Solutions and Colligative Properties - Result Question 5-2
5. The osmotic pressure of a dilute solution of an ionic compound $X Y$ in water is four times that of a solution of $0.01$ $\mathrm{M} $ $\mathrm{BaCl}_2$ in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of $X Y$ (in mol $\mathrm{L}^{-1}$ ) in solution is
(2019 Main, 9 April I)
(a) $4 \times 10^{-2}$
(b) $16 \times 10^{-4}$
(c) $4 \times 10^{-4}$
(d) $6 \times 10^{-2}$
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Answer:
Correct Answer: 5. (d)
Solution:
Key Idea: Osmotic pressure is proportional to the molarity (C) of the solution at a given temperature, $\pi=C R T$
(Given)
$\text { Concentration of } \mathrm{BaCl}_2 =0.01 \mathrm{M} $
$\pi_{X Y} =4 \pi_{\mathrm{BaCl}_2} $
$i \times C R T =4 \times i \times C R T\quad$ ……(i)
For the calculation of $i$,
$ X Y \longrightarrow X^{+}+Y^{-} $ (Here, $i=2$ )
$ \mathrm{BaCl}_2 \longrightarrow \mathrm{Ba}^{2+}+2 \mathrm{Cl}^{-}$ (Here, $i=3$ )
Putting the values of $i$ in (i)
$ \begin{aligned} 2 \times[X Y] & =4 \times 3 \times\left[\mathrm{BaCl}_2\right] \\ 2 \times[X Y] & =12 \times 0.01 \\ {[X Y] } & =\frac{12 \times 0.01}{2} \end{aligned} $
So, the concentration of $X Y=0.06 \mathrm{~mol} \mathrm{~L}^{-1}$
$ =6 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} $
BETA
