Welcome Number average molecular weight.

This presentation is about Number average molecular weight.

1. WelcomeWelcome
To To
our our
PresenTaTionPresenTaTion

2. This presentation is This presentation is
prepared byprepared by
NameName
1.1.Md. Mehedi HasanMd. Mehedi Hasan
2.2.Md. Mehedi HasanMd. Mehedi Hasan
3.3.Joy Kumar DeyJoy Kumar Dey
4.4.Md. Salahuddin Md. Salahuddin
5.5.Md. Omer FarukMd. Omer Faruk
IDID
……. 2012000400127. 2012000400127
……. 2012000400130. 2012000400130
……. 2012000400131. 2012000400131
……. 2012000400137. 2012000400137
……. 2012000400155. 2012000400155

4. Molecular weight:Molecular weight: The molecular weight (M.W.) of a The molecular weight (M.W.) of a
molecule is the sum of the weights of all the atoms which molecule is the sum of the weights of all the atoms which
make up the molecule. For example, [R-(-CHmake up the molecule. For example, [R-(-CH22-CH-CH22-)-R]-)-R]500,500,
the molecular weight of this structure is 14,000.the molecular weight of this structure is 14,000.

Different types of molecular weightDifferent types of molecular weight

Number average molecular weight (Number average molecular weight (MnMn))

Weight average molecular weight (Weight average molecular weight (MwMw))

Zet average molecular weight (Zet average molecular weight (MzMz))

Viscosity average molecular weight (Viscosity average molecular weight (MvMv))

5. The number - average molar mass Mn
Definition = the sum of the products of the molar mass of each fraction
multiplied by its mole fraction.
Mn = åX
i
M
i
..………1.1
where : X
i
is the mole fraction of the molecules of molar mass Mi

X
i
= N
i
/ åN
i
,N = number of moles
\Mn= åN
i
M
i
/

åN
i
= åW
i


/ åW
i
= W/ åN
i
……….. 1.2
Sometimes weight fraction are used in place of mole fraction.
The weight fraction W
i
is defined as the mass of molecules of molar mass
M
i
divided by the total mass of all the molecules present.

6. Wi = N
i
M
i

/ åN
i
M
i
………..1.3
å ( å N
i

/W
i
)

= M
i
/åN
i
M
i
………….1.4
Combining equations 1.2 & 1.4 gives
Mn in terms of weight fraction.
Mn = 1 / åW
i
/M
i
or å W
i
/ M
i
= 1 / Mn
……1.6

7. Different method of determination Number average molecular weight (Mn)
Determination of Mn
In practical the number average molecular weight (Mn)
may be determined by the following method
1.Cryoscopy method i.e. Depression of freezing
point
2.Ebullioscopy i.e. Elevation of boiling point
3.Osmometry A. Vapor phase osmometry
B. Membrane osmometry
4.End group analysis.

Continue…..

8. ◦Freezing point of a solvent is lowered when a non-
volatile solute is dissolved in it.
◦Freezing point of the solution will be depressed.
◦This phenomenon of depressing the freezing point
of a liquid by the addition of a solute is known as
Cryoscopy.
◦The extent of the freezing point depends on the
number of solute molecules dissolved per unit
volume of solution and its independent of the size
and nature of the solute molecule.

9. 1.So, Number average molecular wt. is
measured by this technique.
2.If depression of the freezing point is denoted
by ,Its related to the Number-average
Molecular wt. and concentration through
following equation.
3.Where, C is concentration of the solution, ρ
the density of the solvent, R the universal gas
constant; Tf the freezing point of the solvent,
B is a constant and ΔHf is the heat of fusion of
the solvent.
DT
f
/C = (RT
f
2
/rDH
f
)1/+MBC
DT
f

10. 1.Graphical representation.
2.To find out the freezing point, solvent or solution is
carefully super cooled to a temperature that is
about 5C lower than the freezing point.
3.Once the freezing points of the solvent and
solutions Tf different concentrations are known,
ΔTf can be calculated for all these concentrations.
4.Drawback of this method is, measurement of
temperatures.
5.Highly precised temperature sensors are required.
6.This method can measure molecular wt. up to
30,000.
Continue…..

11. Ebullioscopy (Elevation of boiling point)
This technique is based on boiling point of solutions.
Boiling point of solutions is higher than the pure
solvents. This phenomenon is used to determine the
molecular wt. of polymers.
Where ΔHv and Tb are the heat of vaporization and
boiling of the solvent.
DT
b/C=(RT
b
2
/rDH
v)1/M
n+BC
Continue…..

12. There are two types of ebulliometers.
In first type, the solution of the polymer whose
molecular wt. is to be determined is heated in a
boiler. The solution is then brought in contact with a
sensor. Another in pure solvent.
In second type, both of solution and pure solvent are
heated in identical containers and uniform boiling is
achieved.
It can also be used to determine the molecular wt.
up to 30,000.

13. Osmometry
Osmometry is the mostly used method to determine the
number average molecular weight. There are two
method of osmometry they are –
 Vapor phase osmometry
 Membrane osmometry
These techniques are useful in different Mn ranges and
depend on the change in osmotic pressure and the
lowering of vapor pressure (respectively) by polymers in
solution. These method are very effected to find out the
molecular weight of a polymer.

14. Vapor phase osmometry
The determination of Mn by the use of vapor pressure osmometry operates
on the principle that the vapor pressure of a solution is lower than that of
the pure solvent at the same temperature and pressure. At sufficiently low
concentrations, the magnitude of the vapor pressure decrease is directly
proportional to the molar concentration of solute. Monitoring vapor
pressure versus a change in concentration of solute can be used in a manner
similar to that of membrane osmometry.
The relationship between the vapor pressure difference of solvent and
solution,
and number average molecular wt. is given as

15. Continue….
•Vapor phase osmometry is a experimental method.
•Vapor pressure is not measured directly due to difficulties
in sensitivity, but is measured indirectly by using
thermistors to measure voltage changes caused by changes
in temperature.
•If experimental factors are controlled very carefully, very
accurate Mn numbers can be achieved. MW’s below 1000
are determinable with a precision of 0.5 %. The lower limit
of MW is technically only limited by the vapor pressure of
the sample, but useful lower limits are in the 250 level.

16. Membrane osmometry is an absolute technique which
determines Mn. The solvent is separated from the polymer
solution by a semipermeable membrane which is tightly
held between the two chambers.
It is most widely used technique to determine number
average molecular wt.
It is based on the phenomenon of osmosis.
The equation of Osmotic pressure is given below-
here Π is the osmotic pressure.

17. Membrane osmometry is also a experimental process. The
instrument by which this method done contains two main
components, the cell assembly and the electronics-recorder
assembly. Membrane conditioning is extremely important in
using this technique. Membranes are usually cellulose derivatives
and shipped in alcohol or aqueous solution.
Figure : Schematic representation of a membrane
osmometer.

18. Figure : Automatic membrane osmometer
The problems of this technique are caused mainly by the membrane.
There are problems with membrane leakage and asymmetry. The main
advantage of membrane osmometry is that it yields an absolute Mn for a
polymer and calibration with standards is not required. The most common
membranes typically can determine Mn as low as 10000-20000.
Membrane osmometry also provides information about polymer-solvent
interactions.

19. End group analysis
The end group analysis is a chemical method
used for calculating the Mn of polymer samples
whose molecules contain reactive functional
groups at one ends of the molecules.
From knowledge of the functional group
equivalent and the functionality, the molecular
weight can be calculated by using the equation.
Mn = Functionality/ Functional group
End functional groups are hydroxyl, carboxyl,
aldehyde, amino, ester or methyl.

20. It can be used reliably only for samples consisting of linear
molecules with determinable end groups.
This method can be conveniently used to find out the average
functionality at any polymer sample.
The method cannot be applied to branched polymers. In a linear
polymer there are twice as many end of the chain and groups as
polymer molecules. If having different end group, the number
of detected end group is average molecular weight. End group
analysis could be applied for polymerization
mechanism identified . In this method molecular weight
limitation up to 50,000.

21. THANK YOU