When 5 g of a nonelectrolyte is added to 25 g of water, the new freezing point is -2.5 degrees Celsius. What is the molecular mass of the . ....

When a substance is dissolved in a solvent it reduces the
freezing point of the solvent. The decrease in the temperature at which the liquid freezes is
given by a relation derived by Ebbing as dT = Kf*cm, where Kf is a constant for every liquid and
cm is the molality of the solution after the impurity has been
dissolved.

For water the freezing-point-depression constant is
1.858.

Let the molecular mass of the unknown substance be m, when 5
g of this is added to 25 g of water the molality is (5/m)/25. The new freezing point is -2.5
degrees Celsius, or there is a drop of 2.5 degree Celsius.

This
gives dT = 2.5 = 1.858*mc

=> mc = 2.5/1.858 =
1.345

(5/m)/25 = 1.345

=> m =
0.1486 g

This gives the molecular mass of the unknown
compound as 0.1486 g