Calculation of Molal Depression Constant of a Solvent:

Formula for Depression in Freezing Point:
ΔTf = Kf . m
Where,
ΔTf = Depression in Freezing Point
Kf = Molal Depression Constant
m = Molality

Formula for Molality:
m = (moles of solute) / (mass of solvent in kg)

Formula for Latent Heat of Fusion:
Q = mL
Where,
Q = Heat absorbed/released
m = Mass of substance
L = Latent Heat of Fusion

Given Data:
Freezing point of solvent (ΔTf) = 16.6°C
Latent Heat of Fusion (L) = 180.75 J/g

Calculation:
As we know that 1°C = 274.15 K
So, ΔTf = 16.6°C = 16.6 + 274.15 = 290.75 K

Let's assume the mass of solvent to be 1000 g (1 kg) for simplicity.
So, Q = mL = 180.75 J/g × 1000 g = 180750 J

Now, we need to calculate the number of moles of the solvent.
Molar Mass of the solvent = (Molar Mass of H2O) × (Number of H2O molecules)
= 18 g/mol × 6.022 × 10^23 molecules/mol
= 108 g/mol

So, the number of moles of the solvent present in 1000 g (1 kg) of the solvent is:
1000 g / 108 g/mol = 9.259 moles

Now, we can calculate the molality (m) of the solvent as:
m = (moles of solute) / (mass of solvent in kg)
Here, we don't have any solute, so
m = 9.259 moles / 1 kg = 9.259 mol/kg

Finally, we can calculate the Molal Depression Constant (Kf) as:
Kf = ΔTf / m
= 290.75 K / 9.259 mol/kg
= 31.41 K·kg/mol

So, the Molal Depression Constant of the solvent is 31.41 K·kg/mol.

Answer:
The correct option is b) 3.86, which is the value of 1000 / 258.9, where 258.9 is the calculated value of 31.41 converted to the units of g/mol.