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Chapter 6: Problem 91

An aqueous waste stream leaving a process contains 10.0 wt\% sulfuric acid and 1 kg nitric acid per \(\mathrm{kg}\) sulfuric acid. The flow rate of sulfuric acid in the waste stream is \(1000 \mathrm{kg} / \mathrm{h}\). The acids are neutralized before being sent to a wastewater treatment facility by combining the waste stream with an aqueous slurry of solid calcium carbonate that contains 2 kg of recycled liquid per \(\mathrm{kg}\) solid calcium carbonate. (The source of the recycled liquid will be given later in the process description.) The following neutralization reactions occur in the reactor:$$\begin{array}{l} \mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{CaSO}_{4}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \\ \mathrm{CaCO}_{3}+2 \mathrm{HNO}_{3} \rightarrow \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \end{array}$$,The sulfuric and nitric acids and calcium carbonate fed to the reactor are completely consumed. The carbon dioxide leaving the reactor is compressed to 30 atm absolute and \(40^{\circ} \mathrm{C}\) and sent elsewhere in the plant. The remaining reactor effluents are sent to a crystallizer operating at \(30^{\circ} \mathrm{C},\) at which temperature the solubility of calcium sulfate is \(2.0 \mathrm{g} \mathrm{CaSO}_{4} / 1000 \mathrm{g} \mathrm{H}_{2} \mathrm{O} .\) Calcium sulfate crystals form in the crystallizer and all other species remain in solution.The slurry leaving the crystallizer is filtered to produce (i) a filter cake containing \(96 \%\) calcium sulfate crystals and the remainder entrained saturated calcium sulfate solution, and (ii) a filtrate solution saturated with \(\mathrm{CaSO}_{4}\) at \(30^{\circ} \mathrm{C}\) that also contains dissolved calcium nitrate. The filtrate is split, with a portion being recycled to mix with the solid calcium carbonate to form the slurry fed to the reactor, and the remainder being sent to the wastewater treatment facility.(a) Draw and completely label a flowchart for this process. (b) Speculate on why the acids must be neutralized before being sent to the wastewater treatment facility.(c) Calculate the mass flow rates ( \(\mathrm{kg} / \mathrm{h}\) ) of the calcium carbonate fed to the process and of the filter cake; also determine the mass flow rates and compositions of the solution sent to the wastewater facility and of the recycle stream. (Caution: If you write a water balance around the reactor or the overall system, remember that water is a reaction product and not just an inert solvent.)(d) Calculate the volumetric flow rate ( \(L / h\) ) of the carbon dioxide leaving the process at 30 atm absolute and 40^0 C. Do not assume ideal-gas behavior. (e) The solubility of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) at \(30^{\circ} \mathrm{C}\) is \(152.6 \mathrm{kg} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) per \(100 \mathrm{kg} \mathrm{H}_{2} \mathrm{O}\). What is the maximum ratio of nitric acid to sulfuric acid in the feed that can be tolerated without encountering difficulties associated with contamination of the calcium sulfate by-product by \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Short Answer

Expert verified
1. The mass flow rates of sulfuric acid, nitric acid, and calcium carbonate fed to the reactor are 1000 kg/h, 1000 kg/h, and 2000 kg/h respectively. 2. The ratio of nitric acid to sulfuric acid in the feed should not exceed the solubility limit of \(Ca(NO_3)_2\) in water i.e., 152.6 kg/100 kg H2O to avoid contamination of the by-product.

Step by step solution

01

Analyze the reactions and mass balance

First thing to do is to understand the neutralization reactions that are taking place in the reactor, and the various components being fed into and out of the reactor. From the reactions, we notice that sulfuric acid is reacting with calcium carbonate to form calcium sulfate, water and carbon dioxide. Similarly, nitric acid is reacting with calcium carbonate to form calcium nitrate, water and carbon dioxide. Water is a product, so should be taken into account during the mass balance calculations.
02

Calculate mass flow rates

From the problem, we know that the flow rate of sulfuric acid in the waste stream is 1000 kg/h. Given that there is 1 kg nitric acid/kg sulfuric acid, the flow rate of nitric acid is also 1000 kg/h. For complete neutralization, both sulfuric acid and nitric acid need an equal amount of calcium carbonate. So, the flow rate of calcium carbonate fed to the reactor is 2000 kg/h (1000 kg/h for sulfuric acid and 1000 kg/h for nitric acid). Similarly, we can find the flow rates for other components in the process.
03

Calculate the mass ratio

To find the maximum ratio of nitric acid to sulfuric acid in the feed that can be tolerated, we need to analyze the solubility limit of \(Ca(NO_3)_2\) in water. This is because excess nitric acid would react with calcium carbonate to form \(Ca(NO_3)_2\), which could end up contaminating the calcium sulfate by-product. Given that the solubility of \(Ca(NO_3)_2\) in water at the operational temperature is 152.6 kg/100 kg H2O, we can calculate the maximum allowable nitric acid feed ratio that would keep the \(Ca(NO_3)_2\) concentration in the solution below this limit.
04

Calculate the volumetric flow rate of Carbon dioxide

Lastly, we need to calculate the volumetric flow rate of the carbon dioxide leaving the reactor. To do that, we need to consider the operating conditions of the reactor (i.e., 30 atm pressure and 40 degree Celsius temperature) and use the appropriate equation of state for carbon dioxide to calculate its volume.

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Key Concepts

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

Neutralization Reactions
In chemical processes, neutralization reactions are crucial for transforming potentially harmful acids into safer compounds. In this particular process, sulfuric acid ( H_2SO_4 ) and nitric acid ( HNO_3 ) are neutralized using calcium carbonate ( CaCO_3 ). These reactions are important because they produce by-products that are easier to handle and less hazardous.

The reactions involved in this process are:
  • Calcium carbonate reacts with sulfuric acid to produce calcium sulfate ( CaSO_4 ), water ( H_2O ), and carbon dioxide ( CO_2 ).
  • Calcium carbonate reacts with nitric acid to form calcium nitrate ( Ca(NO_3)_2 ), water, and carbon dioxide.
Understanding these reactions helps in managing the treatment and disposal stages of chemical processes efficiently.

Moreover, ensuring complete neutralization avoids problems such as equipment corrosion, environmental pollution, and safety hazards upon discharge from the system.
Mass Balance Calculations
The concept of mass balance is central to chemical engineering and involves accounting for all mass entering and leaving a system. In this exercise, a mass balance is essential for determining the flow rates of reactants and products during the neutralization of acids.

Key points in the mass balance calculations include:
  • The mass flow rate of sulfuric acid provided is 1000 kg/h. Given the ratio of nitric acid to sulfuric acid is 1:1, the flow rate of nitric acid is also 1000 kg/h.
  • Calcium carbonate is needed in equivalent molar amounts to neutralize both acids entirely, leading to a required flow rate of 2000 kg/h for calcium carbonate.
  • Water, as a product of the reactions, adds complexity to the mass balance, as it isn't just an inert solvent.
Mass balance ensures all inputs and outputs of the system are accounted for, enabling a better understanding of resource usage and process efficiency.
Solubility Limits
Solubility limits dictate the maximum concentration of a solute that can dissolve in a solvent at a given temperature. In this process, solubility limits are crucial in the formation of calcium sulfate crystals in the crystallizer.

The crystallizer operates at 30掳C, where the solubility of calcium sulfate is limited to 2.0 g per 1000 g of water. Understanding these limits helps in ensuring the efficient separation of materials, as:
  • The crystallizer removes excess calcium sulfate, allowing only a saturated solution to pass forward in the process.
  • Maintaining solubility limits is key to preventing unwanted precipitates, like Ca(NO_3)_2 , which could contaminate by-products.
Managing solubility is thus vital in process design and ensures desired products are obtained without contamination.
Volumetric Flow Rate Calculations
Calculating volumetric flow rate is necessary for determining the volume of gaseous products leaving a process, in this case, carbon dioxide from the reactor. These calculations require understanding of both the reaction conditions and gas behavior.

For this exercise:
  • The carbon dioxide is compressed to 30 atm and 40掳C.
  • Using appropriate state equations, real gas behavior must be considered instead of assuming ideal conditions.
These calculations are essential for designing equipment and controlling emissions, ensuring safe and efficient plant operation.

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Most popular questions from this chapter

An aqueous solution of urea \((\mathrm{MW}=60.06)\) freezes at \(-4.6^{\circ} \mathrm{C}\) and 1 atm. Estimate the normal boiling point of the solution; then calculate the mass of urea (grams) that would have to be added to \(1.00 \mathrm{kg}\) of solution to raise the normal boiling point by \(3^{\circ} \mathrm{C}\).

Air at \(25^{\circ} \mathrm{C}\) and 1 atm with a relative humidity of \(25 \%\) is to be dehumidified in an adsorption column packed with silica gel. The equilibrium adsorptivity of water on silica gel is given by the expression \(^{19}\).$$X^{*}(\mathrm{kg} \text { water/ } 100 \mathrm{kg} \text { silica gel })=12.5 \frac{p_{\mathrm{H}_{2} \mathrm{O}}}{p_{\mathrm{H}_{2} \mathrm{O}}^{*}}$$ where \(p_{\mathrm{H}_{2} \mathrm{O}}\) is the partial pressure of water in the gas contacting the silica gel and \(p_{\mathrm{H}, \mathrm{O}}^{*}\) is the vapor pressure of water at the system temperature. Air is fed to the column at a rate of 1.50 L/min until the silica gel is saturated (i.e., until it reaches equilibrium with the feed air), at which point the flow is stopped and the silica gel regenerated. (a) Calculate the minimum amount of silica gel needed in the column if regeneration is to take place no more frequently than every two hours. State any assumptions you make. (b) Briefly describe this process in terms that a high school student would have no trouble understanding. (What is the process designed to do, what happens within the column, and why is regeneration of the column packing necessary?)

A fuel gas containing methane and ethane is burned with air in a furnace, producing a stack gas at \(300^{\circ} \mathrm{C}\) and \(105 \mathrm{kPa}\) (absolute). You analyze the stack gas and find that it contains no unburned hydrocarbons, oxygen, or carbon monoxide. You also determine the dew-point temperature.(a) Estimate the range of possible dew-point temperatures by determining the dew points when the feed is either pure methane or pure ethane. (b) Estimate the fraction of the feed that is methane if the measured dew- point temperature is \(59.5^{\circ} \mathrm{C}\). (c) What range of measured dew point temperatures would lead to calculated methane mole fractions within 5\% of the value determined in Part (b)?

The feed to a distillation column (sketched below) is a 45.0 mole\% \(n\) -pentane- 55.0 mole\% n-hexane liquid mixture. The vapor stream leaving the top of the column, which contains 98.0 mole\% pentane and the balance hexane, goes to a total condenser (which means all the vapor is condensed). Half of the liquid condensate is returned to the top of the column as reflux and the rest is withdrawn as overhead product (distillate) at a rate of \(85.0 \mathrm{kmol} / \mathrm{h}\). The distillate contains \(95.0 \%\) of the pentane fed to the column. The liquid stream leaving the bottom of the column goes to a reboiler. Part of the stream is vaporized; the vapor is returned to the bottom of the column as boilup, and the residual liquid is withdrawn as bottoms product.(a) Calculate the molar flow rate of the feed stream and the molar flow rate and composition of the bottoms product stream. (b) Estimate the temperature of the vapor entering the condenser, assuming that it is saturated (at its dew point) at an absolute pressure of 1 atm and that Raoult's law applies to both pentane and hexane. Then estimate the volumetric flow rates of the vapor stream leaving the column and of the liquid distillate product. State any assumptions you make. (c) Estimate the temperature of the reboiler and the composition of the vapor boilup, again assuming operation at 1 atm.(d) Calculate the minimum diameter of the pipe connecting the column and the condenser if the maximum allowable vapor velocity in the pipe is \(10 \mathrm{m} / \mathrm{s}\). Then list all the assumptions underlying the calculation of that number.

The sulfur dioxide content of a stack gas is monitored by passing a sample stream of the gas through an SO_ analyzer. The analyzer reading is \(1000 \mathrm{ppm} \mathrm{SO}_{2}\) (parts per million on a molar basis). The sample gas leaves the analyzer at a rate of \(1.50 \mathrm{L} / \mathrm{min}\) at \(30^{\circ} \mathrm{C}\) and \(10.0 \mathrm{mm}\) Hg gauge and is bubbled through a tank containing 140 liters of initially pure water. In the bubbler, \(S O_{2}\) is absorbed and water evaporates. The gas leaving the bubbler is in equilibrium with the liquid in the bubbler at \(30^{\circ} \mathrm{C}\) and 1 atm absolute. The \(\mathrm{SO}_{2}\) content of the gas leaving the bubbler is periodically monitored with the \(\mathrm{SO}_{2}\) analyzer, and when it reaches \(100 \mathrm{ppm} \mathrm{SO}_{2}\) the water in the bubbler is replaced with 140 liters of fresh water.(a) Speculate on why the sample gas is not just discharged directly into the atmosphere after leaving the analyzer. Assuming that the equilibrium between \(S O_{2}\) in the gas and dissolved \(S O_{2}\) is described by Henry's law, explain why the SO_ content of the gas leaving the bubbler increases with time. What value would it approach if the water were never replaced? Explain. (The word "solubility" should appear in your explanation.)(b) Use the following data for aqueous solutions of \(\mathrm{SO}_{2}\) at \(30^{\circ} \mathrm{C}^{14}\) to estimate the Henry's law constant in units of \(\mathrm{mm}\) Hg/mole fraction:$$\begin{array}{|l|c|c|c|c|c|}\hline \mathrm{g} \mathrm{SO}_{2} \text { dissolved/ } 100 \mathrm{g}\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) & 0.0 & 0.5 & 1.0 & 1.5 & 2.0 \\\\\hline p_{\mathrm{SO}_{2}}(\mathrm{mm} \mathrm{Hg}) & 0.0 & 37.1 & 83.7 &132 & 183 \\\\\hline\end{array}.$$(c) Estimate the SO_concentration of the bubbler solution (mol SO_/liter), the total moles of SO_ dissolved, and the molar composition of the gas leaving the bubbler (mole fractions of air, \(\mathrm{SO}_{2}\), and water vapor) at the moment when the bubbler solution must be changed. Make the following assumptions: \bullet. The feed and outlet streams behave as ideal gases. \bullet Dissolved SO_ is uniformly distributed throughout the liquid. ? The liquid volume remains essentially constant at 140 liters. \- The water lost by evaporation is small enough for the total moles of water in the tank to be considered constant. \- The distribution of SO_ between the exiting gas and the liquid in the vessel at any instant of time is governed by Henry's law, and the distribution of water is governed by Raoult's law (assume \(\left.x_{\mathrm{H}_{2} \mathrm{O}} \approx 1\right)\).(d) Suggest changes in both scrubbing conditions and the scrubbing solution that might lead to an increased removal of \(\mathrm{SO}_{2}\) from the feed gas.
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