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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

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