Question

$1.4275\, g$ sample of $[Cr(NH_3)_6]SO_4Cl$ (mol. wt. $= 285.5$) is dissolved to prepare $250 \,mL$ solution showing an osmotic pressure of $1.478 \,atm$ at $27^°C$. Which of the following statements are correct about this solution?
(I) Each molecule furnishes three ions in solution.
(II) The vant Hoff factor is $3$.
(III) Equilibrium molarity of $[Cr(NH_3)_6] SO_4Cl = 0$
(IV) Equilibrium molarity of $[Cr(NH_3)_6]^{3+} = 0.02\, M$

• A. I and III only
• B. II and IV only
• C. I, II and IV only
• D. All of these

Answer 1

Answer: (D)

Molarity $= \frac{1.4275 \times1000}{285.5 \times 250}= 0.02\,M$,
$\pi = CRT$
$\therefore \pi_{cal} = 0.02 \times 0.0821 \times 300$
$= 0.4926\,atm$
$\frac{\pi_{obs}}{\pi_{cal}} = i = \frac{1.478}{0.4926} = 3$
$\because \alpha = \frac{i-1}{n-1}$
$\Rightarrow \alpha = 1 \quad\left(\because n = 3\right)$
Also,
$\begin{matrix}&\left[Cr\left(NH_{3}\right)_{6}\right]SO_{4}.Cl&\rightleftharpoons&\left[Cr\left(NH_{3}\right)_{6}\right]^{3+}&+&SO^{2-}_{4}&+&Cl^{-}\\ &0.02\,M&&0&&0&&0\\ \text{Eq. conc.}&0&&0.02\,M&&0.02\,M&&0.02\,M\end{matrix}$