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Chapter 9: Problem 24

Synthetically produced ethanol is an important industrial commodity used for various purposes, including as a solvent (especially for substances intended for human contact or consumption); in coatings, inks, and personal-care products; for sterilization; and as a fuel. Industrial cthanol is a petrochemical synthesized by the hydrolysis of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{v})$$ Some of the product is converted to diethyl ether in the undesired side reaction $$2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{v}) \rightleftharpoons\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}(\mathrm{v})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) $$The combined feed to the reactor contains 53.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{4}, 36.7 \% \mathrm{H}_{2} \mathrm{O}\) and the balance nitrogen, and enters the reactor at \(310^{\circ} \mathrm{C}\). The reactor operates isothermally at \(310^{\circ} \mathrm{C}\). An ethylene conversion of \(5 \%\) is achieved, and the yield of ethanol (moles cthanol produced/mole cthylene consumed) is 0.900 . Data for Diethyl Ether $$\begin{aligned}&\Delta \hat{H}_{f}^{\circ}=-271.2 \mathrm{kJ} / \mathrm{mol} \text { for the liquid }\\\ &\left.\Delta \hat{H}_{v}=26.05 \mathrm{kJ} / \mathrm{mol} \quad \text { (assume independent of } T\right)\end{aligned}$$ $$C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]=0.08945+40.33 \times 10^{-5} T\left(^{\circ} \mathrm{C}\right)-2.244 \times 10^{-7} T^{2}$$ (a) Calculate the reactor heating or cooling requirement in \(\mathrm{kJ} / \mathrm{mol}\) feed. (b) Why would the reactor be designed to yield such a low conversion of ethylene? What processing step (or steps) would probably follow the reactor in a commercial implementation of this process?

Short Answer

Expert verified
(a) The reactor heating or cooling requirement should be calculated according to the steps above, considering the enthalpies of the main and side reactions and the stoichiometry of each reaction. (b) The reactor may be designed to yield such a low conversion of ethylene to limit the production of undesired side product and manage safety or financial concerns. A commercial process could likely include a purification step after the reactor to isolate the desired ethanol product.

Step by step solution

01

Determining chemical reactions

From the problem, there are two reactions taking place: The main reaction is from ethylene and water to produce ethanol \(C_{2}H_{4}(g) + H_{2}O(v) \rightarrow C_{2}H_{5}OH(v)\) and the side reaction is from ethanol to produce diethyl ether \(2C_{2}H_{5}OH(v) \rightarrow {(C_{2}H_{5})}_{2}O(v) + H_{2}O(v)\). For every mole of ethylene consumed, 0.900 moles of ethanol are produced, the remaining 0.100 moles must have reacted to produce diethyl ether.
02

Calculating the enthalpy of reactions

We know that for every mole ethylene used, 0.900 moles of ethanol are produced and 0.100 moles of diethyl ether are produced. Thus, using the given enthalpy data, we can figure out the total enthalpy of reactions. The enthalpy of reaction for the main reaction can be estimated using standard enthalpies of formation from stable forms. The same can be done for the side reaction. As an important detail, care should be taken to use the enthalpy of vaporization for diethyl ether in the side reaction.
03

Calculating the reactor heat

Using the calculated enthalpies of reactions for two reactions, we calculate the total heat or enthalpy change in the reactor per mole of ethylene consumed. As 5% of the incoming ethylene is consumed, we can extrapolate this value to kJ/mol of feed. An important point is to take into consideration that the process is performed at constant temperature, so any heat produced or consumed in the reaction will either have to be added (in case the reaction is endothermic) or removed (if the reaction is exothermic) to keep the temperature steady.
04

Understanding low conversion in a reactor

This is more of a theoretical question, but it essentially brings up concepts of product selectivity and avoiding unwanted side reactions. In this case, a high yield of unnecessary products in unfavorable conditions may be the reason for such a low conversion rate. A probable further step in commercial process may be purification, to extract the required ethanol product while minimizing the side product caused by the side reaction.

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Key Concepts

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

Enthalpy of Reaction
Enthalpy of reaction, often represented as \( \Delta H_{\text{reaction}} \) in chemistry, is a crucial concept when discussing chemical reactions. It defines the total heat content change during a chemical process. When we examine the synthesis of ethanol through the hydrolysis of ethylene, understanding the enthalpy of the main reaction and side reactions is essential.

The enthalpy of the desired ethanol-producing reaction and the undesired diethyl ether-producing side reaction are determined using standard heats of formation and, when applicable, enthalpy of vaporization. These values are critical for engineers to calculate the total energy change within the reactor, which will indicate whether the reactor will require heating or cooling to maintain its isothermal condition. If the reactions are endothermic (absorbing heat), energy must be supplied. Conversely, if they are exothermic (releasing heat), energy must be dissipated.

To accurately calculate the enthalpy of reactions in the synthesis of ethanol, one must take into account not only the standard conditions but also the specific conditions of the reactor, such as temperature and pressure, to make necessary adjustments to the standard enthalpy values.
Reactor Design
In the context of synthesizing industrial ethanol, reactor design plays a crucial role in achieving the desired conversion and selectivity of the desired product. The particular low ethylene conversion of 5% mentioned in the exercise raises the question of why the reactor is designed this way.

A key reason is the trade-off between conversion and selectivity. High conversions often drive the reaction towards more side products, like diethyl ether in this case, which are not desired. A reactor designed to favor higher selectivity towards ethanol at the cost of conversion might be preferable. Additionally, low conversion reactors are often set up in a series to gradually achieve the desired overall conversion while maintaining high selectivity.

Following the chemical reaction, further processing steps such as distillation or separation are common. These processes are designed to purify the ethanol from other substances, like diethyl ether and water. This reactor design approach reflects a careful balance between efficiency, product quality, and overall cost of the process.
Chemical Process Optimization
Chemical process optimization is about improving chemical reaction processes to achieve a set of objectives, such as increasing yield, improving product quality, and reducing energy consumption. It combines principles of chemistry, engineering, and economics.

For the industrial production of ethanol, optimization could focus on adjusting the proportion of reactants, improving catalyst effectiveness, or tweaking reaction conditions, such as temperature and pressure. Optimization considerations include reducing the formation of by-products like diethyl ether, conserving energy, and optimizing the use of feed materials.

Engineers and chemists must work in tandem to adjust variables, potentially using computational models to predict how changes will affect the process before physically implementing them. The exercise of calculating reactor heating or cooling requirements represents a basic form of optimization aimed at maintaining energy efficiency during the isothermal operation of the reactor.

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Most popular questions from this chapter

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.

In the production of many microelectronic devices, continuous chemical vapor deposition (CVD) processes are used to deposit thin and exceptionally uniform silicon dioxide films on silicon wafers. One CVD process involves the reaction between silane and oxygen at a very low pressure. $$\mathrm{SiH}_{4}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g})$$ The feed gas, which contains oxygen and silane in a ratio \(8.00 \mathrm{mol} \mathrm{O}_{2} / \mathrm{mol} \mathrm{SiH}_{4},\) enters the reactor at 298 \(\mathrm{K}\) and 3.00 torr absolute. The reaction products emerge at \(1375 \mathrm{K}\) and 3.00 torr absolute. Essentially all of the silane in the feed is consumed. (a) Taking a basis of \(1 \mathrm{m}^{3}\) of feed gas, calculate the moles of each component of the feed and product mixtures and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the silane oxidation reaction (kJ). Then, taking the feed and product species at \(298 \mathrm{K}\left(25^{\circ} \mathrm{C}\right)\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in the component amounts (mol) and specific enthalpies (kJ/mol). (See Example 9.5-1.) Data $$\left(\Delta \hat{H}_{\mathrm{f}}\right)_{\mathrm{SiH}_{4}(\mathrm{g})}=-61.9 \mathrm{kJ} / \mathrm{mol}, \quad\left(\Delta \hat{H}_{\mathrm{f}}^{\mathrm{o}}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}=-851 \mathrm{kJ} / \mathrm{mol}$$ $$\left(C_{p}\right)_{\mathrm{SiH}_{4}(g)}[\mathrm{k} \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})]=0.01118+12.2 \times 10^{-5} T-5.548 \times 10^{-8} T^{2}+6.84 \times 10^{-12} T^{3}$$ $$\left(C_{p}\right)_{\mathrm{SiO}_{2}(\mathrm{s})}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]=0.04548+3.646 \times 10^{-5} T-1.009 \times 10^{3} / T^{2}$$ The temperatures in the formulas for \(C_{p}\) are in kelvins. (c) Calculate the heat ( \(k\) J) that must be transferred to or from the reactor (state which it is). Then determine the required heat transfer rate ( \(\mathrm{kW}\) ) required for a reactor feed of \(27.5 \mathrm{m}^{3} / \mathrm{h}\).

A gas stream consisting of \(n\) -hexane in methane is fed to a condenser at \(60^{\circ} \mathrm{C}\) and 1.2 atm. The dew point of the gas (considering hexane as the only condensable component) is \(55^{\circ} \mathrm{C}\). The gas is cooled to \(5^{\circ} \mathrm{C}\) in the condenser, recovering pure hexane as a liquid. The effluent gas leaves the condenser saturated with hexane at \(5^{\circ} \mathrm{C}\) and 1.1 atm and is fed to a boiler furnace at a rate of \(207.4 \mathrm{L} / \mathrm{s}\), where it is burned with \(100 \%\) excess air that enters the furnace at \(200^{\circ} \mathrm{C}\). The stack gas emerges at \(400^{\circ} \mathrm{C}\) and 1 atm and contains no carbon monoxide or unburned hydrocarbons. The heat transferred from the furnace is used to generate saturated steam at 10 bar from liquid water at \(25^{\circ} \mathrm{C}\). (a) Calculate the mole fractions of hexane in the condenser feed and product gas streams and the rate of hexane condensation (liters condensate/s). (b) Calculate the rate at which heat must be transferred from the condenser (kW) and the rate of generation of steam in the boiler ( \(\mathrm{kg} / \mathrm{s}\) ).

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).

Methane is burned completely with 40\% excess air. The methane enters the combustion chamber at \(25^{\circ} \mathrm{C},\) the combustion air enters at \(150^{\circ} \mathrm{C},\) and the stack gas \(\left[\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O}(\mathrm{v}), \mathrm{O}_{2}, \mathrm{N}_{2}\right]\) exits at \(450^{\circ} \mathrm{C} .\) The chamber functions as a preheater for an air stream flowing in a pipe through the chamber to a spray dryer. The air enters the chamber at \(25^{\circ} \mathrm{C}\) at a rate of \(1.57 \times 10^{4} \mathrm{m}^{3}(\mathrm{STP}) / \mathrm{h}\) and is heated to \(181^{\circ} \mathrm{C}\). All of the heat generated by combustion is used to heat the combustion products and the air going to the spray dryer (i.e., the combustion chamber may be considered adiabatic). (a) Draw and completely label the process flow diagram and perform a degree- of-freedom analysis. (b) Calculate the required molar flow rates of methane and combustion air (kmol/h) and the volumetric flow rates \(\left(\mathrm{m}^{3} / \mathrm{h}\right)\) of the two effluent streams. State all assumptions you make. (c) When the system goes on line for the first time, environmental monitoring of the stack gas reveals a considerable quantity of CO, suggesting a problem with either the design or the operation of the combustion chamber. What changes from your calculated values would you expect to see in the temperatures and volumetric flow rates of the effluent streams [increase, decrease, cannot tell without doing the calculations]?
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