Question

2 litres of a 1 molar solution of a complex salt $CrC{l}_3.6H_{2}O$ (molar mass $266.5{\text{g mol}}^{-1})$ shows an osmotic pressure of $98.52\text{atm}$. The solution is now treated with 1 litre of $6\text{M}AgN{O}_3$. Which of the following statements is/are correct?

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

Answer 1

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

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

$\pi =C\times R\times T\times i$
As strong electrolyte then i = n.
$\pi =C\times R\times T\times n$
$98.52=1\times 0.0821\times 300\times n$
n = 4

$CrC{l}_3.6H_{2}O$ can be written as:
$\left[Cr\right(H_{2}O{)}_6]C{l}_3\rightleftharpoons [Cr(H_{2}O{)}_6{]}^{3+}+3C{l}^{-1}$
1
1- $\alpha$ $\alpha$ 3$\alpha$

therefore
3 mole of $AgN{O}_3$ will react with 1 mole of $\left[Cr\right(H_{2}O{)}_6]C{l}_3$

$\left[Cr\right(H_{2}O{)}_6]C{l}_3+AgN{O}_3\to [Cr\left(H_{2}O{)}_6\right](N{O}_3{)}_3+3AgCl$
2 6
0 0 2 6
therefore
moles of $AgCl$ formed = 6
mass of $AgCl$ formed = 6$\times$ 143.5= 861$g$

$\left[Cr\right(H_{2}O{)}_6\left]\right(N{O}_3{)}_3$ =$\frac{2}{3}$
$\pi =\frac{2}{3}\times 0.0821\times 300\times 4$
= 65.68 $atm$