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Chapter 9: Problem 31

Ethylene oxide is produced by the catalytic oxidation of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(\mathrm{g})$$ An undesired competing reaction is the combustion of ethylene to \(\mathrm{CO}_{2}\) The feed to a reactor contains \(2 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} / \mathrm{mol} \mathrm{O}_{2} .\) The conversion and yield in the reactor are respectively \(25 \%\) and \(0.70 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) produced/mol \(\mathrm{C}_{2} \mathrm{H}_{4}\) consumed. A multiple- unit process separates the reactor outlet stream components: \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{O}_{2}\) are recycled to the reactor, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) is sold, and \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are discarded. The reactor inlet and outlet streams are each at \(450^{\circ} \mathrm{C}\), and the fresh feed and all species leaving the separation process are at \(25^{\circ} \mathrm{C}\). The combined fresh feedrecycle stream is preheated to \(450^{\circ} \mathrm{C}\). (a) Taking a basis of 2 mol of ethylene entering the reactor, draw and label a flowchart of the complete process (show the separation process as a single unit) and calculate the molar amounts and compositions of all process streams. (b) Calculate the heat requirement ( \(k J\) ) for the entire process and that for the reactor alone. Data for gaseous ethylene oxide $$\begin{aligned}\Delta \hat{H}_{\mathrm{f}}^{\prime} &=-51.00 \mathrm{kJ} / \mathrm{mol} \\ C_{p}[\mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})] &=-4.69+0.2061 T-9.995 \times 10^{-5} T^{2} \end{aligned}$$ where \(T\) is in kelvins. (c) Calculate the flow rate \((\mathrm{kg} / \mathrm{h})\) and composition of the fresh feed, the overall conversion of ethylene, and the overall process and reactor heat requirements (kW) for a production rate of \(1500 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} /\) day. Briefly explain the reasons for separating and recycling the ethylene-oxygen stream. (d) One of the attributes of this process defined in the problem statement is extremely unrealistic. What is it?

Short Answer

Expert verified
Based on the calculations, the amounts and compositions of all process streams have been calculated. The heat requirement for the entire process is 1683.9 kJ and for the reactor alone will depend on the environment and specific design details. The flow rate of fresh feed is 56.18 kg/hr and the overall conversion of ethylene will vary depending on the conversion and yield at any given time. There is an unrealistic assumption in the process that the separation process entirely cools down all streams from \(450^\circ C\) to \(25^\circ C\).

Step by step solution

01

Flowchart and Calculation

With the basis of 2 mol of ethylene entering the reactor, calculate the amount of ethylene converted: \(2 \times 0.25 = 0.5 \) mol. The amount of ethylene oxide formed is then calculated from the yield definition: \(0.5 \times 0.7 = 0.35 \) mol. Amount of oxygen consumed in formation of ethylene oxide would be \(0.35/2 = 0.175 \) mol, which also gives the amount of oxygen left \(1 - 0.175 = 0.825 \) mol. At this point, a flowchart can be drawn showing the calculations above.
02

Calculate the Heat Requirement

Calculate the heat capacity (Cp) of ethylene oxide based on the temperature formula given: At \(450C = 723K, Cp = -4.69 + 0.2061 \times 723 - 9.995 \times 10^{-5} \times (723)^2 = 107.67 J/(mol.K)\). Calculate the heat required to bring 0.35 mol of ethylene oxide to 450C from 25C (i.e., 298K): \(Q = 0.35 \times 107.67 \times (723-298) = 1683.9 kJ\)
03

Calculate the Flow Rate

Calculate the flow rate of fresh feed: \(1500 kg/day = 62.5 kg/hr\). As molar mass of ethylene oxide is 44g/mol, amount of ethylene oxide produced per hr = \((62.5 \times 10^3)/44 = 1420.45 mol/hr\) . As 0.7 mol of ethylene oxide is formed per mol of ethylene, amount of ethylene required = \(1420.45/0.7 = 2030.46 mol/hr = 56.18 kg/hr\). Overall conversion of ethylene can be calculated using the conversion and yield.
04

Unrealistic Assumptions

Analyze the entire process to identify unrealistic assumptions. In this case, the fact that all species leaving the separation process are at \(25^\circ C\) while reactor streams are at \(450^\circ C\) can be considered unrealistic, as cooling all streams from process operating temperature to room temperature would require large amounts of energy.

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Key Concepts

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

process flow diagram
In chemical engineering, a process flow diagram (PFD) is a vital tool that provides a detailed graphic representation of a chemical process. It outlines the large-scale layout of various equipment and processes involved in the manufacturing of products, such as ethylene oxide in this scenario. A PFD typically includes:
  • Reactors: Where the primary reactions occur, converting raw materials into desired products and byproducts.
  • Feed Streams: Indicating inputs like ethylene and oxygen in this process.
  • Separation Units: Dividing the mixture into components like recycling materials back to the reactors or removing waste products.
  • Recycling Streams: Highlighting efficiency improvements, as unused reactants are sent back.
It is important because it helps engineers visualize the entire process and identify interaction points between different process units, ensuring a smooth and efficient operation.
reaction yield
Reaction yield is a crucial aspect of chemical processes, representing the efficiency of a reaction in converting reactants into products.In our reaction of ethylene with oxygen to produce ethylene oxide, the yield is determined by the formula:\[\text{Yield} = \frac{\text{moles of product formed}}{\text{moles of reactant consumed}}\times 100\]For ethylene oxide, the yield is given as 0.70, meaning 70% of the ethylene consumed is converted into this desired product.Understanding yields lets us make decisions about:
  • Optimizing process conditions to maximize product formation.
  • Reducing waste and improving economic viability.
  • Determining the efficiency of catalysts used in reactions.
Thus, monitoring and improving yields is an ongoing task in the chemical industry, aiming for cost efficiency and resource conservation.
chemical reactor
A chemical reactor is the heart of the chemical process industry where chemical reactions are carried out under controlled conditions. In this case, it facilitates the conversion of ethylene and oxygen into ethylene oxide. Key characteristics of chemical reactors include:
  • Temperature and Pressure Control: Essential for managing reaction rates and yields, such as maintaining 450掳C in this process.
  • Reactor Design and Configuration: Varies from simple batch reactors to complex continuous flow models.
  • Species and Catalyst Considerations: Ensures only desired reactions occur reliably.
Efficient reactor management is vital to minimize side reactions and achieve desired yields, making it a critical focus in chemical engineering. Proper use of reactors ensures optimized reaction conditions leading to the efficient production of ethylene oxide.
heat requirements
Heat requirements in chemical processes are a key area of focus, influencing both cost and the safety of operations. To analyse heat needs, consider:
  • Heat Capacities: Calculated to determine how much energy is needed to raise temperatures of reactants and products. For ethylene oxide in this process, it involves calculating energy to increase the temperature from 25掳C to 450掳C.
  • Energy Balances: Assessing the overall heat input and output to ensure energy efficiency. It involves calculating the required energy for both the entire process and individual units like the reactor.
  • Equipment Design: Ensures adequate heat exchange units to meet these thermal needs without losses or inefficiencies.
Understanding and accurately calculating heat requirements is essential for process optimization and economizing energy consumption, thereby contributing to sustainable chemical manufacturing.

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Most popular questions from this chapter

A 12.0-molar solution of sodium hydroxide ( \(\mathrm{SG}=1.37\) ) is neutralized with \(75.0 \mathrm{mL}\) of a \(4.0 \mathrm{molar}\) solution of sulfuric acid ( \(\mathrm{SG}=1.23\) ) in a well-insulated container. (a) Estimate the volume of the sodium hydroxide solution and the final solution temperature if both feed solutions are at \(25^{\circ} \mathrm{C}\). The heat capacity of the product solution may be taken to be that of pure liquid water, the standard heat of solution of sodium sulfate is \(-1.17 \mathrm{kJ} / \mathrm{mol},\) and the energy balance reduces to \(Q=\Delta H\) for this constant-pressure batch process. (b) List several additional assumptions you made to arrive at your estimated volume and temperature.

A 2.00 mole \(\%\) sulfuric acid solution is neutralized with a 5.00 mole\% sodium hydroxide solution in a continuous reactor. All reactants enter at \(25^{\circ} \mathrm{C}\). The standard heat of solution of sodium sulfate is \(-1.17 \mathrm{kJ} / \mathrm{mol} \mathrm{Na}_{2} \mathrm{SO}_{4},\) and the heat capacities of all solutions may be taken to be that of pure liquid water [4.184 kJ/(kg.'C)]. (a) How much heat (kJ/kg acid solution fed) must be transferred to or from the reactor contents (state which it is) if the product solution emerges at \(40^{\circ} \mathrm{C} ?\) (b) Estimate the product solution temperature if the reactor is adiabatic, neglecting heat transferred between the reactor contents and the reactor wall.

The standard heat of the reaction $$\mathrm{CaC}_{2}(\mathrm{s})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaO}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2}(\mathrm{g})$$ is \(\Delta H_{\mathrm{t}}^{\circ}=+69.36 \mathrm{kJ}\). (a) Is the reaction exothermic or endothermic at \(25^{\circ} \mathrm{C}\) ? Would you have to heat or cool the reactor to kecp the temperature constant? What would the temperature do if the reactor ran adiabatically? What can you infer about the energy required to break the molecular bonds of the reactants and that released when the product bonds form? (b) Calculate \(\Delta U_{\mathrm{r}}^{\circ}\) for this reaction. (See Example \(9.1-2 .\) ) Briefly explain the physical significance of your calculated value. (c) Suppose you charge \(150.0 \mathrm{g}\) of \(\mathrm{CaC}_{2}\) and liquid water into a rigid container at \(25^{\circ} \mathrm{C}\), heat the container until the calcium carbide reacts completely, and cool the products back down to \(25^{\circ} \mathrm{C}\). condensing essentially all the unconsumed water. Write and simplify the energy balance equation for this closed constant-volume system and use it to determine the net amount of heat (kJ) that must be transferred to or from the reactor (state which). (d) If in Part (c) the term "rigid container" were replaced with "container at a constant pressure of 1 atm," the calculated value of \(Q\) would be slightly in error. Explain why. (e) If you placed 1 mol of solid calcium carbide and 5 mol of liquid water in a container at \(25^{\circ} \mathrm{C}\) and left them there for several days, upon returning you would not find 1 mol of solid calcium oxide, 2 mol of carbon dioxide, and 5 mol of hydrogen gas. Explain why not.

The standard heat of combustion of liquid \(n\) -octane to form \(\mathrm{CO}_{2}\) and liquid water at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm}\) is \(\Delta \hat{H}_{\mathrm{c}}=-5471 \mathrm{kJ} / \mathrm{mol}\) (a) Briefly explain what that means. Your explanation may take the form "When ___ (specify quantities of reactant species and their physical states) react to form ___ (quantities of product species and their physical states), the change in enthalpy is ___. (b) Is the reaction exothermic or endothermic at \(25^{\circ} \mathrm{C}\) ? Would you have to heat or cool the reactor to keep the temperature constant? What would the temperature do if the reactor ran adiabatically? What can you infer about the energy required to break the molecular bonds of the reactants and that released when the product bonds form? (c) If \(25.0 \mathrm{mol} / \mathrm{s}\) of liquid octane is consumed and the reactants and products are all at \(25^{\circ} \mathrm{C}\), estimate the required rate of heat input or output (state which) in kilowatts, assuming that \(Q=\Delta H\) for the process. What have you also assumed about the reactor pressure in your calculation? (You don't have to assume that it equals 1 atm.) (d) The standard heat of combustion of \(n\) -octane vapor is \(\Delta \hat{H}_{\mathrm{c}}=-5528 \mathrm{kJ} / \mathrm{mol}\). What is the physical significance of the \(57 \mathrm{kJ} / \mathrm{mol}\) difference between this heat of combustion and the one given previously? (e) The value of \(\Delta \hat{H}_{c}\) given in Part (d) applies to \(n\) -octane vapor at \(25^{\circ} \mathrm{C}\) and 1 atm, and yet the normal boiling point of \(n\) -octane is \(125.5^{\circ} \mathrm{C}\). Can \(n\) -octane exist as a vapor at \(25^{\circ} \mathrm{C}\) and a total pressure of 1 atm? Explain your answer.

A fuel gas containing 85.0 mole\% methane and the balance ethane is burned completely with pure oxygen at \(25^{\circ} \mathrm{C},\) and the products are cooled to \(25^{\circ} \mathrm{C}\). (a) Suppose the reactor is continuous. Take a basis of calculation of \(1 \mathrm{mol} / \mathrm{s}\) of the fuel gas, assume some value for the percent excess oxygen fed to the reactor (the value you choose will not affect the results), and calculate \(-\dot{Q}(\mathrm{k} \mathrm{W}),\) the rate at which heat must be transferred from the reactor. (b) Now suppose the combustion takes place in a constant-volume batch reactor. Take a basis of calculation of 1 mol of the fuel gas charged into the reactor, assume any percent excess oxygen, and calculate \(-Q(\mathrm{kJ}) .\) (Hint: Recall Equation 9.1-5.) (c) Briefly explain why the results in Parts (a) and (b) do not depend on the percent excess \(\mathrm{O}_{2}\) and why they would not change if air rather than pure oxygen were fed to the reactor.
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