Answer: Van't Hoff factor for [tex]BaCl_2[/tex] is 1.15
Explanation:
Depression in freezing point:
[tex]T_f^0-T^f=i\times k_f\times \frac{w_2\times 1000}{M_2\times w_1}[/tex]
where,
[tex]T_f[/tex] = freezing point of solution = [tex]-0.33^oC[/tex]
[tex]T^o_f[/tex] = freezing point of water = [tex]0.22^oC[/tex]
[tex]k_f[/tex] = freezing point constant of water = [tex]1.86^0C/m[/tex]
m = molality
i = Van't Hoff factor = ?
[tex]w_2[/tex] = mass of solute = 1.168 g
[tex]w_1[/tex]= mass of solvent (water) = 21.797 g
[tex]M_2[/tex] = molar mass of solute = 208 g/mol
Now put all the given values in the above formula, we get:
[tex](0.22-(-0.33))=i\times (1.86)\times \frac{(1.168)\times 1000}{208\times (21.797)}[/tex]
[tex]i=1.15[/tex]
Thus van't Hoff factor for [tex]BaCl_2[/tex] is 1.15