Question

$1.4275g$ sample of $[Cr(N{H}_3{)}_6]S{O}_{4}Cl$ (mol. wt. $=285.5$) is dissolved to prepare $250mL$ solution showing an osmotic pressure of $1.478atm$ 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 $[Cr(N{H}_3{)}_6]S{O}_{4}Cl=0$
(IV) Equilibrium molarity of $[Cr(N{H}_3{)}_6{]}^{3+}=0.02M$

• 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 $=\frac{1.4275\times 1000}{285.5\times 250}=0.02M$,
$\pi =CRT$
$\therefore {\pi }_{cal}=0.02\times 0.0821\times 300$
$=0.4926atm$
$\frac{{\pi }_{obs}}{{\pi }_{cal}}=i=\frac{1.478}{0.4926}=3$
$\because \alpha =\frac{i-1}{n-1}$
$\Rightarrow \alpha =1\left(\because n=3\right)$
Also,
$\begin{array}{cccccccc}& \left[Cr{\left(N{H}_3\right)}_6\right]S{O}_4.Cl& \rightleftharpoons & {\left[Cr{\left(N{H}_3\right)}_6\right]}^{3+}& +& S{O}_4^{2-}& +& C{l}^{-}\\ & 0.02M& & 0& & 0& & 0\\ \text{Eq. conc.}& 0& & 0.02M& & 0.02M& & 0.02M\end{array}$