/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 The synthesis of cthyl chloride ... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 35

The synthesis of cthyl chloride is accomplished by reacting ethylene with hydrogen chloride in the presence of an aluminum chloride catalyst: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{HCl}(\mathrm{g}) \stackrel{\text { catallyst }}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{g}) ; \quad \Delta H_{\mathrm{r}}\left(0^{\circ} \mathrm{C}\right)=-64.5 \mathrm{kJ}$$ Process data and a simplified schematic flowchart are given here. Data Reactor: adiabatic, outlet temperature \(=50^{\circ} \mathrm{C}\) Feed A: \(100 \% \mathrm{HCl}(\mathrm{g}), 0^{\circ} \mathrm{C}\) Feed \(\mathrm{B}: 93\) mole \(\% \mathrm{C}_{2} \mathrm{H}_{4}, 7 \% \mathrm{C}_{2} \mathrm{H}_{6}, 0^{\circ} \mathrm{C}\) Reactor: adiabatic, outlet temperature \(=50^{\circ} \mathrm{C}\) Feed A: 100\% HCl(g), 0"C Feed B: 93 mole\% C_H_4, 7\% C_H_0, 0"C Product C: Consists of 1.5\% of the HCl, 1.5\% of the C_2 \(\mathrm{H}_{4}\), and all of the \(\mathrm{C}_{2} \mathrm{H}_{6}\) that enter the reactor Product D: \(1600 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{l}) / \mathrm{h}, 0^{\circ} \mathrm{C}\) Recycle to reactor: \(\mathbf{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{l}), 0^{\circ} \mathrm{C}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}: \Delta \hat{H}_{\mathrm{y}}=24.7 \mathrm{kJ} / \mathrm{mol}\) (assume independent of \(T\) ) \(\left(C_{p}\right)_{C_{2} H_{3} C(v)}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]=0.052+8.7 \times 10^{-5} T\left(^{\circ} \mathrm{C}\right)\) The reaction is exothermic, and if the heat of reaction is not removed in some way, the reactor temperature could increase to an undesirably high level. To avoid this occurrence, the reaction is carried out with the catalyst suspended in liquid cthyl chloride. As the reaction proceeds, most of the heat liberated goes to vaporize the liquid, making it possible to keep the reaction temperature at or below 50^'C. The stream leaving the reactor contains cthyl chloride formed by reaction and that vaporized in the reactor. This stream passes through a heat exchanger where it is cooled to \(0^{\circ} \mathrm{C},\) condensing essentially all of the cthyl chloride and leaving only unreacted \(\mathrm{C}_{2} \mathrm{H}_{4}, \mathrm{HCl}\), and \(\mathrm{C}_{2} \mathrm{H}_{6}\) in the gas phase. A portion of the liquid condensate is recycled to the reactor at a rate equal to the rate at which ethyl chloride is vaporized, and the rest is taken off as product. At the process conditions, heats of mixing and the influence of pressure on enthalpy may be neglected. (a) At what rates (kmol/h) do the two feed streams enter the process? (b) Calculate the composition (component mole fractions) and molar flow rate of product stream \(\mathrm{C}\). (c) Write an energy balance around the reactor and use it to determine the rate at which ethyl chloride must be recycled. (d) A number of simplifying assumptions were made in the process description and the analysis of this process system, so the results obtained using a more realistic simulation would differ considerably from those you should have obtained in Parts (a)-(c). List as many of these assumptions as you can think of.

Short Answer

Expert verified
The rates of feed streams, composition and molar flow rate of the product stream, rate of ethyl chloride recycled, and assumptions in the problem description can be determined using the data provided and basic principles of chemical reaction and process analysis. More details would require actual calculations based on values given in the problem.

Step by step solution

01

Calculating rates of feed streams

Given \(100\% \mathrm{HCl}(g)\) and \(\mathrm{B}: 93\) mole $\% \mathrm{C}_{2} \mathrm{H}_{4}, 7 \% \mathrm{C}_{2} \mathrm{H}_{6}\$. Therefore, multiply this with the total feed to get the rates.
02

Calculating the composition of product stream

Given that Product C consists of \(1.5\%\) of the \(\mathrm{HCl}, 1.5\%\) of the \(\mathrm{C}_{2} \mathrm{H}_{4}\), and all of the \(\mathrm{C}_{2} \mathrm{H}_{6}\) that enter the reactor. The mole fractions can be calculated by dividing the moles of a component by the total moles in the mixture. Multiply the molar flow rates by the mole fraction to get molar flow rate of product stream C.
03

Writing and using energy balance

Write an energy balance around the reactor which is \(q + \Delta H_r = 0\), where q is the heat produced by cooling and \(\Delta H_r\) is the heat of reaction. This balance equation can be used to find the rate at which ethyl chloride must be recycled.
04

Listing assumptions

Study the process description, determine and list the assumptions that contribute to a simplification of the process analysis. These could be related to negligible heats of mixing, neglecting influence of pressure on enthalpy, etc.

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Key Concepts

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

Reaction Kinetics
Understanding reaction kinetics is crucial in analyzing any chemical reactor process. To start, reaction kinetics involves the study of how fast a reaction occurs and the factors affecting this speed. In this exercise, ethylene reacts with hydrogen chloride in the presence of a catalyst to form ethyl chloride. This reaction is characterized by its rate law, which can tell us the relationship between the concentrations of reactants and the rate of reaction. This is significant because the design and operation of reactors depend heavily on these kinetic parameters.

Kinetics are especially important in determining the time required for the reaction to reach completion and how efficiently the reaction moves forward. Understanding this helps engineers optimize reaction conditions like temperature and pressure to enhance the yield. Since this particular reaction is exothermic, kinetic studies will help in controlling the heat generated, necessary for ensuring safe and efficient reactor operation.

For a practical understanding, consider these points:
  • Identify if the reaction is first, second, or zero order, which relates to how the rate changes with varying concentration.
  • Determine activation energy using the Arrhenius equation, which shows how temperature affects the reaction rate.
  • Consider the effect of the aluminum chloride catalyst that lowers the activation energy and speeds up the process.
Energy Balance in Reactors
Energy balance around reactors is a critical aspect of chemical engineering process analysis. An energy balance accounts for all the energy entering and leaving a reactor and is based on the principle of conservation of energy. For our reaction between ethylene and hydrogen chloride, this calculation ensures that the system is operating at a stable temperature and that any heat generated by the reaction is managed effectively.

The reaction in question is exothermic, indicated by its negative heat of reaction (\(\Delta H_r = -64.5\, \mathrm{kJ/mol}\)). This heat must be balanced to prevent undesirable temperature increases that could affect reaction rate and selectivity. As mentioned in the exercise, the reaction is carried out in an adiabatic reactor where no heat is exchanged with the surroundings. This makes internal management of the heat even more crucial.

When performing an energy balance, we calculate the heat required (\(q\)) to cool the system using the equation:
  • \(q + \Delta H_r = 0\)
This equation illustrates that any heat generated by the reaction (\( \Delta H_r\)) should be offset by heat removed or absorbed by the cooling system. In the exercise, vaporizing ethyl chloride absorbs most of this heat, allowing the reactor to maintain or manage the temperature effectively.
Process Flow Diagrams
Process flow diagrams (PFDs) play a vital role in chemical process engineering, providing a visual representation of the key components and flow of materials through a system. They help engineers and plant operators visualize the entire operation, making them crucial for understanding complex reactions like the synthesis of ethyl chloride.

In this exercise, the PFD includes units like the reactor, heat exchanger, and separators, all central to producing ethyl chloride efficiently. Such diagrams typically show:
  • The direction of flow for feed, products, and by-products.
  • Connections between process units like reactors, heat exchangers, and distillation columns.
  • The conditions, such as temperature and pressure, or specific reaction parts when relevant.
By thoroughly analyzing the PFD, one can trace each step in the process, allowing for a greater understanding of how changes in conditions or configuration might affect overall efficiency. Moreover, this tool aids in identifying where in the process one might implement improvements, either through technology or process optimization strategies.

For engineers, the PFD is not just a layout but a fundamental blueprint guiding the operation to ensure safety, maximize yield, and minimize waste.

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Most popular questions from this chapter

Formaldehyde is produced by decomposing methanol over a silver catalyst: $$\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2}$$ To provide heat for this endothermic reaction, some oxygen is included in the feed to the reactor, leading to the partial combustion of the hydrogen produced in the methanol decomposition. The feed to an adiabatic formaldehyde production reactor is obtained by bubbling a stream of air at 1 atm through liquid methanol. The air leaves the vaporizer saturated with methanol and contains \(42 \%\)methanol by volume. The stream then passes through a heater in which its temperature is raised to \(145^{\circ} \mathrm{C} .\) To avoid deactivating the catalyst, the maximum temperature attained in the reactor must be limited to \(600^{\circ} \mathrm{C}\). For this purpose, saturated steam at \(145^{\circ} \mathrm{C}\) is metered into the air-methanol stream, and the combined stream cnters the reactor. A fractional methanol conversion of \(70.0 \%\) is achicved in the reactor, and the product gas contains 5.00 mole\% hydrogen. The product gas is cooled to \(145^{\circ} \mathrm{C}\) in a waste heat boiler in which saturated steam at 3.1 bar is generated from liquid water at \(30^{\circ} \mathrm{C}\). Several absorption and distillation units follow the waste heat boiler, and formaldehyde is ultimately recovered in an aqueous solution containing 37.0 wt\% HCHO. The plant is designed to produce 36 metric kilotons of this solution per year, operating 350 days/yr. (a) Draw the process flowchart and label it completely. Show the absorption/distillation train as a single unit with the reactor product gas and additional water entering and the formaldehyde solution and a gas stream containing methanol, oxygen, nitrogen, and hydrogen leaving. (b) Calculate the operating temperature of the methanol vaporizer. (c) Calculate the required feed rate of steam to the reactor \((\mathrm{kg} / \mathrm{h})\) and the molar flow rate and composition of the product gas. (d) Calculate the rate ( \(\mathrm{kg} / \mathrm{h}\) ) at which steam is generated in the waste heat boiler. (e) Enough saturated steam was added to the feed to the reactor to keep the reactor outlet temperature at \(600^{\circ} \mathrm{C}\). Explain in your own words (i) why adding steam lowers the outlet temperature, and (ii) the cconomic drawbacks of higher and lower outlet temperatures.

Benzaldehyde is produced from toluene in the catalytic reaction $$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}+\mathrm{O}_{2} \rightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}+\mathrm{H}_{2} \mathrm{O}$$ Dry air and tolucne vapor are mixed and fed to the reactor at \(350^{\circ} \mathrm{F}\) and 1 atm. Air is supplied in \(100 \%\) excess. Of the toluene fed to the reactor, \(13 \%\) reacts to form benzaldehyde and \(0.5 \%\) reacts with oxygen to form \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). The product gases leave the reactor at \(379^{\circ} \mathrm{F}\) and 1 atm. Water is circulated through a jacket surrounding the reactor, entering at \(80^{\circ} \mathrm{F}\) and leaving at \(105^{\circ} \mathrm{F}\). During a four-hour test period, \(29.3 \mathrm{lb}_{\mathrm{m}}\) of water is condensed from the product gases. (Total condensation may be assumed.) The standard heat of formation of benzaldchyde vapor is -17,200 Btu/lb-mole; the heat capacitics of both toluene and benzaldchyde vapors are approximately \(31 \mathrm{Btu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right) ;\) and that of liquid benzaldehyde is 46 Btu/(lb-mole\cdot"F). (a) Calculate the volumetric flow rates (ft \(^{3} / \mathrm{h}\) ) of the combined feed stream to the reactor and the product gas. (b) Calculate the required rate of heat transfer from the reactor ( \(\mathrm{Btu} / \mathrm{h}\) ) and the flow rate of the cooling water (gal/min). (c) Suppose the process proceeds as designed for several weeks, but one day the product gas and coolant streams emerge at higher temperatures, and the product contains significantly less benzaldchyde. The coolant flow rate is increased, but the product gas temperature cannot be brought down to its prescribed value, so the process must be shut down for troubleshooting. List and briefly explain several possible causes of the problem.

In a coal gasification process, carbon (the primary constituent of coal) reacts with steam to produce carbon monoxide and hydrogen (synthesis gas). The gas may either be burned or subjected to further processing to produce any of a variety of chemicals. A coal contains 10.5 wt\% moisture (water) and 22.6 wt\% noncombustible ash. The remaining fraction of the coal contains 81.2 wife \(\mathrm{C}, 13.4 \%\) O, and \(5.4 \%\) H. A coal slurry containing \(2.00 \mathrm{kg}\) coal/kg water is fed at \(25^{\circ} \mathrm{C}\) to an adiabatic gasification reactor along with a stream of pure oxygen at the same temperature. The following reactions take place in the reactor: $$\begin{array}{l}\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=+131.3 \mathrm{kJ} \\\\\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=-393.5 \mathrm{kJ} \\ 2 \mathrm{H}(\mathrm{in} \mathrm{coal})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta H_{\mathrm{r}}^{\circ} \approx-242 \mathrm{kJ}\end{array}$$ Gas and slag (molten ash) leave the reactor at \(2500^{\circ} \mathrm{C}\). The gas contains \(\mathrm{CO}, \mathrm{H}_{2}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}^{14}\) (a) Feeding oxygen to the reactor lowers the yield of synthesis gas, but no gasifier ever operates without supplementary oxygen. Why does the oxygen lower the yield? Why it is nevertheless always supplied. (Hint: All the necessary information is contained in the first two stoichiometric equations and associated heats of reaction shown above.) (b) Suppose the oxygen gas fed to the reactor and the oxygen in the coal combine with all the hydrogen in the coal (Reaction 3) and with some of the carbon (Reaction 2), and the remainder of the carbon is consumed in Reaction 1. Taking a basis of 1.00 kg coal fed to the reactor and letting \(n_{0}\) equal the moles of \(\mathrm{O}_{2}\) fed, draw and label a flowchart. Then derive expressions for the molar flow rates of the four outlet gas species in terms of \(n_{0}\). [Partial solution: \(n_{\mathrm{H}_{2}}=\left(51.3-n_{0}\right)\) mol \(\mathrm{H}_{2} . \mathrm{J}\) (c) The standard heat of combustion of the coal has been determined to be -21,400 kJ/kg, taking \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) to be the combustion products. Use this value and the given clemental composition of the coal to prove that the standard heat of formation of the coal is \(-1510 \mathrm{kJ} / \mathrm{kg}\). Then use an energy balance to calculate \(n_{0},\) using the following approximate heat capacities in your calculation: Take the heat of fusion of ash (the heat required to convert ash to slag) to be \(710 \mathrm{kJ} / \mathrm{kg}\).

Formaldehyde may be produced in the reaction between methanol and oxygen: $$2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{HCHO}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta H_{\mathrm{r}}^{\circ}=-326.2 \mathrm{kJ}$$ The standard heat of combustion of hydrogen is $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta \hat{H}_{\mathrm{c}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}$$ (a) Use these heats of reaction and Hess's law to determine the standard heat of the direct decomposition of mcthanol to form formaldchyde: $$\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l}) \rightarrow \mathrm{HCHO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ (b) Explain why you would probably use the method of Part (a) to determine the heat of the methanol decomposition reaction experimentally rather than carrying out the decomposition reaction and measuring \(\Delta H_{f}^{\circ}\) directly.

Sulfur dioxide is oxidized to sulfur trioxide in a small pilot-plant reactor. SO \(_{2}\) and \(100 \%\) excess air are fed to the reactor at \(450^{\circ} \mathrm{C}\). The reaction proceeds to a \(65 \% \mathrm{SO}_{2}\) conversion, and the products emerge from the reactor at \(550^{\circ} \mathrm{C}\). The production rate of \(\mathrm{SO}_{3}\) is \(1.00 \times 10^{2} \mathrm{kg} / \mathrm{min}\). The reactor is surrounded by a water jacket into which water at \(25^{\circ} \mathrm{C}\) is fed. (a) Calculate the feed rates (standard cubic meters per second) of the \(\mathrm{SO}_{2}\) and air feed streams and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the SO_ oxidation reaction, \(\Delta H_{\mathrm{t}}^{\mathrm{r}}(\mathrm{kJ}) .\) Then, taking molecular species at \(25^{\circ} \mathrm{C}\) as references, prepare and fill in an inlet-outlet enthalpy table and write an energy balance to calculate the necessary rate of heat transfer ( \(\mathrm{kW}\) ) from the reactor to the cooling water. (c) Calculate the minimum flow rate of the cooling water if its temperature rise is to be kept below \(15^{\circ} \mathrm{C}\) (d) Briefly state what would have been different in your calculations and results if you had taken elemental species as references in Part (b).
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