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Question: Calculate the osmotic pressure of \[0.01\;M\;\] solution of cane sugar at \[300\;K\]. \[(R = 0.082...

Calculate the osmotic pressure of 0.01  M  0.01\;M\; solution of cane sugar at 300  K300\;K.
(R=0.08212   atm   degree−1mol−1).(R = 0.08212\;\,atm\,\;degre{e^{ - 1}}mo{l^{ - 1}}).
(A) 0.3568 atm0.3568\,atm
(B) 0.2463 atm0.2463\,atm
(C) 0.1562 atm0.1562\,atm
(D) 0.5623  atm0.5623\,\,atm

Explanation

Solution

In the process of osmosis molecules of a solvent shift from a solution having low concentration to a solution having high concentration via a semipermeable membrane. To calculate the osmotic pressure of the given solution we will apply the formula of osmotic pressure and then put the values by converting them in the SI unit and will solve for the same.

Formula Used: The osmotic pressure of any solution is given by:
π=CRT\pi = CRT
Where C=C = Concentration or Molarity
R=R = gas constant =0.8212 = 0.8212
T=T = Temperature (in Kelvin)

Complete step by step answer:
The net movement of solvent molecules from the solvent to the solution via the semipermeable membrane can be stopped by applying an extra pressure over the solution side. This extra pressure that is applied is called osmotic pressure. This pressure is applied so that the osmosis is stopped. It is denoted by Osmotic pressure and is a colligative property.
Now we are given, concentration =0.01 = 0.01
R=0.08212   atm   degree−1mol−1R = 0.08212\;\,atm\,\;degre{e^{ - 1}}mo{l^{ - 1}}
T=300  KT = 300\,\,K
So, we will put these values in the formula to calculate the osmotic pressure;
π=CRT\pi = CRT
π=0.01  × 0.8212 ×300\pi = 0.01\,\, \times \,0.8212\, \times 300
π=0.2463 \pi = 0.2463\,
Hence, the osmotic pressure of 0.01  M  0.01\;M\; the solution of cane sugar is 0.2463  atm0.2463\,\,atm.

Therefore, Option (B) is correct.

Note:
During osmosis, only solvent molecules are allowed to pass through the semipermeable membrane meaning that the solute particles cannot pass through it. Being a colligative property Osmotic pressure depends on the concentration of the solute particles. Due to osmotic pressure plants can maintain their correct shape and it also helps in the desalination and purification of the seawater in reverse osmosis. Osmosis also affects the transport of nutrients and the release of metabolic waste products in plants.