/*! 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 55 Ammonia scrubbing is one of many... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 55

Ammonia scrubbing is one of many processes for removing sulfur dioxide from flue gases. The gases are bubbled through an aqueous solution of ammonium sulfite, and the SO_reacts to form ammonium bisulfite: $$\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3}(\mathrm{aq})+\mathrm{SO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{NH}_{4} \mathrm{HSO}_{3}(\mathrm{aq})$$ Subsequent process steps yield concentrated SO \(_{2}\) and regenerate ammonium sulfite, which is recycled to the scrubber. The sulfur dioxide is either oxidized and absorbed in water to form sulfuric acid or reduced to elemental sulfur. Flue gas from a power-plant boiler containing \(0.30 \% \mathrm{SO}_{2}\) by volume enters a scrubber at a rate of \(50,000 \mathrm{mol} / \mathrm{h}\) at \(50^{\circ} \mathrm{C} .\) The gas is bubbled through an aqueous solution containing \(10.0 \mathrm{mole} \%\) ammonium sulfite that enters the scrubber at \(25^{\circ} \mathrm{C}\). The gas and liquid effluents from the scrubber both emerge at \(35^{\circ} \mathrm{C}\). The scrubber removes \(90 \%\) of the \(S O_{2}\) entering with the flue gas. The effluent liquid is analyzed and is found to contain 1.5 moles \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3}\) per mole of \(\mathrm{NH}_{4} \mathrm{HSO}_{3}\). The heat of formation of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{3}(\mathrm{aq})\) at \(25^{\circ} \mathrm{C}\) is \(-890.0 \mathrm{kJ} / \mathrm{mol},\) and that of \(\mathrm{NH}_{4} \mathrm{HSO}_{3}(\mathrm{aq})\) is \(-760 \mathrm{kJ} / \mathrm{mol} .\) The heat capacities of all liquid solutions may be taken to be \(4.0 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right)\) and that of the flue gas may be taken to be that of nitrogen. Evaporation of water may be neglected. Calculate the required rate of heat transfer to or from the scrubber ( \(\mathrm{kW}\) ).

Short Answer

Expert verified
The required rate of heat transfer to the scrubber is -23.65 kW. The negative sign shows that heat is being absorbed by the scrubber from its surroundings.

Step by step solution

01

Determine the amount of incoming SO2

First, the amount of sulfur dioxide (SO2) in mols entering the scrubber must be calculated. This can be done by multiplying the given volume rate (50,000 mol/h) with the SO2 percentage (0.30%). Giving, \(SO2_{incoming} = 0.30/100 * 50000 = 150\, mol/h\)
02

Calculate the SO2 removed

Next, calculate the amount of SO2 removed by the scrubber by using the given removal efficiency (90%). This is \(SO2_{removed} = 90/100 * 150 = 135\, mol/h.\)
03

Determine the heat associated with the reaction

The heat absorbed or released in the reaction \(NH4_2SO3 + SO2 + H2O \rightarrow 2NH4HSO3\) can be determined by the difference in heats of formation of the products and the reactants, \(\Delta H = (2 \times -760.0) - (-890.0) = -630\, kJ/mol.\)
04

Determine the total heat transfer

Since 135 mol of SO2 reacts per hour and each reaction absorbs -630 kJ of heat, the total heat transferred due to this reaction is \(\Delta Q_{reaction} = 135 \times -630 = -85150\, kJ/h.\) To change it into kW, divide it by 3600 \(\Rightarrow \Delta Q_{reaction} = -85150/3600 = -23.65\, kW\).

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Key Concepts

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

Chemical Reactions
Chemical reactions are at the heart of ammonia scrubbing as they describe the transformation of reactants into products. In this process, the reaction formula used shows the interaction between ammonium sulfite, sulfur dioxide, and water to yield ammonium bisulfite. The pertinent chemical equation is:

\[(\text{NH}_4)_2 \text{SO}_3(aq) + \text{SO}_2(g) + \text{H}_2\text{O}(l) \rightarrow 2 \text{NH}_4\text{HSO}_3(aq)\]
During this transformation, certain heat changes occur due to different energy requirements of the bonds formed and broken. This is captured as the heat of reaction \( \Delta H \), allowing us to understand how the reaction absorbs or gives off energy. Each mole of this reaction absorbs 630 kJ, a crucial detail in determining the energy balance needed in the scrubber system.
Sulfur Dioxide Removal
Ammonia scrubbing is an efficient technique for sulfur dioxide (SO鈧�) removal from flue gases. This is significant as SO鈧� is a major air pollutant released from fossil-fuel-burning power plants. The process dissolves SO鈧� in a liquid reagent, where chemical reactions transform it into non-gaseous substances, making it easier to isolate and remove.

Key aspects of SO鈧� removal involve:
  • Using a 90% removal efficiency, i.e., removing 90% of SO鈧� entering the scrubber.
  • Reacting with 10% ammonium sulfite solution in the scrubber.
  • Transforming SO鈧� to ammonium bisulfite, which is further processed.
Given a flow rate of 50,000 mol/h of flue gas, an effective removal strategy ensures significant trapping of SO鈧�, which is chemically altered, reducing emissions to the environment.
Heat Transfer Calculation
Heat transfer calculations in the ammonia scrubbing process involve determining the energy change associated with the reaction, along with temperature conditions of incoming and outgoing effluents. Here, precise calculations ensure that the scrubber operates efficiently without energy wastage.

The heat absorbed for the transformation of around 135 mol/h of SO鈧� involves a computation of the reaction enthalpy, resulting in \[ \Delta Q_{reaction} = 135 \times 630 = 85150 \, \text{kJ/h} \]
The conversion to watts simplifies to:
\[\Delta Q_{reaction} \text{ in kW} = \frac{-85150 \, \text{kJ/h}}{3600 \, \text{s/h}} = -23.65 \, \text{kW}\]This step naturally involves heat capacity understanding, ensuring all temperature changes in the system are accounted for, allowing practical adjustments to operating conditions.
Environmental Engineering
Environmental engineering heavily involves processes like ammonia scrubbing to reduce industrial emissions and protect air quality. Using chemical principles to design systems for pollutant removal, it allows conversion of harmful gases like SO鈧� into benign forms.

The focus in such engineering solutions includes:
  • Effectively managing reactant input and waste output.
  • Ensuring a high-efficiency rate (90% in this case) for pollutant removal.
  • Understanding the energy dynamics to optimize scrubbing operations.
These techniques collectively aid in compliance with environmental laws and reduction of acid rain causatives, making industrial operations more sustainable and environmentally conscious.

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Most popular questions from this chapter

In the preliminary design of a furnace for industrial boiler, methane at \(25^{\circ} \mathrm{C}\) is burned completely with \(20 \%\) excess air, also at \(25^{\circ} \mathrm{C} .\) The feed rate of methane is \(450 \mathrm{kmol} / \mathrm{h}\). The hot combustion gases leave the furnace at \(300^{\circ} \mathrm{C}\) and are discharged to the atmosphere. The heat transferred from the furnace \((\dot{Q})\) is used to convert boiler feedwater at \(25^{\circ} \mathrm{C}\) into superheated steam at 17 bar and \(250^{\circ} \mathrm{C}\). (a) Draw and label a flowchart of this process [the chart should look like the one shown in Part (b) without the preheater] and calculate the composition of the gas leaving the furnace. Then, calculate \(\dot{Q}(\mathrm{kJ} / \mathrm{h})\) and the rate of steam production in the boiler \((\mathrm{kg} / \mathrm{h})\). (b) In the actual boiler design, the air feed at \(25^{\circ} \mathrm{C}\) and the combustion gas leaving the furnace at \(300^{\circ} \mathrm{C}\) pass through a heat exchanger (the air preheater). The combustion (flue) gas is cooled to \(150^{\circ} \mathrm{C}\) in the preheater and is then discharged to the atmosphere, and the heated air is fed to the furnace. Calculate the temperature of the air entering the furnace (a computer solution is required) and the rate of steam production (kg/h). (c) Explain why preheating the air increases the rate of steam production. (Suggestion: Use the energy balance on the furnace in your explanation.) Why does it make sense economically to use the combustion gas as the heating medium?

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.

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?

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

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.
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