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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

A gaseous fuel containing methane and ethane is burned with excess air. The fuel enters the furnace at \(25^{\circ} \mathrm{C}\) and 1 atm, and the air enters at \(200^{\circ} \mathrm{C}\) and 1 atm. The stack gas leaves the furnace at \(800^{\circ} \mathrm{C}\) and 1 atm and contains 5.32 mole\% \(\mathrm{CO}_{2}, 1.60 \%\) CO, \(7.32 \%\) O \(_{2}, 12.24 \% \mathrm{H}_{2} \mathrm{O}\), and the balance \(\mathrm{N}_{2}\). (a) Calculate the molar percentages of methane and ethane in the fuel gas and the percentage excess air fed to the reactor. (b) Calculate the heat (kJ) transferred from the reactor per cubic meter of fuel gas fed. (c) A proposal has been made to lower the feed rate of air to the furnace. State advantages and a drawback of doing so.

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.

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.

Biodiesel fuel - a sustainable alternative to petroleum diesel as a transportation fuel- -is produced via the transesterification of triglyceride molecules derived from vegetable oils or animal fats. For every \(9 \mathrm{kg}\) of biodiesel produced in this process, \(1 \mathrm{kg}\) of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is produced as a byproduct. Finding a market for the glycerol is important for biodiesel manufacturing to be economically viable. A process for converting glycerol to the industrially important specialty chemical intermediates acrolein, \(C_{3} \mathrm{H}_{4} \mathrm{O},\) and hydroxyacetone (acetol), \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2},\) has been proposed. $$\begin{array}{l}\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \end{array}$$ The reactions take place in the vapor phase at \(325^{\circ} \mathrm{C}\) in a fixed bed reactor over an acid catalyst. The feed to the reactor is a vapor stream at \(325^{\circ} \mathrm{C}\) containing 25 mol\% glycerol, \(25 \%\) water, and the balance nitrogen. All of the glycerol is consumed in the reactor, and the product stream contains acrolein and hydroxyacctone in a 9: 1 mole ratio. Data for the process species are shown below. $$\begin{array}{|l|c|c|}\hline \text { Species } & \Delta \hat{H}_{\mathrm{f}}(\mathrm{kJ} / \mathrm{mol}) & C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \\ \hline \text { glycerol(v) } & -620 & 0.1745 \\ \hline \text { acrolein(v) } & -65 & 0.0762 \\\\\hline \text { hydroxyacetone(v) } & -372 & 0.1096 \\ \hline \text { water(v) } & -242 & 0.0340 \\\\\hline \text { nitrogen(g) } & 0 & 0.0291 \\ \hline\end{array}$$ (a) Assume a basis of 100 mol fed to the reactor, and draw and completely label a flowchart. Carry out a degree-of-freedom analysis assuming that you will use extents of reaction for the material balances. Then calculate the molar amounts of all product species. (b) Calculate the total heat added or removed from the reactor (state which it is), using the constant heat capacities given in the above table. (c) Assuming this process is implemented along with biodiesel production, how would you determine whether the biodiesel is an cconomically viable alternative to petroleum diesel? (d) If you do a degree-of-freedom analysis based on atomic species balances, you are likely to count one more equation than you have unknowns, and yet you know the system has zero degrees of freedom. Guess what the problem is, and then prove it.

A natural gas containing 82.0 mole \(\% \mathrm{CH}_{4}\) and the balance \(\mathrm{C}_{2} \mathrm{H}_{6}\) is burned with \(20 \%\) excess air in a boiler furnace. The fuel gas enters the furnace at \(298 \mathrm{K}\), and the air is preheated to 423 \(\mathrm{K}\). The heat capacities of the stack-gas components may be assumed to have the following constant values: $$\begin{aligned}\mathrm{CO}_{2}: & C_{p}=50.0 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\ \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): & C_{p}=38.5 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\\\\mathrm{O}_{2}: & C_{p}=33.1 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K}) \\ \mathrm{N}_{2}: & C_{p}=31.3 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})\end{aligned}$$ (a) Assuming complete combustion of the fuel, calculate the adiabatic flame temperature. (b) How would the flame temperature change if the percent excess air were increased? How would it change if the percentage of methane in the fuel increased? Briefly explain both of your answers.
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