Which of the following solutions are isotonic with respect to an aqueous $N a C l$ solution having molarity $0.2 M$ and $50 %$ dissociation?

0.3 M

aqueous glucose solution

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0.15 M

aqueous

N a_{2} S O_{4}

solution showing complete dissociation

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0.15 M

aqueous

K H F_{2}

solution showing complete dissociation

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0.1 M

aqueous

B a C l_{2}

solution showing

80 %

dissociation

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Solution

The correct option is C $0.15 M$ aqueous $K H F_{2}$ solution showing complete dissociation
Given, molarity of $N a C l$ solution $(C) = 0.2 M$ and
$percentage of dissociation (α) = 50$ %
For $N a C l$ solution
$π_{N a C l} = i \times C R T$
$i = 1 + (n - 1) α$
For $N a C l, n = 2 i = 1 + (2 - 1) 0.5 = \frac{3}{2}$
$\Rightarrow π_{N a C l} = \frac{3}{2} \times 0.2 R T = 0.3 R T$
(A) $π_{G l u c o s e} = 1 \times 0.3 \times R T = 0.3 R T$

(B) $π_{N a_{2} S O_{4}} = i \times C R T$
Now, $i_{N a_{2} S O_{4}} = 1 + (n - 1) α = 1 + (3 - 1)$

$\Rightarrow π_{N a_{2} S O_{4}} = 3 \times 0.15 R T = 0.45 R T$

(C) $π_{K H F_{2}} = i C R T$
$i_{K H F_{2}} = 1 + (n - 1) α$
$i_{K H F_{2}} = 1 + (2 - 1) 1$
$\Rightarrow π_{K H F_{2}} = 2 \times 0.15 R T = 0.3 R T$

(D) $π_{B a C l_{2}} = i C R T$
$i B a C l_{2} = 1 + (n - 1) α$
$= 1 + (3 - 1) 0.8$
$\Rightarrow π_{B a C l_{2}} = 2.6 \times 0.1 R T = 0.26 R T$
Solutions having the same value of $π$ are isotonic solution. Therefore, A and C are isotonic to given $N a C l$ solution.

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