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Chapter 3: Problem 22

A mixture of methanol and propyl acetate contains 25.0 wt\% methanol. (a) Using a single dimensional equation, determine the g-moles of methanol in \(200.0 \mathrm{kg}\) of the mixture. (b) The flow rate of propyl acetate in the mixture is to be 100.0 ib-mole/h. What must the mixture flow rate be in \(\mathrm{Ib}_{\mathrm{m}} / \mathrm{h} ?\)

Short Answer

Expert verified
The g-moles of methanol in 200.0 kg of the mixture approximately equals 1562.5 g-moles. The mixture flow rate should be about 133.33 ib-mole/h.

Step by step solution

01

Calculate the mass of methanol

The mass of methanol in the mixture can be calculated by multiplying the total mass of the mixture with the percent of methanol present by weight. Mathematically, this is represented as:\[\text{Mass of methanol} = \text{Mass of mixture} \times \left(\frac{\text{% of Methanol}}{100}\right)\]Thus,\[\text{Mass of methanol} = 200.0\, \mathrm{kg} \times \left(\frac{25.0}{100}\right)\]
02

Convert the mass of methanol to g-moles

Knowing that the molar mass of methanol is approximately 32 g/mol, we can convert the mass of methanol (in kg) to g-moles:\[\text{Moles of methanol} = \text{Mass of methanol} \times \left(\frac{1\, \mathrm{mol}}{0.032\, \mathrm{kg}}\right)\]
03

Determine the mixture flow rate

Given the flow rate of propyl acetate, which is 100.0 ib-mole/h, and knowing that this represents 75% of the mixture (since methanol is 25%), we can calculate the total flow rate of the mixture. Mathematically, this can be represented as\[\text{Mixture flow rate} = \frac{\text{Flow rate of propyl acetate}}{\left(\frac{75.0}{100}\right)}\]Substituting the given value:\[\text{Mixture flow rate} = \frac{100.0\, \mathrm{ib-mole/h}}{\left(\frac{75.0}{100}\right)}\]

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Key Concepts

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

Mass Percent in Mixtures
Understanding mass percent is crucial in chemical process calculations. It helps in identifying the proportion of one substance within a mixture. This percentage implies how much of the entire mass is due to a specific component, like methanol in our case. To calculate this, you multiply the total mass with the mass percent (given as a fraction).

In the provided exercise, the mixture contains 25.0 wt% methanol. Given that the entire mass is 200 kg, you can find the mass of methanol using the formula:
  • Mass of Methanol = Total Mass of Mixture 脳 (Mass Percent of Methanol / 100)
This calculation results in 50 kg of methanol after applying:
  • 200.0 kg 脳 (25.0 / 100) = 50.0 kg
Knowing these basics can help you tackle more complex problems efficiently!
Mole Conversion in Chemical Processes
Mole conversion simplifies dealing with chemical substances by converting mass to moles using molar mass. Methanol has a molar mass of about 32 g/mol. In our scenario, we begin with methanol's mass in kilograms and convert it to moles.
  • First, convert the mass in kg to grams (since 1 kg = 1000 g).
  • Calculate the moles using Methanol's molar mass: Moles = Mass (in kg) 脳 (1000 g/kg) / Molar Mass
This converts 50 kg of methanol to moles as shown:
  • Moles of Methanol = 50.0 kg 脳 (1000 g / kg) 脳 (1 mol / 32 g)
  • Resulting in approximately 1562.5 g-moles of methanol
Understanding mole conversion is key because it translates the amount of a substance into something more useful for chemical equations and reactions.
Flow Rate Calculations in Mixtures
Flow rate calculations are vital in determining how much of a material moves through a system over time, often critical in industrial applications. Here, we need to find the total mixture flow rate knowing one component's rate.
  • Propyl acetate has a flow rate of 100.0 ib-mole/h, which makes up 75% of the entire mixture.
  • This implies methanol makes up the remaining 25%.
To determine the full mixture flow rate, use:
  • Mixture Flow Rate = Flow Rate of Component / (Percentage by Component / 100)
In the exercise, this calculates as follows:
  • Mixture Flow Rate = 100.0 ib-mole/h / (75.0 / 100)
  • Resulting in approximately 133.3 ib_{m}/h
Mastering flow rate calculations will facilitate more efficient chemical process operations and optimizations.

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Most popular questions from this chapter

The reaction \(A \rightarrow B\) is carried out in a laboratory reactor. According to a published article the concentration of A should vary with time as follows: \(C_{\mathrm{A}}=C_{\mathrm{A} 0} \exp (-k t)\) where \(C_{\mathrm{A} 0}\) is the initial concentration of \(\mathrm{A}\) in the reactor and \(k\) is a constant. (a) If \(C_{\mathrm{A}}\) and \(C_{\mathrm{A} 0}\) are in \(\mathrm{Ib}-\) moles \(/ \mathrm{ft}^{3}\) and \(t\) is in minutes, what are the units of \(k ?\) (b) The following data are taken for \(C_{\mathrm{A}}(t):\) $$\begin{array}{cc}\hline t(\min ) & C_{\mathrm{A}}\left(\mathrm{lb}-\mathrm{mole} / \mathrm{ft}^{3}\right) \\\\\hline 0.5 & 1.02 \\\1.0 & 0.84 \\\1.5 & 0.69 \\\2.0 & 0.56 \\\3.0 & 0.38 \\\ 5.0 & 0.17 \\\10.0 & 0.02 \\\\\hline\end{array}$$ Verify the proposed rate law graphically (first determine what plot should yield a straight line), and calculate \(C_{\mathrm{A} 0}\) and \(k\) (c) Convert the formula with the calculated constants included to an expression for the molarity of A in the reaction mixture in terms of \(t\) (seconds). Calculate the molarity at \(t=265 \mathrm{s}\).

In September 2014 the average price of gasoline in France was 1.54 euro/liter, and the exchange rate was \(\$ 1.29\) per euro ( \(\epsilon\) ). How much would you have paid, in dollars, for 50.0 kg of gasoline in France, assuming gasoline has a specific gravity of \(0.71 ?\) What would the same quantity of gasoline have cost in the United States at the prevailing average price of \(\$ 3.81 /\) gal?

The feed to an ammonia synthesis reactor contains 25 mole \(\%\) nitrogen and the balance hydrogen. The flow rate of the stream is \(3000 \mathrm{kg} / \mathrm{h}\). Calculate the rate of flow of nitrogen into the reactor in \(\mathrm{kg} / \mathrm{h}\). (Suggestion: First calculate the average molecular weight of the mixture.)

The little-known rare earth element nauseum (atomic weight \(=172\) ) has the interesting property of being completely insoluble in everything but 25 -year- old single-malt Scotch. This curious fact was discovered in the laboratory of Professor Ludwig von Schlimazel, the eminent German chemist whose invention of the bathtub ring won him the Nobel Prize. Having unsuccessfully tried to dissolve nauseum in 7642 different solvents over a 10 -year period, Schlimazel finally came to the \(30 \mathrm{mL}\) of The Macsporran that was the only remaining liquid in his laboratory. Always willing to suffer personal loss in the name of science, Schlimazel calculated the amount of nauseum needed to make up a 0.03 molar solution, put the Macsporran bottle on the desk of his faithful technician Edgar P. Settera, weighed out the calculated amount of nauseum and put it next to the bottle, and then wrote the message that has become part of history: "Ed Settera. Add nauseum/" How many grams of nauseum did he weigh out? (Neglect the change in liquid volume resulting from the nauseum addition.)

since the 1960 s, the Free Expression Tunnel at North Carolina State University has been the University's way to combat graffiti on campus. The tunnel is painted almost daily by various student groups to advertise club meetings, praise athletic accomplishments, and declare undying love. You and your engineering classmates decide to decorate the tunnel with chemical process flowcharts and key equations found in your favorite text, so you purchase a can of spray paint. The label indicates that the can holds nine fluid ounces, which should cover an area of approximately \(25 \mathrm{ft}^{2}\). (a) You measure the tunnel and find that it is roughly 8 feet wide, 12 feet high, and 148 feet long. Based on the stated coverage, how many cans of spray paint would it take to apply one coat to the walls and ceiling of the tunnel? (b) Having just heard a lecture on process safety in your engineering class, you want to take appropriate safety precautions while painting the tunnel. One useful source for this type of information is the Safety Data Sheet (SDS), a document used in industry to provide workers and emergency personnel with procedures for safely handling or working with a specified chemical. Other sources of information about hazardous substances can be found in handbooks, and some countries, including the United States, have laws that require employers to provide their employees with Safety Data Sheets. \(^{6}\) Besides composition information, the SDS contains information such as physical properties (melting point, boiling point, flash point, etc.), other threats to health and safety, recommended protective equipment, and recommended procedures for storage, disposal, first aid, and spill handling. The SDS can typically be found online for most common substances. Search the web for "spray paint SDS" and find a representative SDS for a typical spray paint product. Based on the document you find, what are the top three hazards that you might encounter during your tunnel painting project? Suggest one safety precaution for each listed hazard.
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