pairs of ($x_A, y_A$) using the formula:

$$ P_{A} = \frac{P_{total} \cdot y_A}{760} $$

Where $P_{A} = P_{A}(x_A)$ (Benzene vapor pressure corresponding to $x_A$).

5. Plot the Equilibrium Diagram

Using the ($x, y$) pairs generated in the previous step, plot the equilibrium data on an x-y diagram. This can be done using graphing software or manual plotting techniques based on the calculated values.