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Chapter 4: Problem 59

Titanium dioxide \(\left(\mathrm{Ti} \mathrm{O}_{2}\right)\) is used extensively as a white pigment. It is produced from an ore that contains ilmenite \(\left(\mathrm{FeTiO}_{3}\right)\) and ferric oxide \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right) .\) The ore is digested with an aqueous sulfuric acid solution to produce an aqueous solution of titanyl sulfate \(\left[(\mathrm{TiO}) \mathrm{SO}_{4}\right]\) and ferrous sulfate (FeSO \(_{4}\) ). Water is added to hydrolyze the titanyl sulfate to \(\mathrm{H}_{2} \mathrm{TiO}_{3},\) which precipitates, and \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) The precipitate is then roasted, driving off water and leaving a residue of pure titanium dioxide. (Several steps to remove iron from the intermediate solutions as iron sulfate have been omitted from this description.) Suppose an ore containing \(24.3 \%\) Ti by mass is digested with an \(80 \% \mathrm{H}_{2} \mathrm{SO}_{4}\) solution, supplied in \(50 \%\) excess of the amount needed to convert all the ilmenite to titanyl sulfate and all the ferric oxide to ferric sulfate \(\left[\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\right] .\) Further suppose that \(89 \%\) of the ilmenite actually decomposes. Calculate the masses (kg) of ore and 80\% sulfuric acid solution that must be fed to produce \(1000 \mathrm{kg}\) of pure \(\mathrm{TiO}_{2}\)

Short Answer

Expert verified
To produce 1000 kg of \(TiO_{2}\), you need approximately 4625 kg of ore and 8661 kg of 80% sulfuric acid solution.

Step by step solution

01

Calculate the mass of \(\mathrm{TiO}_{2}\) obtained from ilmenite

We're given that the ore is composed of 24.3% Ti by mass and there is 89% decomposition of ilmenite. So, the mass of \(\mathrm{TiO}_{2}\) obtained from 100% decomposition is \(0.243 \times 1000 = 243 \mathrm{kg}\). However, since only 89% decomposes, the actual yield of \(\mathrm{TiO}_{2}\) would be \(0.89 \times 243 = 216.27 \mathrm{kg}\).
02

Determine the mass of ore

To get 1000 kg of \(\mathrm{TiO}_{2}\), the required ore is calculated as \( \frac{1000 \mathrm{kg}}{216.27 \mathrm{kg}} \times 1000 \mathrm{kg} = 4624.57 \mathrm{kg}\). So, the amount of ore needed is approximately 4625 kg.
03

Determine the mass of sulfuric acid

Given the sulfuric acid solution is supplied in 50% excess of the amount needed, the amount of 80% sulfuric acid solution required is calculated as \( \frac{4624.57 \mathrm{kg}}{0.8} \times 1.5 = 8661.06 \mathrm{kg}\). So, approximately 8661 kg of 80% sulfuric acid solution is needed.
04

Conclusion

Therefore, to produce 1000 kg of titanium dioxide, approximately 4625 kg of the ore and 8661 kg of 80% sulfuric acid solution would need to be used.

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Key Concepts

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

Titanium Dioxide Production
Titanium dioxide, known by its chemical symbol \(\mathrm{TiO}_2\), is a versatile compound used in products ranging from paint to sunscreen. Its brilliance and opacity make it a sought-after white pigment. This compound is primarily produced through processes involving ilmenite \(\left(\mathrm{FeTiO}_3\right)\) and ferric oxide \(\left(\mathrm{Fe}_2\mathrm{O}_3\right)\).
The process begins with digesting the ore in an acid, producing titanyl sulfate \(\left((\mathrm{TiO}) \mathrm{SO}_4\right)\) and ferrous sulfate (\(\mathrm{FeSO}_4\)). Water is then introduced to trigger the hydrolysis of titanyl sulfate, forming a titanium hydroxide precipitate \(\mathrm{H}_2\mathrm{TiO}_3\), which is later turned into \(\mathrm{TiO}_2\) upon roasting. By removing excess water, pure titanium dioxide is obtained. Understanding this chain of chemical reactions is vital for efficient \(\mathrm{TiO}_2\) production.
This elaborative process ensures purity while maintaining the essential properties that make titanium dioxide a valuable industrial compound.
Stoichiometry
Stoichiometry is fundamental in chemical engineering and is especially crucial in calculating the quantities needed and produced in reactions. In our context, it involves determining how much ore and sulfuric acid is required to yield a target quantity of titanium dioxide.
In the problem, stoichiometry is applied by accounting for decomposition percentages and purity constraints. Approximately 24.3% of the ore consists of titanium, and out of this, 89% actually decomposes. Hence, for a 1000 kg target of \(\mathrm{TiO}_2\), the stoichiometric calculations reveal how to scale up the input of raw materials.
Such precise calculations prevent excess waste, ensuring resources are efficiently used without compromising the production targets.
Material Balance
Material balance or mass balance is a key principle in process engineering. It is the concept of balancing inputs and outputs in chemical reactions and unit operations. The main idea is what enters a process must either come out or accumulate within it.
In this exercise, we address material balance by calculating both the ore and the sulfuric acid required to achieve the desired output of 1000 kg of \(\mathrm{TiO}_2\).
Using principles of conservation, we estimate that 4625 kg of ore and 8661 kg of sulfuric acid are necessary to meet this output. By assuming a 50% excess of the acid, the calculations ensure all reactants fully participate in forming products, illustrating sound material management in chemical processes.

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Most popular questions from this chapter

L-Serine is an amino acid that often is provided when intravenous feeding solutions are used to maintain the health of a patient. It has a molecular weight of \(105,\) is produced by fermentation and recovered and purified by crystallization at \(10^{\circ} \mathrm{C}\). Yield is enhanced by adding methanol to the system, thereby reducing serine solubility in aqueous solutions. An aqueous serine solution containing 30 wt\% serine and \(70 \%\) water is added along with methanol to a batch crystallizer that is allowed to equilibrate at \(10^{\circ} \mathrm{C}\). The resulting crystals are recovered by filtration; liquid passing through the filter is known as filtrate, and the recovered crystals may be assumed in this problem to be free of adhering filtrate. The crystals contain a mole of water for every mole of serine and are known as a monohydrate. The crystal mass recovered in a particular laboratory run is \(500 \mathrm{g},\) and the filtrate is determined to be \(2.4 \mathrm{wt} \%\) serine, \(48.8 \%\) water, and \(48.8 \%\) methanol. (a) Draw and label a flowchart for the operation and carry out a degree-of- freedom analysis. Determine the ratio of mass of methanol added per unit mass of feed. (b) The laboratory process is to be scaled to produce \(750 \mathrm{kg} / \mathrm{h}\) of product crystals. Determine the required aqueous serine solution rates of aqueous serine solution and methanol.

Inside a distillation column (see Problem 4.8), a downward-flowing liquid and an upward-flowing vapor maintain contact with each other. For reasons we will discuss in greater detail in Chapter \(6,\) the vapor stream becomes increasingly rich in the more volatile components of the mixture as it moves up the column, and the liquid stream is enriched in the less volatile components as it moves down. The vapor leaving the top of the column goes to a condenser. A portion of the condensate is taken off as a product (the overhead product), and the remainder (the reflux) is returned to the top of the column to begin its downward journey as the liquid stream. The condensation process can be represented as shown below: A distillation column is being used to separate a liquid mixture of ethanol (more volatile) and water (less volatile). A vapor mixture containing 89.0 mole \(\%\) ethanol and the balance water enters the overhead condenser at a rate of \(100 \mathrm{lb}\) -mole/h. The liquid condensate has a density of \(49.01 \mathrm{b}_{\mathrm{m}} / \mathrm{ft}^{3},\) and the reflux ratio is \(3 \mathrm{lb}_{\mathrm{m}}\) reflux/lb \(_{\mathrm{m}}\) overhead product. When the system is operating at steady state, the tank collecting the condensate is half full of liquid and the mean residence time in the tank (volume of liquid/volumetric flow rate of liquid) is 10.0 minutes. Determine the overhead product volumetric flow rate (ft \(^{3}\) /min) and the condenser tank volume (gal).

Under the FutureGen 2.0 project (http:///www.futuregenalliance.org/) sponsored by the U.S. Department of Energy, a novel process is used to convert coal into electricity with minimal greenhouse gas \(\left(\mathrm{CO}_{2}\right)\) emissions to the atmosphere. In the process, coal is combusted in a boiler with pure \(\mathrm{O}_{2}\); the heat released produces steam, which is then used for heating and to drive turbines that generate electricity. An excess of \(\mathrm{O}_{2}\) is supplied to the boiler to convert all the coal into a flue gas consisting of carbon dioxide, steam, and any unreacted oxygen. The mass flow rate of coal to the boiler is \(50 \mathrm{kg} / \mathrm{s}\), and \(\mathrm{O}_{2}\) is fed in \(8.33 \%\) excess. For the purposes of this analysis, the chemical formula of coal can be approximated as \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{2}\) (a) Draw and label the flowchart and carry out the degree-of-freedom analysis using balances on atomic species. (b) Determine the molar flow of oxygen supplied to the boiler. (c) Solve for the remaining unknown flow rates and mole fractions. Determine the molar composition of the flue gas on a dry basis. (d) A feature that makes the FutureGen power plant unique is the intent to capture the \(\mathrm{CO}_{2}\) generated, compress it, and pump it into deep geological formations in which it will be permanently stored. List at least two safety or environmental issues that should be considered in the construction and operation of this plant. (e) List at least two pros and two cons of using pure \(O_{2}\) versus air.

Two aqueous sulfuric acid solutions containing \(20.0 \mathrm{wt} \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{SG}=1.139)\) and \(60.0 \mathrm{wt} \% \mathrm{H}_{2} \mathrm{SO}_{4}\) (SG = 1.498) are mixed to form a 4.00 molar solution (SG = 1.213). (a) Calculate the mass fraction of sulfuric acid in the product solution. (b) Taking \(100 \mathrm{kg}\) of the \(20 \%\) feed solution as a basis, draw and label a flowchart of this process, labeling both masses and volumes, and do the degree-of-freedom analysis. Calculate the feed ratio (liters 20\% solution/liter 60\% solution). (c) What feed rate of the \(60 \%\) solution (L/h) would be required to produce \(1250 \mathrm{kg} / \mathrm{h}\) of the product?

A fuel distributor supplies four liquid fuels, each of which has a different ratio of ethanol to gasoline. Five percent of the demand is for E100 (pure ethanol), 15\% for E85 (85.0 volume\% ethanol), 40\% for E10 (10.0\% ethanol), and the remainder for pure gasoline. The distributor blends gasoline and ethanol to produce E85 and E10, and the four products are produced continuously. (a) Draw and label a flowchart for the blending operation, letting \(\dot{V}\) represent the combined volumetric flow rate of all four fuels and \(\dot{V}_{\mathrm{G}}\) and \(\dot{V}_{\mathrm{E}}\) represent the volumetric flow rates of gasoline and ethanol sold as fuels and sent to the blending operation. (b) Assuming volume additivity when blending ethanol and gasoline, determine the volumetric flow rates of all streams when delivery of 100,000 L/d of \(\mathrm{E} 10\) is specified. (c) Tank trucks are to transport the fuel from the blending operation to service stations in the area. The gross weight of a loaded truck, which has a tare (empty) weight of \(12,700 \mathrm{kg}\), cannot exceed \(36,000 \mathrm{kg} .\) Assuming the specific gravity of pure gasoline is \(0.73,\) estimate the maximum volume (L) of each fuel that can be loaded onto a truck.
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