Find the molecular mass of element knowing the solvent's Kf, mass, freezing point and element's mass & fp

Question

After heating solid naphthalene to convert it to a liquid, an element is then dissolved in the naphthalene. If the Kf of naphthalene is 6.9 K/mc, its freezing point is 80 C, and its mass is 7 grams. And if the element's freezing point is 70 C and its mass is 0.6 grams, how would you calculate the element's molecular mass?

Answer 1

molality = moles solute / kg solvent =
= mole solute / mass solvent (in kg)
= 1000* mole solute / mass solvent (in g)

but mole solute = mass solute (in g) / Molecular Weight solute

Let's use some symbols to make life easier

m= molality
g= mass solute in grams
MW= molecular weight of solute
G= mass solvent in grams

Thus we get that

m= 1000*g /(MW*G)

In our case
ΔTf= Kf*m =Kf*1000*g/(MW*G) =>

MW= Kf*1000*g / (ΔTf*G) = 6.9*1000*0.6/((80-70)*7)= 59.14

Note: It is not the element's freezing point that is 70 deg C, but the freezing point of the element's solution in naphthalene.