Solutions and Colligative Properties - Result Question 39
39. If the freezing point of a $0.01$ molal aqueous solution of a cobalt (III) chloride-ammonia complex (which behaves as a strong electrolyte) is $-0.0558^{\circ} \mathrm{C}$, the number of chloride(s) in the coordination sphere of the complex is
$[K_f \text { of water }=1.86$ $ K $ $kg $ $\mathrm{mol}^{-1}]$
(2015 Adv.)
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Solution:
$ \begin{aligned} & 1+\Delta T_f=i K_f m \\ & \begin{aligned} \Delta T_f & =0-\left(-0.0558^{\circ} \mathrm{C}\right) \\ & =0.0558^{\circ} \mathrm{C} \end{aligned} \\ & \Rightarrow i(\text { vant Hoff’s factor })=\frac{0.0558}{1.86 \times 0.01}=3 \end{aligned} $
This indicates that complex upon ionisation produces three ions as:
$ \left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right] \mathrm{Cl}_2 \rightarrow\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q)\right. $
Thus, only one $Cl$ is inside the coordination sphere.
BETA
