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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

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).

Two streams flow into a 500 -gallon tank. The first stream is 10.0 wt\% ethanol and \(90.0 \%\) hexane (the mixture density, \(\rho_{1},\) is \(0.68 \mathrm{g} / \mathrm{cm}^{3}\) ) and the second is \(90.0 \mathrm{wt} \%\) ethanol, \(10.0 \%\) hexane \(\left(\rho_{2}=0.78 \mathrm{g} / \mathrm{cm}^{3}\right) .\) After the tank has been filled, which takes 22 \(\mathrm{min}\), an analysis of its contents determines that the mixture is 60.0 wt\% ethanol, \(40.0 \%\) hexane. You wish to estimate the density of the final mixture and the mass and volumetric flow rates of the two feed streams. (a) Draw and label a flowchart of the mixing process and do the degree-of- freedom analysis. (b) Perform the calculations and state what you assumed.

\- 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).

The gas-phase reaction between methanol and acetic acid to form methyl acetate and water takes place in a batch reactor. When the reaction mixture comes to equilibrium, the mole fractions of the four reactive species are related by the reaction equilibrium constant $$K_{y}=\frac{y_{C} y_{D}}{y_{A} y_{B}}=4.87$$ (a) Suppose the feed to the reactor consists of \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0}, n_{\mathrm{D} 0},\) and \(n_{10}\) gram-moles of \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},\) and an inert gas, I, respectively. Let \(\xi\) be the extent of reaction. Write expressions for the gram-moles of each reactive species in the final product, \(n_{\mathrm{A}}(\xi), n_{\mathrm{B}}(\xi), n_{\mathrm{C}}(\xi),\) and \(n_{\mathrm{D}}(\xi) .\) Then use these expressions and the given equilibrium constant to derive an equation for \(\xi_{c}\), the equilibrium extent of reaction, in terms of \(\left.n_{\mathrm{A} 0}, \ldots, n_{10} . \text { (see Example } 4.6-2 .\right)\) (b) If the feed to the reactor contains equimolar quantities of methanol and acetic acid and no other species, calculate the equilibrium fractional conversion. (c) It is desired to produce 70 mol of methyl acetate starting with 75 mol of methanol. If the reaction proceeds to equilibrium, how much acetic acid must be fed? What is the composition of the final product? (d) Suppose it is important to reduce the concentration of methanol by making its conversion at equilibrium as high as possible, say 99\%. Again assuming the feed to the reactor contains only methanol and acetic acid and that it is desired to produce 70 mol of methyl acetate, determine the extent of reaction and quantities of methanol and acetic acid that must be fed to the reactor. (e) If you wanted to carry out the process of Part (b) or (c) commercially, what would you need to know besides the equilibrium composition to determine whether the process would be profitable? (List several things.)

A stream consisting of 44.6 mole \(\%\) benzene and \(55.4 \%\) toluene is fed at a constant rate to a process unit that produces two product streams, one a vapor and the other a liquid. The vapor flow rate is initially zero and asymptotically approaches half of the molar flow rate of the feed stream. Throughout this entire period, no material accumulates in the unit. When the vapor flow rate has become constant, the liquid is analyzed and found to be 28.0 mole\% benzene. (a) Sketch a plot of liquid and vapor flow rates versus time from startup to when the flow rates become constant. (b) Is this process batch or continuous? Is it transient or steady-state before the vapor flow rate reaches its asymptotic limit? What about after it becomes constant? (c) For a feed rate of 100 mol/min, draw and fully label a flowchart for the process after the vapor flow rate has reached its limiting value, and then use balances to calculate the molar flow rate of the liquid and the composition of the vapor in mole fractions.
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