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^(@)C`, the number of chloride (s) in the coordination sphere of the complex if `[K_(f)` of water `=1.86 K kg mol^(-1)]`

Explanation

`DeltaT_(f)=iK_(f)m`
Given `m=0.01 " molal, "T_(f)=-0.0558^(@)C`,
`K_(f)="1.86 K kg mol"^(-1)`
`DeltaT_(f)=T_(f)^(@)-T_(f)=0-(-0.0558)=0.0558^(@)`
`i=(DeltaT_(f))/(K_(f)m)=(0.0588)/(1.86xx0.01)=3`
As 3 ions are produced on dissociation of the complex, the molecular formula of the complex is `[Co(NH_(3))_(5)Cl]Cl_(2)`. Thus, only one chloride ion is present in the coordination sphere.