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 K_{f}.

As we know,

depression in freezing point

△T_{f} = K_{f} m

where,

m = molality

K_{f} = Cryoscopic constant

△T_{f }= depression in freezing point

we have given

△T_{f }= 177.5 - 147

= 30.5 °C

Number of moles of Naphthalene = \(\frac1{128}\) mole

molality = \(\cfrac{\frac1{128}}{10}\times1000\)

= 0.78 m

Therefore,

K_{f} = \(\frac{30.5}{0.78}\)

K_{f} = 39.1 °C kg mol^{-1}

**Hence, the cryosopic constant will be 39.1 °C kg mol**^{-1}