Finding mole fraction of polymers from weight percents %

[watsup]

Watsup! I'm taking this nano class which is awesome but I am getting stuck on the gen chem material! no bueno. just want to make sure i did this right. Thanks!

Homework Statement

[/B]
"A blend contains 45wt% polystyrene and 55wt% polypropylene. What is the mole fraction of polystyrene in the blend?"

The Attempt at a Solution

I think I remember having to change the percents into grams,
then find the molar masses of the total blend and the polystyrene.
Then divide the grams by the molar masses leaving moles/moles --> so unitless
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45[g(PS)]/100[g(total)]
Polystyrene: (12*8 + 1*8) = 104[g/mol]
Polypropylene: (12*3 + 6*1) = 42[g/mol]
total= 146[g/mol]

(45/104)/(100/146) ≈ 0.632

 

[Borek]

This is at least strange. Unless they mean something else than they asked, to calculate molar fraction you need to know molar mass - of the polymer, not of the monomer.

Unless for some reason they decided to use a definition of molar fraction that is different from the definition used in general chemistry.

 

[watsup]

Why wouldn't the molar mass for the polymer be the sum of the molar masses of the two different monomers?

 

[Borek]

Molar mass depends on how many monomers reacted when producing one polymer molecule. And it is (almost) never a strict value, it is an average.

 

[chemisttree]

You are using 100g of polymer in your calculation. You have determined that 45g of this is PS. Where you went wrong is with the factor 100/146. You assume here that the molecular wt of the polymer is the algebraic sum of the molecular weights of the individual monomers. This would be true only for a polymer derived from an equimolar mixture of the two monomers.