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Chapter 4: Problem 57

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?

Short Answer

Expert verified
The mole fractions for each component will be calculated using both atomic species balances and extent of the reaction. Cost implications and savings from using pure oxygen will also be discussed. Ultimately, the production should be run in the way that is more cost-effective, balancing the costs of using pure oxygen against the efficiency of the process.

Step by step solution

01

Calculate the mole fractions using atomic species balances

First establish the balanced chemical equation for the Deacon process: 4HCl + O2 -> 2Cl2 + 2H2O. From there, we can calculate the amount of moles for each substance. Consider an initial amount of 100 moles of HCl which would react with 25 moles of O2 from air, thereby leaving 35% of the oxygen at 8.75 moles. Given 85% of HCl reacts, 15 moles of HCl is left unreacted. The reaction produces 42.5 moles of Cl2 and 42.5 moles of H2O. Yet, Nitrogen is unaffected and remains the same. Now, calculate the mole fraction by dividing the amount of each component by the total moles in the system.
02

Calculate the mole fractions using extent of reaction

The stoichiometric number (尉) can be used which is a measure of the progress of the reaction. It is advantageous because it allows us to track the amount of reactants and products directly without calculating balance. Again, consider the reaction of 4HCl + O2 -> 2CL2 + 2H2O. The stoichiometric number for HCl was found to be -4; it was -1 for O2 (reactants side) and was +2 for Cl2 and H2O (products side). The extent of reaction can be utilized to calculate the final quantities of reactants and products. Using the relation (final state = initial state + 尉* stoichiometric coefficient), you can find the new quantities. Afterwards, the mole fractions can be calculated in the same way as before.
03

Speculating the cost implications and savings of using pure Oxygen

Considerable cost implications and savings might occur if pure Oxygen was used instead of air. On the one side there are higher costs for using pure oxygen, as it requires additional steps of filtration and purification. On the other side, the potential savings could stem from increased efficiency of the process, as there would be more oxygen available for the reaction, potentially making it faster and yielding a higher conversion rate of Hydrogen Chloride to Chlorine. The decision would depend on whether the extra costs are outweighed by the savings made from the increased efficiency.

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Key Concepts

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

Deacon Process
The Deacon Process is an industrial method for producing chlorine gas. It involves the chemical reaction where hydrochloric acid (HCl) and oxygen (\(O_2\)) react to form chlorine (\(Cl_2\)) and water (\(H_2O\)). This process is important for industries that need a large supply of chlorine, such as in the production of PVC (polyvinyl chloride).
\[4 ext{ HCl} + ext{O}_2 ightarrow 2 ext{ Cl}_2 + 2 ext{ H}_2 ext{O}\]
The Deacon Process is notable for its use of air, which contains a high amount of nitrogen (79%), as an economical oxygen source. This makes the process cost-effective. However, using air can lead to efficiency issues as only 21% of it is \(O_2\), requiring specific management of excess oxygen to drive the process effectively.
Atomic Species Balances
Atomic species balances help us understand and account for the amount of each element present in a chemical reaction. It's a method of ensuring that all atoms are balanced before and after the reaction takes place.
In the Deacon Process exercise, assume we start with 100 moles of HCl. When it reacts with oxygen (\(O_2\)), the atomic balance requires that all atoms from the reactants must equal the atoms in the products. An atomic species balance for the Deacon Process can be set as follows:
  • Chlorine balance: All the chlorine in HCl ends up as \(Cl_2\).
  • Oxygen balance: The oxygen reacts with HCl to form \(H_2O\) and some remains unreacted.
  • Hydrogen balance: The hydrogen in HCl forms \(H_2O\).
  • Nitrogen balance: It stays unchanged as it is inert in this reaction.
Atomic species balances are a reliable method to derive the system's stoichiometry and to calculate mole fractions.
Extent of Reaction
The extent of reaction, denoted by \(\xi\), measures how far the reaction has proceeded. It simplifies calculations about changes in moles of reactants and products.
In terms of the Deacon Process, we use the extent of reaction to keep track of reactants and products. The stoichiometric coefficients from the balanced chemical equation (\(\text{HCl}: -4, \ O_2: -1, \ Cl_2: +2, \ H_2O: +2\)) relate to \(\xi\). These describe how the quantities of each reactant decrease or increase.
The final amount of any component is given by:\[n_{final} = n_{initial} + \xi \times \text{stoichiometric coefficient}\]This formula allows us to determine the quantities of products formed or reactants consumed. By calculating \(\xi\), we can directly calculate mole fractions, as \(\xi\) relates to how much of the initial substances have reacted to form the products.
Mole Fractions
Mole fractions are a way to express the concentration of each component in a mixture. They are the ratio of the number of moles of a substance to the total number of moles in the mixture.
In the Deacon Process, after calculating the moles of all substances, these are used to find mole fractions. For any substance A, the mole fraction, \(x_A\), is calculated using:\[x_A = \frac{n_A}{n_{total}}\]Where \(n_A\) is the number of moles of substance A and \(n_{total}\) is the total moles in the system.
This fraction helps in understanding the composition of the product stream. For the Deacon Process, you would calculate for \(HCl\), \(Cl_2\), \(H_2O\), \(O_2\), and \(N_2\) to see how they compare against each other in terms of concentration.

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Most popular questions from this chapter

Chlorobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right),\) an important solvent and intermediate in the production of many other chemicals, is produced by bubbling chlorine gas through liquid benzene in the presence of ferric chloride catalyst. In an undesired side reaction, the product is further chlorinated to dichlorobenzene, and in a third reaction the dichlorobenzene is chlorinated to trichlorobenzene. The feed to a chlorination reactor consists of essentially pure benzene and a technical grade of chlorine gas (98 wt\% \(\mathrm{Cl}_{2}\), the balance gaseous impurities with an average molecular weight of 25.0 ). The liquid output from the reactor contains \(65.0 \mathrm{wt} \% \mathrm{C}_{6} \mathrm{H}_{6}, 32.0 \% \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}, 2.5 \% \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2},\) and \(0.5 \%\) \(\mathrm{C}_{6} \mathrm{H}_{3} \mathrm{Cl}_{3} .\) The gaseous output contains only \(\mathrm{HCl}\) and the impurities that entered with the chlorine. (a) You wish to determine (i) the percentage by which benzene is fed in excess, (ii) the fractional conversion of benzene, (iii) the fractional yield of monochlorobenzene, and (iv) the mass ratio of the gas feed to the liquid feed. Without doing any calculations, prove that you have enough information about the process to determine these quantities. (b) Perform the calculations. (c) Why would benzene be fed in excess and the fractional conversion kept low? (d) What might be done with the gaseous effluent? (e) It is possible to use 99.9\% pure ("reagent-grade") chlorine instead of the technical grade actually used in the process. Why is this probably not done? Under what conditions might extremely pure reactants be called for in a commercial process? (Hint: Think about possible problems associated with the impurities in technical grade chemicals.)

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.

Effluents from metal-finishing plants have the potential of discharging undesirable quantities of metals, such as cadmium, nickel, lead, manganese, and chromium, in forms that are detrimental to water and air quality. A local metal-finishing plant has identified a wastewater stream that contains 5.15 wt\% chromium (Cr) and devised the following approach to lowering risk and recovering the valuable metal. The wastewater stream is fed to a treatment unit that removes \(95 \%\) of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above \(4500 \mathrm{kg} / \mathrm{h}\) ) bypasses the unit and combines with the residual liquid leaving the unit, and the combined stream goes to the waste lagoon. (a) Without assuming a basis of calculation, draw and label a flowchart of the process. (b) Wastewater leaves the finishing plant at a rate \(\dot{m}_{1}=6000 \mathrm{kg} / \mathrm{h}\). Calculate the flow rate of liquid to the waste lagoon, \(\dot{m}_{6}(\mathrm{kg} / \mathrm{h}),\) and the mass fraction of \(\mathrm{Cr}\) in this liquid, \(x_{6}(\mathrm{kg} \mathrm{Cr} / \mathrm{kg})\) (c) Calculate the flow rate of liquid to the waste lagoon and the mass fraction of Crin this liquid for \(\dot{m}_{1}\) varying from \(1000 \mathrm{kg} / \mathrm{h}\) to \(10,000 \mathrm{kg} / \mathrm{h}\) in \(1000 \mathrm{kg} / \mathrm{h}\) increments. Generate a plot of \(x_{6}\) versus \(\dot{m}_{1}\). (Suggestion: Use a spreadsheet for these calculations.) (d) The company has hired you as a consultant to help them determine whether or not to add capacity to the treatment unit to increase the recovery of chromium. What would you need to know to make this determination? (e) What concerns might need to be addressed regarding the waste lagoon?

Strawberries contain about \(15 \mathrm{wt} \%\) solids and \(85 \mathrm{wt} \%\) water. To make strawberry jam, crushed strawberries and sugar are mixed in a 45: 55 mass ratio, and the mixture is heated to evaporate water until the residue contains one-third water by mass. (a) Draw and label a flowchart of this process. (b) Do the degree-of-freedom analysis and show that the system has zero degrees of freedom (i.e., the number of unknown process variables equals the number of equations relating them). If you have too many unknowns, think about what you might have forgotten to do. (c) Calculate how many pounds of strawberries are needed to make a pound of jam. (d) Making a pound of jam is something you could accomplish in your own kitchen (or maybe even a dorm room). However, a typical manufacturing line for jam might produce 1500 1b_m/h. List technical and economic factors you would have to take into account as you scaled up this process from your kitchen to a commercial operation.

One thousand kilograms per hour of a mixture containing equal parts by mass of methanol and water is distilled. Product streams leave the top and the bottom of the distillation column. The flow rate of the bottom stream is measured and found to be \(673 \mathrm{kg} / \mathrm{h}\), and the overhead stream is analyzed and found to contain 96.0 wt\% methanol. (a) Draw and label a flowchart of the process and do the degree-of-freedom analysis. (b) Calculate the mass and mole fractions of methanol and the molar flow rates of methanol and water in the bottom product stream. (c) Suppose the bottom product stream is analyzed and the mole fraction of methanol is found to be significantly higher than the value calculated in Part (b). List as many possible reasons for the discrepancy as you can think of. Include in your list possible violations of assumptions made in Part (b).
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