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Chapter 5: Problem 61

Most of the concrete used in the construction of buildings, roads, dams, and bridges is made from Portland cement, a substance obtained by pulverizing the hard, granular residue (clinker) from the roasting of a mixture of clay and limestone and adding other materials to modify the setting properties of the cement and the mechanical properties of the concrete. The charge to a Portland cement rotary kiln contains \(17 \%\) of a dried building clay \(\left(72 \mathrm{wt} \% \mathrm{SiO}_{2}\right.\) \(\left.16 \% \mathrm{Al}_{2} \mathrm{O}_{3}, 7 \% \mathrm{Fe}_{2} \mathrm{O}_{3}, 1.7 \% \mathrm{K}_{2} \mathrm{O}, 3.3 \% \mathrm{Na}_{2} \mathrm{O}\right)\) and \(83 \%\) limestone \(\left(95 \mathrm{wt} \% \mathrm{CaCO}_{3}, 5 \% \text { impuritics }\right)\) When the solid temperature reaches about \(900^{\circ} \mathrm{C},\) calcination of the limestone to lime (CaO) and carbon dioxide occurs. As the temperature continues to rise to about \(1450^{\circ} \mathrm{C},\) the lime reacts with the minerals in the clay to form such compounds as \(3 \mathrm{CaO} \cdot \mathrm{SiO}_{2}, 3 \mathrm{CaO} \cdot \mathrm{Al}_{2} \mathrm{O}_{3},\) and \(4 \mathrm{CaO} \cdot \mathrm{Al}_{2} \mathrm{O}_{3} \cdot \mathrm{Fe}_{2} \mathrm{O}_{3} .\) The flow rate of \(\mathrm{CO}_{2}\) from the kiln is \(1350 \mathrm{m}^{3} / \mathrm{h}\) at \(1000^{\circ} \mathrm{C}\) and 1 atm. Calculate the feed rates of clay and limestone ( \(\mathrm{kg} / \mathrm{h}\) ) and the weight percent of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the final cement.

Short Answer

Expert verified
To calculate the feed rates of clay and limestone, one needs to break down the given weight percentages, calculate the feed rate of limestone from CO2 emission using stoichiometric principle, and then use this feed rate to calculate feed rate of clay. For calculating the weight percent of Fe2O3, one needs the mass contribution of Fe2O3 in the total mass.

Step by step solution

01

Derive expressions for the mass percentages

Calculate the mass percentages of the constituting elements from the given weight percentages. Mathematically, these can be given as follows assuming 'm' as the total mass of feed: mass of SiO2 = 0.17 * 0.72 * m, mass of Al2O3 = 0.17 * 0.16 * m, mass of Fe2O3 = 0.17 * 0.07 * m, and mass of CaCO3 = 0.83 * 0.95 * m.
02

Use CO2 emission to calculate feed rate

We have been given that CO2 is emitted at 1350 m3/hr at 1000 degrees Celsius and 1 atm. Considering the ideal gas law, this amounts to 1350 mol/hr of CO2. Given that CaCO3 -> CaO + CO2, stoichiometrically 1 mol of CaCO3 gives 1 mol of CO2. Hence from the given CO2 emission rate, the rate of usage or feed of CaCO3 = 1350 mol/hr. This can now be converted to kg/hr using molecular weights. Calculating these would yield the feed rate of limestone (which is mostly CaCO3).
03

Calculate the feed rate of clay

From the feed rate of limestone calculated in Step 2, we can now calculate the feed rate of clay. As per the given mix, clay is 17% by weight. Therefore feed rate of clay = 0.17 / 0.83 times the feed rate of limestone calculated in last step. This would yield the desired feed rate of clay in kg/hr.
04

Determine the weight percent of Fe2O3

From the calculations in Step 1, we know the mass contribution of Fe2O3 in the feed. Taking the ratio of this mass to the total feed mass would yield the weight percent of Fe2O3 in the final cement. This ratio needs to be expressed as a percentage.

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Key Concepts

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

Portland Cement Composition
Portland cement is the principal ingredient in concrete, which is essential in constructing infrastructure like buildings, roads, and bridges. Its composition is a finely tuned mixture resulting from the pulverization of clinker鈥攁 product of calcining a blend of clay and limestone鈥攁t high temperatures. To tailor the cement's setting time and enhance the mechanical properties of concrete, additional materials can be added to the clinker base during the manufacturing process.

The composition of Portland cement typically includes a combination of calcium silicates, calcium aluminates, and calcium aluminoferrites, which are chemical compounds that impart strength and setting characteristics. These compounds are created through a high-temperature reaction between limestone, which predominantly consists of calcium carbonate (CaCO鈧�), and clay containing silica (SiO鈧�), alumina (Al鈧侽鈧�), iron oxide (Fe鈧侽鈧�), and other minor constituents. It's essential for students to understand that the composition of clay and limestone in the cement manufacturing process is crucial, as it defines the final properties of the Portland cement.
Calcination Process
Calcination is a thermal treatment process in chemical engineering and material sciences that involves heating a substance to a high temperature but below its melting point, to bring about thermal decomposition or phase transition. In the production of Portland cement, calcination occurs when limestone, composed primarily of CaCO鈧�, is heated. At around 900掳C, the limestone decomposes into lime (CaO) and carbon dioxide (CO鈧�).

The importance of understanding the calcination process lies in the changes that occur to the raw materials: it's the heart of cement chemistry. As CaCO鈧� decomposes to CaO, it subsequently reacts with the minerals in the clay to form compounds like tricalcium silicate (3 CaO路SiO鈧�) and dicalcium silicate (2 CaO路SiO鈧�), which are responsible for the eventual hardening of cement. Cement engineers must control the rate of calcination and temperature to ensure that the final product possesses the desired physical and chemical properties.
Stoichiometry Calculations
Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions. In the context of chemical engineering and specifically Portland cement production, using stoichiometric calculations is essential to determine the correct proportions of raw materials needed for the reaction. These calculations ensure that the materials react completely without any excess or shortfall.

When applied to Portland cement production, stoichiometry allows predicting and controlling the quantities of clay and limestone to be fed into the kiln. Based on the exercise provided, using stoichiometric principles, you can determine the amount of limestone decomposing to produce a given volume of CO鈧�. This is calculated using the ideal gas law and the molar mass of CaCO鈧�. Subsequently, the feed rate of clay is deduced from its percentage in the initial mixture with limestone. Proper comprehension of stoichiometry is vital for students not only for solving textbook exercises but also for applying similar calculations in real-world cement production scenarios.

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Most popular questions from this chapter

The oxidation of nitric oxide $$\mathrm{NO}+\frac{1}{2} \mathrm{O}_{2} \rightleftharpoons \mathrm{NO}_{2}$$ takes place in an isothermal batch reactor. The reactor is charged with a mixture containing 20.0 volume percent NO and the balance air at an initial pressure of \(380 \mathrm{kPa}\) (absolute). (a) Assuming ideal-gas behavior, determine the composition of the mixture (component mole fractions) and the final pressure (kPa) if the conversion of NO is 90\%. (b) Suppose the pressure in the reactor eventually equilibrates (levels out) at \(360 \mathrm{kPa}\). What is the equilibrium percent conversion of NO? Calculate the reaction equilibrium constant at the prevailing temperature, \(K_{p}\left[(\mathrm{atm})^{-0.5}\right]\), defined as $$K_{p}=\frac{\left(p_{\mathrm{NO}_{2}}\right)}{\left(p_{\mathrm{NO}}\right)\left(p_{\mathrm{O}_{2}}\right)^{0.5}}$$ where \(p_{i}(\mathrm{atm})\) is the partial pressure of species \(i\left(\mathrm{NO}_{2}, \mathrm{NO}, \mathrm{O}_{2}\right)\) at equilibrium. (c) Assuming that \(K_{\mathrm{p}}\) depends only on temperature, estimate the final pressure and composition in the reactor if the feed ratio of NO to \(\mathrm{O}_{2}\) and the initial pressure are the same as in \(\operatorname{Part}(\) a), but the feed to the reactor is pure \(\mathrm{O}_{2}\) instead of air. (d) Replace the partial pressures in the expression for \(K_{\mathrm{p}}\), and use the result to explain how reactor pressure influences the conversion of NO to \(\mathrm{NO}_{2}\)

During your summer vacation, you plan an epic adventure trip to scale Mt. Kilimanjaro in Tanzania. Dehydration is a great danger on such a climb, and it is essential to drink enough water to make up for the amount you lose by breathing. (a) During your pre-trip physical, your physician measured the average flow rate and composition of the gas you exhaled (expired air) while performing light activity. The results were \(11.36 \mathrm{L} / \mathrm{min}\) at body temperature (37^) C) and 1 atm, 17.08 mole\% oxygen, 3.25\% carbon dioxide, 6.12 mole\% \(\mathrm{H}_{2} \mathrm{O},\) and the balance nitrogen. The ambient (inspired) air contained 1.67 mole\% water and a negligible amount of carbon dioxide. Calculate the rate of mass lost through the breathing process (kg/day) and the volume of water in liters you would have to drink per day just to replace the water lost in respiration. Consider your lungs to be a continuous steady-state system, with input streams being inspired air and water and \(\mathrm{CO}_{2}\) transferred from the blood and output streams being expired air and \(\mathrm{O}_{2}\) transferred to the blood. Assume no nitrogen is transferred to or from the blood. (b) You made the trip to Tanzania and completed the climb to Uhuru Peak, the summit of Kilimanjaro, at an altitude of 5895 meters above sea level. The ambient temperature and pressure there averaged \(-9.4^{\circ} \mathrm{C}\) and \(360 \mathrm{mm} \mathrm{Hg},\) and the air contained \(0.46 \mathrm{mole} \%\) water. The molar flow rate of your expired air was roughly the same as it had been at sea level, and the expired air contained \(14.86 \% \mathrm{O}_{2}\) \(3.80 \% \mathrm{CO}_{2},\) and \(13.20 \% \mathrm{H}_{2} \mathrm{O} .\) Calculate the rate of mass lost (g/day) through breathing and water you would have to drink (L/day) just to replace the water lost in respiration. (c) The equality of the molar flow rates of expired air at sea level and at Uhuru Peak is due to a cancellation of effects, one of which would tend to increase the rate at higher altitudes and the other to decrease it. What are those effects? (Hint: Use the ideal-gas equation of state in your solution, and think about how the oxygen concentration at a high altitude would likely affect your breathing rate.)

A fuel cell is an electrochemical device that reacts hydrogen with oxygen from the air to produce water and DC electricity. A proposed application is replacement of the gasoline-fueled internal combustion engine in an automobile with a \(100 \mathrm{kW}\) fuel cell. You are on a summer internship with a gas supplier planning to transport hydrogen to service stations for use in cars powered by fuel cells. The hydrogen is to be transported in tube trailers, each of which has 10 tubes of length \(10.5 \mathrm{m}\) and diameter \(0.56 \mathrm{m}\). Hydrogen in the tubes at 2600 psig and an average temperature of \(298 \mathrm{K}\) is discharged at service stations to a final pressure of 55 psig. Refueling cach fuel-cell-powered automobile is estimated to require 4.0 kg of hydrogen. (a) You and your office-mate- an intern from a different university - have been asked to estimate the number of automobiles that can be refueled by one tube-trailer load of hydrogen. He does a very quick calculation and comes up with a value of 95 cars. Speculate how he did it and provide support for your speculation. What was his mistake? (b) Do the calculation using the SRK equation of state. Instead of using Eqs. \(5.3-11\) and \(5.3-13\) for the parameter \(\alpha,\) use the following correlation developed specifically for hydrogen: \(^{23}\) \(\alpha=1.202 \exp \left(-0.3228 T_{\mathrm{r}}\right)\) (c) Do the calculation using the law of corresponding states. (d) In which of the three estimates would you have the greatest confidence, and why?

Terephthalic acid (TPA), a raw material in the manufacture of polyester fiber, film, and soft drink bottles, is synthesized from \(p\) -xylene (PX) in the process shown below. A fresh feed of pure liquid \(\mathrm{PX}\) combines with a recycle stream containing \(\mathrm{PX}\) and a solution (S) of a catalyst (a cobalt salt) in a solvent (methanol). The combined stream, which contains \(S\) and \(P X\) in a 3: 1 mass ratio, is fed to a reactor in which \(90 \%\) of the \(\mathrm{PX}\) is converted to TPA. A stream of air at \(25^{\circ} \mathrm{C}\) and 6.0 atm absolute is also fed to the reactor. The air bubbles through the liquid and the reaction given above takes place under the influence of the catalyst. A liquid stream containing unreacted \(\mathrm{PX}\), dissolved TPA, and all the S that entered the reactor goes to a separator in which solid TPA crystals are formed and filtered out of the solution. The filtrate, which contains all the \(S\) and \(P X\) leaving the reactor, is the recycle stream. A gas stream containing unreacted oxygen, nitrogen, and the water formed in the reaction leaves the reactor at \(105^{\circ} \mathrm{C}\) and 5.5 atm absolute and goes through a condenser in which essentially all the water is condensed. The uncondensed gas contains 4.0 mole \(\%\) O. (a) Taking \(100 \mathrm{kmol}\) TPA produced/h as a basis of calculation, draw and label a flowchart for the process. (b) What is the required fresh feed rate (kmol PX/h)? (c) What are the volumetric flow rates \(\left(\mathrm{m}^{3} / \mathrm{h}\right)\) of the air fed to the reactor, the gas leaving the reactor, and the liquid water leaving the condenser? Assume ideal-gas behavior for the two gas streams. (d) What is the mass flow rate ( \(\mathrm{kg} / \mathrm{h}\) ) of the recycle stream? (e) Briefly explain in your own words the functions of the oxygen, nitrogen, catalyst, and solvent in the process. (f) In the actual process, the liquid condensate stream contains both water and PX. Speculate on what might be done with the latter stream to improve the economics of the process. [Hint: Note that PX is expensive, and recall what is said about oil (hydrocarbons) and water.]

Lewis \(^{12}\) describes the hazards of breathing air containing appreciable amounts of an asphyxiant (a gas that has no specific toxicity but, when inhaled, excludes oxygen from the lungs). When the mole percent of the asphyxiant in the air reaches \(50 \%,\) marked symptoms of distress appear, and at \(75 \%\) death occurs in a matter of minutes. A small storage room whose dimensions are \(2 \mathrm{m} \times 1.5 \mathrm{m} \times 3 \mathrm{m}\) contains a number of expensive and dangerous chemicals. To prevent unauthorized entry, the door to the room is always locked and can be opened with a key from either side. A cylinder of liquid carbon dioxide is stored in the room. The valve on the cylinder is faulty and some of the contents have escaped over the weekend. The room temperature is \(25^{\circ} \mathrm{C}\). (a) If the concentration of \(\mathrm{CO}_{2}\) reaches the lethal 75 mole \(\%\) level, what would be the mole percent of \(\mathrm{O}_{2} ?\) (b) How much \(\mathrm{CO}_{2}(\mathrm{kg})\) is present in the room when the lethal concentration is reached? Why would more than that amount have to escape from the cylinder for this concentration to be reached? (c) Describe a set of events that could result in a fatality in the given situation. Suggest at least two measures that would reduce the hazards associated with storage of this scemingly harmless substance.
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