Question

The osmotic pressure of a solution containing \[0.1~\] mol of solute per litre at \[273\text{ }K\] is :
A. \[\frac{0.1}{1}\times 0.08205\times 273\text{ }atm\]
B. \[0.1\text{ }\times \text{ }2\text{ }0.08205\text{ }\times \text{ }273\text{ }atm\]
C. \[\frac{1}{0.1}\text{ }\times \text{ }0.08205\text{ }\times \text{ }273\text{ }atm\]
D. \[\frac{0.1}{1}\times \frac{273}{0.08205}\text{ }atm\]

Answer 1

Hint: Osmotic pressure is the quantitative measure of the force with which the osmosis process occurs. Osmotic pressure or force with which osmosis takes place will increase with the increase in the concentration of solute molecules in the solution. And the relationship between osmotic pressure with concentration of diluted molecules is given as \[p\text{ }=\text{ }cRT\].

Complete Step by Step Answer:
Let us take two solutions in one beaker separated through a semipermeable membrane, one solution containing fewer solute particles (less concentrated or dilute) and the other containing a large number of solute particles (more concentrated).

It is very interesting to know that a semi-permeable membrane only allows the passage of solvent molecules from the solution but not solute. Now the solvent of the solution which is less concentrated moves towards the solution which is highly concentrated through a semipermeable membrane. And this process is known as osmosis. And this process is spontaneous.

As solvent molecules move toward the highly concentrated solution thus we fit the piston on the highly concentrated solution and push it until osmosis stops. Thus, the pressure we apply to stop the osmosis process is equal to the force with which solvent molecules move towards a concentrated solution. This pressure which we applied is known as osmotic pressure.

Osmotic pressure is directly proportional to the force with which osmosis coccus which in turn is directly proportional to the difference between the concentration of one solution and with another. Indirectly osmotic pressure depends on the concentration of solute molecules in one solution as compared to another.

It was first derived by Dutch chemist, Jacobus and given as
p (osmotic pressure) = c (concentration of solute molecules in moles per litre) R (gas constant) T(temperature in kelvin)
\[p\text{ }=\text{ }cRT\]

In the given question, c is given which is equal to \[0.1~\]M (Where M is moles/litre). Value of gas constant is always fixed and that is \[0.0821\]and temperature is already given in Kelvin \[273\text{ }K\]. Putting all the values in given equation we get
\[p\text{ }=\text{ }0.1\text{ }\times \text{ }0.0821\text{ }\times \text{ }273\]
Thus, the correct option is A.

Additional information: When a solute is added to a solvent (generally water) it gives out a solution. Now if in any solution the number of moles of solute is present in a large amount then the solution is concentrated otherwise dilute or less concentrated. An osmosis process occurs due to the difference in concentration between two solutions.

Note: It is important to note that when pressure is applied to the highly concentrated solution, we need to take care not to apply pressure more than required to stop osmosis otherwise reverse osmosis will take place, and solvent molecules from highly concentrated solution move towards a low concentrated solution through a semipermeable membrane.