# Assuming equal concentrations and complete dissociation, rank these aqueous solutions by their freezing points from highest to lowest.

Assuming equal concentrations and complete dissociation, rank these aqueous solutions by their freezing points from highest to lowest. CoCl3, NH4Cl, Li2SO4

The order of increasing freezing points is   Explanation: The expression of depression in freezing point is given as: where, = Depression in freezing point i = Van’t Hoff factor = freezing point constant m = molality Let the molarity of the given solutions is ‘1 m’ For the given options: Option 1:  1 m Value of i = 4 So, molal concentration will be = Option 2:  1 m Value of i = 3 So, molal concentration will be = Option 3:  1 m Value of i = 2 So, molal concentration will be = As, the molal concentration of is the highest, so its freezing point will be the highest. Hence, the order of increasing freezing points follows:

By using the formula of depression in freezing, it can easily identify the rank of the given compounds. where, = freezing point depression i = van ‘t Hoff factor (number of ions per individual molecule of solute) m = molality of the solute = molal freezing point According to question, if concentration (m) and is same, then only van ‘t Hoff factor will change. For , i = 2 For , i = 4 For , i= 3 Now, the solute with the largest i value results in low freezing point. The highest value of i is 4 (), thus   has lowest freezing point. And, has highest freezing point. The order of freezing point is :

CoCl₃ > Li₂SO₄ > NH₄I. Explanation: Adding solute to water causes depression of the boiling point.The depression in freezing point (ΔTf) can be calculated using the relation: ΔTf = i.Kf.m, where, ΔTf is the depression in freezing point. i is the van ‘t Hoff factor. van ‘t Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the van ‘t Hoff factor is essentially 1. Kf is the molal depression constant of water. m is the molality of the solution. (1) Li₂SO₄: i for Li₂SO₄ = no. of particles produced when the substance is dissolved/no. of original particle = 3/1 = 3. ∴ ΔTb for (Li₂SO₄) = i.Kb.m = (3)(Kf)(m) = 3(Kf)(m). (2) NH₄I: i for NH₄I = no. of particles produced when the substance is dissolved/no. of original particle = 2/1 = 2. ∴ ΔTb for (NH₄I) = i.Kb.m = (2)(Kf)(m) = 2(Kf)(m). (3) CoCl₃: i for CoCl₃ = no. of particles produced when the substance is dissolved/no. of original particle = 4/1 = 4. ∴ ΔTb for (CoCl₃) = i.Kb.m = (4)(Kf)(m) = 4(Kf)(m). So, the ranking of the freezing point from the highest to the lowest is: CoCl₃ > Li₂SO₄ > NH₄I.

CoCl₃ > Li₂SO₄ > NH₄I. Explanation: Adding solute to water causes depression of the boiling point.The elevation in boiling point (ΔTf) can be calculated using the relation: ΔTf = i.Kf.m, where, ΔTf is the depression in freezing point. i is the van ‘t Hoff factor. van ‘t Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the van ‘t Hoff factor is essentially 1. Kf is the molal depression constant of water. m is the molality of the solution. (1) Li₂SO₄: i for Li₂SO₄ = no. of particles produced when the substance is dissolved/no. of original particle = 3/1 = 3. ∴ ΔTb for (Li₂SO₄) = i.Kb.m = (3)(Kf)(m) = 3(Kf)(m). (2) NH₄I: i for NH₄I = no. of particles produced when the substance is dissolved/no. of original particle = 2/1 = 2. ∴ ΔTb for (NH₄I) = i.Kb.m = (2)(Kf)(m) = 2(Kf)(m). (3) CoCl₃: i for CoCl₃ = no. of particles produced when the substance is dissolved/no. of original particle = 4/1 = 4. ∴ ΔTb for (CoCl₃) = i.Kb.m = (4)(Kf)(m) = 4(Kf)(m). So, the ranking of the freezing point from the highest to the lowest is: CoCl₃ > Li₂SO₄ > NH₄I.

The freezing order from the largest to the smallest is:
NH4Cl> K2SO4> COBr3
Further explanation For electrolyte solutions: ΔTb = Kb.m. i ΔTf = Kf.m. i Kb = molal boiling point increase Kf = molal freezing point constant m = molal solution i = van’t Hoff factor i = 1 + (n-1) α The formula above shows that the freezing point depends on •molal value •degree of ionization/dissociation •number of ions in solution In the statement of the matter, it is known that there are solutions which have the same concentration and are completely dissociated (α = 1) So the value of the freezing point drop depends only on the number of ions in the solution The more ions produced, the greater the value of the freezing point (the freezing point is smaller) There are several solutions •1. NH4Cl ionization: NH4Cl —> NH4+ + Cl- There are 2 ions in the solution •2. COBr3 ionization: COBr3 —> CO3++ 3Br- There are 4 ions in the solution •3. ionization K2SO4 K2SO4 —> 2K ++ SO42- There are 3 ions in the solution So the order of freezing from the largest to the smallest is: NH4Cl> K2SO4> COBr3 Learn more The freezing point of a solution Keywords: freezing point,  properties, van’t Hoff factor

Assuming equal concentrations and complete dissociation, the aqueous solutions with the highest freezing point is NA3PO4 floowed by K2SO4, and then NH4I. This is due tot he number of ions being dissociated in the solution that will help in depressing the freezing point of a solution.