The molar masses determined from the colligative properties of substances that associate or dissociate in solution are abnormal and are called abnormal molar masses. Ionic substances such as NaCl, BaCl2 and AlCl3 dissociate into ions in solution. Their colligative properties are higher than those of solutions of non-electrolytes such as glucose of the same concentration, because the number of particles in solution increases. When molecules of a substance such as ethanoic acid (acetic acid) associate in benzene to form dimers, the number of particles decreases and the colligative properties also decrease. The van’t Hoff factor, i, accounts for the extent of dissociation or association:
\(\displaystyle i = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}\)
\(\displaystyle i = \frac{\text{Total number of moles of particles after association/dissociation}}{\text{Number of moles of particles before association/dissociation}}\)
The value of i is greater than 1 for ionic substances and less than 1 for substances that associate in solution.
For which of the following, in a dilute aqueous solution, will the van’t Hoff factor i be equal to 3? (Assume complete dissociation of the electrolytes.)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Na2SO4
The passage states that the van’t Hoff factor i is the total number of moles of particles after dissociation divided by the number of moles of particles before it. On complete dissociation, i is the number of ions given by one formula unit.
NaCl — \( \ce{NaCl -> Na^+ + Cl^-} \): 2 ions, so i = 2.
Urea — a non-electrolyte; it does not dissociate, so i = 1.
\( \ce{MgSO4} \) — \( \ce{MgSO4 -> Mg^2+ + SO4^2-} \): 2 ions, so i = 2.
\( \ce{Na2SO4} \) — \( \ce{Na2SO4 -> 2Na^+ + SO4^2-} \): 3 ions, so i = 3.
Only \( \ce{Na2SO4} \) has i = 3.