What is the freezing point of 0.4 molal solution of acetic acid in benzene in which it dimerises to the extent of 85%. Freezing point of benzene is 278.4k and its molar heat of fusion is 10.042kj mol-1 .

To determine the freezing point of a 0.4 molal solution of acetic acid in benzene, where acetic acid dimerizes to 85%, we can follow a systematic approach using colligative properties. Colligative properties depend on the number of solute particles in a solution, rather than the identity of the solute. In this case, we will use the freezing point depression formula to find the new freezing point.

Understanding the Components

First, let's break down the information we have:

• Concentration of acetic acid solution: 0.4 molal (m)
• Freezing point of pure benzene: 278.4 K
• Molar heat of fusion of benzene: 10.042 kJ/mol
• Dimerization extent of acetic acid: 85%

Calculating the Effective Concentration

Acetic acid (CH₃COOH) dimerizes in solution to form (CH₃COOH)₂. When it dimerizes, two molecules of acetic acid combine to form one dimer. Since the dimerization is 85%, we need to calculate how many moles of acetic acid remain as monomers and how many form dimers.

In a 0.4 molal solution, we start with 0.4 moles of acetic acid. If 85% dimerizes, then:

• Moles dimerized = 0.4 moles × 0.85 = 0.34 moles
• Moles remaining as monomers = 0.4 moles - 0.34 moles = 0.06 moles

Each dimer counts as one particle, while the remaining monomers count as individual particles. Thus, the total number of particles in solution is:

• Total particles = Moles of dimers + Moles of monomers = 0.34 + 0.06 = 0.4 moles

Applying the Freezing Point Depression Formula

The freezing point depression can be calculated using the formula:

ΔTf = i × Kf × m

Where:

• ΔTf = change in freezing point
• i = van 't Hoff factor (number of particles after dissociation)
• Kf = freezing point depression constant of the solvent (for benzene, Kf = 5.12 °C kg/mol)
• m = molality of the solution

In our case, since we have 0.4 moles of particles, the van 't Hoff factor (i) is 1 (for the dimer) + 0.15 (for the remaining monomer) = 1.15. Now, substituting the values:

• ΔTf = 1.15 × 5.12 °C kg/mol × 0.4 mol/kg
• ΔTf = 1.15 × 5.12 × 0.4 = 2.3584 °C

Finding the New Freezing Point

Now, we can find the new freezing point of the solution:

• New freezing point = Freezing point of pure benzene - ΔTf
• New freezing point = 278.4 K - 2.3584 °C

Converting the temperature change to Kelvin (since 1 °C change is equivalent to 1 K change):

• New freezing point = 278.4 K - 2.3584 K = 276.0416 K

Final Result

Therefore, the freezing point of the 0.4 molal solution of acetic acid in benzene, considering the dimerization, is approximately 276.04 K. This demonstrates how colligative properties can significantly affect the physical properties of solutions, depending on the interactions between solute and solvent.