/*! 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 13 A process is carried out in whic... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A process is carried out in which a mixture containing 25.0 wt\% methanol, \(42.5 \%\) ethanol, and the balance water is separated into two fractions. A technician draws and analyzes samples of both product streams and reports that one stream contains \(39.8 \%\) methanol and \(31.5 \%\) ethanol and the other contains 19.7\% methanol and 41.2\% ethanol. You examine the reported figures and tell the technician that they must be wrong and that stream analyses should be carried out again. (a) Prove your statement. (b) How many streams do you ask the technician to analyze? Explain.

Short Answer

Expert verified
The reported figures are incorrect as the weight percentage of methanol, ethanol, and water in both product streams doesn't add up to 100%. Thereby, both streams need to be analyzed again.

Step by step solution

01

Calculation of water percentage in the original mixture

The weight percentage of each substance in the given mixture is calculated. The percent weight of methanol is 25%, ethanol is 42.5%, and the balance, i.e. 100 - 25 - 42.5 = 32.5%, is water.
02

Validation of the product stream data

The total weight percentage in both product streams must add up to 100%. For the first product stream, it sums up to 39.8% methanol + 31.5% ethanol = 71.3% which implies that the rest 28.7% should be water. For the second product stream, the sum is 19.7% methanol + 41.2% ethanol = 60.9%, implying 39.1% should be water. It is clear that the total weight percentage in both product streams does not add to 100%. Hence, the reported figures are incorrect.
03

Verification of streams to be analyzed

The technician needs to analyze the same two streams again because the sum of the percentages of methanol, ethanol, and water in both streams should always add up to 100%. Since it's not the case for the provided data, there must be a mistake in the measurement or calculation process.

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 91Ó°ÊÓ!

Key Concepts

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

Weight Percentage Calculation
Understanding weight percentage calculation is fundamental in chemical process analysis. It is a method to express the concentration of an ingredient in a mixture by weight. For instance, if you have a mixture of various substances, the weight percentage tells you how much of each component you have, compared to the total mixture's weight.

For a proper calculation, you would add up the weight of each ingredient and divide the weight of the individual component by the total weight, then multiply by 100 to get a percentage. This form of calculation is crucial because in chemistry, the composition of mixtures must conform to the law of conservation of mass. That means when you sum the weight percentages of all components in a mixture, it should always equal 100%. If it doesn’t, an error has occurred, indicating that the analysis needs to be revisited to correct the mistakes.
Separation Processes
In the field of chemical engineering, separation processes are essential operations used to purify or separate mixtures into their constituent parts. These processes include distillation, filtration, crystallization, and others. For example, when a mixture of liquids with different boiling points is heated, the one with the lower boiling point will vaporize first, enabling its separation from the rest.

During these processes, rigorous monitoring and analysis are performed to ensure the desired level of purity is achieved. Efficacy is judged not only by the quality of the separated products but also by how well the original mixture's components are distributed across the resulting product streams. Misjudgments or errors in separation can lead to reduced efficiency, product contamination, or process malfunction. Therefore, separation processes are closely linked with accurate weight percentage calculations and data validation.
Validation of Analytical Data
The validation of analytical data is a critical step that ensures integrity and accuracy in chemical analysis. This involves confirming that the data aligns with theoretically expected values, following laws such as the conservation of mass. Data validation detects errors in measurement, calculation, or procedural steps within analytical processes.

When discrepancies appear, such as sums of percentages not equating to 100%, a red flag is raised for analysts to re-examine their results. Validation includes cross-checking calculations, redoing measurements, and sometimes using alternative methods for comparison. Effective validation practices are the safeguard against making potentially costly or hazardous errors in both academia and industry. In the case of our exercise, the technician's reported data failing to validate against expected norms prompted a repetition of the analysis, highlighting the importance of meticulous validation procedures.

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

Methanol is produced by reacting carbon monoxide and hydrogen. A fresh feed stream containing \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) joins a recycle stream and the combined stream is fed to a reactor. The reactor outlet stream flows at a rate of \(350 \mathrm{mol} / \mathrm{min}\) and contains \(10.6 \mathrm{wt} \% \mathrm{H}_{2}, 64.0 \mathrm{wt} \% \mathrm{CO},\) and \(25.4 \mathrm{wt} \% \mathrm{CH}_{3} \mathrm{OH} .\) (Notice that those are percentages by mass, not mole percents.) This stream enters a cooler in which most of the methanol is condensed. The liquid methanol condensate is withdrawn as a product, and the gas stream leaving the condenser- -which contains \(\mathrm{CO}, \mathrm{H}_{2},\) and \(0.40 \mathrm{mole} \%\) uncondensed \(\mathrm{CH}_{3} \mathrm{OH}\) vapor \(-\mathrm{is}\) the recycle stream that combines with the fresh feed. (a) Without doing any calculations, prove that you have enough information to determine (i) the molar flow rates of CO and \(\mathrm{H}_{2}\) in the fresh feed, (ii) the production rate of liquid methanol, and (iii) the single-pass and overall conversions of carbon monoxide. Then perform the calculations. (b) After several months of operation, the flow rate of liquid methanol leaving the condenser begins to decrease. List at least three possible explanations of this behavior and state how you might check the validity of each one. (What would you measure and what would you expect to find if the explanation is valid?)

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.

Oxygen consumed by a living organism in aerobic reactions is used in adding mass to the organism and/or the production of chemicals and carbon dioxide. since we may not know the molecular compositions of all species in such a reaction, it is common to define the ratio of moles of \(\mathrm{CO}_{2}\) produced per mole of \(\mathrm{O}_{2}\) consumed as the respiratory quotient, \(R Q,\) where $$R Q=\frac{n_{\mathrm{CO}_{2}}}{n_{\mathrm{O}_{2}}}\left(\text { or } \frac{\dot{n}_{\mathrm{CO}_{2}}}{\dot{n}_{\mathrm{O}_{2}}}\right)$$ since it generally is impossible to predict values of \(R Q\), they must be determined from operating data. Mammalian cells are used in a bioreactor to convert glucose to glutamic acid by the reaction $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+a \mathrm{NH}_{3}+b \mathrm{O}_{2} \rightarrow p \mathrm{C}_{5} \mathrm{H}_{9} \mathrm{NO}_{4}+q \mathrm{CO}_{2}+r \mathrm{H}_{2} \mathrm{O}$$ The feed to the bioreactor comprises \(1.00 \times 10^{2} \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} / \mathrm{day}, 1.20 \times 10^{2} \mathrm{mol} \mathrm{NH}_{3} / \mathrm{day},\) and \(1.10 \times\) \(10^{2}\) mol \(\mathrm{O}_{2} /\) day. Data on the system show that \(R Q=0.45 \mathrm{mol} \mathrm{CO}_{2}\) produced/mol \(\mathrm{O}_{2}\) consumed. (a) Determine the five stoichiometric coefficients and the limiting reactant. (b) Assuming that the limiting reactant is consumed completely, calculate the molar and mass flow rates of all species leaving the reactor and the fractional conversions of the non-limiting reactants.

A stream containing \(\mathrm{H}_{2} \mathrm{S}\) and inert gases and a second stream of pure \(\mathrm{SO}_{2}\) are fed to a sulfur recovery reactor, where the reaction $$2 \mathrm{H}_{2} \mathrm{S}+\mathrm{SO}_{2} \rightarrow 3 \mathrm{S}+2 \mathrm{H}_{2} \mathrm{O}$$ takes place. The feed rates are adjusted so that the ratio of \(\mathrm{H}_{2} \mathrm{S}\) to \(\mathrm{SO}_{2}\) in the combined feed is always stoichiometric. In the normal operation of the reactor the flow rate and composition of the \(\mathrm{H}_{2} \mathrm{S}\) feed stream both fluctuate. In the past, each time either variable changed the required \(\mathrm{SO}_{2}\) feed rate had to be reset by adjusting a valve in the feed line. A control system has been installed to automate this process. The \(\mathrm{H}_{2} \mathrm{S}\) feed stream passes through an electronic flowmeter that transmits a signal \(R_{\mathrm{f}}\) directly proportional to the molar flow rate of the stream, \(\dot{n}_{\mathrm{f}}\). When \(\dot{n}_{\mathrm{f}}=100 \mathrm{kmol} / \mathrm{h}\), the transmitted signal \(R_{\mathrm{f}}=15 \mathrm{mV}\). The mole fraction of \(\mathrm{H}_{2} \mathrm{S}\) in this stream is measured with a thermal conductivity detector, which transmits a signal \(R_{\mathrm{a}} .\) Analyzer calibration data are as follows: $$\begin{array}{|l|c|c|c|c|c|c|}\hline R_{\mathrm{a}}(\mathrm{mV}) & 0 & 25.4 & 42.8 & 58.0 & 71.9 & 85.1 \\ \hline x\left(\mathrm{mol} \mathrm{H}_{2} \mathrm{S} / \mathrm{mol}\right) & 0.00 & 0.20 & 0.40 & 0.60 &0.80 & 1.00 \\\\\hline\end{array}$$ The controller takes as input the transmitted values of \(R_{\mathrm{f}}\) and \(R_{\mathrm{a}}\) and calculates and transmits a voltage signal \(R_{\mathrm{c}}\) to a flow control valve in the \(\mathrm{SO}_{2}\) line, which opens and closes to an extent dependent on the value of \(R_{c} .\) A plot of the \(S O_{2}\) flow rate, \(\dot{n}_{c},\) versus \(R_{c}\) on rectangular coordinates is a straight line through the points \(\left(R_{c}=10.0 \mathrm{mV}, \dot{n}_{c}=25.0 \mathrm{kmol} / \mathrm{h}\right)\) and \(\left(R_{c}=25.0 \mathrm{mV}, \dot{n}_{c}=60.0 \mathrm{kmol} / \mathrm{h}\right)\) (a) Why would it be important to feed the reactants in stoichiometric proportion? (Hint: \(\mathrm{SO}_{2}\) and especially \(\mathrm{H}_{2} \mathrm{S}\) are serious pollutants.) What are several likely reasons for wanting to automate the \(\mathrm{SO}_{2}\) feed rate adjustment? (b) If the first stream contains 85.0 mole \(\% \mathrm{H}_{2} \mathrm{S}\) and enters the unit at a rate of \(\dot{n}_{\mathrm{f}}=3.00 \times 10^{2} \mathrm{kmol} / \mathrm{h}\) what must the value of \(\dot{n}_{c}\left(\mathrm{kmol} \mathrm{SO}_{2} / \mathrm{h}\right)\) be? (c) Fit a function to the \(\mathrm{H}_{2} \mathrm{S}\) analyzer calibration data to derive an expression for \(x\) as a function of \(R_{\mathrm{a}}\) Check the fit by plotting both the function and the calibration data on the same graph. (d) Derive a formula for \(R_{\mathrm{c}}\) from specified values of \(R_{\mathrm{f}}\) and \(R_{\mathrm{a}},\) using the result of Part (c) in the derivation. (This formula would be built into the controller.) Test the formula using the flow rate and composition data of Part (a). (e) The system has been installed and made operational, and at some point the concentration of \(\mathrm{H}_{2} \mathrm{S}\) in the feed stream suddenly changes. A sample of the blended gas is collected and analyzed a short time later and the mole ratio of \(\mathrm{H}_{2} \mathrm{S}\) to \(\mathrm{SO}_{2}\) is not the required 2: 1 . List as many possible reasons as you can think of for this apparent failure of the control system.

An evaporation-crystallization process of the type described in Example \(4.5-2\) is used to obtain solid potassium sulfate from an aqueous solution of this salt. The fresh feed to the process contains 19.6 wt\% \(\mathrm{K}_{2} \mathrm{SO}_{4}\). The wet filter cake consists of solid \(\mathrm{K}_{2} \mathrm{SO}_{4}\) crystals and a \(40.0 \mathrm{wt} \% \mathrm{K}_{2} \mathrm{SO}_{4}\) solution, in a ratio \(10 \mathrm{kg}\) crystals/kg solution. The filtrate, also a \(40.0 \%\) solution, is recycled to join the fresh feed. Of the water fed to the evaporator, 45.0\% is evaporated. The evaporator has a maximum capacity of 175 kg water evaporated/s. (a) Assume the process is operating at maximum capacity. Draw and label a flowchart and do the degree-of-freedom analysis for the overall system, the recycle-fresh feed mixing point, the evaporator, and the crystallizer. Then write in an efficient order (minimizing simultaneous equations) the equations you would solve to determine all unknown stream variables. In each equation, circle the variable for which you would solve, but don't do the calculations. (b) Calculate the maximum production rate of solid \(\mathrm{K}_{2} \mathrm{SO}_{4}\), the rate at which fresh feed must be supplied to achieve this production rate, and the ratio kg recycle/kg fresh feed. (c) Calculate the composition and feed rate of the stream entering the crystallizer if the process is scaled to 75\% of its maximum capacity. (d) The wet filter cake is subjected to another operation after leaving the filter. Suggest what it might be. Also, list what you think the principal operating costs for this process might be. (e) Use an equation-solving computer program to solve the equations derived in Part (a). Verify that you get the same solutions determined in Part (b).

See all solutions

Recommended explanations on Chemistry Textbooks

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.