17
Molar mass:
There are different ways to report a molar mass like
(a) Number average
molar mass, (b) mass average molar mass, (c) Viscosity average molar
mass, (d) Z- Average molar mass
Number Average Molar Mass
Colligative properties (like vapor pressure lowering, freezing point
depression, osmotic pressure etc) depend on the number of molecules
and not on their size.
M
n
=
Σ
x
i
M
i
=
(Eq 1)
Σ
N
i
M
i
Σ
N
i
i
where, x
i
= Number fraction = mole fraction =
Σ
N
i
N
i
Mass Average Molar Mass
Mass average molar mass depends on size (mass/volume) as well as
number of molecules. Properties like diffusion, sedimentation, light
scattering depends both on size and mass of the molecules.
M
w
=
Σ
y
i
M
i
=
=
(Eq
2))
Σ
w
i
M
i
Σ
w
i
i
Σ
N
i
M
i
2
Σ
N
i
M
i
i
where, y
i
= mass or weight fraction =
Σ
w
i
w
i
i
w
i
= N
i
M
i
Z-Average Molar Mass
The molar mass depends both on size and mass of the molecules.
However, the contribution of the mass of the particle are weighted
further
in this type of molar mass. M
z
can be determined by
ultracentrifugation technique.
M
z
=
(Eq
3
Σ
N
i
M
i
3
)
Σ
N
i
M
i
2
i

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