Arrange the following in increasing order of freezing point : 0.2 M NaOH, 0.2 M 2 3 , Na CO 0.1 M 3, AgNO 0.1M ( )4 4 2 .NH SO

To arrange the solutions in increasing order of freezing point, we need to consider the concept of freezing point depression, which is influenced by the number of particles that a solute dissociates into when dissolved in a solvent. The more particles produced, the greater the freezing point depression, leading to a lower freezing point. Let's analyze each solution step by step.

Understanding Freezing Point Depression

Freezing point depression is a colligative property, meaning it depends on the number of solute particles in a solution rather than the identity of the solute. The formula for freezing point depression is:

ΔTf = i * Kf * m

Where:

• ΔTf = change in freezing point
• i = van 't Hoff factor (number of particles the solute dissociates into)
• Kf = freezing point depression constant (depends on the solvent)
• m = molality of the solution

Analyzing Each Solution

Now, let's evaluate the van 't Hoff factor (i) for each of the given solutions:

• 0.2 M NaOH: Sodium hydroxide dissociates into Na⁺ and OH^-, giving us i = 2.
• 0.2 M Ca(NO₃)₂: Calcium nitrate dissociates into Ca²⁺ and 2 NO₃^-, resulting in i = 3.
• 0.1 M Na₂SO₄: Sodium sulfate dissociates into 2 Na⁺ and SO₄^2-, leading to i = 3.
• 0.1 M AgNO₃: Silver nitrate dissociates into Ag⁺ and NO₃^-, so i = 2.

Calculating Effective Concentration

To find the effective concentration of particles in each solution, we multiply the molarity by the van 't Hoff factor:

• For 0.2 M NaOH: 0.2 M * 2 = 0.4 particles
• For 0.2 M Ca(NO₃)₂: 0.2 M * 3 = 0.6 particles
• For 0.1 M Na₂SO₄: 0.1 M * 3 = 0.3 particles
• For 0.1 M AgNO₃: 0.1 M * 2 = 0.2 particles

Arranging in Order

Now that we have the effective concentrations, we can arrange the solutions in increasing order of freezing point (from lowest to highest freezing point):

• 0.1 M AgNO₃ (0.2 particles)
• 0.1 M Na₂SO₄ (0.3 particles)
• 0.2 M NaOH (0.4 particles)
• 0.2 M Ca(NO₃)₂ (0.6 particles)

Thus, the final arrangement in increasing order of freezing point is:

0.1 M AgNO₃ < 0.1 M Na₂SO₄ < 0.2 M NaOH < 0.2 M Ca(NO₃)₂