1. Use depression in freezing point formula

For a strong electrolyte: $\Delta T_f = i K_f m$ where:

• $\Delta T_f = 0.0558\,^\circ\mathrm{C}$
• $K_f = 1.86\,\mathrm{K\,kg\,mol^{-1}}$
• $m = 0.01\,\mathrm{molal}$

So, $i = \frac{\Delta T_f}{K_f m} = \frac{0.0558}{1.86 \times 0.01}$

$i = \frac{0.0558}{0.0186} = 3$

Thus, the van't Hoff factor is: $i=3$

2. Interpret $i = 3$

Since the complex behaves as a strong electrolyte, it dissociates completely into ions.

Let the complex be of the type: $[\mathrm{Co}(\mathrm{NH}_3)_x\mathrm{Cl}_y]\mathrm{Cl}_{3-y}$

Here:

• $y$ chloride ions are inside the coordination sphere.
• $(3-y)$ chloride ions are outside the coordination sphere and dissociate as counter ions.

On dissociation: $[\mathrm{Co}(\mathrm{NH}_3)_x\mathrm{Cl}_y]\mathrm{Cl}_{3-y} \rightarrow [\mathrm{Co}(\mathrm{NH}_3)_x\mathrm{Cl}_y]^{(3-y)+} + (3-y)\mathrm{Cl}^-$

So total number of ions formed is: $1 + (3-y) = 4-y$

Since for complete dissociation, number of ions equals van't Hoff factor: $4-y = 3$

Therefore, $y=1$

3. Conclusion

The number of chloride ions in the coordination sphere is: $\boxed{1}$