/*! 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 15 Two streams flow into a 500 -gal... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 15

Two streams flow into a 500 -gallon tank. The first stream is 10.0 wt\% ethanol and \(90.0 \%\) hexane (the mixture density, \(\rho_{1},\) is \(0.68 \mathrm{g} / \mathrm{cm}^{3}\) ) and the second is \(90.0 \mathrm{wt} \%\) ethanol, \(10.0 \%\) hexane \(\left(\rho_{2}=0.78 \mathrm{g} / \mathrm{cm}^{3}\right) .\) After the tank has been filled, which takes 22 \(\mathrm{min}\), an analysis of its contents determines that the mixture is 60.0 wt\% ethanol, \(40.0 \%\) hexane. You wish to estimate the density of the final mixture and the mass and volumetric flow rates of the two feed streams. (a) Draw and label a flowchart of the mixing process and do the degree-of- freedom analysis. (b) Perform the calculations and state what you assumed.

Short Answer

Expert verified
The solution involves creating a flowchart and carrying out degree-of-freedom analysis, formulating equations based on mass and volume conservation, and finally solving these equations to find the mass flow rates of the feed streams and the density of the resulting mixture.

Step by step solution

01

Draw and analyze the flowchart

First, a flowchart is to be drawn, showing all the inputs and outputs. There are two inputs, stream 1 and 2, and one output, the mixture in the tank. Each stream has its concentration of ethanol and hexane given. The mix in the tank also has its concentration specified. A degree-of-freedom analysis will show that there are 5 components (ethanol and hexane in both streams and the tank) and 3 independent equations (two for conservation of mass and one relating mass and volume for the mixture). Thus, there are \(5-3 = 2\) degrees of freedom, indicating there are enough data to solve the problem with 2 unknown variables.
02

Mathematical formulation for the mixture density

The mass (m1 + m2) of the mixture in the tank is found assuming volume is conserved. The volume is 500 gallons, which is equivalent to 1892,705924 Liters (or 1892705,924 cm鲁, since 1L = 1000 cm鲁). So total mass is the sum of ethanol and hexane and can be calculated using the equation \( m = V * \rho \), where \( m \) is mass, \( V \) is volume, and \( \rho \) is density. So, \( m = 1892705,924 * \rho \) where \( \rho \) is the final mixture density which is unknown.
03

Calculating Mass Flow Rates of the Feed Streams

Recognized that the mass of the mixture is made up of the streams flowing in, so \( m = m1_{ethanol} + m2_{ethanol} + m1_{hexane} + m2_{hexane} \). Given the mass fractions of ethanol and hexane in each flow streams, the mass flow rates (g/min) can be expressed. The volumetric flow rates (cm鲁/min) is found by dividing the mass flow rate by its respective density.
04

Solving the Equation

Solving the equations formed would give the values of the mass flow rates of the streams and the density of the mixture, which are the unknown variables.

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.

Mass and Energy Balance
Understanding mass and energy balances is fundamental in analyzing any chemical process. It is based on the law of conservation of mass and energy, which states that, within a closed system, mass and energy can neither be created nor destroyed, only converted from one form to another. In our exercise, we performed a mass balance to determine the composition and flow rates of a mixture based on the amount of ethanol and hexane from two separate streams entering a tank.

Determining the mass balance requires accounting for all the mass entering and leaving the system. In this case, we know the contents and volume of the tank, the composition of the inputs, and the time it takes to fill. With this information, we can calculate the overall mass of each component within the tank by using the mass balance equation:

\( m_{total} = m_{inlet_1} + m_{inlet_2} - m_{outlet} \).

Since the tank is just being filled and has no outlet stream, the mass of ethanol and hexane is simply the sum of what has been introduced into the tank. This calculation is essential for quantifying the mass flow rates of individual streams.
Density Calculation
The concept of density plays a critical role in determining the characteristics of a mixture within a process. Density is defined as mass per unit volume (\( \rho = \frac{m}{V} \)). In our exercise, to compute the density of the final mixture, the total mass of the mixture was first determined. Since the volume of the tank is known (500 gallons), the density calculation can be inferred using the derived mass balance information.

To find the density (\

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

A fuel distributor supplies four liquid fuels, each of which has a different ratio of ethanol to gasoline. Five percent of the demand is for E100 (pure ethanol), 15\% for E85 (85.0 volume\% ethanol), 40\% for E10 (10.0\% ethanol), and the remainder for pure gasoline. The distributor blends gasoline and ethanol to produce E85 and E10, and the four products are produced continuously. (a) Draw and label a flowchart for the blending operation, letting \(\dot{V}\) represent the combined volumetric flow rate of all four fuels and \(\dot{V}_{\mathrm{G}}\) and \(\dot{V}_{\mathrm{E}}\) represent the volumetric flow rates of gasoline and ethanol sold as fuels and sent to the blending operation. (b) Assuming volume additivity when blending ethanol and gasoline, determine the volumetric flow rates of all streams when delivery of 100,000 L/d of \(\mathrm{E} 10\) is specified. (c) Tank trucks are to transport the fuel from the blending operation to service stations in the area. The gross weight of a loaded truck, which has a tare (empty) weight of \(12,700 \mathrm{kg}\), cannot exceed \(36,000 \mathrm{kg} .\) Assuming the specific gravity of pure gasoline is \(0.73,\) estimate the maximum volume (L) of each fuel that can be loaded onto a truck.

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?

A stream of humid air containing 1.50 mole \(\% \mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) and the balance dry air is to be humidified to a water content of 10.0 mole\% \(\mathrm{H}_{2} \mathrm{O}\). For this purpose, liquid water is fed through a flowmeter and evaporated into the air stream. The flowmeter reading, \(R\), is \(95 .\) The only available calibration data for the flowmeter are two points scribbled on a sheet of paper, indicating that readings \(R=15\) and \(R=50\) correspond to flow rates \(\dot{V}=40.0 \mathrm{ft}^{3} / \mathrm{h}\) and \(\dot{V}=96.9 \mathrm{ft}^{3} / \mathrm{h},\) respectively. (a) Assuming that the process is working as intended, draw and label the flowchart, do the degree-offreedom analysis, and estimate the molar flow rate (lb-mole/h) of the humidified (outlet) air if (i) the volumetric flow rate is a linear function of \(R\) and (ii) the reading \(R\) is a linear function of \(\dot{V}^{0.5}\) (b) Suppose the outlet air is analyzed and found to contain only \(7 \%\) water instead of the desired \(10 \%\) List as many possible reasons as you can think of for the discrepancy, concentrating on assumptions made in the calculation of Part (a) that might be violated in the real process.

If the percentage of fuel in a fuel-air mixture falls below a certain value called the lower flammability limit (LFL), which sometimes is referred to as the lower explosion limit (LEL), the mixture cannot be ignited. In addition there is an upper flammability limit (UFL), which also is known as the upper explosion limit (UEL). For example, the LFL of propane in air is 2.3 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) and the UFL is \(9.5 \%^{14}\). If the percentage of propane in a propane-air mixture is greater than \(2.3 \%\) and less than \(9.5 \%,\) the gas mixture can ignite if it is exposed to a flame or spark. A mixture of propane in air containing 4.03 mole \(\% \mathrm{C}_{3} \mathrm{H}_{8}\) (fuel gas) is the feed to a combustion furnace. If there is a problem in the furnace, a stream of pure air (dilution air) is added to the fuel mixture prior to the furnace inlet to make sure that ignition is not possible. (a) Draw and label a flowchart of the fuel gas-dilution air mixing unit, presuming that the gas entering the furnace contains propane at the LFL, and do the degree-of-freedom analysis. (b) If propane flows at a rate of \(150 \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8} / \mathrm{s}\) in the original fuel-air mixture, what is the minimum molar flow rate of the dilution air? (c) How would the actual dilution air feed rate probably compare with the value calculated in Part (b)? (>, \(<,=\) ) Explain.

The popularity of orange juice, especially as a breakfast drink, makes this beverage an important factor in the economy of orange-growing regions. Most marketed juice is concentrated and frozen and then reconstituted before consumption, and some is "not-from-concentrate." Although concentrated juices are less popular in the United States than they were at one time, they still have a major segment of the market for orange juice. The approaches to concentrating orange juice include evaporation, freeze concentration, and reverse osmosis. Here we examine the evaporation process by focusing only on two constituents in the juice: solids and water. Fresh orange juice contains approximately 10 wt\% solids (sugar, citric acid, and other ingredients) and frozen concentrate contains approximately 42 wt\% solids. The frozen concentrate is obtained by evaporating water from the fresh juice to produce a mixture that is approximately 65 wt\% solids. However, so that the flavor of the concentrate will closely approximate that of fresh juice, the concentrate from the evaporator is blended with fresh orange juice (and other additives) to produce a final concentrate that is approximately 42 wt\% solids. (a) Draw and label a flowchart of this process, neglecting the vaporization of everything in the juice but water. First prove that the subsystem containing the point where the bypass stream splits off from the evaporator feed has one degree of freedom. (If you think it has zero degrees, try determining the unknown variables associated with this system.) Then perform the degree- offreedom analysis for the overall system, the evaporator, and the bypass- evaporator product mixing point, and write in order 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 any calculations. (b) Calculate the amount of product (42\% concentrate) produced per 100 kg fresh juice fed to the process and the fraction of the feed that bypasses the evaporator. (c) Most of the volatile ingredients that provide the taste of the concentrate are contained in the fresh juice that bypasses the evaporator. You could get more of these ingredients in the final product by evaporating to (say) 90\% solids instead of 65\%; you could then bypass a greater fraction of the fresh juice and thereby obtain an even better tasting product. Suggest possible drawbacks to this proposal.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Organic Chemistry

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.