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Chapter 4: Problem 20

A \(100 \mathrm{kmol} / \mathrm{h}\) stream that is 97 mole \(\%\) carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\) and \(3 \%\) carbon disulfide \(\left(\mathrm{CS}_{2}\right)\) is to be recovered from the bottom of a distillation column. The feed to the column is 16 mole \(\% \mathrm{CS}_{2}\) and \(84 \% \mathrm{CCl}_{4},\) and \(2 \%\) of the \(\mathrm{CCl}_{4}\) entering the column is contained in the overhead stream leaving the top of the column. (a) Draw and label a flowchart of the process and do the degree-of-freedom analysis. (b) Calculate the mass and mole fractions of \(\mathrm{CCl}_{4}\) in the overhead stream, and determine the molar flow rates of \(\mathrm{CCl}_{4}\) and \(\mathrm{CS}_{2}\) in the overhead and feed streams. (c) Suppose the overhead stream is analyzed and the mole fraction of \(\mathrm{CS}_{2}\) is found to be significantly lower than the value calculated in Part (b). List as many reasons as you can for the discrepancy, including possible violations of assumptions made in Part (b).

Short Answer

Expert verified
Degrees of Freedom (DOF) for the system is 2. The molar and mass fractions of CCl4 in the overhead stream were found to be 0.02 and can be calculated respectively. The molar flow rate for the feed stream is found from the CCl4 balance and total molar balance equations, and then molar flow rates of CCl4 and CS2 are calculated for the overhead and feed streams. Discrepancies between the calculated and real mole fraction of CS2 could be due to reasons such as: lack of steady state, system losses/leaks, errors in feed mixture analysis, and non-idealized behaviors.

Step by step solution

01

Draw and label a flowchart of the process and do the degree-of-freedom analysis

Begin by drawing a simple flowchart to represent this process. The feed enters the column and the two outputs are the bottom stream and the overhead stream leaving the top of the column. The degree of freedom for a separation unit without chemical reaction like the distillation column can be calculated using the formula: DOF = Unknowns - Equations. In this case, the unknowns are F (feed), B (bottom product), D (distillate), xF (mole fraction of CS2 in the feed), xB (mole fraction of CS2 in the bottom product), and xD (mole fraction of CS2 in the distillate) which is total 6. The equations are: overall mole balance, CCl4 balance, CS2 balance and the column specification which is total 4. So, the DOF = 6 鈥� 4 = 2.
02

Calculate the mass and mole fractions; determine the molar flow rate

Make use of the information provided to calculate the required values. Start by finding the mass and mole fractions of CCl4 in the overhead stream. Since 2% of the CCl4 entering the column is contained in the overhead stream, this means that the mole fraction is 0.02. Mass fraction can be calculated using the formula: mass fraction = (mole fraction * molar mass of CCl4) / molar mass of mixture. For the molar flow rates, this can be done using the feed conditions and the mole fractions. Given that P is a bottom product with flow rate of 100 kmol/h and 97% CCl4, F (feed) can be calculated by CCl4 balance equation: F x 0.84 = 100 x 0.97 + 0.02 x F, which we can solve to find F. From this, D (overhead stream) can be found from the material balance equation: F = D + P. After that, molar flow rates of CCl4 and CS2 in overhead and feed streams can be calculated by multiplying the total flow rates by their respective mole fractions.
03

Analyzing discrepancies

There are a few explanations that could account for why the CS2 mole fraction is found to be lower than expected. Firstly, the distillation process might not be at steady state, which is an assumption made for calculations in Part (b). Secondly, there may be losses or leaks in the system that were not accounted for. Thirdly, there could be errors in the initial analysis of the feed mixture. Lastly, one might have assumed ideal behaviors and no interactions between the two species in the mixture, which may not necessarily reflect the reality.

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Key Concepts

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

Flowchart Analysis
In distillation column problems, drawing a flowchart helps visualize the process. It's a graphical representation that maps the inputs, outputs, and flow of materials in the system. In this specific problem, you have:
- A feed stream entering the distillation column.
- Two output streams: an overhead and a bottom stream.
The degree-of-freedom analysis allows you to determine whether you have sufficient information to solve the system. The formula used is \( \text{DOF} = \text{Unknowns} - \text{Equations} \). For separation processes, key assumptions include no chemical reactions, known inlet compositions, and typically constant pressure and temperature conditions.

In our case, we evaluated components in terms of three streams and performed an overall mole balance, along with specific balances for each compound (CCl4 and CS2). This provides a means to ensure that all necessary calculations can be performed without ambiguity.
Mass and Mole Fractions
Mass and mole fractions are useful measurements for describing the composition of mixtures. The mole fraction (\( x \)) is simply the ratio of moles of a component to the total moles in a mixture. Here, 2\% of CCl4 in the overhead stream translates to a mole fraction of 0.02 for CCl4.

The mass fraction involves considering the molar masses of the components and can be found using the formula:\[\text{Mass fraction} = \frac{\text{mole fraction} \times \text{molar mass of component}}{\text{molar mass of mixture}}\]
This conversion is especially relevant for processes like distillation where compositions need to be managed between different phases. Knowing these fractions allows for precise control of the distillation process and verification of design and operating parameters.
Material Balance
In distillation and other separation processes, the material balance is an essential tool for determining unknown stream properties, flow rates, and concentrations. In essence, it ensures that mass is conserved across the system.

This problem requires applying material balance equations for the overall system and individual components, specifically CCl4 and CS2. You use these balances to find values like the feed flow rate \( F \) and the molar flow rates within the distillation system:
  • Overall mole balance: \( F = D + P \) where \( F \) is feed, \( D \) is distillate overhead, and \( P \) is bottoms product.
  • Component balance, e.g., CCl4 balance: \( F \times 0.84 = 100 \times 0.97 + D \times 0.02 \).
Through these balances, you ensure that all inputs and outputs are accounted for, yielding accurate process predictions.
Molar Flow Rates
Understanding molar flow rates is crucial when analyzing chemical processing systems like distillation columns. They signify how much of a substance is moving through a given section of the system per unit time.

Calculating molar flow rates involves using both the feed stream composition and the separation specifications provided in the problem. You essentially apply the mole fractions to the total flow rates to determine individual component flow rates:
  • For example: If the mole fraction of CCl4 in the feed is 0.84, and the feed rate is determined through material balances, then the molar flow rate of CCl4 in the feed will be \( 0.84 \times F \).
This information helps ensure that desired purities and recoveries are achieved and informs any necessary adjustments to the column's operation.

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Most popular questions from this chapter

If the percentage of fuel in a fuel-air mixture falls below a certain value called the lower flammability limit (LFL), which sometimes is referred to as the lower explosion limit (LEL), the mixture cannot be ignited. In addition there is an upper flammability limit (UFL), which also is known as the upper explosion limit (UEL). For example, the LFL of propane in air is 2.3 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) and the UFL is \(9.5 \%^{14}\). If the percentage of propane in a propane-air mixture is greater than \(2.3 \%\) and less than \(9.5 \%,\) the gas mixture can ignite if it is exposed to a flame or spark. A mixture of propane in air containing 4.03 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) (fuel gas) is the feed to a combustion furnace. If there is a problem in the furnace, a stream of pure air (dilution air) is added to the fuel mixture prior to the furnace inlet to make sure that ignition is not possible. (a) Draw and label a flowchart of the fuel gas-dilution air mixing unit, presuming that the gas entering the furnace contains propane at the LFL, and do the degree-of-freedom analysis. (b) If propane flows at a rate of \(150 \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8} / \mathrm{s}\) in the original fuel-air mixture, what is the minimum molar flow rate of the dilution air? (c) How would the actual dilution air feed rate probably compare with the value calculated in Part (b)? (>, \(<,=\) ) Explain.

Under the FutureGen 2.0 project (http:///www.futuregenalliance.org/) sponsored by the U.S. Department of Energy, a novel process is used to convert coal into electricity with minimal greenhouse gas \(\left(\mathrm{CO}_{2}\right)\) emissions to the atmosphere. In the process, coal is combusted in a boiler with pure \(\mathrm{O}_{2}\); the heat released produces steam, which is then used for heating and to drive turbines that generate electricity. An excess of \(\mathrm{O}_{2}\) is supplied to the boiler to convert all the coal into a flue gas consisting of carbon dioxide, steam, and any unreacted oxygen. The mass flow rate of coal to the boiler is \(50 \mathrm{kg} / \mathrm{s}\), and \(\mathrm{O}_{2}\) is fed in \(8.33 \%\) excess. For the purposes of this analysis, the chemical formula of coal can be approximated as \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{2}\) (a) Draw and label the flowchart and carry out the degree-of-freedom analysis using balances on atomic species. (b) Determine the molar flow of oxygen supplied to the boiler. (c) Solve for the remaining unknown flow rates and mole fractions. Determine the molar composition of the flue gas on a dry basis. (d) A feature that makes the FutureGen power plant unique is the intent to capture the \(\mathrm{CO}_{2}\) generated, compress it, and pump it into deep geological formations in which it will be permanently stored. List at least two safety or environmental issues that should be considered in the construction and operation of this plant. (e) List at least two pros and two cons of using pure \(O_{2}\) versus air.

Two aqueous sulfuric acid solutions containing \(20.0 \mathrm{wt} \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{SG}=1.139)\) and \(60.0 \mathrm{wt} \% \mathrm{H}_{2} \mathrm{SO}_{4}\) (SG = 1.498) are mixed to form a 4.00 molar solution (SG = 1.213). (a) Calculate the mass fraction of sulfuric acid in the product solution. (b) Taking \(100 \mathrm{kg}\) of the \(20 \%\) feed solution as a basis, draw and label a flowchart of this process, labeling both masses and volumes, and do the degree-of-freedom analysis. Calculate the feed ratio (liters 20\% solution/liter 60\% solution). (c) What feed rate of the \(60 \%\) solution (L/h) would be required to produce \(1250 \mathrm{kg} / \mathrm{h}\) of the product?

A fuel oil is analyzed and found to contain 85.0 wt\% carbon, \(12.0 \%\) elemental hydrogen (H), \(1.7 \%\) sulfur, and the remainder noncombustible matter. The oil is burned with \(20.0 \%\) excess air, based on complete combustion of the carbon to \(\mathrm{CO}_{2}\), the hydrogen to \(\mathrm{H}_{2} \mathrm{O}\), and the sulfur to \(\mathrm{SO}_{2}\). The oil is burned completely, but \(8 \%\) of the carbon forms CO. Calculate the molar composition of the stack gas.

A paint mixture containing \(25.0 \%\) of a pigment and the balance binders (which help the pigment stick to the surface) and solvents (which ensure that the paint stays in liquid form) sells for 18.00 dollar/kg, and a mixture containing 12.0\% sells for 10.00 dollar /kg. (a) If a paint retailer produces a blend containing \(17.0 \%\) pigment, for how much (S/kg) should it be sold to yield a 10\% profit? (b) Paint manufacturers have begun to market "low VOC" paint as a more environmentally friendly product. What are VOCs? List some ways in which paint products can be altered to lower the VOC content.
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