Question

The osmotic pressure of \[0.1M\] sodium chloride solution at ${27^o}C$ is:
(A) \[4.0{\text{ }}atm\]
(B) \[2.46{\text{ }}atm\]
(C) \[4.92{\text{ }}atm\]
(D) \[1.23{\text{ }}atm\]

Answer 1

Hint: 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
$\pi = CRT$
Where, $\pi = $ osmotic pressure
$C = $ concentration of solution
$R = $ gas constant
$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.
${\text Van’t\,\, Hoff\,\, factors\,(i)} =\dfrac{\pi\,\,observed}{\pi}$ theoretical. And osmotic pressure of solution containing non-electrolyte as solute is,$\pi = iCRT$

In given problem: $NaCl \to N{a^ + } + C{l^ - }$
Number of ions$ = 2$
$\therefore i = 2$

$C = 0.1M$
$R = 0.0821atm$$mo{l^{ - 1}}{k^{ - 1}}$

$\Rightarrow \pi = 2 \times 0.1mol \times 0.0821atm$$mo{l^{ - 1}}{k^{ - 1}} \times 300k$
$\Rightarrow T = 27 + 273$
$\Rightarrow 300k.$
$\Rightarrow \pi = 4.92atm.$

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

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 $NaCl$ is strong electrolyte therefore it dissociates completely in solution and increases solute particles. Therefore, osmotic pressure of solution also increases.