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Chapter 4: Problem 52

Acetylene is hydrogenated to form ethane. The feed to the reactor contains \(1.50 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{2}\) (a) Calculate the stoichiometric reactant ratio (mol \(\mathrm{H}_{2}\) react/mol \(\mathrm{C}_{2} \mathrm{H}_{2}\) react) and the yield ratio (kmol \(\mathbf{C}_{2} \mathbf{H}_{6}\) formed/kmol \(\mathbf{H}_{2}\) react (b) Determine the limiting reactant and calculate the percentage by which the other reactant is in excess. (c) Calculate the mass feed rate of hydrogen ( \(\mathrm{kg} / \mathrm{s}\) ) required to produce \(4 \times 10^{6}\) metric tons of ethane per year, assuming that the reaction goes to completion and that the process operates for 24 hours a day, 300 days a year. (d) There is a definite drawback to running with one reactant in excess rather than feeding the reactants in stoichiometric proportion. What is it? [Hint: In the process of Part (c), what does the reactor effluent consist of and what will probably have to be done before the product ethane can be sold or used?]

Short Answer

Expert verified
Stoichiometric reactant ratio is \(2.00 \, \text{mol H}_2/\text{mol C}_2\text{H}_2\), yield ratio is \(1.00 \, \text{kmol C}_2\text{H}_6/\text{kmol H}_2\). \(\text{H}_2\) is the limiting reactant, and \(\text{C}_2\text{H}_2\) is in excess by 25%. Feed rate of hydrogen required to meet production goal can be calculated but depends on molecular weights and time. Potential drawbacks of running the process with one reactant in excess include the need for expensive and energy-intensive separation processes.

Step by step solution

01

Calculate the stoichiometric reactant ratio and the yield ratio

We know that the reaction is \(C_2H_2 + 2H_2 鈫� C_2H_6\). This tells us that for every mole of acetylene, we need two moles of hydrogen gas, and we form 1 mole of ethane. Therefore, the stoichiometric reactant ratio is \(2.00 \, \text{mol H}_2/\text{mol C}_2\text{H}_2\) and the yield ratio is \(1.00 \, \text{kmol C}_2\text{H}_6/\text{kmol H}_2\).
02

Determine the limiting reactant and the percentage by which the other reactant is in excess

Since the feed to the reactor contains only \(1.50 \, \text{mol H}_2/\text{mol C}_2\text{H}_2\), there is less hydrogen than needed for every mole of acetylene, making \(H_2\) the limiting reactant. The reactant \(C_2H_2\) is in excess by \((2.00 - 1.50)/2.00 * 100 = 25%\).
03

Calculate the mass feed rate of hydrogen required to produce the desired amount of ethane

We know that 1 mole of \(H_2\) is needed to produce 1 mole of \(C_2H_6\). With a molecular weight of \(2.016 \, \text{kg/kmol}\) for \(H_2\) and \(30.069 \, \text{kg/kmol}\) for \(C_2H_6\), the yearly required feed rate of \(H_2\) to produce \(4 * 10^9 \, \text{kg}\) of \(C_2H_6\) is \((4 * 10^9 \, \text{kg C}_2\text{H}_6)(\text{kmol C}_2\text{H}_6/30.069 \, \text{kg C}_2\text{H}_6)(2.016 \, \text{kg H}_2/\text{kmol H}_2)\). Dividing this by the number of seconds in a year ( \(24 * 60 * 60 * 300 = 25,920,000\) s) gives the required mass feed rate of \(H_2\).
04

Discuss the drawbacks of running the process with one reactant in excess

Feeding the reactor with an excess of acetylene means that unreacted acetylene will be present in the effluent from the reactor. This unreacted acetylene needs to be separated from the product ethane before the ethane can be sold or used. This separation could be costly and energy-intensive, reducing the overall efficiency of the process.

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Key Concepts

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

Stoichiometric Reactant Ratio
In any chemical reaction, understanding the stoichiometric reactant ratio is crucial. This ratio tells us the exact amount of reactants needed to perfectly balance a chemical equation, ensuring that all reactants are used up to form the intended products without anything left over. This is important for efficient chemical process principles.

In our given problem involving the hydrogenation of acetylene (\[C_2H_2 + 2H_2 \rightarrow C_2H_6\]), the stoichiometric reactant ratio informs us that for every mole of acetylene (\(C_2H_2\)), we require two moles of hydrogen gas (\(H_2\)). Thus, the stoichiometric reactant ratio is \(2 \text{ mol H}_2/\text{mol C}_2\text{H}_2\). This means to convert acetylene to ethane completely, the ideal proportion of hydrogen to acetylene must be maintained at this ratio. Deviating from this ratio can lead to inefficiencies, such as having excess reactants.
Limiting Reactant
The concept of a limiting reactant is fundamental in chemical reactions because it dictates how much product can be formed. The limiting reactant is the reactant that gets completely used up first, thus determining the maximum amount of product formed.

In our scenario, the feed has only \(1.50 \text{ mol H}_2/\text{mol C}_2\text{H}_2\), which is less than the stoichiometric ratio of \(2.00 \text{ mol H}_2/\text{mol C}_2\text{H}_2\). Therefore, hydrogen (\(H_2\)) is the limiting reactant, as it runs out first, halting the reaction despite having unreacted acetylene.

The acetylene (\(C_2H_2\)) is in excess by \([\,(2.00 - 1.50)/2.00 \,] \times 100 = 25\%\). Identifying the limiting reactant helps in calculating the reaction's yield and understanding the reaction's efficiency.
Mass Feed Rate Calculation
Mass feed rate calculation is critical in ensuring that a chemical process is economically feasible and efficient. It determines the amount of reactant that needs to be supplied to achieve a desired production level.

In the problem, we are tasked to calculate the mass feed rate of hydrogen required to produce \(4 \times 10^6\) metric tons of ethane annually. Given ethane's molecular weight \( (30.069 \, \text{kg/kmol})\) and hydrogen's molecular weight \( (2.016 \, \text{kg/kmol})\), the mass of hydrogen needed is derived through a series of conversions:
  • First, calculate the moles of ethane required: \[\,(4 \times 10^9 \, \text{kg C}_2\text{H}_6) \, (\text{kmol C}_2\text{H}_6/30.069 \, \text{kg C}_2\text{H}_6)\,\]
  • Convert it based on the reaction ratio to find required moles of hydrogen.
  • Finally, divide the total mass of hydrogen by the total operational seconds in a year \((24 \times 60 \times 60 \times 300)\) to determine the continuous feed rate in \(\text{kg/s}\)
By tackling these calculations, you ensure the process operates smoothly, continuously, and economically viable for the given production requirements.

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Most popular questions from this chapter

Carbon nanotubes (CNT) are among the most versatile building blocks in nanotechnology. These unique pure carbon materials resemble rolled-up sheets of graphite with diameters of several nanometers and lengths up to several micrometers. They are stronger than steel, have higher thermal conductivities than most known materials, and have electrical conductivities like that of copper but with higher currentcarrying capacity. Molecular transistors and biosensors are among their many applications. While most carbon nanotube research has been based on laboratory-scale synthesis, commercial applications involve large industrial-scale processes. In one such process, carbon monoxide saturated with an organo-metallic compound (iron penta-carbonyl) is decomposed at high temperature and pressure to form CNT, amorphous carbon, and CO_. Each "molecule" of CNT contains roughly 3000 carbon atoms. The reactions by which such molecules are formed are: In the process to be analyzed, a fresh feed of CO saturated with \(\mathrm{Fe}(\mathrm{CO})_{5}(\mathrm{v})\) contains \(19.2 \mathrm{wt} \%\) of the latter component. The feed is joined by a recycle stream of pure CO and fed to the reactor, where all of the iron penta-carbonyl decomposes. Based on laboratory data, \(20.0 \%\) of the CO fed to the reactor is converted, and the selectivity of CNT to amorphous carbon production is (9.00 kmol CNT/kmol C). The reactor effluent passes through a complex separation process that yields three product streams: one consists of solid \(\mathrm{CNT}, \mathrm{C},\) and \(\mathrm{Fe} ;\) a second is \(\mathrm{CO}_{2} ;\) and the third is the recycled \(\mathrm{CO}\). You wish to determine the flow rate of the fresh feed (SCM/h), the total CO_ generated in the process ( \(\mathrm{kg} / \mathrm{h}\) ), and the ratio (kmol CO recycled/kmol CO in fresh feed). (a) Take a basis of \(100 \mathrm{kmol}\) fresh feed. Draw and fully label a process flow chart and do degree-offreedom analyses for the overall process, the fresh-feed/recycle mixing point, the reactor, and the separation process. Base the analyses for reactive systems on atomic balances. (b) Write and solve overall balances, and then scale the process to calculate the flow rate (SCM/h) of fresh feed required to produce \(1000 \mathrm{kg} \mathrm{CNT} / \mathrm{h}\) and the mass flow rate of \(\mathrm{CO}_{2}\) that would be produced. (c) In your degree-of-freedom analysis of the reactor, you might have counted separate balances for C (atomic carbon) and O (atomic oxygen). In fact, those two balances are not independent, so one but not both of them should be counted. Revise your analysis if necessary, and then calculate the ratio (kmol CO recycled/kmol CO in fresh feed). (d) Prove that the atomic carbon and oxygen balances on the reactor are not independent equations.

Methanol is formed from carbon monoxide and hydrogen in the gas-phase reaction The mole fractions of the reactive species at equilibrium satisfy the relation where \(P\) is the total pressure (atm), \(K_{c}\) the reaction equilibrium constant (atm \(^{-2}\) ), and \(T\) the temperature (K). The equilibrium constant \(K_{c}\) equals 10.5 at 373 K, and \(2.316 \times 10^{-4}\) at \(573 \mathrm{K}\). A semilog plot of \(K_{\mathrm{c}}\) (logarithmic scale) versus 1/ \(T\) (rectangular scale) is approximately linear between \(T=300 \mathrm{K}\) and \(T=600 \mathrm{K}\) (a) Derive a formula for \(K_{\mathrm{c}}(T),\) and use it to show that \(K_{\mathrm{e}}(450 \mathrm{K})=0.0548 \mathrm{atm}^{-2}\) (b) Write expressions for \(n_{A}, n_{B},\) and \(n_{C}\) (gram-moles of each species), and then \(y_{A}, y_{B},\) and \(y_{C},\) in terms of \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0},\) and \(\xi,\) the extent of reaction. Then derive an equation involving only \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0}, P, T,\) and \(\xi_{e},\) where \(\xi_{e}\) is the extent of reaction at equilibrium. (c) Suppose you begin with equimolar quantities of CO and \(\mathrm{H}_{2}\) and no \(\mathrm{CH}_{3} \mathrm{OH}\), and the reaction proceeds to equilibrium at 423 K and 2.00 atm. Calculate the molar composition of the product ( \(y_{\mathrm{A}}\), \(\left.y_{\mathrm{B}}, \text { and } y_{\mathrm{C}}\right)\) and the fractional conversion of \(\mathrm{CO}\) (d) The conversion of CO and \(\mathrm{H}_{2}\) can be enhanced by removing methanol from the reactor while leaving unreacted CO and \(\mathrm{H}_{2}\) in the vessel. Review the equations you derived in solving Part (c) and determine any physical constraints on \(\xi_{c}\) associated with \(n_{\mathrm{A} 0}=n_{\mathrm{B} 0}=1\) mol. Now suppose that 90\% of the methanol is removed from the reactor as it is produced; in other words, only 10\% of the methanol formed remains in the reactor. Estimate the fractional conversion of CO and the total gram moles of methanol produced in the modified operation. (e) Repeat Part (d), but now assume that \(n_{\mathrm{B} 0}=2\) mol. Explain the significant increase in fractional conversion of CO. (f) Write a set of equations for \(y_{\mathrm{A}}, y_{\mathrm{B}}, y_{\mathrm{C}},\) and \(f_{\mathrm{A}}\) (the fractional conversion of \(\mathrm{CO}\) ) in terms of \(y_{\mathrm{A} 0}, y_{\mathrm{B} 0}, T,\) and \(P(\) the reactor temperature and pressure at equilibrium). Enter the equations in an equation-solving program. Check the program by running it for the conditions of Part (c), then use it to determine the effects on \(f_{\mathrm{A}}\) (increase, decrease, or no effect) of separately increasing, (i) the fraction of \(\mathrm{CH}_{3} \mathrm{OH}\) in the feed, (ii) temperature, and (iii) pressure.

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?

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.

Seawater containing 3.50 wt\% salt passes through a series of 10 evaporators. Roughly equal quantities of water are vaporized in each of the 10 units and then condensed and combined to obtain a product stream of fresh water. The brine leaving each evaporator but the tenth is fed to the next evaporator. The brine leaving the tenth evaporator contains \(5.00 \mathrm{wt} \%\) salt. (a) Draw a flowchart of the process showing the first, fourth, and tenth evaporators. Label all the streams entering and leaving these three evaporators. (b) Write in order the set of equations you would solve to determine the fractional yield of fresh water from the process \(\left(\mathrm{kg} \mathrm{H}_{2} \mathrm{O} \text { recovered } / \mathrm{kg} \mathrm{H}_{2} \mathrm{O}\) in process feed) and the weight percent of salt in the \right. solution leaving the fourth evaporator. Each equation you write should contain no more than one previously undetermined variable. In each equation, circle the variable for which you would solve. Do not do the calculations. (c) Solve the equations derived in Part (b) for the two specified quantities. (d) The problem statement made no mention of the disposition of the 5 wt\% effluent from the tenth evaporator. Suggest two possibilities for its disposition and describe any environmental concerns that might need to be considered.
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