Please help me with this question. I need to find the number average molecular w
ID: 512233 • Letter: P
Question
Please help me with this question.
I need to find the number average molecular weight (Mn) and the weight average molecular weight (Mw).
11 As part of an investigation into a failed implant, a polymeric impurity has been detected as an inclusion. Owing to the small size of the sample you have been provided with a very dilute solution of this polymer. An analysis provides data as shown in the table below. Given this information, calculate the number average molecular weight (Mn) of the polymer. If the polydis- persity index for the sample is 1.5, what is its weight average molecular weight (MW)? 50000 10000 20000 30 000 40 000 45 000 50 000 52000 Size (Da) Number of chains 100 150 500 1000 5000 8000 7000 6000Explanation / Answer
Number/Chain
(Ni)
Mass of each molecule (Mi)
Number Average mol wt Nw
=mass of molecule/no of molecule
Total mass of each type of molecule
(NiMi)
Weight fraction of the molecule
NiMi/
the weight average molecular weight (Mw)
100
5000
50
500000
0.000395
197.5
150
10000
66.66
1500000
0.001186
1779
500
20000
40
10000000
0.0079
79000
1000
30000
30
30000000
0.0237
71000
5000
40000
4
200000000
0.1582
31640000
8000
45000
5.62
360000000
0.284
102240000
7000
50000
7.14
350000000
0.274
95900000
6000
52000
8.56
312000000
0.246
76752000
Number average mol wt=50+66.66+40+30+4+5.62+7.14+8.56=211.98
Sr no.
Ni x
Mi
= NiMi
1.
100 x
5000
= 500000
2
150 x
10000
= 1500000
3
500 x
20000
= 10000000
4
1000 x
30000
= 30000000
5
5000 x
40000
= 200000000
6
8000 x
45000
= 360000000
7
7000 x
50000
= 350000000
8
6000 x
52000
= 312000000
500000+ 1500000+10000000+30000000+200000000+360000000+350000000+312000000=1264000000
NiMi/
NiMi/=10000000/1264000000=0.0079
NiMi/30000000/1264000000=0.0237
NiMi/200000000/1264000000=0.1582
NiMi/360000000/1264000000=0.284
NiMi/350000000/1264000000=0.276
NiMi/312000000/1264000000=0.246
Weight average molecular weight is
=NiMi/[ NiMi/=
NiMi x
NiMi/
=Weight average mol wt
500000 x
0.000395
=197.5
1500000 x
0.001186
=1779
10000000 x
0.0079
=79000
30000000 x
0.0237
=71000
200000000 x
0.1582
=31640000
360000000 x
0.284
=102240000
350000000 x
0.274
=95900000
312000000 x
0.246
=76752000
Weight average mol. Wt is 306683976.5
Number/Chain
(Ni)
Mass of each molecule (Mi)
Number Average mol wt Nw
=mass of molecule/no of molecule
Total mass of each type of molecule
(NiMi)
Weight fraction of the molecule
NiMi/
the weight average molecular weight (Mw)
100
5000
50
500000
0.000395
197.5
150
10000
66.66
1500000
0.001186
1779
500
20000
40
10000000
0.0079
79000
1000
30000
30
30000000
0.0237
71000
5000
40000
4
200000000
0.1582
31640000
8000
45000
5.62
360000000
0.284
102240000
7000
50000
7.14
350000000
0.274
95900000
6000
52000
8.56
312000000
0.246
76752000
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