A polymer contains 50 molecules with molecular mass 5000, 100 molecules with molecular mass 10,000 and 50 molecules with molecular mass 15,000.Calculate number average molecular mass ?

Options

A. 5000
B. 75000
C. 10000
D. 20000

Answer

C

Explanation

`:'` Number average molecular mass `(M bar(n))`
`(N_(1)M_(1)+N_(2)M_(2)+N_(3)M_(3))/(N_(1)+N_(2)N_(3))`
where `N_(1), N_(2)` and `N_(3)` are number of molecules and `M_(1), M_(2)` and `M_(3)` are respectively their molecular masses.
Given, `N_(1)=50` and `M_(1)=5000`
`N_(2)=100` and `M_(2)=10,000`
`N_(3)=50` and `M_(3)=15,000`
Thus, `M bar(n)=(N_(1)M_(1)+N_(2)M_(2)+N_(3)M_(3))/(N_(1)+N_(2)+N_(3))`
`=((50xx5000)+(100xx10,000)+(50xx15000))/(50+100+50)`
`=((25,0000)+(1,000,000)+(75,00,00))/200`
`M bar(n)=10,000`
Hence, option (c) is the correct answer.