[Rutherford]

The  melting  point  of  cryolite (molar  mass  210  g) is  1282.7K.    However,  by  adding sodium fluoride cryolite is made to melt at 1233K. Calculate the percentage (on w/wbasis) of sodium fluoride needed to be added to reduce the melting point to 1233K assuming that it dissociates completely.  The heat of fusion of cryolite in this temperature range is 114kJmol^-1.

What equation should be used here?

[Borek]

Sigh, I know the equation, but I have no idea what it is called nor how it is derived.

You need to calculate cryoscopic constant from K_f=RT²/L, where L is the heat of fusion (beware of units!). This is probably related to Van 't Hoof equation.

[Rutherford]

Oh, you reminded me now. It should be:
ΔT=RT_m²χ_s/ΔH_f (T_m is the melting point of pure solvent, χ_s is the molar share of the solute).
I got that χ=41.4% while their answer is 4.14%. Can someone check this?

[mjc123]

I agree with χ = 41.4 mol%. By the way, that should be T_m² in your equation.

[Rutherford]

Corrected. Thanks.

[mjc123]

Good, but you still need to answer the question!

[Rutherford]

I got that χ=41.4% while their answer is 4.14%.

[mjc123]

χ is the mole fraction of solute; they ask for the weight % of NaF.

[Rutherford]

Why is their answer 4.14% then? The w/w share won't have this value.