Solutions and Colligative Properties 2 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
$$ \left[K_{f} \text { of water }=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right] $$
(2015 Adv.)
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Solution:
- $1+\Delta T_{f}=i K_{f} m$
$\Delta T_{f}=0-\left(-0.0558^{\circ} \mathrm{C}\right)$
$$ =0.0558^{\circ} \mathrm{C} $$
$\Rightarrow i$ (vant Hoff’s factor) $=\frac{0.0558}{1.86 \times 0.01}=3$
This indicates that complex upon ionisation produces three ions as:
$\left[\mathrm{Co}\left(\mathrm{NH}{3}\right){5} \mathrm{Cl}\right] \mathrm{Cl}{2} \rightarrow\left[\mathrm{Co}\left(\mathrm{NH}{3}\right)_{5} \mathrm{Cl}\right]^{2+}(a q)+2 \mathrm{Cl}^{-}(a q)$
Thus, only one $\mathrm{Cl}$ is inside the coordination sphere.
