Determining colligative properties of ionic solutions: Estimate the freezing point of a `0.010 m` aqueous solution of aluminium sulphate, `Al_(2)(SO_(4))_(3)`. Assume the value of `i` based on the formula of the compound.
Strategy: Use the modified equation `(2.77)` to account for the effect of dissociation of `Al_(2)(SO_(4))_(3)` in water. The van't hoff factor, `i`, is equal to the number of ions furnished per formula unit (assuming `100%` dissociation.)

Explanation

When aluminium sulphate, `Al_(2)(SO_(4))_(3)`, dissolved in water, it dissociates into five ions
`Al_(2)(SO_(4))_(3) overset (H_(2)O) (rarr) 2Al^(3+)(aq)+3SO_(4)^(2-)(aq)`
Thus, we assure `i=5`.
The freezing- point depression is
`DeltaT_(f)=iK_(f)m`
`(5)(1.86^(@)C//m)(0.01 m)`
`=0.093^(@)C`
Thus, the estimated freezing point of the aqueous solution is `0.000^(@) C - 0.093^(@)C = -0.093^(@)C`