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A Polydisperse mixture of a polymer can ...

A Polydisperse mixture of a polymer can be describe by the following composition-molar mass data:
`{:(Ni(mol),0.10,0.20,0.40,0.20,0.10),(Mi(kgmol^(-1)),1.00,1.20,1.40,1.60,1.80):}`
Calculate the number -average,mass-average,and`z`-average molar masses.

Text Solution

Verified by Experts

The number-average molar mass`(Mbar(n))`is defined as:`
`(Mbar(n))=SigmaNiMi//SigmaNi….(i)`
The mass-average molar mass`(Mbar(m))`is defined as:`
`(Mbar(m)=SigmaNiMi^(2)//SigmaNiMi…(ii)`
`z-average molar mass`(Mbar(z))` is defined as:`
`(Mbar(z))=SigmaNiMI^(3)//SigmaNiMI^(2)...(iii)`
Substituting the data into (i)-(iii),we get
`Mbar(n)=([{:((0.10mol)(1.00kg.mol^(-1))),(+(0.20mol)(1.20kg.mol^(-1))),(+(0.40mol)(1.40kg.mol^(-1))),(+(0.20mol)(1.60kg.mol^(-1))),(+(0.10mol)(1.80kg.mol^(-1))):}])/(0.10mol+0.20mol+0.40mol+0.20mol+0.10mol)=1.40kgmol^(-1)`
`Mbar(m)=([{:((0.10)(1.00)^(2)),(+(0.20)(1.20)^(2)),(+(0.40)(1.40)^(2)),(+(0.20)(1.60)^(2)),(+(0.10)(1.80)^(2)):}]Kg^(2)mol^(-1))/([{:((0.10)(1.00)),(+(0.20)(1.20)),(+(0.40)(1.40)),(+(0.20)(1.60)),(+(0.10)(1.80)):}]Kg)=1.43kgmol^(-1)`
`Mbar(z)=([{:((0.10)(1.00)^(3)),(+(0.20)(1.20)^(3)),(+(0.40)(1.40)^(3)),(+(0.20)(1.60)^(3)),(+(0.10)(1.80)^(3)):}]Kg^(3)mol^(-2))/([{:((0.10)(1.00)^(2)),(+(0.20)(1.20)^(2)),(+(0.40)(1.40)^(2)),(+(0.20)(1.60)^(2)),(+(0.10)(1.80)^(2)):}]Kg^(2)mol^(-1))=1.47kgmol^(-1)`
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