Question

If $M$, $W$ and $V$ represent a molar mass of solute, then the mass of solute and volume of solution in litres respectively, which among the following equations is true?
A.$\pi = \dfrac{{MWR}}{{TV}}$
B.$\pi = \dfrac{{MTR}}{{WV}}$
C.$\pi = \dfrac{{TWR}}{{VM}}$
D.$\pi = \dfrac{{TRV}}{{WM}}$

Answer 1

Hint: This question gives the knowledge about the osmotic pressure. Osmotic pressure is the hydrostatic pressure which is built up on the solution to stop the osmosis of pure solvent into the solution via semipermeable membrane.

Complete step by step answer:
Osmotic pressure is the hydrostatic pressure which is built up on the solution to stop the osmosis of pure solvent into the solution via semipermeable membrane. It is also defined as the external pressure which is applied to the solution to stop the osmosis of pure solvent into the solution via semipermeable membrane. Osmometer is the apparatus used to determine the osmotic pressure. Various methods are also there which helps in determining the osmotic pressure such as Pfeffer’s method, Berkeley and Hartley’s method and modern Osmometer.
Osmotic pressure gives the relation between volume of the solution and the concentration of the solute. The formula used for determining the osmotic pressure is as follows:
$ \Rightarrow \pi = CRT$
Where $\pi $ is the osmotic pressure, $C$ is the concentration of solute, $R$ is the gas constant and $T$ is the temperature.
As we know, concentration is the ratio of moles of solute to the volume of the solution.
$ \Rightarrow C = \dfrac{W}{{MV}}$
Where $W$ is the given weight and $M$ is the molar mass whose ratio determines the moles of solute and $V$ is the volume of the solution.
Substitute the value of concentration of solute in the osmotic pressure formula as follows:
$ \Rightarrow \pi = \dfrac{{WRT}}{{MV}}$
Therefore, option $C$ is the correct option.

Note:
Always remember that the osmotic pressure is the hydrostatic pressure which is built up on the solution to stop the osmosis of pure solvent into the solution via semipermeable membrane. Osmometer is used to determine the osmotic pressure.