The main application of osmotic pressure measurement is in the determination of the molar mass of a substance which is either slightly soluble or has a very high molar mass such as proteins, polymers of various types and colloids.This is due to the fact that even a very small concentraion of the solution produces fairly large magnitude of osomotic pressure.In the laboratory the concentrations usually employed are of the order of `10^(-3)` to `10^(-4)` M.At concentration of `10^(-3)` mol `dm^(-3)` , the magnitude of osmotic pressure of 300 K is :
`P=10^(-3)xx0.082xx300=0.0246` atm
or `0.0246xx1.01325xx10^5=2492.595 Pa`
At this concentration, the values of other colligative properties such as boiling point elevation and depression in freezing point are too small to be determined experimentally.
Further polymers have following two types of molar masses :
(A) Number average molar mass `(barM_n)`, which is given by `(undersetisumN_iM_i)/(undersetisumN_i)`
where `N_i` is the number of molecules having molar mass `M_i`.
(B) Molar average molar mass `(barM_m)`, which is given by `(undersetisumN_iM_i^2)/(undersetisumN_iM_i)`
Obviously the former is independent of the individual characteristics of the molecules and gives equal weightage to large and small molecules in the polymer sample.On the other hand later gives more weightage to the heavier molecules.Infact with the help of a colligative property only one type of molar mass of the polymer can be determined.
What will be the observed molecular weight of the above polymer sample generating osomotic pressure equal to the answer in the previous questions at `27^@C`?

Options

A. 4000
B. 3000
C. 2500
D. 1200

Answer

B

Explanation

`0.0164xx1=2/mxx0.082xx300`
`:. M=3000`