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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

Ethane is chlorinated in a continuous reactor: $$\mathrm{C}_{2} \mathrm{H}_{6}+\mathrm{Cl}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{HCl}$$ Some of the product monochloroethane is further chlorinated in an undesired side reaction: $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{Cl}_{2} \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}+\mathrm{HCl}$$ (a) Suppose your principal objective is to maximize the selectivity of monochloroethane production relative to dichloroethane production. Would you design the reactor for a high or low conversion of ethane? Explain your answer. (Hint: If the reactor contents remained in the reactor long enough for most of the ethane in the feed to be consumed, what would the main product constituent probably be?) What additional processing steps would almost certainly be carried out to make the process economically sound? (b) Take a basis of \(100 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) produced. Assume that the feed contains only ethane and chlorine and that all of the chlorine is consumed, and carry out a degree-of-freedom analysis based on atomic species balances. (c) The reactor is designed to yield a \(15 \%\) conversion of ethane and a selectivity of \(14 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl} / \mathrm{mol}\) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2},\) with a negligible amount of chlorine in the product gas. Calculate the feed ratio \(\left(\mathrm{mol} \mathrm{Cl}_{2} /\right.\) mol \(\mathrm{C}_{2} \mathrm{H}_{6}\) ) and the fractional yield of monochloroethane. (d) Suppose the reactor is built and started up and the conversion is only \(14 \% .\) Chromatographic analysis shows that there is no \(\mathrm{Cl}_{2}\) in the product but another species with a molecular weight higher than that of dichloroethane is present. Offer a likely explanation for these results.

The fresh feed to an ammonia production process contains nitrogen and hydrogen in stoichiometric proportion, along with an inert gas (I). The feed is combined with a recycle stream containing the same three species, and the combined stream is fed to a reactor in which a low single-pass conversion of nitrogen is achieved. The reactor effluent flows to a condenser. A liquid stream containing essentially all of the ammonia formed in the reactor and a gas stream containing all the inerts and the unreacted nitrogen and hydrogen leave the condenser. The gas stream is split into two fractions with the same composition: one is removed from the process as a purge stream, and the other is the recycle stream combined with the fresh feed. In every stream containing nitrogen and hydrogen, the two species are in stoichiometric proportion. (a) Let \(x_{10}\) be the mole fraction of inerts in the fresh feed, \(f_{\mathrm{sp}}\) the single-pass conversion of nitrogen (and of hydrogen) in the reactor, and \(y_{p}\) the fraction of the gas leaving the condenser that is purged (mol purged/mol total). Taking a basis of 1 mol fresh feed, draw and fully label a process flowchart, incorporating \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}}\) in the labeling to the greatest possible extent. Then, assuming that the values of these three variables are given, write a set of equations for the total moles fed to the reactor \(\left(n_{\mathrm{r}}\right),\) moles of ammonia produced \(\left(n_{\mathrm{p}}\right),\) and overall nitrogen conversion \(\left(f_{\mathrm{ov}}\right) .\) Each equation should involve only one unknown variable, which should be circled. (b) Solve the equations of Part (a) for \(x_{10}=0.01, f_{\mathrm{sp}}=0.20,\) and \(y_{\mathrm{p}}=0.10\) (c) Briefly explain in your own words the reasons for including (i) the recycle stream and (ii) the purge stream in the process design. (d) Prepare a spreadsheet to perform the calculations of Part (a) for given values of \(x_{10}, f_{\mathrm{sp}},\) and \(y_{\mathrm{p}} .\) Test it with the values in Part (b). Then in successive rows of the spreadsheet, vary each of the three input variables two or three times, holding the other two constant. The first six columns and first five rows of the spreadsheet should appear as follows:Summarize the effects on ammonia production \(\left(n_{\mathrm{P}}\right)\) and reactor throughput \(\left(n_{\mathrm{r}}\right)\) of changing each of the three input variables.

Fermentation of sugars obtained from hydrolysis of starch or cellulosic biomass is an alternative to using petrochemicals as the feedstock in production of ethanol. One of the many commercial processes to do this \(^{16}\) uses an enzyme to hydrolyze starch in corn to maltose (a disaccharide consisting of two glucose units) and oligomers consisting of several glucose units. A yeast culture then converts the maltose to ethyl alcohol and carbon dioxide: $$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O}(+\text { yeast }) \rightarrow 4 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+4 \mathrm{CO}_{2}\left(+\text { yeast }+\mathrm{H}_{2} \mathrm{O}\right)$$ As the yeast grows, \(0.0794 \mathrm{kg}\) of yeast is produced for every \(\mathrm{kg}\) ethyl alcohol formed, and \(0.291 \mathrm{kg}\) water is produced for every kg of yeast formed. For use as a fuel, the product from such a process must be around 99.5 wt\% ethyl alcohol. Corn fed to the process is 72.0 wt\% starch on a moisture-free basis and contains 15.5 wt\% moisture. It is estimated that 101.2 bushels of corn can be harvested from an acre of com, that each bushel is equivalent to \(25.4 \mathrm{lb}_{\mathrm{m}}\) of corn, and that \(6.7 \mathrm{kg}\) of ethanol can be obtained from a bushel of corn. What acreage of farmland is required to produce 100,000 kg of ethanol product? What factors (economic and environmental) must be considered in comparing production of ethanol by this route with other routes involving petrochemical feedstocks?

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.

The indicator-dilution method is a technique used to determine flow rates of fluids in channels for which devices like rotameters and orifice meters cannot be used (e.g., rivers, blood vessels, and largediameter pipelines). A stream of an easily measured substance (the tracer) is injected into the channel at a known rate, and the tracer concentration is measured at a point far enough downstream of the injection point for the tracer to be completely mixed with the flowing fluid. The larger the flow rate of the fluid, the lower the tracer concentration at the measurement point. A gas stream that contains 1.50 mole \(\% \mathrm{CO}_{2}\) flows through a pipeline. Twenty (20.0) kilograms of \(\mathrm{CO}_{2}\) per minute is injected into the line. A sample of the gas is drawn from a point in the line 150 meters (a) Estimate the gas flow rate (kmol/min) upstream of the injection point. (b) Eighteen seconds elapse from the instant the additional \(\mathrm{CO}_{2}\) is first injected to the time the \(\mathrm{CO}_{2}\) concentration at the measurement point begins to rise. Assuming that the tracer travels at the average velocity of the gas in the pipeline (i.e., neglecting diffusion of \(\mathrm{CO}_{2}\) ), estimate the average velocity (m/s). If the molar gas density is \(0.123 \mathrm{kmol} / \mathrm{m}^{3}\), what is the pipe diameter?
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