/*! 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 14 The production of most of the st... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 14

The production of most of the steel manufactured in the United States begins with the reduction of hematite ore (mostly ferric oxide) with coke (carbon) in a blast furnace to obtain pig iron. The basic reaction is $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}\left(77^{\circ} \mathrm{F}\right)=2.111 \times 10^{5} \mathrm{Btu}$$ Suppose that stoichiometric amounts of ferric oxide and carbon are fed at \(77^{\circ} \mathrm{F}\), the reaction is complete, the iron emerges as a liquid at \(2800^{\circ} \mathrm{F}\), and \(\mathrm{CO}\) emerges at \(570^{\circ} \mathrm{F}\). Perform the following calculations for a basis of 1 ton of iron produced. (a) Draw and label a flowchart and perform all the material balance calculations needed to determine the amounts (lb-mole) of each feed and product stream component. (b) Taking the reactant and product species in their normal states at \(77^{\circ} \mathrm{F}\) as references, prepare an inlet-outlet enthalpy table and calculate and fill in all unknown component specific enthalpies (Btu/lb- mole). Use the following physical property data for iron: \(\mathrm{Fe}(\mathrm{s}): \quad C_{p}\left[\mathrm{B} \operatorname{tu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right)\right]=5.90+1.50 \times 10^{-3} T\left(^{\circ} \mathrm{F}\right)\) \(T_{\mathrm{m}}=2794^{\circ} \mathrm{F}, \quad \Delta \hat{H}_{\mathrm{m}}\left(T_{\mathrm{m}}\right)=6496 \mathrm{Btu} / \mathrm{lb}-\mathrm{mole}\) \(\mathrm{Fe}(\mathrm{l}): \quad C_{p}\left[\mathrm{Btu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right)\right]=8.15\) (c) Estimate the furnace heat requirement (Btu/ton Fe produced). (d) List the assumptions that make the value calculated in Part (c) only an approximate estimate of the furnace heat requirement. (One of the assumptions has something to do with the reactor pressure.)

Short Answer

Expert verified
The amounts required are 17.9 lb-moles of Fe2O3 and 53.7 lb-moles of carbon to produce 35.8 lb-moles of Fe and 53.7 lb-moles of CO. Specific enthalpies are calculated using the given Cp values and enthalpy tables. Finally, the furnace heat requirement is calculated using enthalpy values and reaction heat. The values calculated are approximates due to several inherently assumed conditions in the exercise.

Step by step solution

01

Material Balance Calculation

From the balanced chemical equation, it's clear that for every 2 moles of Fe produced, 1 mole of Fe2O3 is used and 3 moles of C are used. The molar mass of iron is \(55.85 \, lb-mol^{-1}\). Therefore, for 2000 lbs of iron, \(2000/55.85 = 35.8 \, moles\) of iron are produced. As a result, we need \(35.8/2 = 17.9 \, moles\) of Fe2O3 and \(3 \times 17.9 = 53.7 \, moles\) of carbon. The products formed would be \(35.8 \, moles\) of Fe and \(53.7 \, moles\) of CO.
02

Inlet-Outlet Enthalpy Table Preparation

First, calculate the specific enthalpy of Fe at 2800 F using the given heat capacity function and its enthalpy of fusion. Then, calculate the enthalpy of CO at 570 F using enthalpy tables. Then, calculate enthalpies of the reactants at 77 F, again using enthalpy tables. Fill these values into a table listing the enthalpy values for the input and output streams so it can be used for downstream calculations.
03

Furnace Heat Requirement Calculation

For this, the enthalpy of the products (at their final temperatures) is subtracted from the enthalpy of the reactants (at 77 F). To this, the reaction heat given (\(2.111 \times 10^{5} \, Btu\)) is added.
04

Discuss Assumptions

The exercise assumes that all reactions are complete and there's no energy loss to the surroundings. It assumes ideal conditions and doesn't account for the pressure in the furnace, the side reactions that may occur, or changes in physical states beyond what's mentioned.

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Key Concepts

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

Stoichiometry
Stoichiometry is a fundamental concept in chemistry that deals with the calculation of reactants and products in chemical reactions. It is essential to understand stoichiometry for performing material balance calculations, especially when dealing with industrial processes like steel manufacturing. In the provided exercise, stoichiometry helps determine the precise amounts of ferric oxide (Fe2O3) and coke (carbon) needed to produce a specific amount of iron (Fe).

The balanced reaction equation teaches us that 1 mole of ferric oxide reacts with 3 moles of carbon to yield 2 moles of iron and 3 moles of carbon monoxide (CO). By working backwards from the target of producing 2000 pounds of iron, we first convert this weight into moles using iron's molar mass (55.85 lb/mol), resulting in 35.8 moles.
  • Dividing by 2, we find that 17.9 moles of Fe2O3 are required.
  • Multiplying the moles of Fe2O3 required by 3 gives us 53.7 moles of carbon needed.
  • The products formed will match the moles of Fe and CO calculated, satisfying both conservation of mass and stoichiometric proportions.
Mastering stoichiometry is key to ensuring that chemical processes are efficient and economical.
Enthalpy Calculation
Enthalpy calculations are crucial for understanding the energy changes in chemical processes. Enthalpy, denoted as \( \Delta H \), represents the heat content of a chemical system at constant pressure. In the context of the steelmaking process, performing these calculations allows engineers to estimate the energy required to convert reactants to products under specific conditions.

For this exercise, the enthalpy calculations involve creating an inlet-outlet enthalpy table, which records the enthalpies of the reactants and products at different temperatures. The given reaction enthalpy at 77掳F (\(2.111 \times 10^{5} \text{ Btu}\)) applies to the process.
  • Calculate the specific enthalpy of iron at 2800掳F using its heat capacity function and enthalpy of fusion.
  • Similarly, determine the specific enthalpy of carbon monoxide at 570掳F.
  • Document the enthalpies of all components at the reference temperature of 77掳F.
This systematic approach helps to establish the heat balance, laying the groundwork for estimating process energy requirements.
Chemical Reaction Engineering
Chemical reaction engineering focuses on reactor design and operation to optimize the production of desired products while minimizing costs and environmental impact. For the steel production process using a blast furnace, this discipline analyzes how to best utilize reaction kinetics and thermodynamics to achieve complete conversion of reactants into products.

Key considerations involve:
  • Ensuring complete reactions by supplying appropriate amounts of reactants and controlling reaction conditions like temperature and pressure.
  • Utilizing efficient heat exchange methods to manage the temperatures of the iron and carbon monoxide as they exit the furnace.
  • Addressing operational challenges like potential side reactions and energy loss, which could affect the overall efficiency.
By applying principles of chemical reaction engineering, engineers can design systems that improve reaction rates, yield, and energy efficiency, contributing to more sustainable industrial practices.
Thermodynamics
Thermodynamics governs the principles of energy transformation, providing insight into the feasibility and efficiency of chemical processes. In our exercise, thermodynamics helps us understand the energy exchanges necessary for the reduction of hematite ore into pig iron within the blast furnace.

The heat requirement estimation involves accounting for the system's enthalpic changes from the blast furnace's operation. Understanding the reaction's thermodynamics includes:
  • Considering the enthalpy of the reaction and its temperature dependence, which indicates the direction and spontaneity of the reaction.
  • Recognizing the implications of the reaction being exothermic or endothermic, influencing the need for heat input or removal.
  • Factoring the specific heat capacities of substances as their temperatures change, further elucidating the energy exchanges internally.
While thermodynamics offers a macro perspective, detailing energy balance and process limits, it helps refine process control to ensure efficient material transformation and energy utilization, crucial in industrial applications like steel manufacturing.

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Most popular questions from this chapter

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.

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?

A gas mixture containing 85 mole\% methane and the balance oxygen is to be charged into an evacuated well-insulated 20-liter reaction vessel at 25^^ C and 200 kPa. An electrical coil in the reactor, which delivers heat at a rate of 100 watts, will be turned on for 85 seconds and then turned off. Formaldehyde will be produced in the reaction $$\mathrm{CH}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2} \mathrm{O}$$ The reaction products will be cooled and discharged from the reactor. (a) Calculate the maximum pressure that the reactor is likely to have to withstand, assuming that there are no side reactions. If you were ordering the reactor, why would you specify an even greater pressure in your order? (Give several reasons.) (b) Why would heat be added to the feed mixture rather than running the reactor adiabatically? (c) Suppose the reaction is run as planned, the reaction products are analyzed chromatographically, and some \(\mathrm{CO}_{2}\) is found. Where did it come from? If you had taken it into account, would your calculated pressure in Part (a) have been larger, smaller, or can't you tell without doing the detailed calculations?

A coal contains \(73.0 \mathrm{wt} \% \mathrm{C}, 4.7 \% \mathrm{H}\) (not including the hydrogen in the coal moisture), \(3.7 \% \mathrm{S}, 6.8 \% \mathrm{H}_{2} \mathrm{O}\) and \(11.8 \%\) ash. The coal is burned at a rate of \(50,000 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}\) in a power-plant boiler with air \(50 \%\) in excess of that needed to oxidize all the carbon in the coal to \(\mathrm{CO}_{2}\). The air and coal are both fedat \(77^{\circ} \mathrm{F}\) and 1 atm. The solid residue from the furnace is analyzed and is found to contain \(28.7 \mathrm{wt} \% \mathrm{C}, 1.6 \% \mathrm{S},\) and the balance ash. The sulfur oxidized in the furnace is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) Of the ash in the coal, \(30 \%\) emerges in the solid residue and the balance is emitted with the stack gases as fly ash. The stack gas and solid residue emerge from the furnace at \(600^{\circ} \mathrm{F}\). The higher heating value of the coal is \(18,000 \mathrm{Btu} / \mathrm{b}_{\mathrm{m}}\). (a) Calculate the mass flow rates of all components in the stack gas and the volumetric flow rate of this gas. (Tgnore the contribution of the fly ash in the latter calculation, and assume that the stack gas contains a negligible amount of CO.) (b) Assume that the heat capacity of the solid furnace residuc is \(0.22 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right),\) that of the stack gas is the heat capacity per unit mass of nitrogen, and \(35 \%\) of the heat generated in the furnace is used to produce electricity. At what rate in \(\mathrm{MW}\) is electricity produced? (c) Calculate the ratio (heat transferred from the furnace)/(heating value of the fuel). Why is this ratio less than one? (d) Suppose the air fed to the furnace were preheated rather than being fed at ambient temperature, but that everything else (feed rates, outlet temperatures, and fractional coal conversion) were the same. What effect would this change have on the ratio calculated in Part (c)? Explain. Suggest an economical way in which this preheating might be accomplished. Exploratory Exercises - Research and Discover (e) At least three components of the stack gas from the power plant raise significant environmental concerns. Identify the components, explain why they are considered problems, and describe how the problems can be addressed in a modern coal-fired power plant. (f) Several minor constituents of coal were not mentioned in the problem statement, and yet they may be part of the stack gas. Identify one such species and, as in Part (e), explain why it is a problem and how the problem cither is or could be addressed in a modern coal-fired power plant.

Formaldehyde may be produced in the reaction between methanol and oxygen: $$2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{HCHO}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta H_{\mathrm{r}}^{\circ}=-326.2 \mathrm{kJ}$$ The standard heat of combustion of hydrogen is $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta \hat{H}_{\mathrm{c}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}$$ (a) Use these heats of reaction and Hess's law to determine the standard heat of the direct decomposition of mcthanol to form formaldchyde: $$\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l}) \rightarrow \mathrm{HCHO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ (b) Explain why you would probably use the method of Part (a) to determine the heat of the methanol decomposition reaction experimentally rather than carrying out the decomposition reaction and measuring \(\Delta H_{f}^{\circ}\) directly.
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