Question

$2\text{litre}$ of $1$ molar solution of a complex salt $CrC{l}_3,6H_{2}O$ (mol. wt. 266.5) shows an osmotic pressure of $98.52\text{atm}$. The solution is now treated with $1\text{litre}$ of $6M$ $AgN{O}_3$, which of the following are correct?

• A. Weight of $AgCl$ precipitated is $861\text{g}$
• B. The clear solution will show an osmotic pressure $=98.52\text{atm}$
• C. The clear solution will show an osmotic pressure $=65.68\text{atm}$
• D. $2$ moles of $\left[Cr\right(H_{2}O{)}_6\left]\right(N{O}_3{)}_3$ will be present in solution

Answer 1

Answer: (A), (C), (D)

$2$ moles of $\left[Cr\right(H_{2}O{)}_6\left]\right(N{O}_3{)}_3$ will be present in solution

$CrC{l}_3.6H_{2}O$
$\pi =CST(1-\alpha +x\alpha +y\alpha )$
$98.52=1\times 0.0821\times 300\times (x+y)(\because \alpha =1)$

$(x+y)=4$
$\begin{array}{c}\left[Cr\right(H_{2}O{)}_6]C{l}_3\rightleftharpoons \\ 1\\ 1-\alpha \end{array}\begin{array}{c}\left[Cr\right(H_{2}O{)}_6{]}^{3+}\\ 0\\ \alpha \end{array}\begin{array}{c}+3C{l}^{-}\\ 0\\ 3\alpha \end{array}$

$\text{moles}\begin{array}{c}Cr(H_{2}O{)}_{6}C{l}_3+\\ 2\times 1=2\\ 0\end{array}\begin{array}{c}3AgN{O}_3\to \\ 1\times 6=6\\ 0\end{array}\begin{array}{c}\left[Cr\right(H_{2}O{)}_6\left]\right(N{O}_3{)}_3+\\ 0\\ 2\end{array}\begin{array}{c}3AgCl\\ 0\\ 6\end{array}$

Weight of $AgCl$ formed $=6\times 143.5=861\text{g}$

$\pi =CST\times (1+3\alpha )=\frac{2}{3}\times 0.0821\times 300\times 4=65.68\text{atm}$