Calculating Mole Fraction from Mass Fraction: Benzene-Toluene Mixture Example

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Discussion Overview

The discussion revolves around calculating the mole fraction of toluene in a benzene-toluene mixture given the mass fraction of benzene. Participants explore methods to connect mass fractions to mole fractions, particularly in the context of a chemical engineering homework problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states the mass fraction of benzene is 0.450 and seeks to find the mole fraction of toluene, expressing uncertainty about the steps to take.
  • Another participant explains that the mass fraction is the ratio of the mass of benzene to the total mass of the mixture and suggests using molecular weights to find the molecular weight of the mixture.
  • A participant questions the logic of simply adding the molecular weights to find the mixture's molecular weight, indicating confusion about the approach.
  • One participant proposes assuming a total mass of 100 grams for the mixture to simplify calculations, which another participant acknowledges as a helpful suggestion.
  • Another participant advises that while assuming a mass simplifies the problem, it is technically better to solve using symbols to maintain generality, noting that the mass would ultimately cancel out.

Areas of Agreement / Disagreement

Participants express differing views on the best approach to solving the problem, with some favoring the assumption of a specific mass for ease of calculation, while others advocate for a more symbolic approach. There is no consensus on a single method to proceed.

Contextual Notes

Participants highlight the importance of understanding the relationship between mass fractions and mole fractions, but there are unresolved questions regarding the validity of certain assumptions and the clarity of the steps involved in the calculations.

Who May Find This Useful

This discussion may be useful for students in chemical engineering or related fields who are grappling with concepts of mass and mole fractions in mixtures, particularly in homework contexts.

GreatEscapist
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This is for my chemical engineering class...for some reason, I am struggling with this problem. I'm not quite sure how to connect the dots..I feel like I know how to do this, though.


Homework Statement


The mass fraction of benzene in a benzene-toluene mixture is 0.450. What is the mole fraction of toluene in the mixture? Molecular weights of benzene and toluene are 78.11 and 92.12 respectively.


Homework Equations


listed


The Attempt at a Solution



Mass fraction of toluene is .550

Now, that is dimensionless, and I don't know how to get going from here. I know it's simple, but I've forgotten my general chemistry...
I was thinking I just multiply that mass fraction by the molecular weight of toluene, but then that's still in g/mol...then I thought about adding them, which would make more sense (since I have the mass fraction). I don't know though, because I don't have the exact chemical formula.


Any tips or steps would be greatly appreciated. Thank you.
 
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well mass fraction is of benzene is mass_benzene/(mass_mixture)=.450

they give you the molecular weights of each component, and you can find the molecular weight of the mixture by just adding the molecular weights.

since the masses are in grams, and moelcular weight is in g/mol, if you divide the mass by molecular weight you get just moles. just make sure what you do to one side of the equation you do to the other.

And then just manipulate the equation the same way you did to get the mass fraction of toluene.Hope that helps
 
Puchinita5 said:
they give you the molecular weights of each component, and you can find the molecular weight of the mixture by just adding the molecular weights.

Huh? Doesn't make any sense to me.

GreatEscapist: assume 100g of the mixture.
 
Aha- I knew I forgot something simple. Thank you for the 100 g suggestion. I didn't know if assuming an amount of grams was a legal move.
 
Technically you should assume mass m and solve with symbols, you would find in the end m cancels out. But 100g is much faster and less cumbersome.
 

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