Question

The osmotic pressure of 1 M solution at \[27\text{ }{}^\circ C\] is
A. \[2.46\text{ }atm\]
B. \[24.6\text{ }atm\]
C. \[1.21\text{ }atm\]
D. \[12.1\text{ }atm\]

Answer 1

Hint: Osmotic pressure is the force applied by solvent molecules of one solution to another solution through a semipermeable membrane because of the difference in concentration of solute molecules between two solutions. It was the Dutch scientist, Jacobus who give the relationship between osmotic pressure represented as p and concentration of solute particles in the solution represented as c such as
\[p\text{ }=\text{ }cRT\]
where R is gas constant, and T is the absolute temperature at which process osmosis occurs.

Complete Step by Step Answer:
In the given question, we need to find the osmotic pressure of 1M solution. The 1M solution means that the solution (formed with the combination of solvent (liquid generally water) and solute (solid)) containing 1 mol of solute in 1 L .
Let the osmotic pressure of 1 M solution is p which is equal to cRT (given in hint).
The concentration of solute in a solution is defined as the number of moles of solute per litre solution such as \[\frac{n}{V}\]. In given question concentration of solution 1 M.
Now osmotic pressure of 1M solution is given as
\[p\text{ }=\text{ }cRT\]
\[p\text{ }=\text{ (1)}RT\]
Where R is a gas constant whose value is \[0.082\]and the temperature of the solution is given in Celcius
\[(27{}^\circ C)\]but we need absolute temperature so, first convert it to kelvin by adding 273 such as
\[\text{27 }+\text{ }273\text{ }=\text{ }300\text{ }K\]
So,
\[p\text{ }=\text{ (1)}\times \text{0}\text{.082}\times 300\]
Solving it we get
\[p\text{ }=\text{ 24}\text{.6 }atm\]
Thus, the correct option is B.

Note: The movement of solvent molecules from a low concentrated solution (less number of solute molecules) to a highly concentrated solution (a large number of solute particles) with some force through a semipermeable membrane and this process is known as osmosis. If we applied pressure against the force of the solvent molecule (less concentrated solution) to stop the osmosis process that pressure is osmotic pressure. The osmotic pressure of the solvent molecule of high concentrated solution will be very negligible as compared to the osmotic pressure of the less concentrated solution. In this question, the osmotic pressure of cane sugar solution is \[24.6\text{ }atm\]so, applying this amount of pressure will stop osmosis process and if we applied more than this pressure then reverse osmosis will take place.