Cryoscopic constant is the depression of the freezing point of the solvent produced on dissolving are mole of substance in 1000g of it. it is also called molal depression constant. it is denoted by Kf.
As we know,
depression in freezing point
△Tf = Kf m
where,
m = molality
Kf = Cryoscopic constant
△Tf = depression in freezing point
we have given
△Tf = 177.5 - 147
= 30.5 °C
Number of moles of Naphthalene = \(\frac1{128}\) mole
molality = \(\cfrac{\frac1{128}}{10}\times1000\)
= 0.78 m
Therefore,
Kf = \(\frac{30.5}{0.78}\)
Kf = 39.1 °C kg mol-1
Hence, the cryosopic constant will be 39.1 °C kg mol-1