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Chapter 4: Problem 78

Ethylene oxide is produced by the catalytic oxidation of ethylene: $$ 2 \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{O}_{2} \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} $$ An undesired competing reaction is the combustion of ethylene: $$ \mathrm{C}_{2} \mathrm{H}_{4}+3 \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} $$ The feed to the reactor (not the fresh feed to the process) contains 3 moles of ethylene per mole of oxygen. The single-pass conversion of ethylene is \(20 \%,\) and for every 100 moles of ethylene consumed in the reactor, 90 moles of ethylene oxide emerge in the reactor products. A multiple-unit process is used to separate the products: ethylene and oxygen are recycled to the reactor, ethylene oxide is sold as a product, and carbon dioxide and water are discarded. (a) Assume a quantity of the reactor feed stream as a basis of calculation, draw and label the flowchart, perform a degree-of-freedom analysis, and write the equations you would use to calculate (i) the molar flow rates of ethylene and oxygen in the fresh feed, (ii) the production rate of ethylene oxide, and (iii) the overall conversion of ethylene. Do no calculations. (b) Calculate the quantities specified in Part (a), either manually or with an equation-solving program. (c) Calculate the molar flow rates of ethylene and oxygen in the fresh feed needed to produce 1 ton per hour of ethylene oxide.

Short Answer

Expert verified
To solve such a problem, be sure to properly set up a flowchart and perform a degree of freedom analysis to understand the constraints of the system. Next, write the stoichiometric relationships for the reactions occuring in the reactor and use them to solve for the molar flow rates and the overall conversion of ethylene. Finally, adapt these calculations for a specific production rate.

Step by step solution

01

Set up a Flowchart

Draw a schematic of the process. Label the influx stream (fresh feed), the reactor, and the product streams. It is known that the reactor feed contains 3 moles of ethylene per mole of oxygen, and that 90 moles of ethylene oxide are produced for every 100 moles of ethylene consumed, hence indicating the stoichiometry of the competing reactions in the reactor.
02

Degree of Freedom Analysis

Perform a degree-of-freedom analysis. It involves identifying how many unknown variables there are in the system and writing the relationships (balance equations) between them. Corresponding to each unit operation (the reactor, the separator), write the balance equations (mass and mole balances). You will need an equation equal to the number of unknown variables to have a solvable system.
03

Write Stoichiometric Equations

Formulate the stoichiometric equations based on the reactions provided in the problem. For every 2 moles of ethylene \(C_{2}H_{4}\), 2 moles of ethylene oxide \(C_{2}H_{4}O\) are produced in the desired reaction. An undesired reaction also takes place where ethylene \(C_{2}H_{4}\) is combusted to yield \(CO_{2}\) and \(H_{2}O\). This will help in developing the reaction rate equations.
04

Calculate Molar Flow Rates

Use the stoichiometric relationships and the balance equations to solve for the molar flow rates of the reactants in fresh feed and the production rate of the product. The equations set up previously provide the necessary relationships between quantities to do this.
05

Calculate Overall Ethylene Conversion

By using the flow rates calculated and the definitions of conversion, the overall conversion of the reactant ethylene can be calculated.
06

Perform Calculation for Specific Production

Extend these calculations for a specific case. Here, calculate the molar flow rates of ethylene and oxygen required to produce 1 ton per hour of ethylene oxide.

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Key Concepts

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

Degree of Freedom Analysis
Degree of Freedom Analysis is an essential method used in chemical engineering to determine the number of independent variables that can be changed without impacting certain constraints. In the context of the given chemical reactions, this analysis helps us understand how many unknowns or variables exist, and how many equations are needed to solve for these unknowns.

For instance, in the provided problem, we identify each stream in the system 鈥� fresh feed, reactor, separator 鈥� and count all the unknown quantities such as molar flow rates of different components. We also consider the number of equations available, including mass or molar balances and stoichiometric relationships, ensuring that we have an equal number of equations to variables, which makes the system solvable.
  • The reactor feed ratio is given (3 moles of ethylene per mole of oxygen), providing one such critical balance difference.
  • We account for each reaction pathway and product formed, each demanding its own unique balance equation link.
The outcome of this analysis tells us whether we can solve the system with the information provided or if additional data is required.
Mass and Mole Balances
In chemical processes, maintaining mass and mole balances is crucial for tracking the materials as they move through the system. These balances ensure that the inputs and outputs of the reactors are accounted for accurately, adhering to the principle of conservation of mass.

For the problem at hand, we start with known initial conditions and quantities, such as the 3:1 ratio of ethylene to oxygen. We consider balances over both the primary (ethylene) and secondary reactants (oxygen) as they undergo transformation through the reactor:
  • The desired reaction pathway yields ethylene oxide, while an undesired reaction forms carbon dioxide and water.
  • We incorporate the conversion rates, crucially using the provided 20% single-pass conversion of ethylene to determine changes in quantities.
These balanced equations help calculate the shift in amounts across different streams, informing us about changes within the system from the reactor feed to the product streams.
Stoichiometric Equations
Stoichiometric equations form the backbone of reaction chemistry, describing the quantitative relationships between reactants and products in a chemical reaction. Understanding these equations allows engineers to predict the quantities of substances consumed and produced.

The primary equation given for ethylene oxide production is: \[ 2 \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} \] From this, it is evident that two moles of ethylene react with one mole of oxygen to produce two moles of ethylene oxide. A competing combustion reaction also must be considered, given by: \[ \mathrm{C}_{2} \mathrm{H}_{4} + 3 \mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \]
  • These equations define how the reactants are transformed, specifying that excessive oxygen consumption leads to undesired byproducts.
  • Knowing the stoichiometric coefficients facilitates determining how reactant feed ratios need to be adjusted depending on the desired product output.
This understanding is crucial when optimizing conditions to maximize ethylene oxide production.
Reaction Rate Equations
When analyzing chemical reactions, Reaction Rate Equations offer insight into how quickly reactants are converted into products. These rates are influenced by factors such as reactant concentration, temperature, pressure, and the presence of catalysts.

For the given reactions, specifying a reaction rate equation necessitates taking into account the conversion efficiency of ethylene. Given a 20% single-pass conversion rate, the reaction rate from ethylene to ethylene oxide can be determined and used to estimate overall system performance:
  • We know that for every 100 moles of ethylene processed, 90 moles of ethylene oxide are produced, informing our calculations.
  • Analyzing competing reaction rates helps identify how much reactant is diverted to byproducts like carbon dioxide and water.
By understanding these rates, engineers can adjust operational parameters of the reactor, such as catalyst effectiveness or reaction time, to optimize output, achieving the desired balance between kinetics and production efficiency.

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Most popular questions from this chapter

A stream of humid air containing 1.50 mole \(\% \mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) and the balance dry air is to be humidified to a water content of 10.0 mole\% \(\mathrm{H}_{2} \mathrm{O}\). For this purpose, liquid water is fed through a flowmeter and evaporated into the air stream. The flowmeter reading, \(R\), is \(95 .\) The only available calibration data for the flowmeter are two points scribbled on a sheet of paper, indicating that readings \(R=15\) and \(R=50\) correspond to flow rates \(\dot{V}=40.0 \mathrm{ft}^{3} / \mathrm{h}\) and \(\dot{V}=96.9 \mathrm{ft}^{3} / \mathrm{h},\) respectively. (a) Assuming that the process is working as intended, draw and label the flowchart, do the degree-offreedom analysis, and estimate the molar flow rate (lb-mole/h) of the humidified (outlet) air if (i) the volumetric flow rate is a linear function of \(R\) and (ii) the reading \(R\) is a linear function of \(\dot{V}^{0.5}\) (b) Suppose the outlet air is analyzed and found to contain only \(7 \%\) water instead of the desired \(10 \%\) List as many possible reasons as you can think of for the discrepancy, concentrating on assumptions made in the calculation of Part (a) that might be violated in the real process.

\- An equimolar liquid mixture of benzene and toluene is separated into two product streams by distillation. A process flowchart and a somewhat oversimplified description of what happens in the process follow: Inside the column a liquid stream flows downward and a vapor stream rises. At each point in the column some of the liquid vaporizes and some of the vapor condenses. The vapor leaving the top of the column, which contains 97 mole\% benzene, is completely condensed and split into two equal fractions: one is taken off as the overhead product stream, and the other (the reflux) is recycled to the top of the column. The overhead product stream contains \(89.2 \%\) of the benzene fed to the column. The liquid leaving the bottom of the column is fed to a partial reboiler in which \(45 \%\) of it is vaporized. The vapor generated in the reboiler (the boilup) is recycled to become the rising vapor stream in the column, and the residual reboiler liquid is taken off as the bottom product stream. The compositions of the streams leaving the reboiler are governed by the relation $$\frac{y_{\mathrm{B}} /\left(1-y_{\mathrm{B}}\right)}{x_{\mathrm{B}} /\left(1-x_{\mathrm{B}}\right)}=2.25$$ where \(y_{\mathrm{B}}\) and \(x_{\mathrm{B}}\) are the mole fractions of benzene in the vapor and liquid streams, respectively. (a) Take a basis of 100 mol fed to the column. Draw and completely label a flowchart, and for each of four systems (overall process, column, condenser, and reboiler), do the degree-of-freedom analysis and identify a system with which the process analysis might appropriately begin (one with zero degrees of freedom). (b) Write in order the equations you would solve to determine all unknown variables on the flowchart, circling the variable for which you would solve in each equation. Do not do the calculations in this part. (c) Calculate the molar amounts of the overhead and bottoms products, the mole fraction of benzene in the bottoms product, and the percentage recovery of toluene in the bottoms product \((100 \times\) moles toluene in bottoms/mole toluene in feed).

A Claus plant converts gaseous sulfur compounds to elemental sulfur, thereby eliminating emission of sulfur into the atmosphere. The process can be especially important in the gasification of coal, which contains significant amounts of sulfur that is converted to \(\mathrm{H}_{2}\) S during gasification. In the Claus process, the \(\mathrm{H}_{2}\) S-rich product gas recovered from an acid-gas removal system following the gasifier is split, with one-third going to a furnace where the hydrogen sulfide is burned at 1 atm with a stoichiometric amount of air to form SO \(_{2}\). $$\mathrm{H}_{2} \mathrm{S}+\frac{3}{2} \mathrm{O}_{2} \rightarrow \mathrm{SO}_{2}+\mathrm{H}_{2} \mathrm{O}$$ The hot gases leave the furnace and are cooled prior to being mixed with the remainder of the \(\mathrm{H}_{2}\) S-rich gases. The mixed gas is then fed to a catalytic reactor where hydrogen sulfide and \(\mathrm{SO}_{2}\) react to form elemental sulfur. $$2 \mathrm{H}_{2} \mathrm{S}+\mathrm{SO}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+3 \mathrm{S}$$ The coal available to the gasification process is 0.6 wt\% sulfur, and you may assume that all of the sulfur is converted to \(\mathrm{H}_{2} \mathrm{S}\), which is then fed to the Claus plant. (a) Estimate the feed rate of air to the Claus plant in \(\mathrm{kg} / \mathrm{kg}\) coal. (b) While the removal of sulfur emissions to the atmosphere is environmentally beneficial, identify an environmental concern that still must be addressed with the products from the Claus plant.

The hormone estrogen is produced in the ovaries of females and elsewhere in the body in men and postmenopausal women, and it is also administered in estrogen replacement therapy, a common treatment for women who have undergone a hysterectomy. Unfortunately, it also binds to estrogen receptors in breast tissue and can activate cells to become cancerous. Tamoxifen is a drug that also binds to estrogen receptors but does not activate cells, in effect blocking the receptors from access to estrogen and inhibiting the growth of breast-cancer cells. Tamoxifen is administered in tablet form. In the manufacturing process, a finely ground powder contains tamoxifen (tam) and two inactive fillers- -lactose monohydrate (lac) and corn starch (cs). The powder is mixed with a second stream containing water and suspended solid particles of polyvinylpymolidone (pvp) binder, which keeps the tablets from easily crumbling. The slurry leaving the mixer goes to a dryer, in which 94.2\% of the water fed to the process is vaporized. The wet powder leaving the dryer contains 8.80 wr\% tam, 66.8\% lac, 21.4\% cs, 2.00\% pvp, and 1.00\% water. After some additional processing, the powder is molded into tablets. To produce a hundred thousand tablets, 17.13 kg of wet powder is required. (a) Taking a basis of 100,000 tablets produced, draw and label a process flowchart, labeling masses of individual components rather than total masses and component mass fractions. It is unnecessary to label the stream between the mixer and the dryer. Carry out a degree-of-freedom analysis of the overall two-unit process. (b) Calculate the masses and compositions of the streams that must enter the mixer to make 100,000 tablets. (c) Why was it unnecessary to label the stream between the mixer and the dryer? Under what circumstances would it have been necessary? (d) Go back to the flowchart of Part (a). Without using the mass of the wet powder (17.13 kg) or any of the results from Part (b) in your calculations, determine the mass fractions of the stream components in the powder fed to the mixer and verify that they match your solution to Part (b). (Hint: Take a basis of \(100 \mathrm{kg}\) of wet powder.) (e) Suppose a student does Part (d) before Part (b), and re-labels the powder feed to the mixer on the flowchart of Part (a) with an unknown total mass ( \(m_{1}\) ) and the three now known mole fractions. (Sketch the resulting flowchart.) The student then does a degree-of-freedom analysis, counts four unknowns (the masses of the powder, pvp, and water fed to the mixer, and the mass of water evaporated in the dryer), and six equations (five material balances for five species and the percentage evaporation), for a net of -2 degrees of freedom. since there are more equations than unknowns, it should not be possible to get a unique solution for the four unknowns. Nevertheless, the student writes four equations, solves for the four unknowns, and verifies that all of the balance equations are satisfied. There must have been a mistake in the degree-of-freedom calculation. What was it?

In the Deacon process for the manufacture of chlorine, HCI and \(\mathrm{O}_{2}\) react to form \(\mathrm{Cl}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) Sufficient air ( 21 mole \(\% \mathrm{O}_{2}, 79 \% \mathrm{N}_{2}\) ) is fed to provide \(35 \%\) excess oxygen, and the fractional conversion of HCl is \(85 \%\) (a) Calculate the mole fractions of the product stream components, using atomic species balances in your calculation. (b) Again calculate the mole fractions of the product stream components, only this time use the extent of reaction in the calculation. (c) An alternative to using air as the oxygen source would be to feed pure oxygen to the reactor. Running with oxygen imposes a significant extra process cost relative to running with air, but also offers the potential for considerable savings. Speculate on what the cost and savings might be. What would determine which way the process should be run?
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