Question

1 gm of polymer having molar mass 1, 60,000 gm dissolve in 800 ml water, so calculate osmotic pressure in pascal at $27{}^oC$ ${\text{(R = 8}}{\text{.314 J /Kmole)}}$.
A 19.4
B 0.90
C 0.50
D 1.20

Answer 1

Osmotic pressure pressure is a colligative property and it is defined as the minimum excess pressure that is applied from the solution side to prevent flow of the solvent into the solution through the semipermeable membrane.

Complete step by step answer:
We know that osmotic pressure is directly proportional to the molar concentration of the solution.
It is also directly proportional to the temperature also.
Hence the expression of osmotic pressure is given as:
$\Pi = CRT$
Here,
$\Pi =$Osmotic pressure of solution.
$T =$Temperature of the solution
$R =$It is known as a solution constant and its value is found to be the same as a gas constant.
Here it is given ,
Mass of polymer=1gm
Molar mass of polymer=1,60,000gm
Volume of water=800ml
Temperature=$27{}^oC$
${\text{R = 8}}{\text{.314 J /Kmole}}$
Now we know that concentration is defined as moles of solute dissolved per litre of solution.
$C = \dfrac{{Mass{\text{ of polymer}}}}{{Molar{\text{ mass of polymer }} \times {\text{Volume}}}}$
$= \dfrac{{1 \times 1000}}{{1,60,000 \times 800}}$
$= \dfrac{1}{{128000}}g/L$
Now calculating the osmotic pressure in pascal we know ,
1 atm=101325 pascal
$\Pi = \dfrac{{1 \times 0.0821 \times 300}}{{128000}} \times 101325$
=19.4 pascal

So, the correct answer is Option A.

Note: It should be noted that osmotic pressure is not preferred for the determination of molecular masses because many experimental difficulties are involved. However for the determination of molecular masses of proteins ,polymers, and other macromolecules, it is considered the best suitable method. Also osmotic pressure has the advantage that it uses molarities that is mass of solute dissolved in per litre of solution instead of molalities that is mass of solvent dissolved per Kg of solvent.