91Ó°ÊÓ

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.

Step by step solution

01

Speculation and Explanation for the SO_2 Discharge Process

The SO_2 gas is dangerous and polluting, hence it cannot be discharged directly into the environment. The SO_2 gas bubbling through water is a process to absorb SO_2 into the water. According to Henry's law, the solubility of a gas in a liquid is directly proportional to the pressure of that gas above the liquid. Hence the SO_2 content in gas leaving the bubbler increases with time because more SO_2 is dissolved in the water due to the continuous supply from gas and the bubbler water could only hold finite amount SO_2.

02

Calculation of Henry's Law Constant

We can calculate the Henry's law constant (K_H) using following formula: K_H= p / x. From the data in table, we can select the third column where we have p=37.1mmHg and x=0.5gSO_2/100gH_2O. Convert the mass of SO_2 to mole (assume Molar mass of SO_2 =64 g/mol) we get x= 0.5g/64 g/mol = 0.0078 mol. And in 100g of H_2O there are 100/18 = 5.56 mol. So mole fraction of SO_2= 0.0078 / (0.0078+5.56) = 0.0014. Hence K_H = 37.1 / 0.0014 ~= 26,500 mmHg.

03

Calculation of SO_2 Concentration at the Point of Change

When the water needs to be changed, the concentration of SO_2 in the leaving gas is 100 ppm. That means the partial pressure of SO_2 in the leaving gas is 100*760/10^6 = 0.076mmHg. Now we can use Henry's law K_H = p / x to calculate the mole fraction of SO_2 in the bubbler solution: x = 0.076 / 26,500 ~=0.000003. So the concentration of SO_2 in the bubbler solution = 0.000003 * 5.56 ~= 0.000017 mol/liter. The total mole of SO_2 in 140 liters of water is then 0.000017 * 140 ~= 0.0024 mol. As for the molar composition of leaving gas, we have SO_2's mole fraction is 100/10^6 = 0.0001, and since the water lost by evaporation is negligible, we can assume H_2O's mole fraction is 1. Hence, air's mole fraction is 1 - 0.0001 = 0.9999.

04

Suggestions for Enhanced SO_2 Removal

To increase the efficiency of SO_2 removal, we could increase the pressure to have more SO_2 dissolve in the water according to Henry's law. More frequent water changes could also increase the SO_2 removal rates. In addition, selecting a more effective scrubbing solution which has a higher SO_2 absorbing capacity could also enhance SO_2 removal.

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Key Concepts

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

Sulfur Dioxide Removal

Sulfur dioxide (SOâ‚‚) is a harmful gas often emitted from industrial processes such as the burning of fossil fuels. Direct discharge of this pollutant into the atmosphere creates environmental issues like acid rain and respiratory problems for living beings. Therefore, it is crucial to remove or significantly reduce SOâ‚‚ before it is released into the environment. One common method used is "gas absorption," where SOâ‚‚ is absorbed into a liquid, typically water, before being emitted. This process not only reduces pollution but also helps to comply with environmental regulations.

Gas Absorption

Gas absorption involves a gas being dissolved into a liquid. In the case of sulfur dioxide removal, the SOâ‚‚ is absorbed into water. The process relies on solubility, which measures how well a gas dissolves in a liquid. The effectiveness of this process can depend on factors like the concentration of gas, temperature, and pressure. By increasing the surface area of contact between the gas and the liquid, the absorption efficiency can be improved. This technique is widely used in chemical engineering to separate or purify components within a process stream. In this scenario, once the SOâ‚‚ gas is absorbed into the water, it no longer poses a direct threat to the atmosphere.

Henry's Law

Henry's Law is essential in understanding how gases dissolve in liquids. It states that the amount of gas dissolved in a liquid is proportional to the partial pressure of the gas above the liquid. Mathematically, it is expressed as \( p = K_H \cdot x \), where \( p \) is the partial pressure of the gas, \( K_H \) is the Henry's Law constant, and \( x \) is the mole fraction of the dissolved gas in the liquid. As the concentration of SOâ‚‚ gas increases in the gas phase, more SOâ‚‚ will dissolve in the water until equilibrium is reached. However, the water can only hold a finite amount of SOâ‚‚, leading to eventual saturation where the rate of gas absorption decreases.

Solubility in Water

Solubility refers to the capacity of a particular substance, such as SOâ‚‚, to dissolve in a solvent like water. Factors that affect solubility include temperature, pressure, and the nature of the solvent. In terms of gas absorption for sulfur dioxide removal, solubility is crucial because it dictates how much of the gas can be captured from the stream. At a given temperature and pressure, solubility helps determine the necessary conditions for an effective absorption process. Increasing pressure can enhance solubility, while rising temperatures can generally decrease it. Understanding solubility is key to optimizing processes for maximum SOâ‚‚ retention in the water.