/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 A gas stream contains 18.0 mole ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 40

A gas stream contains 18.0 mole \(\%\) hexane and the remainder nitrogen. The stream flows to a condenser, where its temperature is reduced and some of the hexane is liquefied. The hexane mole fraction in the gas stream leaving the condenser is \(0.0500 .\) Liquid hexane condensate is recovered at a rate of \(1.50 \mathrm{L} / \mathrm{min}\). (a) What is the flow rate of the gas stream leaving the condenser in mol/min? (Hint: First calculate the molar flow rate of the condensate and note that the rates at which \(C_{6} H_{14}\) and \(N_{2}\) enter the unit must equal the total rates at which they leave in the two exit streams.) (b) What percentage of the hexane entering the condenser is recovered as a liquid? (c) Suggest a change you could make in the process operating conditions to increase the percentage recovery of hexane. What would be the downside?

Short Answer

Expert verified
a) The molar flow rate of the gas leaving condenser is calculated in step 2. b) The percentage of hexane recovered as liquid is computed in step 3. c) To increase the hexane recovery, temperature can be lowered, but it may lead to increased energy cost or freezing of unit components.

Step by step solution

01

Find molar flow rate of liquid hexane

From tables, the density of liquid hexane is 0.659 g/mL. So, convert the volume flow rate of liquid hexane (1.50 L/min) to mass flow rate using density, then convert this to molar flow rate by dividing by the molar mass of hexane (86.18 g/mol).
02

Find the flow rate of hexane in the gas stream

The hexane in the gas stream will be the difference between the total hexane entering and the amount of hexane leaving as liquid. Use the equation: \(f_{\text{hexane, gas}} = f_{\text{hexane, total}} - f_{\text{hexane, liquid}}\). The total hexane entering the condenser is 0.18 times the total flow, so, equating, we get total flow equals hexane in gas divided by 0.05 (the molar fraction of hexane in the gas stream).
03

Find the percentage of hexane recovered as liquid

The percentage of hexane that is recovered as a liquid is given by \(100 \times \frac{\text{hexane liquid molar flow rate}}{\text{total hexane entering the condenser}}\). Calculate this percentage using the determined values.
04

Suggest improvement in operation conditions

To increase the recovery of hexane, lower the temperature of the condenser further since it would cause more hexane to condense. However, downside could be potential increased energy cost or possible freezing of components in the system due to lower temperatures.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Molar Flow Rate
Understanding the molar flow rate is key when dealing with processes involving chemical reactions or separations. In the context of our condensation problem, the molar flow rate measures how many moles of a substance pass through a given point in the process per unit of time, typically expressed in moles per minute (mol/min). To calculate the molar flow rate of the liquid hexane condensate, we utilize the physical property of hexane鈥檚 density and translate the volume flow to a mass flow rate, which we then convert to a molar flow rate using hexane's molar mass.

This step is crucial because it sets the base for understanding how much hexane is actually being recovered from the gas stream. It directly impacts the calculation of the overall efficiency of the condenser unit. The beauty of chemical processes like this is that we can account for every molecule by applying the law of conservation of mass, which essentially states that mass cannot be created nor destroyed in a closed system.
Gas Stream Composition
The gas stream composition details the proportion of different components in the gas mixture. In our example, the stream contains hexane and nitrogen, with the initial composition being 18.0 mole percent hexane, leaving the remainder as nitrogen.

The composition of the gas stream after it leaves the condenser changes due to the condensation of some hexane. Measuring the mole fraction tells us what part of the gas mixture is made up by hexane after the condensation process. By knowing both, the initial and exit compositions, we gain insight into the condenser's efficiency and how effectively it performs the separation. Remember, a clear understanding of the stream composition is essential when optimizing these processes for better performance or economic efficiency.
Percentage Recovery
Percentage recovery quantifies the efficiency of a separation process鈥攊n this case, how much hexane is successfully separated from the original gas stream. We calculate it by comparing the molar flow rate of the condensed hexane to the total moles of hexane that entered the condenser.

To improve the percentage recovery of hexane, we could adjust the operating conditions of the system, such as lowering the temperature of the condenser. This would promote more hexane to condense out of the gas phase. However, when implementing such changes, it's important to evaluate potential downsides. Decreasing the temperature further might increase operational costs due to energy consumption, and too low temperatures pose risks like freezing the contents of the condenser, which could damage equipment or cause process interruptions. Such trade-offs must be carefully considered in chemical engineering to optimize both process efficiency and economic viability.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An open-end mercury manometer is connected to a low-pressure pipeline that supplies a gas to a laboratory. Because paint was spilled on the arm connected to the line during a laboratory renovation, it is impossible to see the level of the manometer fluid in this arm. During a period when the gas supply is connected to the line but there is no gas flow, a Bourdon gauge connected to the line downstream from the manometer gives a reading of 7.5 psig. The level of mercury in the open arm is \(900 \mathrm{mm}\) above the lowest part of the manometer. (a) When the gas is not flowing, the pressure is the same everywhere in the pipe. How high above the bottom of the manometer would the mercury be in the arm connected to the pipe? (b) When gas is flowing, the mercury level in the visible arm drops by \(25 \mathrm{mm}\). What is the gas pressure (psig) at this moment?

The specific gravity of gasoline is approximately 0.70. (a) Estimate the mass (kg) of 50.0 liters of gasoline. (b) The mass flow rate of gasoline exiting a refinery tank is \(1150 \mathrm{kg} / \mathrm{min}\). Estimate the volumetric flow rate in liters/s. (c) Estimate the average mass flow rate ( \(\left(\mathrm{lb}_{\mathrm{m}} / \mathrm{min}\right)\) delivered by a gasoline pump. (d) Gasoline and kerosene (specific gravity \(=0.82\) ) are blended to obtain a mixture with a specific gravity of 0.78. Calculate the volumetric ratio (volume of gasoline/volume of kerosene) of the two compounds in the mixture, assuming \(V_{\text {blend }}=V_{\text {gasoline }}+V_{\text {kerosene. }}\)

In the manufacture of pharmaceuticals, most active pharmaceutical ingredients (APIs) are made in solution and then recovered by separation. Acetaminophen, a pain-killing drug commercially marketed as Tylenol", is synthesized in an aqueous solution and subsequently crystallized. The slurry of crystals is sent to a centrifuge from which two effluent streams emerge: ( 1 ) a wet cake containing 90.0 wt\% solid acetaminophen \((\mathrm{MW}=\) 151 g/mol) and 10.0 wt\% water (plus some acetaminophen and other dissolved substances, which we will neglect), and (2) a highly dilute aqueous solution of acetaminophen that is discharged from the process. The wet cake is fed to a dryer where the water is completely evaporated, leaving the residual acetaminophen solids bone dry. If the evaporated water were condensed, its volumetric flow rate would be \(50.0 \mathrm{Lh}\). Following is a flowchart of the process, which runs 24 h/day, 320 days/yr. A denotes acetaminophen. (a) Calculate the yearly production rate of solid acetaminophen (tonne/yr), using as few dimensional equations as possible. (b) A proposal has been made to subject the liquid solution leaving the centrifuge to further processing to recover more of the dissolved acetaminophen instead of disposing of the solution. On what would the decision depend?

A useful measure of an individual's physical condition is the fraction of his or her body that consists of fat. This problem describes a simple technique for estimating this fraction by weighing the individual twice, once in air and once submerged in water. (a) A man has body mass \(m_{b}=122.5 \mathrm{kg} .\) If he stands on a scale calibrated to read in newtons, what would the reading be? If he then stands on a scale while he is totally submerged in water at \(30^{\circ} \mathrm{C}\) (specific gravity \(=0.996\) ) and the scale reads \(44.0 \mathrm{N},\) what is the volume of his body (liters)? (Hint: Recall from Archimedes' principle that the weight of a submerged object equals the weight in air minus the buoyant force on the object, which in turn equals the weight of water displaced by the object. Neglect the buoyant force of air.) What is his body density, \(\rho_{\mathrm{b}}(\mathrm{kg} / \mathrm{L}) ?\) (b) Suppose the body is divided into fat and nonfat components, and that \(x_{f}\) (kilograms of fat/kilogram of total body mass) is the fraction of the total body mass that is fat: \(x_{\mathrm{f}}=\frac{m_{\mathrm{f}}}{m_{\mathrm{b}}}\) Prove that \(x_{\mathrm{f}}=\frac{\frac{1}{\rho_{\mathrm{b}}}-\frac{1}{\rho_{\mathrm{nf}}}}{\frac{1}{\rho_{\mathrm{f}}}-\frac{1}{\rho_{\mathrm{nf}}}}\) where \(\rho_{\mathrm{b}}, \rho_{\mathrm{f}},\) and \(\rho_{\mathrm{nf}}\) are the average densities of the whole body, the fat component, and the nonfat component, respectively. [Suggestion: Start by labeling the masses ( \(m_{\mathrm{f}}\) and \(m_{\mathrm{b}}\) ) and volumes \(\left(V_{\mathrm{f}} \text { and } V_{\mathrm{b}}\right)\) of the fat component of the body and the whole body, and then write expressions for the three densities in terms of these quantities. Then eliminate volumes algebraically and obtain an expression for \(\left.m_{f} / m_{b} \text { in terms of the densities. }\right]\) (c) If the average specific gravity of body fat is 0.9 and that of nonfat tissue is \(1.1,\) what fraction of the man's body in Part (a) consists of fat? (d) The body volume calculated in Part (a) includes volumes occupied by gas in the digestive tract, sinuses, and lungs. The sum of the first two volumes is roughly \(100 \mathrm{mL}\) and the volume of the lungs is roughly 1.2 liters. The mass of the gas is negligible. Use this information to improve your estimate of \(x_{\mathrm{f}}\).

A rectangular block of solid carbon (graphite) floats at the interface of two immiscible liquids. The bottom liquid is a relatively heavy lubricating oil, and the top liquid is water. Of the total block volume, \(54.2 \%\) is immersed in the oil and the balance is in the water. In a separate experiment, an empty flask is weighed, \(35.3 \mathrm{cm}^{3}\) of the lubricating oil is poured into the flask, and the flask is reweighed. If the scale reading was \(124.8 \mathrm{g}\) in the first weighing, what would it be in the second weighing? (Suggestion: Recall Archimedes' principle, and do a force balance on the block.)
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

The Earths Atmosphere

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.