/*! 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 13 In the production of many microe... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 13

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 \(27.5 \mathrm{m}^{3} / \mathrm{h}\).

Short Answer

Expert verified
The solution of this problem involves a series of calculations. First we find the moles of each component in the feed and product and the extent of reaction. Then, the standard heat of the reaction and enthalpies at reference and final temperatures is calculated. Finally, with these parameters, we calculate the heat transfer and heat transfer rate.

Step by step solution

01

Calculation of Moles in Feed and Product

Given the ratio of \(\mathrm{O}_{2}\) to \(\mathrm{SiH}_{4}\) is 8:1. For 1 cubic meter of feed gas, the number of moles can be calculated as \(n = \frac{P}{RT}\). Here, \(P = 3.00\, \text{torr} = 0.00393\, \text{atm}\), \(R = 0.0821\, \text{atm}\, \text{L/mol}\, \text{K}\), and \(T = 298\, \text{K}\). The total moles is then distributed in the 8:1 ratio for \(\mathrm{O}_{2}\) and \(\mathrm{SiH}_{4}\) respectively. All of \(\mathrm{SiH}_{4}\) is consumed in the reaction, as given. So the change in amount of \(\mathrm{SiH}_{4}\) gives \(\xi\), the extent of reaction.
02

Calculation of Standard Heat and Enthalpy Table

The standard heat of the reaction can be calculated using given enthalpy of formations, \((\Delta H_f)\). Use the equation, \(\Delta H_{rxn} = \sum \Delta H_{f,products} - \sum \Delta H_{f,reactants}\). To prepare the enthalpy table, calculate the change in specific enthalpy from 298 K to 1375 K using the given \(C_p\) equations, first integrating these equations over the temperature range to get enthalpies and then using these enthalpies and the standard heats (if required) to get the final specific enthalpies at 1375 K.
03

Calculation of Heat Transfer

Since the process is at constant pressure, the heat transferred (q) to/from the reactor will be equal to the change of enthalpy for the reaction, \(q=\Delta H_{total} = n_p\Delta H_{p,exit} - n_f\Delta H_{f,entry}\). Here \(n_p\) and \(n_f\) are the total moles in the product and feed, and \(\Delta H_{p,exit}\) and \(\Delta H_{f,entry}\) their respective enthalpies at exit and entry. To find the heat transfer rate, use the given feed rate of 27.5 cubic meters per hour and convert the heat for 1 cubic meter to the heat for 27.5 cubic meters, and then convert it to kW.

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Key Concepts

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

Silane Oxidation Reaction
Understanding the silane oxidation reaction is crucial as it is a fundamental component of the Chemical Vapor Deposition (CVD) process widely used in the production of microelectronic devices. Specifically, this reaction involves the conversion of silane (\text{SiH}_4) and oxygen (\text{O}_2) into silicon dioxide (\text{SiO}_2), a solid, and hydrogen gas (\text{H}_2), as shown by the balanced chemical equation: \[\text{SiH}_4(\text{g}) + \text{O}_2(\text{g}) \rightarrow \text{SiO}_2(\text{s}) + 2 \text{H}_2(\text{g})\]The process typically takes place under very low pressure conditions to ensure the deposition of thin and uniform silicon dioxide films on silicon wafers.

During this reaction, it is crucial that almost all silane is consumed, indicating the reaction goes to completion, making it highly efficient. The actual reaction conditions, such as temperature and pressure (298 K and 3.00 torr absolute, respectively, for feeds), also play a significant role in determining the reaction kinetics.

In practical applications, the correct feed gas ratio and the total pressure determine how much of each reactant is provided for the reaction, and hence, the extent of reaction and purity of the silicon dioxide produced.
Calculation of Moles in Feed and Product
For a thorough grasp of stoichiometry, one must delve into calculating the moles of reactants and products in a chemical reaction. The amount of each substance can be found using the ideal gas law equation \(n = \frac{P}{RT}\)Where \(n\) is the number of moles, \(P\) is the pressure, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. Given the ratio of oxygen to silane and the total pressure of the feed gas entering the reactor, one can distribute the total moles according to the provided molar ratio.

Furthermore, since it is stated that all the silane is used up during the reaction, the moles of silane at the end will be zero, which greatly simplifies calculations for the extent of reaction, denoted as \(\text{尉}\). Deciphering these concepts through an in-depth analysis of the distinct components in both the feed and product mixtures equips students with the knowledge to tackle more complex stoichiometric challenges.
Enthalpy Change and Heat Transfer
Enthalpy change is a central concept in thermochemistry, referring to the heat content in a system at constant pressure. This particular scenario utilizes the silane oxidation reaction's enthalpy change to calculate the heat that must be exchanged within the reactor. Using the equation \(\text{螖}H_{rxn} = \text{危} \text{螖}H_{f,products} - \text{危} \text{螖}H_{f,reactants}\), one can ascertain the standard heat of reaction by utilizing the given enthalpies of formation for the reactants and products.

The next step involves constructing an enthalpy table, considering both the moles and specific enthalpies of the components at different temperatures (298 K for entry and 1375 K for exit). The heat transferred to or from the reactor is fundamentally the difference in total enthalpy between the entry and exit streams, requiring an evaluation of the products' and feed's enthalpies at their respective states.

Finally, calculating the heat transfer rate involves converting the total heat change for the entire feed over a specified time into power units (kilowatts), providing insights into the practical energy requirements for maintaining the CVD process at an industrial scale. This knowledge is not only theoretical but also immensely beneficial for industrial applications, such as semiconductor manufacturing.

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Most popular questions from this chapter

Ethyl alcohol (ethanol) can be produced by the fermentation of sugars derived from agricultural products such as sugarcane and com. Some countries without large petroleum and natural gas reserves - such as Brazil - have found it profitable to convert a portion of their agricultural output to cthanol for fuel or for use as a feedstock in the synthesis of other chemicals. In one such process, a portion of the starch in corn is converted to ethanol in two consecutive reactions. In a saccharification reaction, starch decomposes in the presence of certain enzymes (biological catalysts) to form an aqueous mash containing maltose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right.\), a sugar) and several other decomposition products. The mash is cooled and combined with additional water and a yeast culture in a batch fermentation tank (fermentor). In the fermentation reaction (actually a complex series of reactions), the yeast culture grows and in the process converts maltose to ethanol and carbon dioxide: $$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}+\mathrm{H}_{2} \mathrm{O} \rightarrow 4 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+4 \mathrm{CO}_{2}$$ The fermentor is a 550,000 gallon tank filled to \(90 \%\) of its capacity with a suspension of mash and yeast in water. The mass of the yeast is negligible compared to the total mass of the tank contents. Thermal energy is released by the exothermic conversion of maltose to ethanol. In an adiabatic operating stage, the temperature of the tank contents increases from an initial value of \(85^{\circ} \mathrm{F}\) to \(95^{\circ} \mathrm{F}\), and in a second stage the temperature is kept at \(95^{\circ} \mathrm{F}\) by a reactor cooling system. The final reaction mixture contains carbon dioxide dissolved in a slurry containing 7.1 wt\% ethanol, 6.9 wt\% soluble and suspended solids, and the balance water. The mixture is pumped to a flash evaporator in which \(\mathrm{CO}_{2}\) is vaporized, and the ethanol product is then separated from the remaining mixture components in a series of distillation and stripping operations. Data One bushel ( 56 Ib \(_{m}\) ) of corn yiclds 25 gallons of mash fed to the fermentor, which in turn yields 2.6 gallons of ethanol. Roughly 101 bushels of corn is harvested from an acre of land. A batch fermentation cycle (charging the fermentation tank, running the reaction, discharging the tank, and preparing the tank to receive the next load) takes eight hours. The process operates 24 hours per day, 330 days per year. The specific gravity of the fermentation reaction mixture is approximately constant at \(1.05 .\) The average heat capacity of the mixture is \(0.95 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) The standard heat of combustion of maltose to form \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is \(\Delta H_{\mathrm{c}}^{\mathrm{o}}=-5649 \mathrm{kJ} / \mathrm{mol}\) (a) Calculate (i) the quantity of ethanol ( \(\left(\mathrm{b}_{\mathrm{m}}\right)\) produced per batch, (ii) the quantity of water (gal) that must be added to the mash and yeast in the fermentation tank, and (iii) the acres of land that must be harvested per year to keep the process running. (b) Calculate the standard heat of the maltose conversion reaction, \(\Delta H_{\mathrm{r}}^{\circ}\) (Btu). (c) Estimate the total amount of heat (Btu) that must be transferred from the fermentor during the reaction period. Take only the maltose conversion into account in this calculation (i.c., neglect the yeast growth reaction and any other reactions that may occur in the fermentor), assume that the heat of reaction is independent of temperature in the range from \(77^{\circ} \mathrm{F}\left(=25^{\circ} \mathrm{C}\right)\) to \(95^{\circ} \mathrm{F}\), and neglect the heat of solution of carbon dioxide in water. (d) Although Brazil and Venezuela are neighboring countries, producing ethanol from grain for use as a fuel is an important process in Brazil and an almost nonexistent one in Venezuela. What difference between the two countries probably accounts for this observation?

Use Hess's law to calculate the standard heat of the water-gas shift reaction $$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ from each of the two sets of data given here. (a) \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=+1226 \mathrm{Btu}\) $$\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta \hat{H}_{\mathrm{v}}=+18,935 \mathrm{Btu} / \mathrm{lb}-\mathrm{mole}$$ $$\begin{aligned}&\text { (b) } \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=-121,740 \mathrm{Btu}\\\&\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta H_{\mathrm{r}}^{\circ}=-104,040 \mathrm{Btu} \end{aligned}$$

Lime (calcium oxide) is widely used in the production of cement, steel, medicines, insecticides, plant and animal food, soap, rubber, and many other familiar materials. It is usually produced by heating and decomposing limestone (CaCO \(_{3}\) ), a cheap and abundant mineral, in a calcination process: $$\mathrm{CaCO}_{3}(\mathrm{s}) \stackrel{\text { heat }}{\longrightarrow} \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$ (a) Limestone at \(25^{\circ} \mathrm{C}\) is fed to a continuous calcination reactor. The calcination is complete, and the products leave at \(900^{\circ} \mathrm{C}\). Taking 1 metric ton \((1000 \mathrm{kg})\) of limestone as a basis and clemental species \(\left[\mathrm{Ca}(\mathrm{s}), \mathrm{C}(\mathrm{s}), \mathrm{O}_{2}(\mathrm{g})\right]\) at \(25^{\circ} \mathrm{C}\) as references for enthalpy calculations, prepare and fill in an inlet-outlet enthalpy table and prove that the required heat transfer to the reactor is \(2.7 \times 10^{6} \mathrm{kJ}\) (b) In a common variation of this process, hot combustion gases containing oxygen and carbon monoxide (among other components) are fed into the calcination reactor along with the limestone. The carbon monoxide is oxidized in the reaction $$\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})$$ Suppose the combustion gas fed to a calcination reactor contains 75 mole \(\% \mathrm{N}_{2}, 2.0 \% \mathrm{O}_{2}, 9.0 \% \mathrm{CO},\) and \(14 \% \mathrm{CO}_{2}\) the gas enters the reactor at \(900^{\circ} \mathrm{C}\) in a feed ratio of \(20 \mathrm{kmol}\) gas/kmol limestone; the calcination is complete; all of the oxygen in the gas feed is consumed in the CO oxidation reaction; the reactor effluents are at \(900^{\circ} \mathrm{C}\) Again taking a basis of 1 metric ton of limestone calcined, prepare and fill in an inlet-outlet enthalpy table for this process [don't recalculate enthalpies already calculated in Part (a)] and calculate the required heat transfer to the reactor. (c) You should have found that the heat that must be transferred to the reactor is significantly lower with the combustion gas in the feed than it is without the gas. By what percentage is the heat requirement reduced? Give two reasons for the reduction. State another benefit of feeding the combustion gas, besides the reduction of the heating requirement.

Ethylbenzene is converted to styrene in the catalytic dehydrogenation reaction $$\mathrm{C}_{8} \mathrm{H}_{10}(\mathrm{g}) \rightarrow \mathrm{C}_{8} \mathrm{H}_{8}(\mathrm{g})+\mathrm{H}_{2}: \quad \Delta H_{\mathrm{r}}^{\circ}\left(600^{\circ} \mathrm{C}\right)=+124.5 \mathrm{kJ}$$ A flowchart of a simplified version of the commercial process is shown here. Fresh and recycled liquid ethylbenzene combine and are heated from \(25^{\circ} \mathrm{C}\) to \(500^{\circ} \mathrm{C} \mathrm{C}\) ? and the heated ethylbenzene is mixed adiabatically with steam at \(700^{\circ} \mathrm{C}\) ? to produce the feed to the reactor at \(600^{\circ} \mathrm{C}\) (The steam suppresses undesired side reactions and removes carbon deposited on the catalyst surface.) A once-through conversion of \(35 \%\) is achieved in the reactor ? and the products emerge at \(560^{\circ} \mathrm{C}\).The product stream is cooled to \(25^{\circ} \mathrm{C}\) ? condensing essentially all of the water, ethylbenzene, and styrene and allowing hydrogen to pass out as a recoverable by-product of the process. The water and hydrocarbon liquids are immiscible and are separated in a settling tank decanter ? The water is vaporized and heated ? to produce the steam that mixes with the cthylbenzene feed to the reactor. The hydrocarbon stream leaving the decanter is fed to a distillation tower ? (actually, a seriesof towers), which separates the mixture into essentially pure styrene and ethylbenzene, each at \(25^{\circ} \mathrm{C}\) after cooling and condensation steps have been carried out. The ethylbenzene is recycled to the reactor preheater, and the styrene is taken off as a product. (a) On a basis of \(100 \mathrm{kg} / \mathrm{h}\) styrene produced, calculate the required fresh ethylbenzene feed rate, the flow rate of recycled ethylbenzene, and the circulation rate of water, all in mol/h. (Assume \(P=1\) atm.) (b) Calculate the required rates of heat input or withdrawal in \(\mathrm{kJ} / \mathrm{h}\) for the ethylbenzene preheater ? steam generator ? ind reactor ? (c) Suggest possible ways to improve the energy economy of this process.

Various uses for nitric acid are given in Problem \(6.43,\) along with information about how this important chemical is synthesized industrially. The key reactions are oxidations of ammonia to nitric oxide and of nitric oxide to nitrogen dioxide, followed by dissolution of \(\mathrm{NO}_{2}\) in water: $$\begin{aligned} 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) & \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \\ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) & \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \\ 3 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1) & \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g}) \end{aligned}$$ Nitric oxide generated on dissolution of \(\mathrm{NO}_{2}\) in water is oxidized to produce additional \(\mathrm{NO}_{2},\) which is then combined with water to form more \(\mathrm{HNO}_{3}\). In this problem we neglect side reactions that would lower the product yield. Ammonia vapor at \(275^{\circ} \mathrm{C}\) and 8 atm is mixed with air, also at \(275^{\circ} \mathrm{C}\) and 8 atm, and the combined stream is fed to a converter. Fresh air entering the system at \(30^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(50 \%\) is compressed to \(100^{\circ} \mathrm{C}\) and 8 atm, and the compressed air then exchanges heat with the product gas leaving the converter. The quantity of oxygen in the feed to the converter is \(20 \%\) in excess of the amount theoretically required to convert all of the ammonia to \(\mathrm{HNO}_{3}\). The entire process after the compressor may be taken to operate at a constant pressure of 8 atm. In the converter, the ammonia is completely oxidized, with a negligible amount of \(\mathrm{NO}_{2}\) formed. The product gas leaves the converter at \(850^{\circ} \mathrm{C}\), and, as described in the preceding paragraph, exchanges heat with the air entering the system. The product gas then is fed to a waste-heat boiler that produces superheated steam at \(200^{\circ} \mathrm{C}\) and 10 bar from liquid water at \(35^{\circ} \mathrm{C}\). The product gas leaving the wasteheat boiler is cooled further to \(35^{\circ} \mathrm{C}\) and fed to an absorption column in which the NO is completely oxidized to \(\mathrm{NO}_{2},\) which in turn combines with water (some of which is present in the product gas). Water is fed to the absorber at \(25^{\circ} \mathrm{C},\) at a rate sufficient to form a 55 wt\% aqueous nitric acid solution. The NO formed in the reaction of \(\mathrm{NO}_{2}\) to produce \(\mathrm{HNO}_{3}\) is oxidized, and the NO \(_{2}\) produced is hydrated to form still more \(\mathrm{HNO}_{3}\). The off-gas from the process may be taken to contain only \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) (a) Construct a flowchart showing all process streams, including input and output from the process and the following equipment: converter, air compressor, exchanger recovering heat from the converter product, waste-heat boiler producing superheated steam, exchanger cooling the product gas before it is fed to the absorber, and absorber. (b) Taking a basis of \(100 \mathrm{kmol}\) of ammonia fed to the process, develop spreadsheets (preferably incorporating the use of APEx) to determine the following: (i) Molar amounts (kmol) of oxygen, nitrogen, and water vapor in the air fed to the process, cubic meters of air fed to the process, and kmol of water fed to the absorber. (ii) Molar amounts, molar composition, and volume of the off-gas leaving the absorber. (iii) Mass (kg) of product nitric acid solution. (iv) Molar amounts and composition of the gas leaving the converter. (v) Heat removed from or added to (state which) the converter. (vi) Temperature of the product gas after it has exchanged heat with the air, assuming no heat is transferred between the heat exchanger and the surroundings. (vii) Production rate of superheated steam if the gas temperature leaving the boiler is \(205^{\circ} \mathrm{C}\). Before performing this calculation, determine if condensation of water occurs when the gas is cooled to \(205^{\circ} \mathrm{C}\). Since the superheated steam temperature is \(200^{\circ} \mathrm{C}\), explain why the selected temperature of the product gas is reasonable. (viii) Heat removed from the product gas before it is fed to the absorber (Hint: Check the condition of the gas at \(35^{\circ} \mathrm{C}\) ) and mass of cooling water required to remove that heat if the water temperature can only be increased by \(5^{\circ} \mathrm{C}\). Assume no heat is transferred between the heat exchanger and the surroundings. (ix) Heat removed from or added to the absorber. Assume the heat capacity of the nitric acid solution is approximately the same as that of liquid water and the outlet temperatures of the off-gas and product streams are \(25^{\circ} \mathrm{C}\) and \(35^{\circ} \mathrm{C}\), respectively. (c) Scale up the results calculated in Part (b) to determine all stream flow rates and heat transfer rates for a production rate of \(5.0 \times 10^{3} \mathrm{kg} / \mathrm{h}\) of the product solution.
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