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Question: The osmotic pressure of \[0.1M\] sodium chloride solution at \({27^o}C\) is: (A) \[4.0{\text{ }}at...

The osmotic pressure of 0.1M0.1M sodium chloride solution at 27oC{27^o}C is:
(A) 4.0 atm4.0{\text{ }}atm
(B) 2.46 atm2.46{\text{ }}atm
(C) 4.92 atm4.92{\text{ }}atm
(D) 1.23 atm1.23{\text{ }}atm

Explanation

Solution

Osmotic pressure is pressure on the side of solution that stops net flow of solvent into solution through semipermeable membrane.
Osmotic pressure only exists when a solution of two different concentrations is represented by a semipermeable membrane.

Complete step by step answer:
Let us discuss different types of solutions before studying osmotic pressure.
There are there types of solutions:
(1) Isotonic solution: Two or more solutions of the same osmotic pressure.
(2) Hypertonic solution: A solution having osmotic pressure higher than other solution.
(3) Hypotonic solution: A solution having osmotic pressure less than other solution.

Osmotic pressure of solution having non-volatile solute is given by
π=CRT\pi = CRT
Where, π=\pi = osmotic pressure
C=C = concentration of solution
R=R = gas constant
T=T = absolute temperature

But when a solution contains electrolyte as a solute osmotic pressure of solution cannot be calculated by the above equation.Since osmotic pressure is a colligative property therefore the number of solute particles increases in solution and thus osmotic pressure also increases.

Therefore, Van’t Hoff factor (i) should be introduced while calculating osmotic pressure.
Van’t  Hoff  factors (i)=π  observedπ{\text Van’t\,\, Hoff\,\, factors\,(i)} =\dfrac{\pi\,\,observed}{\pi} theoretical. And osmotic pressure of solution containing non-electrolyte as solute is,π=iCRT\pi = iCRT

In given problem: NaCl→Na++Cl−NaCl \to N{a^ + } + C{l^ - }
Number of ions=2 = 2
∴i=2\therefore i = 2

C=0.1MC = 0.1M
R=0.0821atmR = 0.0821atm mol−1k−1mo{l^{ - 1}}{k^{ - 1}}

⇒π=2×0.1mol×0.0821atm\Rightarrow \pi = 2 \times 0.1mol \times 0.0821atm mol−1k−1×300kmo{l^{ - 1}}{k^{ - 1}} \times 300k
⇒T=27+273\Rightarrow T = 27 + 273
⇒300k.\Rightarrow 300k.
⇒π=4.92atm.\Rightarrow \pi = 4.92atm.

Therefore, from the above explanation the correct option is (C) 492atm.492atm.

Note:
Osmotic pressure is a colligative property which depends on the number of solute particles present in solution.
Osmotic pressure increases or decreases when the number of solute particles dissociate or associate in solution.
Since NaClNaCl is strong electrolyte therefore it dissociates completely in solution and increases solute particles. Therefore, osmotic pressure of solution also increases.