/*! 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 32 Gas streams containing hydrogen ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 32

Gas streams containing hydrogen and nitrogen in different proportions are produced on request by blending gases from two feed tanks: Tank A (hydrogen mole fraction \(=x_{\mathrm{A}}\) ) and Tank \(\mathrm{B}\) (hydrogen mole fraction \(=x_{\mathrm{B}}\) ). The requests specify the desired hydrogen mole fraction, \(x_{\mathrm{p}}\), and mass flow rate of the product stream, \(\dot{m}_{\mathrm{P}}(\mathrm{kg} / \mathrm{h})\) (a) Suppose the feed tank compositions are \(x_{\mathrm{A}}=0.10 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol}\) and \(x_{\mathrm{B}}=0.50 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol},\) and the desired blend-stream mole fraction and mass flow rate are \(x_{\mathrm{P}}=0.20 \mathrm{mol} \mathrm{H}_{2} / \mathrm{mol}\) and \(\dot{m}_{\mathrm{P}}=100 \mathrm{kg} / \mathrm{h} .\) Draw and label a flowchart and calculate the required molar flow rates of the feed mixtures, \(\dot{n}_{\mathrm{A}}(\mathrm{kmol} / \mathrm{h})\) and \(\dot{n}_{\mathrm{B}}(\mathrm{kmol} / \mathrm{h})\) (b) Derive a series of formulas for \(\dot{n}_{\mathrm{A}}\) and \(\dot{n}_{\mathrm{B}}\) in terms of \(x_{\mathrm{A}}, x_{\mathrm{B}}, x_{\mathrm{P}},\) and \(\dot{m}_{\mathrm{P}} .\) Test them using the values in Part (a). (c) Write a spreadsheet that has column headings \(x_{\mathrm{A}}, x_{\mathrm{B}}, x_{\mathrm{P}}, \dot{m}_{\mathrm{P}}, \dot{n}_{\mathrm{A}},\) and \(\dot{n}_{\mathrm{B}}\). The spreadsheet should calculate entries in the last two columns corresponding to data in the first four. In the first six data rows of the spreadsheet, do the calculations for \(x_{\mathrm{A}}=0.10, x_{\mathrm{B}}=0.50,\) and \(x_{\mathrm{P}}=\) \(0.10,0.20,0.30,0.40,0.50,\) and \(0.60,\) all for \(\dot{m}_{\mathrm{P}}=100 \mathrm{kg} / \mathrm{h} .\) Then in the next six rows repeat the calculations for the same values of \(x_{\mathrm{A}}, x_{\mathrm{B}},\) and \(x_{\mathrm{p}}\) for \(\dot{m}_{\mathrm{p}}=250 \mathrm{kg} / \mathrm{h} .\) Explain any of your results that appear strange or impossible. (d) Enter the formulas of Part (b) into an equation-solving program. Run the program to determine \(\dot{n}_{\mathrm{A}}\) and \(\dot{n}_{\mathrm{B}}\) for the 12 sets of input variable values given in Part (c) and explain any physically impossible results.

Short Answer

Expert verified
This exercise requires knowledge of mole and mass fractions, molar flow rates, and mass balance principles to find the required molar flow rates of feed mixtures that will yield a desired product mixture. After deriving the formulas for molar flow rates, they are tested using the known feed compositions and desired product conditions. Subsequently, a spreadsheet is used to perform calculations for different mole fractions and mass flow rates, prompting certain impossible results which means those input conditions are unfeasible in real-life scenarios.

Step by step solution

01

Calculate Molar Flow Rates for the Feed Mixtures

Use the given mass flow rate and molecular weight for the feed and product streams to establish a mass balance for hydrogen. This mass balance enables the calculation of molar flow rates for the feed mixtures. The molecular weight of H2 is 2 kg/kmol.
02

Derive Formulas for Molar Flow Rates

The derived formulas will create a relationship between the molar flow rates of the feed mixture and the mole fractions and mass flow rate of the hydrogen. By setting up a mass balance around the mixing point and doing some algebraic manipulations, the formulas can be generalized to represent any input condition.
03

Create Spreadsheet for Calculations

With the given inputs, the formulas developed in Step 2 can be used to compute the molar flow rates in a spreadsheet. The spreadsheet can then calculate the molar flow rates corresponding to data in the first four columns for different mole fractions and mass flow rates. Notably, some of the results obtained may seem strange or impossible. For instance, a negative molar flow rate is physically impossible.
04

Compute Molar Flow Rates using an Equation-Solving Program

By inputting the formulas into an equation-solving program, the molar flow rates can be determined for the 12 sets of input variable values given. While running the program, any physically impossible results, like negative molar flow rates, will prove the input conditions unfeasible to carry out in reality.

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.

Understanding Molecular Flow Rate
In chemical engineering, the term "molecular flow rate" refers to the number of moles of a substance that passes through a section of a process per unit time. This is crucial in processes like gas blending, where different gases are mixed to achieve a desired composition. For example, when blending hydrogen and nitrogen from two tanks, knowing the molecular flow rate of each feed is necessary to achieve a desired hydrogen mole fraction in the product stream.
The molecular flow rate is often denoted as \(\dot{n}\), with units of moles per hour or \(\text{kmol/h}\). Calculating this involves understanding the mass balance in the system and the mole fractions of the components in the feed and the product. By setting up a mass balance equation around a mixing point, you can determine the molar flow rates required from each tank to meet a specific product composition. This concept helps ensure that the process operates efficiently and meets the specifications set by the system demand.
Principles of Mass Balance
Mass balance is a fundamental concept in chemical engineering used to calculate the flow rates of substances in a chemical process. It is based on the principle of conservation of mass, stating that mass cannot be created or destroyed. Everything that enters a process must either leave the process as output or accumulate within the system. This is summed up in the equation: \[\text{Input} - \text{Output} = \text{Accumulation}\]Applying this to a gas blending scenario, where gases like hydrogen are blended from different sources to achieve a desired composition, involves considering the hydrogen molecules entering and leaving the system.
Consider Tank A and Tank B, each with known hydrogen mole fractions. To find the necessary molar flow rates to achieve a certain hydrogen content in the final blend, you balance the masses: the total hydrogen in the output must equal the total hydrogen coming from the inputs. This often requires solving equations that combine these mole fractions with known mass flow rates. Understanding mass balance is critical for designing and operating processes that are safe, efficient, and environmentally friendly.
Using a Chemical Engineering Spreadsheet
In modern chemical engineering, spreadsheets play a crucial role in calculations and data analysis. A spreadsheet for chemical process calculations allows engineers to systematically organize data, apply equations, and visualize results.
In the context of the gas blending exercise, a spreadsheet can be set up to calculate the molar flow rates based on varying inputs like mole fractions and mass flow rates. Columns are typically organized to represent each variable involved in the process. For example:
  • Mole fractions of hydrogen from each tank \(x_{A}, x_{B}, x_{P}\)
  • The mass flow rate of the product \(\dot{m}_{P}\)
  • The molar flow rates from each tank \(\dot{n}_{A}, \dot{n}_{B}\)
By entering the input variables, the spreadsheet automatically performs calculations using the formulas derived for molar flow rates, providing instant feedback on the feasibility and optimization of process designs. Spreadsheets thus offer a powerful tool for chemical engineers to test different scenarios, identify anomalies, such as negative flow rates, and optimize the blending process effectively.

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

Draw and label the given streams and derive expressions for the indicated quantities in terms of labeled variables. The solution of Part (a) is given as an illustration. (a) A continuous stream contains 40.0 mole\% benzene and the balance toluene. Write expressions for the molar and mass flow rates of benzene, \(\dot{n}_{\mathrm{B}}\left(\operatorname{mol} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right)\) and \(\dot{m}_{\mathrm{B}}\left(\mathrm{kg} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right),\) in terms of the total molar flow rate of the stream, \(\dot{n}(\mathrm{mol} / \mathrm{s})\) (b) The feed to a batch process contains equimolar quantities of nitrogen and methane. Write an expression for the kilograms of nitrogen in terms of the total moles \(n(\) mol) of this mixture. (c) A stream containing ethane, propane, and butane has a mass flow rate of \(100.0 \mathrm{g} / \mathrm{s}\). Write an expression for the molar flow rate of ethane, \(\dot{n}_{\mathrm{E}}\left(\text { Ib-mole } \mathrm{C}_{2} \mathrm{H}_{6} / \mathrm{h}\right)\), in terms of the mass fraction of this species, \(x_{\mathrm{E}}\). (d) A continuous stream of humid air contains water vapor and dry air, the latter containing approximately 21 mole \(\% \mathrm{O}_{2}\) and \(79 \% \mathrm{N}_{2}\). Write expressions for the molar flow rate of \(\mathrm{O}_{2}\) and for the mole fractions of \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{O}_{2}\) in the gas in terms of \(\dot{n}_{1}\left(\mathrm{lb}-\mathrm{mole} \mathrm{H}_{2} \mathrm{O} / \mathrm{s}\right)\) and \(\dot{n}_{2}(\text { lb- mole dry air/s })\) (e) The product from a batch reactor contains \(\mathrm{NO}, \mathrm{NO}_{2},\) and \(\mathrm{N}_{2} \mathrm{O}_{4} .\) The mole fraction of \(\mathrm{NO}\) is 0.400. Write an expression for the gram-moles of \(\mathrm{N}_{2} \mathrm{O}_{4}\) in terms of \(n(\mathrm{mol}\) mixture) and \(y_{\mathrm{NO}_{2}}\left(\operatorname{mol} \mathrm{NO}_{2} / \mathrm{mol}\right)\)

Methane and oxygen react in the presence of a catalyst to form formaldehyde. In a parallel reaction, methane is oxidized to carbon dioxide and water: $$\begin{aligned} \mathrm{CH}_{4}+\mathrm{O}_{2} & \rightarrow \mathrm{HCHO}+\mathrm{H}_{2} \mathrm{O} \\ \mathrm{CH}_{4}+2 \mathrm{O}_{2} & \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \end{aligned}$$ The feed to the reactor contains equimolar amounts of methane and oxygen. Assume a basis of \(100 \mathrm{mol}\) feed/s. (a) Draw and label a flowchart. Use a degree-of-freedom analysis based on extents of reaction to determine how many process variable values must be specified for the remaining variable values to be calculated. (b) Use Equation 4.6-7 to derive expressions for the product stream component flow rates in terms of the two extents of reaction, \(\xi_{1}\) and \(\xi_{2}\) (c) The fractional conversion of methane is 0.900 and the fractional yield of formaldehyde is 0.855 . Calculate the molar composition of the reactor output stream and the selectivity of formaldehyde production relative to carbon dioxide production. (d) A classmate of yours makes the following observation: "If you add the stoichiometric equations for the two reactions, you get the balanced equation $$2 \mathrm{CH}_{4}+3 \mathrm{O}_{2} \rightarrow \mathrm{HCHO}+\mathrm{CO}_{2}+3 \mathrm{H}_{2} \mathrm{O}$$ The reactor output must therefore contain one mole of \(\mathrm{CO}_{2}\) for every mole of HCHO, so the selectivity of formaldehyde to carbon dioxide must be \(1.0 .\) Doing it the way the book said to do it, \(I\) got a different selectivity. Which way is right, and why is the other way wrong?" What is your response?

The gas-phase reaction between methanol and acetic acid to form methyl acetate and water takes place in a batch reactor. When the reaction mixture comes to equilibrium, the mole fractions of the four reactive species are related by the reaction equilibrium constant $$K_{y}=\frac{y_{C} y_{D}}{y_{A} y_{B}}=4.87$$ (a) Suppose the feed to the reactor consists of \(n_{\mathrm{A} 0}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0}, n_{\mathrm{D} 0},\) and \(n_{10}\) gram-moles of \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D},\) and an inert gas, I, respectively. Let \(\xi\) be the extent of reaction. Write expressions for the gram-moles of each reactive species in the final product, \(n_{\mathrm{A}}(\xi), n_{\mathrm{B}}(\xi), n_{\mathrm{C}}(\xi),\) and \(n_{\mathrm{D}}(\xi) .\) Then use these expressions and the given equilibrium constant to derive an equation for \(\xi_{c}\), the equilibrium extent of reaction, in terms of \(\left.n_{\mathrm{A} 0}, \ldots, n_{10} . \text { (see Example } 4.6-2 .\right)\) (b) If the feed to the reactor contains equimolar quantities of methanol and acetic acid and no other species, calculate the equilibrium fractional conversion. (c) It is desired to produce 70 mol of methyl acetate starting with 75 mol of methanol. If the reaction proceeds to equilibrium, how much acetic acid must be fed? What is the composition of the final product? (d) Suppose it is important to reduce the concentration of methanol by making its conversion at equilibrium as high as possible, say 99\%. Again assuming the feed to the reactor contains only methanol and acetic acid and that it is desired to produce 70 mol of methyl acetate, determine the extent of reaction and quantities of methanol and acetic acid that must be fed to the reactor. (e) If you wanted to carry out the process of Part (b) or (c) commercially, what would you need to know besides the equilibrium composition to determine whether the process would be profitable? (List several things.)

n-Pentane is burned with excess air in a continuous combustion chamber. (a) A technician runs an analysis and reports that the product gas contains 0.270 mole\% pentane, \(5.3 \%\) oxygen, \(9.1 \%\) carbon dioxide, and the balance nitrogen on \(a\) dry basis. Assume 100 mol of dry product gas as a basis of calculation, draw and label a flowchart, perform a degree-offreedom analysis based on atomic species balances, and show that the system has -1 degree of freedom. Interpret this result. (b) Use balances to prove that the reported percentages could not possibly be correct. (c) The technician reruns the analysis and reports new values of 0.304 mole\% pentane, \(5.9 \%\) oxygen, \(10.2 \%\) carbon dioxide, and the balance nitrogen. Verify that this result could be correct and, assuming that it is, calculate the percent excess air fed to the reactor and the fractional conversion of pentane. (d) It was emphasized in Part (c) that the new composition could be correct. Explain why it isn't possible to say for sure; illustrate your response by considering a set of equations with -1 degree of freedom.

Carbon nanotubes (CNT) are among the most versatile building blocks in nanotechnology. These unique pure carbon materials resemble rolled-up sheets of graphite with diameters of several nanometers and lengths up to several micrometers. They are stronger than steel, have higher thermal conductivities than most known materials, and have electrical conductivities like that of copper but with higher currentcarrying capacity. Molecular transistors and biosensors are among their many applications. While most carbon nanotube research has been based on laboratory-scale synthesis, commercial applications involve large industrial-scale processes. In one such process, carbon monoxide saturated with an organo-metallic compound (iron penta-carbonyl) is decomposed at high temperature and pressure to form CNT, amorphous carbon, and CO_. Each "molecule" of CNT contains roughly 3000 carbon atoms. The reactions by which such molecules are formed are: In the process to be analyzed, a fresh feed of CO saturated with \(\mathrm{Fe}(\mathrm{CO})_{5}(\mathrm{v})\) contains \(19.2 \mathrm{wt} \%\) of the latter component. The feed is joined by a recycle stream of pure CO and fed to the reactor, where all of the iron penta-carbonyl decomposes. Based on laboratory data, \(20.0 \%\) of the CO fed to the reactor is converted, and the selectivity of CNT to amorphous carbon production is (9.00 kmol CNT/kmol C). The reactor effluent passes through a complex separation process that yields three product streams: one consists of solid \(\mathrm{CNT}, \mathrm{C},\) and \(\mathrm{Fe} ;\) a second is \(\mathrm{CO}_{2} ;\) and the third is the recycled \(\mathrm{CO}\). You wish to determine the flow rate of the fresh feed (SCM/h), the total CO_ generated in the process ( \(\mathrm{kg} / \mathrm{h}\) ), and the ratio (kmol CO recycled/kmol CO in fresh feed). (a) Take a basis of \(100 \mathrm{kmol}\) fresh feed. Draw and fully label a process flow chart and do degree-offreedom analyses for the overall process, the fresh-feed/recycle mixing point, the reactor, and the separation process. Base the analyses for reactive systems on atomic balances. (b) Write and solve overall balances, and then scale the process to calculate the flow rate (SCM/h) of fresh feed required to produce \(1000 \mathrm{kg} \mathrm{CNT} / \mathrm{h}\) and the mass flow rate of \(\mathrm{CO}_{2}\) that would be produced. (c) In your degree-of-freedom analysis of the reactor, you might have counted separate balances for C (atomic carbon) and O (atomic oxygen). In fact, those two balances are not independent, so one but not both of them should be counted. Revise your analysis if necessary, and then calculate the ratio (kmol CO recycled/kmol CO in fresh feed). (d) Prove that the atomic carbon and oxygen balances on the reactor are not independent equations.
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Making Measurements

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.