Question

A column of dishes with countercurrent flow must be designed to absorb acetone,

contained in a mixture with air, using non-volatile oil. The gas entering the column contains 25% of acetone, and the oil that enters is free of acetone. 90% of the acetone contained in the air is absorbed. A equilibrium relationship is given by the equation:

`(Y)/(1+Y)=0,3(X)/(1+X)`
A) Carry out a study of the minimum flow rate of solvent necessary to treat 0.01 kmol/s of the gas mixture;
B) Determine the composition of the concentrated liquor at the bottom of the column, knowing that the operating solvent flow rate must be equal to 5 times the minimum flow rate;
C) Determine the number of theoretical stages analytically and through the operation diagram.

Answer 1

To calculate the minimum flow rate of solvent, use the equilibrium relationship equation with the initial composition of the gas mixture. The composition of the concentrated liquor can be found by using the solvent flow rate and the equilibrium relationship equation. The number of theoretical stages can be determined analytically or with an operation diagram.

Step-by-step explanation:

In order to determine the minimum flow rate of solvent necessary to treat 0.01 kmol/s of the gas mixture, we can use the equilibrium relationship given by the equation
`(Y)/(1+Y)=0,3(X)/(1+X)`. Since the gas entering the column contains 25% acetone, we can substitute X=0.25 into the equation to find the corresponding value of Y. The flow rate of solvent necessary to treat the gas mixture will be the difference between the initial and final moles of acetone in the gas, divided by the time interval in seconds.

To determine the composition of the concentrated liquor at the bottom of the column, we need to know the operating solvent flow rate. Since the operating solvent flow rate must be equal to 5 times the minimum flow rate, we can multiply the minimum flow rate by 5 to find the solvent flow rate. By knowing the solvent flow rate and using the equilibrium relationship equation, we can calculate the concentrations of acetone and oil in the concentrated liquor.

The number of theoretical stages can be determined analytically by using the equilibrium equation and solving for the number of stages. Alternatively, an operation diagram can be used to determine the number of stages, by plotting the equilibrium curve and operating line for the system and identifying the points where the lines intersect.