Solutions and Colligative Properties 2 Question 5
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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Solution:
- Key Idea Osmotic pressure is proportional to the molarity $(C)$ of the solution at a given temperature, $\pi=C R T$
Concentration of $\mathrm{BaCl}_{2}=0.01 \mathrm{M}$
$$ \pi_{X Y}=4 \pi_{\mathrm{BaCl}_{2}} $$
$$ i \times C R T=4 \times i \times C R T $$
For the calculation of $i$,
$$ \begin{aligned} X Y & \longrightarrow X^{+}+Y^{-} & & (\text {Here }, i=2) \ \mathrm{BaCl}_{2} & \longrightarrow \mathrm{Ba}^{2+}+2 \mathrm{Cl}^{-} & & (\text {Here, } i=3) \end{aligned} $$
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 $X Y=0.06 \mathrm{~mol} \mathrm{~L}^{-1}$
$$ =6 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} $$
