Finding Molecular Mass and Formula

Question

A compound known to be a pain reliever had the empirical formula C₈H₈O₄. When a mixture of 5.02 mg of the unknown and 50.37 mg of camphor was prepared, the melting point of a portion of this mixture was determined. The observed melting point of the mixture was 156°C. What is the molecular mass and formula of this substance?

Answer 1

This is a problem dealing with the colligative property of change in melting/freezing point. To solve this problem, one will need to know/look up the Kf value of camphor. One such literature value is Kf = 39.7ºC/m.

One will also need to know the normal melting point of pure camphor. Again, a literature value is 178,.4ºC. If you have different values for these constants, use them in place of these values in the following calculations. You may get a slightly different answer.

Also, are you sure the stated empirical formula is C₈H₈O₄, because that isn't really an empirical formula. The empirical formula for that compound would be C₂H₂O. So, you might want to check that out.

The useful equation for change in melting point is ∆T = imK

∆T = change in melting point = 178.4º - 156º = 22.4ºC

i = van't Hoff factor = 1 since the empirical formula shows it to be molecular and not ionic.

m = molality = moles solute/kg solvent = ?

K = constant for camphor = 39.7ºC/m

22.4 = (1)(m)(39.7)

m = 22.4/39.7 = 0.564 moles of unknown/kg camphor

kg camphor = 50.37 mg x 1 g/1000 mg x 1 kg/1000 g = 5.037x10^-5 kg

moles of unknown = 0.564 moles/kg x 5.037x10^-5 kg = 2.84x10^-5 moles of unknown

molar mass of unknown = 5.02 mg x 1 g/1000 mg /2.84x10^-5 moles = 5.02x10^-3 g/2.84x10^-5 moles = 1.77x10² g/mole = 177 g/mole

molar mass of empirical formula = 96+8+64 = 168

This value is close to the molar mass of unknown and considering there are various literature values of Kf, this is a reasonable approximation that the molecular formula of the unknown is C8H8O4 with a molar mass of 168.