Gewichtsmittlere Molmasse aus zahlenmittlerer Molmasse berechnen?
Ich bin gerade in der Klausurvorbereitung für Makromolekulare Chemie, und eine der Übungsaufgaben verwirrt mich. Mein Professor darf mir dabei anscheinend auch nicht helfen, da die Aufgabe in der Klausur drankommen könnte (er konnte mir jedoch Tipps geben).
Die Aufgabe:
Man soll die zahlenmittlere Molmasse Mn und die gewichtsmittlere Molmasse Mw berechnen. Gegeben ist lediglich der Polymerisationsgrad P = 900 und das Monomer Isopren mit einer Molmasse von 68,12 g/mol.
Die Definition von P ist P = Mn/M0 (mit M0 = Molmasse von Isopren). Darüber komme ich dann auf eine zahlenmittlere Molmasse Mn = 61308 g/mol. Dies ist auch laut meinem Professor richtig.
Nun fehlt nur noch Mw, und hierfür soll ich die direkten Definitionen von Mn und Mw verwenden.
Also Mn = (ΣNi*Mi)/(ΣNi) und Mw = (ΣNi*Mi^2)/(ΣNi*Mi). Hierbei steht Ni für die Anzahl an Molekülen und Mi für die Masse.
Allerdings habe ich leider keine Ahnung wie ich die eine Definition in die andere überführen kann und wie ich schlussendlich auf Mw kommen kann.
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So if I get that right, that’s Carother’s equation.
Then you would be using the equation for the degree of polymerization X
X = 1/(1-p)
calculate the conversion p of the reaction. You can then calculate the number-average molar mass Mn and mass-average molar mass by:
Mn = M0 * 1/(1-p)
and
Mw = M0 * (1+p)/(1-p)
See more equations for this here under related equations.
That sounds very promising. Carother’s equation we didn’t have in the lecture and actually the lecture of this professor is very close…
In any case, I come to a turnover p of 899/900, which leads to an Mn of 61308 g/mol (as in my original approach!) and an Mw of 122547.88 g/mol.
I’ll ask my professor if my Mw is right, but a thousand thanks! Now I really wonder what his originally planned solution approach was? So the one about the definitions with the Σ sums.
Look at the Wikipedia article, there should be something in there where it comes from.
Yes ask
Either you only tell half the story, or the task is super-fishy.
The molar masses Mn and MW are the same for uniformly assembled polymers. If all polymers have the same degree of polymerization P and the monomer has the mass Mm, then Mn=MW = P⋅Mm.
In contrast, when different degrees of polymerization are present in the polymer, i.e. shorter and longer chains occur as a mixture. In this case, however, a distribution must be specified, i.e. what proportion of the polymer molecules xi have a certain degree of polymerization Pi and therefore the molar mass Mi=Pi⋅Mm. Then Mn=ΣxiMi and MW=ΣxiMiM/ΣxiMi. Often, the distribution is also specified by a function (e.g., cast-shaped by an average of a given width), and then, of course, an integral must be evaluated instead of the sum.
Your information does not appear to contain any information on the distribution. If this is the case, one must assume a uniform chain length and the task is trivial (see above) and almost a catch question. Alternatively, it may be natural that you have misunderstood the essential part of the question, ignored, swallowed or not reproduced here for other reasons (or that your teacher has blew anything). I can only guess.
The complete task (including spelling errors) is: “Calculate the Mw and Mn of a polyisoprene with 900 degree of polymerization”. No further information is given.
Therefore, in his email, my professor referred to the “definitions with Σ” to be able to calculate Mw, I do not think this is a catch question.
Then I do not know — the sum must go beyond anything, but there is nothing to do with it.