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Chapter 4: Problem 30

A garment to protect the wearer from toxic agents may be made of a fabric that contains an adsorbent, such as activated carbon. In a test of such a fabric, a gas stream containing \(7.76 \mathrm{mg} / \mathrm{L}\) of carbon tetrachloride (CCl_) was passed through a 7.71-g sample of the fabric at a rate of 1.0 L/min, and the concentration of \(\mathrm{CCl}_{4}\) in the gas leaving the fabric was monitored. The run was continued for \(15.5 \mathrm{min}\) with no \(\mathrm{CCl}_{4}\) being detected, after which the \(\mathrm{CCl}_{4}\) concentration began to rise. (a) How much CCl_ was fed to the system during the first 15.5 min of the run? How much was adsorbed? Using this information as a guide, sketch the expected concentration of \(\mathrm{CCl}_{4}\) in the exit gas as a function of time, showing the curve from \(t=0\) to \(t \gg 15.5\) min. (b) Assuming a linear relationship between amount of \(\mathrm{CCl}_{4}\) adsorbed and mass of fabric, what fabric mass would be required if the feed concentration is \(5 \mathrm{mg} / \mathrm{L},\) the feed rate \(1.4 \mathrm{L} / \mathrm{min},\) and it is desired that no \(\mathrm{CCl}_{4}\) leave the fabric earlier than 30 min?

Short Answer

Expert verified
For part (a), the total fed amount and the quantity of CCl_4 adsorbed by the fabric is \(120 \, \text{mg}\), and the concentration profile would be at zero for the first 15.5 min, then increase progressively. For part (b), approximately \(16.8 \, \text{g}\) of fabric is required to adsorb all CCl_4 for the first 30 minutes under the new conditions.

Step by step solution

01

Calculate Carbon tetrachloride (CCl4) fed to the system

Use the formula: \[ \text{Mass}_{\text{fed}} = C \times Q \times t \] Where: \(C = 7.76 \, \text{mg/L}\) (Concentration), \(Q = 1.0 \, \text{L/min}\) (Flow rate), and \(t = 15.5 \, \text{min}\) (Time).
02

Calculate adsorbed CCl4

Since there is no CCl4 detected in the exiting gas stream for the first 15.5 minutes, all of it is adsorbed by the fabric. Thus the total adsorbed quantity is equal to the fed quantity.
03

Sketch concentration profile

The concentration profile would be a straight line along the time-axis for the first 15.5 min, indicating zero concentration of CCl4. After this point, the concentration will start to increase progressively as the fabric becomes saturated and cannot adsorb any more CCl4.
04

Calculate Required Fabric Mass for new Conditions

From Step 2, we know that a 7.71 g fabric sample can adsorb all CCl4 fed in the first 15.5 min. With the new conditions, calculation will use the formula: \[ \text{Mass}_{\text{fabric}} = (C_{\text{new}} \times Q_{\text{new}} \times t_{\text{new}} / \text{Mass}_{\text{CCl4, adsorbed}} ) \times \text{Mass}_{\text{fabric}} \] Where: \(C_{\text{new}} = 5 \, \text{mg/L}\), \(Q_{\text{new}} = 1.4 \, \text{L/min}\), \(t_{\text{new}} = 30 \, \text{min}\), \(\text{Mass}_{\text{CCl4, adsorbed}}\) is from step 2 and \(\text{Mass}_{\text{fabric}} = 7.71 \, \text{g}\)

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Key Concepts

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

Adsorbent Materials
Adsorbent materials play a crucial role in protective garments for filtering toxic agents, like in the case of the exercise involving activated carbon and carbon tetrachloride (CCl4). These materials, by virtue of their porous structure, offer extensive surface area for the attachment, or 'adsorption', of molecules from gases or liquids.

Activated carbon, a commonly used adsorbent, is made by processing carbon-rich materials, such as wood, coconut shells, or coal, to increase porosity and surface area. During adsorption, the pollutants adhere to the surface of the activated carbon, getting trapped in the internal pore structure, thereby cleaning the medium (gas or liquid) passing through it.

Understanding the capacity of an adsorbent material is essential, as in the textbook exercise, to determine how long it will effectively filter a specific contaminant before becoming saturated. Once saturated, no more adsorption can occur, and the toxic agents will pass through, hence the rise of CCl4 concentration after 15.5 minutes as indicated in the exercise.
Mass Transfer in Chemical Engineering
Mass transfer is one of the foundational pillars of chemical engineering, dealing with the movement and distribution of a substance from one location to another, which may occur due to concentration gradients or differences in chemical potential. In the context of our exercise, mass transfer explains how the CCl4 moves from the gas stream into the fabric's adsorbent material.

The efficiency of mass transfer in a system such as the gas stream through fabric relates directly to the adsorption kinetics - the rate at which CCl4 molecules come into contact and adhere to the activated carbon in the fabric. Initially, when the adsorbent is fresh, the mass transfer rate is high because there are many available sites for adsorption. However, as these sites fill up over time, the rate decreases, which is why we observe no CCl4 in the exit gas for the first 15.5 minutes in the exercise. Eventually, the fabric becomes saturated, and the mass transfer effectively ceases, leading to a detectable concentration of CCl4 in the exiting gas.
Activated Carbon Filtration
Activated carbon filtration is a common method used in both protective wear and various industrial processes. It leverages the porous nature of activated carbon to remove contaminants via physical adsorption. The adsorption capacity highly depends on factors such as the concentration of contaminants, flow rate, temperature, and contact time.

In the exercise scenario, activated carbon is used in a fabric to filter out CCl4 from the air. The filtration performance relies on the amount of activated carbon present, which is directly proportional to the mass of the fabric. This is demonstrated in part (b) of the exercise, which requires calculation of fabric mass needed for extended filtration time using ratios derived from the initial experiment conditions.

Furthermore, activated carbon filtration is not infinite 鈥� it has a finite capacity for adsorbing pollutants, after which it must be replaced or regenerated. This is apparent when the fabric starts to allow CCl4 to pass through after 15.5 minutes, indicating it is a critical factor to consider while designing filtration systems for protective garments or other applications.

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Most popular questions from this chapter

A liquid mixture contains \(60.0 \mathrm{wt} \%\) ethanol \((\mathrm{E}), 5.0 \mathrm{wt} \%\) of a dissolved solute \((\mathrm{S}),\) and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Product streams emerge at the top and bottom of the column. The column design calls for the product streams to have equal mass flow rates and for the top stream to contain 90.0 wt\% ethanol and no S. (a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions can be calculated. (Don't do any calculations yet.) (b) Calculate (i) the mass fraction of \(S\) in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., \(\mathrm{kg} \mathrm{E}\) in bottom stream/kg \(\mathrm{E}\) in feed) if the process operates as designed. (c) An analyzer is available to determine the composition of ethanol-water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, \(x\) (kg E/kg mixture), versus analyzer reading, \(R\). The line passes through the points \((R=15, x=\) 0.100) and \((R=38, x=0.400)\). Derive an expression for \(x\) as a function of \(R(x=\cdots\) ) based on the calibration, and use it to determine the value of \(R\) that should be obtained if the top product stream from the distillation column is analyzed. (d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in Part (c). Assume that the calculation in Part (c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between \(R_{\text {measured and }} R_{\text {prediced }}\), including several assumptions made when writing the balances of Part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.

Eggs are sorted into two sizes (large and extra large) at the Cheerful Chicken Coop. Recently, the economic downturn has not allowed Cheerful Chicken to repair the egg-sorting machine bought in 2000. Instead, the company has Chick Poulet, one of the firm's sharper-eyed employees, stamp the big eggs with a "Large" rubber stamp in her right hand and the really big eggs with an "X-large" stamp in her left as the eggs go by on a conveyor belt. Down the line, another employee puts the eggs into one of two hoppers, each egg according to its stamp. On average Chick breaks \(8 \%\) of the 120 eggs that pass by her each minute. At the same time, a check of the "X-large" stream reveals a flow rate of 70 eggs/min, of which 8 eggs/min are broken. (a) Draw and label a flowchart for this process. (b) Write and solve balances about the egg sorter on total eggs and broken eggs. (c) How many "large" eggs leave the plant each minute, and what fraction of them are broken? (d) Is Chick right- or left-handed?

One thousand kilograms per hour of a mixture containing equal parts by mass of methanol and water is distilled. Product streams leave the top and the bottom of the distillation column. The flow rate of the bottom stream is measured and found to be \(673 \mathrm{kg} / \mathrm{h}\), and the overhead stream is analyzed and found to contain 96.0 wt\% methanol. (a) Draw and label a flowchart of the process and do the degree-of-freedom analysis. (b) Calculate the mass and mole fractions of methanol and the molar flow rates of methanol and water in the bottom product stream. (c) Suppose the bottom product stream is analyzed and the mole fraction of methanol is found to be significantly higher than the value calculated in Part (b). List as many possible reasons for the discrepancy as you can think of. Include in your list possible violations of assumptions made in Part (b).

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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 \(\mathrm{TiO}_{2}\)
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