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

Answer: 6

$\left(\Delta T_f\right)=i\times k_f\times m$

$\left(\Delta T_f\right)=i\times k_f\times$ 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 $=2\times 3=6$