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A dry gas containing \(10.0 \% \mathrm{NH}_{3}\) by volume is contacted with water at \(10^{\circ} \mathrm{C}\) and 1 atm in a singlestage bubble contactor. The effluent liquid and gas streams may be considered to be in equilibrium with each other. A small slip stream taken from the effluent liquid is fed to a continuous densitometer, which indicates that the liquid density is \(0.9534 \mathrm{g} / \mathrm{mL}\) (a) Using tabulated data from Perry's Chemical Engineers' Handbook,12 estimate the percentage of the ammonia in the feed that is removed in the contactor. (b) Why is it important to maintain the slip stream and densitometer chamber at a known temperature at or below the temperature of the contactor?

Short Answer

Expert verified
The percentage of ammonia removed will vary depending on the actual data from Perry’s Handbook. For part (b), maintaining slipstream and densitometer chamber's temperature at or below the contactor temperature ensures accurate density readings and consistent solubility.

Step by step solution

01

Understand and use tabulated data

First, refer to Perry’s Chemical Engineers’ Handbook to understand the solubility of NH3 in water at \(10 ^{\circ} C\). Find the mole fraction of NH3 in the solution using the given liquid and NH3 densities. The mole fraction of NH3 (\(y\)) can be calculated using the formula : \(y = \frac{{\text{Density of NH3}}}{{\text{Density of solution}}}\)
02

Compute the mole fractions

Using the molar masses of NH3 and water and the densities of liquid and NH3, calculate the mole fraction of NH3 in the liquid phase. Let's denote this mole fraction as \(X_{NH3}\).
03

Determine the mole fraction of ammonia in gas phase

Next, determine the mole fraction of NH3 in the gas phase, denoted by \(Y_{NH3}\), by consulting the tabulated data in Perry's Handbook. This data will provide information about the equilibrium relation for NH3 between the gas and liquid phases at \(10 ^{\circ} C\) and 1 atm.
04

Computing the percentage ammonia removed

The percentage of ammonia in the feed removed in the contactor can be estimated as \[\text{Percentage NH3 removed} = \frac{{(Y_{NH3,initial}-Y_{NH3,final})}}{{Y_{NH3,initial}}}\times 100 \%\] where \(Y_{NH3,initial}\) is the initial mole fraction in the feed (10%) and \(Y_{NH3, final}\) is the final mole fraction in the effluent gas.
05

Provide an explanation regarding the temperature

The densitometer measures the density of the solution which is temperature-dependent. The solubility of gases in liquids typically decreases with increasing temperature. Therefore, to ensure accurate readings, the slipstream and densitometer chamber must be maintained at a temperature at or below the contactor temperature.

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Key Concepts

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

Ammonia Solubility
Ammonia solubility refers to the ability of ammonia gas to dissolve in a liquid—in this case, water. Ammonia is highly soluble in water due to the formation of hydrogen bonds. The solubility can be significantly affected by temperature, pressure, and the nature of the solvent. In our context, at a lower temperature of 10°C, ammonia's solubility is higher. This means more ammonia can dissolve in the water at this temperature, impacting the efficiency of gas-liquid contact devices like bubble contactors. Keep in mind that solubility data is often referenced from reliable sources like Perry’s Chemical Engineers’ Handbook, helping to predict the extent of ammonia removal in gas-liquid equilibrium processes.
Mole Fraction Calculation
Calculating the mole fraction is essential in chemical equilibrium because it helps express the concentration of a component in a mixture. A mole fraction is simply the ratio of the number of moles of a component to the total number of moles in the mixture. For ammonia in the solution, you'll calculate it using its density and the density of the solution:
  • Find the density of ammonia as a gas at the specified conditions.
  • Determine the density of the liquid mixture from the problem data.
  • Apply the formula: \( y = \frac{\text{Density of NH3}}{\text{Density of solution}} \) to compute the ammonia mole fraction (\( y \)).
This fraction is crucial for determining the equilibrium between the gas and liquid phases.
Gas-Liquid Contacting
Gas-liquid contacting is a process where a gas mixture is brought into contact with a liquid to exchange a soluble component between the two phases. In a bubble contactor, the gas rises through the liquid as bubbles, allowing ammonia to dissolve. This technique enhances surface area contact, improving mass transfer. The exchange leads to an equilibrium state where the concentration of ammonia is equal in both phases. By achieving equilibrium, you effectively remove ammonia from the gas stream efficiently. This description aligns with typical operations in chemical engineering fields, mainly focusing on equilibrium and enhancing solubility through optimal contact engineering.
Density Measurement
Density measurement is a critical aspect of calculating solubility and understanding chemical processes like ammonia absorption. The density of the liquid is provided using a densitometer, which measures it accurately. This data allows us to:
  • Calculate the mole fraction of ammonia, as density plays a key role in these calculations.
  • Ensure readings are done at constant conditions, as changes in temperature affect density.
Maintaining a known temperature ensures that the results reflect the correct equilibrium state and solubility conditions. Consistent measurements ensure reliable data for understanding how much ammonia remains soluble in the liquid, crucial for equilibrium predictions and performance assessment of gas-liquid contact systems.

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Most popular questions from this chapter

A stream of 5.00 wt\% oleic acid in cottonseed oil enters an extraction unit at a rate of \(100.0 \mathrm{kg} / \mathrm{h}\). The unit operates as a single equilibrium stage (the streams leaving the unit are in equilibrium) at \(85^{\circ} \mathrm{C} . \mathrm{At}\) this temperature, propane and cottonseed oil are essentially immiscible, the vapor pressure of propane is 34 atm, and the distribution coefficient (oleic acid mass fraction in propane/oleic acid mass fraction in cottonseed oil) is \(0.15 .\)(a) Calculate the rate at which liquid propane must be fed to the unit to extract \(90 \%\) of the oleic acid. (b) Estimate the minimum operating pressure of the extraction unit. Explain your answer.(c) High-pressure operation is costly and introduces potential safety hazards. Suggest two possible reasons for using propane as the solvent when other less volatile hydrocarbons are equally good solvents for oleic acid.

The solubility of sodium bicarbonate in water is \(11.1 \mathrm{g} \mathrm{NaHCO}_{3} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) at \(30^{\circ} \mathrm{C}\) and \(16.4 \mathrm{g}\) \(\mathrm{NaHCO}_{3} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) at \(60^{\circ} \mathrm{C} .\) If a saturated solution of \(\mathrm{NaHCO}_{3}\) at \(60^{\circ} \mathrm{C}\) is cooled and comes to equilibrium at \(30^{\circ} \mathrm{C},\) what percentage of the dissolved salt crystallizes?

State whether you would use Raoult's law or Henry's law to perform vapor- liquid equilibrium calculations for each component in the following liquid mixtures: (a) water and dissolved nitrogen; (b) hexane, octane, and decane; and (c) \(\mathrm{CO}_{2}\) and water in club soda or any other carbonated beverage.

Various amino acids have utility as food additives and in medical applications. They are often synthesized by fermentation using a specific microorganism to convert a substrate (e.g., a sugar) into the desired product. Small quantities of other species also may be formed and must be removed to meet product specifications. For example, isoleucine (Ile), which has a molecular weight of \(131.2,\) is an essential amino acid \(^{16}\) produced by fermentation, and other amino acids such as leucine and valine also are found in the fermentation broth. The broth is subjected to several processing steps to remove these and other impurities, but final processing by crystallization is required to meet stringent specifications on purity. The strategy is to crystallize the hydrated acid form of Ile (Ile. \(\mathrm{HCl} \cdot \mathrm{H}_{2} \mathrm{O}\) ), whose crystals exclude other amino acids, and then to redissolve, neutralize, and crystallize the final Ile product. In a batch process designed to manufacture \(2500 \mathrm{kg}\) of Ile per batch, an aqueous feed solution containing 35 g Ile/dL and much lower concentrations of leucine and valine is fed to the final purification stages. The pH of the solution is 1.1 and its specific gravity is 1.02. The solution is heated to \(60^{\circ} \mathrm{C}\) and 35-wt\% HCl solution is added in a ratio of 0.4 kg per kg of feed. The addition of HCl causes the formation of crystals of Ile\cdotHCl\cdot \(\mathrm{H}_{2} \mathrm{O},\) and the production of these crystals is further increased by slowly lowering the temperature to \(20^{\circ} \mathrm{C}\). At the final crystallizer conditions the Ile solubility is \(5 \mathrm{g}\) Ile/ \(100 \mathrm{g}\) solution. The resulting slurry is sent to a centrifuge where the crystals are separated from the liquid solution and the crystal cake is washed with water. The solids leaving the centrifuge contain \(12 \%\) free water (i.e., not part of the crystal structure) and \(88 \%\) pure crystals of Ile\(\cdot \mathrm{HCl} \cdot \mathrm{H}_{2} \mathrm{O}\). \(\mathrm{H}_{2} \mathrm{O}\).The washed crystals "water to form a solution that is 4.0 g Ile/dL with gravity of 1.1. The solution is sent to an ion exchange unit where HCl is removed. Upon leaving the ion exchange unit the solution has a pH of about \(5.5 .\) It is sent to a second crystallizer where the temperature is gradually reduced to \(10^{\circ} \mathrm{C}\) and the Ile solubility is \(3.4 \mathrm{g} \mathrm{Ile} / 100 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\). The crystals are separated from the slurry by centrifugation, washed with pure water, and sent to a dryer for final processing. (a) Construct a labeled flowchart for the process. (b) Choosing a basis of 1 kg of feed solution, estimate (i) the mass of HCl solution added to the system, (ii) the water added to redissolve the Ile.HCI. \(\mathrm{H}_{2} \mathrm{O}\) crystals, (iii) the mass of \(\mathrm{HCl}\) removed in the ion exchange unit, and (iv) the mass of final Ile product. (c) Scale the quantities calculated in Part (b) to the production rate of 2500 kg Ile/batch. (d) Estimate the active volume (in liters) of each of the crystallizers. (e) Amino acids are amphoteric, which means they can either donate or accept a proton \(\left(\mathrm{H}^{+}\right) .\) At low pH they tend to accept a proton and become acidic while at high pH they tend to donate a proton and become basic. They also are known as zwitterions because their ends are oppositely charged, even though the overall molecule is neutral. Isoleucine is reported to have an isoelectric point (pI) of 6.02 and \(\mathrm{pK}_{\mathrm{a}}\) values of 2.36 and \(9.60 .\) Look up the meaning of these terms and prepare a plot showing how these values are used in plotting the distribution of Ile between acid, zwitterionic (neutral), and basic forms as a function of pH. Explain why such a distribution is important in carrying out the separations described in the process.

A storage tank for liquid \(n\) -octane has a diameter of \(30 \mathrm{ft}\) and a height of \(20 \mathrm{ft}\). During a typical \(24-\mathrm{h}\) period the level of liquid octane falls from 18 ft to 8 ft, after which fresh octane is pumped into the tank to return the level to \(18 \mathrm{ft}\). As the level in the tank falls, nitrogen is fed into the free space to maintain the pressure at 16 psia; when the tank is being refilled, the pressure is maintained at 16 psia by discharging gas from the vapor space to the environment. The nitrogen in the tank may be considered saturated with octane vapor at all times. The average tank temperature is \(90^{\circ} \mathrm{F}\). (a) What is the daily rate, in gallons and \(1 \mathrm{b}_{\mathrm{m}}\), at which octane is used? (b) What is the variation in absolute pressure at the bottom of the tank in inches of mercury? (c) How much octane is lost to the environment during a 24 -h period? (d) Why is nitrogen used in the vapor space of the tank when air would be cheaper? (e) Suggest a means by which the octane can be recovered from the gas stream discharged to the atmosphere.

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