Question

$\text{0} \text{.002}$ molal aqueous solution of an ionic compound with moleciular formula $\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{NO}_2\right) \mathrm{Cl}$ freezes at $-0.00744^{\circ} \mathrm{C}$. How many moles of ions does $3$ moles of the salt produce on being dissolved in water?

[Given: $\text{K}_{\text{f}}$ of water $= 1.86 \, \text{K} \, \text{kg} \, \text{mol}^{- 1}$ ]

Answer 1

$\left(\Delta T _{ f }\right)= i \times k _{ f } \times m$

$\left(\Delta T _{ f }\right)= i \times k _{ f } \times$ Molality

$0.00744= i \times 1.86 \times 0.002$

$i \cong 2$

$\Rightarrow i =1+\alpha( n -1)$

$\Rightarrow 2=1+1( n -1)$

$\Rightarrow n -1=1$

$\therefore n =2$

$\therefore $ number of ions produced from 3 moles of compound $=2 \times 3=6$