The freezing point (in 0c) of a solution containing 0.1 g of K3[Fe(CN)6 (Mol. Wt. 329) in 100 g of water Kf= 1.86 K kg mol-1) is (A) -2.3 × 10-2 (B) -5.7 × 10-2 (C) -5.7 × 10-3 (D) -1.2 × 10-2

To determine the freezing point of the solution containing potassium ferricyanide (K3[Fe(CN)6]), we can use the concept of freezing point depression. This phenomenon occurs when a solute is added to a solvent, resulting in a lower freezing point than that of the pure solvent. The formula for calculating the freezing point depression is:

Freezing Point Depression Formula

The equation is given by:

ΔTf = Kf × m

Where:

• ΔTf = change in freezing point
• Kf = freezing point depression constant of the solvent (for water, Kf = 1.86 K kg mol^-1)
• m = molality of the solution

Step 1: Calculate the number of moles of K3[Fe(CN)6

First, we need to find the number of moles of the solute. The molar mass of K3[Fe(CN)6] is 329 g/mol. Given that we have 0.1 g of the solute, we can calculate the moles:

Number of moles = mass (g) / molar mass (g/mol)

Number of moles = 0.1 g / 329 g/mol ≈ 0.000304 moles

Step 2: Calculate the molality of the solution

Molality (m) is defined as the number of moles of solute per kilogram of solvent. Since we have 100 g of water, we convert this to kilograms:

100 g = 0.1 kg

Now we can calculate the molality:

Molality (m) = moles of solute / kg of solvent

Molality (m) = 0.000304 moles / 0.1 kg = 0.00304 mol/kg

Step 3: Calculate the freezing point depression

Now that we have the molality, we can find the freezing point depression:

ΔTf = Kf × m

ΔTf = 1.86 K kg mol^-1 × 0.00304 mol/kg ≈ 0.00566 K

Step 4: Determine the new freezing point

The normal freezing point of pure water is 0 °C. To find the new freezing point, we subtract the freezing point depression from the original freezing point:

New freezing point = 0 °C - ΔTf

New freezing point = 0 °C - 0.00566 °C ≈ -0.00566 °C

Final Result

Expressing this in scientific notation gives us approximately -5.66 × 10^-3 °C. Therefore, the closest answer from the options provided is:

(C) -5.7 × 10^-3