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148
polydisperse solution. In osmometry the total osmotic pressure is the sum of
the pressure for each molecular weight:
Π
=
Π
i
i
∑
We further choose to analyse the situation in the limit c
2
→
0, hence A
2
c
2
= 0
and therefore:
Π
=
RT
c
i
M
i
i
∑
By dividing and multiplying by c
2
, which equals
c
1
i
∑
we obtain:
Π
=
RT
c
i
M
i
i
∑
=
RT
c
2
c
2
⎛
⎝⎜
⎞
⎠⎟
c
i
M
i
i
∑
=
RT
c
2
c
i
i
∑
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
c
i
M
i
i
∑
=
RTc
2
c
i
M
i
i
∑
c
i
i
∑
Since M
n
is given by:
M
n
=
c
i
i
∑
c
i
M
i
i
∑
it follows directly that
Π
=
RTc
2
c
i
M
i
i
∑
c
i
i
∑
=
RTc
2
M
n
Π
c
2
=
RT
1
M
n
⎛
⎝⎜
⎞
⎠⎟
(in the limit c
2
→
0)
Hence, the molecular weight obtained by osmometry is M
n
.