Answer: Freezing point of this solution is [tex]-8.58^0C[/tex]
Explanation:
Depression in freezing point is given by:
[tex]\Delta T_f=i\times K_f\times m[/tex]
[tex]\Delta T_f=T_f^0-T_f=(0-T_f)^0C[/tex] = Depression in freezing point
i= vant hoff factor = 3 (for [tex]MgCl_2[/tex] as it dissociates to give three ions.
[tex]K_f[/tex] = freezing point constant = [tex]1.86^0C/m[/tex]
m= molality
Weight of solvent (water)= 650g = 0.65 kg
Molar mass of solute = 95.21 g
Molar mass of solute= 95.21 g/mol
[tex]0-T_f=3\times 1.86\times \frac{\95.21g}{95.21g/mol}\times 0.65kg[/tex]
[tex]T_f=-8.58^0C[/tex]
Thus freezing point of this solution is [tex]-8.58^0C[/tex]